Wolfgang Pauli Institute (WPI) Vienna |
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| Dominik Wodarz (UC San Diego) | WPI, OMP 1, Seminar Room 08.135 | Fri, 2. Aug 24, 11:45 |
| Stem cell dynamics and mutant invasion in the hematopoietic system of mice | ||
The maintenance of the hematopoietic system is a complex and highly dynamic process where cell division, self-renewal, and differentiation events are regulated by homeostatic control networks. An evolutionary mathematical model with feedback control that is parameterized with data from label propagation experiments in mice predicts the existence of major invasion barriers for advantageous mutants (such as TET2 or DNMT3A mutants) in short term stem cell and multipotent progenitor cell compartments. It further provides an evolutionary explanation or why mutant invasion can become more likely with age, and suggests that evolutionary niche construction dynamics, based on mutant-induced inflammation, could be central to mutant emergence. The mathematical analysis further provides new interpretations of experimentally estimated rates of cellular self-renewal and differentiation. | ||
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| Juliane Winkler (Medical University, Vienna) | WPI, OMP 1, Seminar Room 08.135 | Fri, 2. Aug 24, 11:00 |
| Dissecting tumor heterogeneity in breast cancer metastasis | ||
About 30% of breast cancer patients develop metastases and eventually succumb to the disease. Tumor cell adaptations to distant microenvironments during the multistep process of metastasis contribute to the heterogeneity of metastatic tumors and the remodeling of tumor-promoting metastatic niches. This inherent complexity challenges the development of effective metastatic treatment strategies. To gain a holistic view of the metastatic process we profile tumor and immune cells in breast cancer metastasis on single-cell resolution. We dissect the tumor heterogeneity contributing to metastasis progression and describe the dynamic changes in the metastatic immune niche. Ultimately, we aim to develop novel immuno-oncology strategies in metastasis. | ||
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| Thomas Vogl (Medical University, Vienna) | WPI, OMP 1, Seminar Room 08.135 | Fri, 2. Aug 24, 9:55 |
| Deciphering human immune responses against the microbiome in health and disease | ||
My research combines experimental biology (robotic high-throughput immunoassays) with data science (machine learning, bioinformatics) to gain a holistic view of interactions between microbes and the immune system. Our current conception of these immune responses is mostly based on DNA sequencing of antibody genes, whereas the actual functional consequences thereof (the molecular structures “antigens” recognized) are vastly unknown. I strive to unravel the functional capacity of these enormous immune repertoires targeting microbes and to shed light on their role in human health. Here, I will be giving and brief overview of the experimental methods we are using to generate large datasets, and then discuss machine learning and bioinformatics approaches we are using to interpret this data. | ||
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| Thomas Stiehl (RWTH Aachen University Hospital) | WPI, OMP 1, Seminar Room 08.135 | Fri, 2. Aug 24, 9:10 |
| Understanding pre-malignant stem cell dynamics – insights from mechanistic mathematical modeling | ||
The expansion of pre-malignant, i.e., mutated but not yet malignant cells is an important prerequisite for cancer. It is well accepted that the frequency of pre-malignant stem cells increases with age. However, the underlying mechanisms are not well understood. Potential explanations include immune dysfunction, increase of chronic inflammation and age-related accumulation of mutations. A detailed understanding of pre-malignant stem cell dynamics is crucial to identify patients with a high risk of cancer. Since pre-malignant cells do not cause symptoms, it is challenging to study them in humans. A suitable scenario to invest their dynamics under stress conditions is hematopoietic stem cell transplantation (bone marrow transplantation), a curative treatment for many diseases of the blood forming (hematopoietic) system. In case of allogeneic stem cell transplantation, the stem cells are harvested from a donor who might, as a significant proportion of healthy individuals, harbor pre-malignant cells. Before the transplantation, the recipient’s marrow is eradicated using high dose chemotherapy or radio-chemotherapy. Therefore, the donor cells are exposed to strong proliferative stimuli in the host environment, which potentially unmask differences between healthy and pre-malignant stem cells. We propose quantitative non-linear ordinary differential equation models to investigate the dynamics of pre-malignant hematopoietic stem cells. The models account for key mechanisms mediating clonal expansion, such as mutationrelated changes of stem cell proliferation & self-renewal, aberrant response of mutated cells to systemic signals and chronic inflammation. Combining model simulations, longitudinal patient data and in silico clinical trials, we address the following questions: (i) Why do pre-malignant cells expand in some individuals but not in others? (ii) How do pre-malignant cells respond to systemic cues such as chronic inflammation & physiological feedbacks? (iii) How do cell-intrinsic and host-specific factors contribute to cell expansion? (iv) What does stem cell transplantation data tell us about the differences between healthy and pre-malignant stem cells? | ||
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| Jörg Menche (CEMM & University of Vienna) | WPI, OMP 1, Seminar Room 08.135 | Thu, 1. Aug 24, 16:00 |
| Network Medicine | ||
Virtually all processes in health and disease rely on the careful orchestration of a large number of diverse individual components ranging from molecules to cells and entire organs. Networks provide a powerful framework for describing and understanding these complex systems in a holistic fashion. They offer a unique combination of a highly intuitive, qualitative description, and a plethora of analytical, quantitative tools. In my presentation, I will first review how molecular networks can be understood as maps for elucidating the relation between molecular-level perturbations and their phenotypic manifestations. I will then sketch out a number of challenges in the areas of network biology and network medicine, as well as recent efforts of my group to address them. These efforts range from methodological work on the visualization and interpretation of large biomedical data combining artificial intelligence with virtual reality technology, to translational efforts towards concrete clinical applications in rare diseases and drug repurposing. | ||
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| Natalia Komarova (UC San Diego) | WPI, OMP 1, Seminar Room 08.135 | Thu, 1. Aug 24, 15:15 |
| Mathematical methods in evolution and medicine | ||
Evolutionary dynamics permeates life and life-like systems. Mathematical methods can be used to study evolutionary processes, such as selection, mutation, and drift, and to make sense of many phenomena in the life sciences. How likely is a single mutant to take over a population of individuals? What is the speed of evolution, if things have to get worse before they can get better (aka, fitness valley crossing)? Can cooperation, hierarchical relationships between individuals, spatial interactions, or randomness influence the speed or direction of evolution? Applications to biomedicine will be discussed. | ||
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| Philip Maini (Oxford University) | WPI, OMP 1, Seminar Room 08.135 | Thu, 1. Aug 24, 14:00 |
| Modelling cancer cell invasion | ||
How various processes combine to enable cancer cells to invade tissue is still an open question. We have been using non-linear partial differential equation models to investigate how different processes can enhance cancer cell invasion. Here, I shall investigate the impact of the Allee effect on one cancer cell type invading, and then consider how different specialised cancer cell phenotypes can co-operate to overcome the obstacles that normal cells and extracellular matrix provide, and determine if this is more efficient than invasion by a single generalist cell type. | ||
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| Luca Gerardo-Giorda (Johannes Kepler University, Linz) | WPI, OMP 1, Seminar Room 08.135 | Thu, 1. Aug 24, 11:45 |
| Towards personalized treatment of low grade glioma: modeling the invasive proces | ||
One of the most prevalent forms of central nervous system tumors, diffuse low grade gliomas (LGG) have distinct clinical outcomes and require different treatment strategies based on their clinicopathological characteristics. In contrast to extraaxial or extracranial tumors, LGG diffusely infiltrate the brain parenchyma and can extend well beyond the original tumor mass detectable by standard radiological means. Although a comprehensive neuropsychological evaluation reveals abnormalities in the majority of patients at the time of diagnosis, subjective and clinical symptoms are typically subtle. LGG are thus diagnosed at various stages, depending on the size, location, and growth kinetics of the tumor. Feasible total onco-functional resection of LGG within the brain is often deemed impossible due to its extent or location. Understanding tumor infiltration patterns can thus be of paramount importance to maximize tumor resection and improve patient outcome. In this talk, I will discuss our current project, in collaboration with the Department of Neurosurgery of the Kepler University Klinikum in Linz, aiming at understanding which role do the brain fibers (assessed by DTI data) have on the low grade glioma progression, and whether they have any. | ||
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| Angelika Manhart (University of Vienna) | WPI, OMP 1, Seminar Room 08.135 | Thu, 1. Aug 24, 11:00 |
| Nuclear positioning and size scaling – using modelling for hypothesis testing | ||
How a cell organizes its organelles is fundamental to its function. I will focus on the nucleus, a cell’s central organ, and its properties, such as number, size and position. I will discuss nuclear positioning and size scaling in multi-nucleated muscle cells. Mispositioned nuclei are associated with muscle disease. Using coarse, deterministic, as well as detailed, stochastic models, we use data from drosophila larval muscles to identify the most plausible model. This model assumes repulsive forces created by microtubules between nuclei and the cell sides and correctly reproduces and predicts bifurcating nuclear positioning patterns and nuclear shapes. Finally, we show that nuclear size scaling is driven by nuclear positioning, evidenced in the data and predicted by a partialdifferential- equations size sensing model. This creates a plausible link between mispositioned nuclei and muscle disease. | ||
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| Morten Andersen (Roskilde University) | WPI, OMP 1, Seminar Room 08.135 | Thu, 1. Aug 24, 9:55 |
| Mathematical modeling of phosphate kinetics for kidney malfunction treated by hemodialysis | ||
Chronic kidney diseases imply an ongoing need to remove toxins, with hemodialysis as the preferred treatment modality. We investigate and find expressions for phosphate clearance during dialysis based on the single pass (SP) model corresponding to a standard clinical hemodialysis and the multi pass (MP) model, where dialysate is recycled and therefore makes a smaller clinical setting possible such as a novel transportable dialysis suitcase. For both cases we find that the convective contribution to the dialysate is negligible for the phosphate kinetics. The SP and MP models are calibrated to clinical data of ten patients showing consistency between the models and provide estimates of the kinetic parameters. Immediately after dialysis a rebound effect in the phosphate level is observed. We give a simple formula describing this effect which is valid both posterior to SP or MP dialysis. The analytical formulas provide explanations to observations of previous clinical studies. The work is based on an interdisciplinary collaboration between mathematicians and a nephrologist and I will touch upon the benefits and challenges of such a collaboration. | ||
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| Anna Marciniak-Czochra (Heidelberg University) | WPI, OMP 1, Seminar Room 08.135 | Thu, 1. Aug 24, 9:10 |
| Cellular hierarchies in cancer: Mathematics of stem cell dynamics and model-based data analysis | ||
This talk is devoted to the mathematical modelling of a glioblastoma tumour dynamics structured by a cellular hierarchy. The work is motivated by recent experimental data and their analysis, which indicate the impact of the cellular structure of tumour cell populations on disease dynamics and patient prognosis. We propose new mechanistic mathematical models that allow linking the observed cellular patterns to the key parameters of different cell populations, which in turn characterise their dynamics and allow predictions. The results are discussed in the context of tumour evolution, but also from the perspective of mathematical challenges arising in coupling spatial and structured dynamics. We discuss different modelling and data analysis approaches. | ||
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| Walter Berger (Medical University, Vienna) | WPI, OMP 1, Seminar Room 08.135 | Wed, 31. Jul 24, 16:00 |
| Complexity of BOLD-100 anticancer activity: targeting the oncometabolism network | ||
The anticancer ruthenium complex KP1339 (BOLD-100), globally evaluated currently in clinical phase II studies, was developed for improved tumor-targeting and to reduce chemotherapyassociated side effects. Mechanistically, BOLD-100 is delivered to malignant tissue bound to serum albumin. Intratumorally, BOLD-100 induces endoplasmic reticulum (ER) stress via chaperone GRP78 inhibition, leading to unfolded protein response and apoptosis induction. Resistance acquisition presents a major limitation for effective cancer therapy. Additionally, treatment success is often regulated by tumor microenvironmental cells. Thus, dissection of these aspects is essential for promoting (pre)clinical development of BOLD-100. Here we report on the identification of BOLD-100 as a multi-faceted onco-metabolism-regulating compound by targeting several aspects of cancer cell metabolism. BOLD-100 massively interfered with cancer cell glycolysis, inducing downregulation of cellular pyruvate and citrate contents. This, in turn, impacted on lipid metabolism – specifically, de novo fatty acid synthesis and beta-oxidation - translating into epigenetic gene expression deregulation via depletion of acetyl-coenzyme A. Alterations in glycolysis-driven lipid processing also contributed to BOLD-100 resistance acquisition. Distinct lipid metabolism routes were identified as vulnerabilities of BOLD-100-resistant in vitro and in vivo models. Additionally, the anti-Warburg compound BOLD-100 significantly reduced release of the immunosuppressive metabolite lactate. Despite increased glycose uptake, lactate secretion was diminished in the resistant subline linked to loss of monocarboxylate transporter 1 (MCT1) expression, based on a frame-shift mutation in the MCT1 chaperone basigin (CD147). Preliminary data suggest that BOLD-100 also decreases lactate production in cancer-associated fibroblasts, associated with altered expression of MCT-1 and CD147. This suggests an impact of BOLD-100 on the metabolic crosstalk between cancer cells and the immune microenvironment. Summarizing, we uncover novel modes of action of BOLD-100 and unravel molecular mechanisms driving resistance acquisition. BOLD-100-induced lactate reduction indicates a potential to overcome the immune-suppressive environment of solid tumors. The impact on metabolic cross-talks between cancer cells and the components of the microenvironment are currently evaluated. This is a joint work with Dina Baier, Theresa Mendrina, Mate Rusz, Christine Pirker, Samuel Meier-Menches, Gunda Koellensperger, and Bernhard K. Keppler. | ||
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| Quentin Bedel (University Toulouse III) | WPI, OMP 1, Seminar Room 08.135 | Wed, 31. Jul 24, 15:15 |
| Immunological synapse modelling : numerical mesoscale simulation accounting for the segregation of the TCR/pMHC and LFA1/ICAM1 molecular couples | ||
T lymphocytes are key cellular components of the immune system since they can eliminate virusinfected cells and tumor cells. T cells recognize target cells by forming tight contacts known as immunological synapses (IS). The mechanisms and parameters responsible for the assembly and the spatial patterning of the IS are still poorly understood. In particular the mechanism leading to the segregation between the T-cell receptor (TCR) recognizing the foreign antigens and the LFA-1 integrin responsible of cell adhesion is subject to debate. In this work we propose an analytical and numerical modeling of the IS, with the hypothesis that the TCR-LFA-1 segregation is driven by the difference of height between the TCR-pMHC ligandreceptor couple on the one hand, and the LFA1-ICAM1 ligand-receptor couple on the other hand, together with an inhomogeneous pressure field exerted by the cortical actin cytoskeleton. Our numerical mesoscale simulation is based on the Dynamically Triangulated Surface (DTS) modeling, using Monte Carlo Metropolis algorithm. It validates qualitatively our hypothesis. However, to quantitatively validate this mechanism, we need to know the true pressure field driven by the cortical actin cytoskeleton that the lymphocyte exerts on its target cell. We propose an analytical approach based on elasticity theory to determine the single solution of the 3D force field exerted by the lymphocyte while knowing only the one- dimensional height deformation measured by traction-force microscopy (TFM) experiments, compensating the lack of information by minimizing the residual force on the lymphocyte-free region. This approach will be used in a near future to extract pressure field from TFM experiments. This is a joint work with Loïc Dupré and Nicolas Destainville. | ||
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| Jasmine Foo (University of Minnesota) | WPI, OMP 1, Seminar Room 08.135 | Wed, 31. Jul 24, 14:00 |
| Computational methods for inferring tumor evolution and heterogeneity | ||
Tumors are typically comprised of heterogeneous cell populations exhibiting diverse phenotypes. This heterogeneity, which is correlated with tumor aggressiveness and treatment-failure, confounds current drug screening efforts to identify effective candidate therapies for individual tumors. In the first part of the talk I will present a modeling-driven statistical framework that enables the deconvolution of tumor samples into individual subcomponents exhibiting differential drug-response, using standard bulk drug-screen measurements. In the second part of the talk I will present some efforts towards obtaining insights about tumor evolution from standard genomic data. In particular, we analyze the site frequency spectrum (SFS), a population summary statistic of genomic data, for exponentially growing tumor populations, and we demonstrate how these results can in principle be used to gain insights into tumor evolutionary parameters. | ||
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| Loïc Dupre (INSERM Toulouse) | WPI, OMP 1, Seminar Room 08.135 | Wed, 31. Jul 24, 11:45 |
| Calibration of T cell responses across the molecular, cellular and population scales | ||
T cells are a subset of white blood cells that can be protective by controlling infections and tumors on one side, but that can also be deleterious by triggering autoimmunity and autoinflammation. A central quest of my research activity as a cellular immunologist is to elucidate how T cell responses are calibrated to ensure enough protection against infectious agents and tumors, while avoiding inflicting damages to healthy tissues. Calibration of T cell responses occurs through various molecular switches that tune the abilities of T cells to explore their environment, to establish tight contacts with potential target cells and to deliver bioactive molecules such as lytic granules that can kill target cells. How calibration operates from the molecular scale up to the functional output of T cell populations remains poorly understood. To first provide a background on this topic, I will briefly present recent projects in which collaboration with computational scientists has been decisive to grasp some of the calibration mechanisms at play in T cells. This includes: • the digital activation of individual nanoclusters of an adhesive receptor to allow graded adhesion. • a share of labor mechanism accounting for the efficacy of T cells at eliminating target cells. • the emergence of collective migratory behaviors in cell populations facing chemoattractant gradients. I will also present ongoing applications of machine learning approaches to extract refined signatures from T cell image datasets. Such applications include: • the discrimination of T cell alterations in patients with highly related genetic defects • the prediction of the efficacy of therapeutic antibodies for the treatment of autoimmune diseases. To further stimulate interdisciplinary exchange, I will expose some of the most advanced experimental approaches in the field of cellular immunology and explain the nature of the generated datasets. I will then formulate a series of unsolved questions around the topic of T cell response calibration, for which mathematical modeling or analytical approaches are expected to provide solutions. | ||
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| Iros Barozzi (Medical University, Vienna) | WPI, OMP 1, Seminar Room 08.135 | Wed, 31. Jul 24, 11:05 |
| Identifying mechanisms of evolvability of breast cancer cells | ||
Hormone-responsive breast cancer is among the most prevalent tumor types in women. While adjuvant endocrine therapy, targeting non-mutated estrogen receptor alpha (Er-alpha), represents a highly efficient option for these patients, three percent of them relapse each year, often with metastasis. Genetic alterations that might drive relapse could be previously identified only in a fraction of these tumors, suggesting the need to identify alternative scenarios for the evolution of therapy resistant tumors. These include non-genetic sources of cell intrinsic tolerance to therapies, as well as of adaptability and plasticity. While intra-tumor heterogeneity is a recognized hallmark of cancer, the mechanisms that generate such heterogeneity, which in turn increases the chances of the cancer cell population to evolve when challenged, are currently less understood. By combining single-cell technologies, perturbation screens, and computational modeling, we aim at dissecting the evolvability of hormone-responsive breast cancer cells. While increasing our knowledge on the evolution of breast cancer, our study could provide insights into potentially new combinatorial therapies, that might limit tumor evolution and increase the efficacy of the current standard of care. | ||
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| Tommaso Lorenzi (Politechnico di Torino) | WPI, OMP 1, Seminar Room 08.135 | Wed, 31. Jul 24, 10:05 |
| Modelling the spatial spread and evolutionary dynamics of heterogeneous cell populations | ||
In this talk, mathematical models for the spatial spread and evolutionary dynamics of heterogeneous cell populations will be considered. In these models, which are formulated as partial differential equations, a continuous structuring variable captures intercellular heterogeneity in cell proliferation and migration rates. Analytical and numerical results summarising the behaviour of the solutions to the model equations will be presented, and the main biological insights generated by these results will be discussed. | ||
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| Elena Ambrogi (Sorbonne Université & Università di Bologna) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Thu, 18. Jul 24, 11:20 |
| Comparison of two results of long time convergence for the solutions to the random discharge Integrate and Fire model | ||
The analysis of equations arising in neuroscience raises many challenging questions that always require the development of new tools to answer them. In this presentation we will illustrate two exponential convergence results obtained using the two different techniques of Relative Entropy with Poincaré-type inequality on the one hand and Harris theory on the other. In particular, the presentation will be motivated by the case study of the Integrate and Fire model with random discharge used in mathematical neuroscience to describe the spiking activity of neurons [1, 2]. This study will be an opportunity to highlight some peculiar differences between the two techniques mentioned above [3]. The results we present are an ongoing collaboration with Professor J. A. Canizo and Professor M. J. Caceres from University of Granada, Professor D. Salort from Sorbonne University and Doctor A. Lora-Ramos from University of Granada. | ||
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| Michele Romanos (CNRS - Université Claude Bernard Lyon 1 ) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Thu, 18. Jul 24, 10:40 |
| Mathematical modeling, analysis and simulation of crowd dynamics in Myxococcus xanthus bacteria | ||
Myxococcus xanthus, a social bacterium, exhibits intriguing collective behavior, characterized by coordinated group movement and the ability of each bacterium to change its movement direction by reversing its body axis. This behavior results in the formation of interesting patterns, such as rippling, where cells self-organize into colliding counter-propagating waves, and swarming, where cells align and move together in large groups. The complex nature of this behavior has captured the attention of biologists, physicists, and mathematicians, driving extensive research efforts. This talk has two main goals. First, we present new biological data on Myxococcus xanthus, featuring high-resolution movies of their collective movements. Using advanced algorithms, we segment these movies, track cell trajectories, and analyze reversals. From these observations, we propose a kinetic model explaining the emergence of rippling patterns. Second, we develop a 2D agent-based model where bacterial reversals are closely linked to congestion, a hypothesis confirmed by our data. This model accurately replicates the rippling and swarming dynamics and highlights the crucial role of background anisotropy in the formation and persistence of these patterns. It also shows that the emergence of both rippling and swarming can be explained by the same rules at the individual level. This project is in collaboration with Vincent Calvez (Laboratoire de Mathématiques de Bretagne Atlantique), Tâm Mignot (Laboratoire de Chimie Bactérienne - Marseille) and Jean-Baptiste Saulnier (Laboratoire de Chimie Bactérienne). | ||
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| Leo Meyer (Universität Wien) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Thu, 18. Jul 24, 9:30 |
| Mathematical modeling of the size distribution of adipose cells | ||
In this talk, I’ll be present some recent advancement in the modelling of the size dynamics of adipose cells. Adipose cells or adipocytes are the specialized cells composing the adipose tissue in a variety of species. Their role is the storage of energy in the form of a lipid droplet inside their membrane. Based on the amount of lipid they contain, one can consider the distribution of adipocyte per amount of lipid and observe a peculiar feature : the resulting distribution is bimodal, thus having two local maxima. The aim of this talk is to introduce a model built from the Lifshitz-Slyozov equations that is able to replicate this bimodale feature. I also introduce a microscopic scale model build from the Becker-Döring equations and show a new convergence result toward the Lifshitz-Slyozov-inspired model, which provides a rate of convergence. I will also present some extension to stochastic models, which support some extension of the deterministic model to better approximate data. Regarding the data, I’ll present some parameter estimation on measures from rats. | ||
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| Marie-José Chaava (Aix-Marseille Université) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Wed, 17. Jul 24, 14:40 |
| A continuous approach of modeling tumorigenesis and axons regulation for the pancreatic cancer. | ||
The pancreatic innervation undergoes dynamic remodeling during the development of pancreatic ductal adenocarcinoma (PDAC). Denervation experiments have shown that different types of axons can exert either pro- or anti-tumor effects, but conflicting results exist in the literature, leaving the overall influence of the nervous system on PDAC incompletely understood. To address this gap, we propose a continuous mathematical model of nerve-tumor interactions that allows in silico simulation of denervation at different phases of tumor development. This model takes into account the pro- or anti-tumor properties of different types of axons (sympathetic or sensory) and their distinct remodeling dynamics during PDAC development. We observe a “shift effect” where an initial pro-tumor effect of sympathetic axon denervation is later outweighed by the anti-tumor effect of sensory axon denervation, leading to a transition from an overall protective to a deleterious role of the nervous system on PDAC tumorigenesis. Our model also highlights the importance of the impact of sympathetic axon remodeling dynamics on tumor progression. These findings may guide strategies targeting the nervous system to improve PDAC treatment. | ||
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| Marcella Szopos (Université Paris Cité) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Wed, 17. Jul 24, 13:30 |
| Mathematical and computational modeling of ocular flows: challenges and opportunities | ||
Despite significant advances in the in silico modeling of human physiology, understanding the complex behavior of fluids in the eye and identifying the main factors that influence their dynamics is still a very challenging field. On the one hand, the description requires a multi-scale characterization, since these phenomena encompass a wide range of spatial and temporal scales, from the molecular level to networks of a few meters, between a one-second heartbeat and a lifetime. On the other hand, the fluid dynamics is influenced by the interaction with surrounding tissues and their temperature, which calls for a multi-physics approach. In addition, the geometric representation can be very complex and the availability of real data is scarce. In this challenging context, the aim of this talk is to present our continuous efforts from a modeling and numerical viewpoint to develop a powerful and flexible mathematical and computational framework called the Ocular Mathematical Virtual Simulator. The combined effects of ocular blood flow and different ocular tissues are described by a coupled hemodynamics and biomechanics model. The multi-scale aspect, essential to properly account for systemic effects of the blood circulation coupled with local effects on the tissues of interest, is represented by a coupled partial and ordinary differential equations for fluid flow. The PDE/ODE coupling is handled via (i) operator splitting for the time discretization, which provides modularity of the solution algorithm while preserving the physical energy at the discrete level; and (ii) Hybridizable Discontinuous Galerkin (HDG) method for the PDE discretization, which ensures conservation of fluxes of mass and linear momentum at the discrete level. A special interest is devoted to the issues of verification, validation and treatment of inherent uncertainties. Finally, we discuss some specific applications related to glaucoma, a leading cause of irreversible blindness worldwide, that currently lacks cure and for which existing treatments focus on managing the condition and slowing its progression. | ||
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| Carmella Moschella (Universität Wien) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Wed, 17. Jul 24, 11:20 |
| A model for non-instantaneous collisions with alignment | ||
In this talk I am going to consider a Boltzmann-type equation for the description of a collision dynamic which is not instantaneous. This new class of kinetic equations has been introduced by Kanzler, Schmeiser, and Tora to model ensembles of living agents, where the changes of state are the result of complicated internal processes, and not simple mechanical interactions. We extend their work introducing a first-order approximation to the instantaneous equation, where non-binary collisions are included. This is motivated by the fact that during an extended collision period there is a positive probability that a colliding pair is joined by additional particles. The interaction kernel is of alignment type, where the states of the particles approach each other. For this spatially homogeneous approximation, we check that the formal properties of the system are kept. Furthermore, existence and uniqueness of solutions and instantaneous limit are examined. | ||
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| Simon Labarthe (INRAe – Université de Bordeaux) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Wed, 17. Jul 24, 10:40 |
| Towards digital twins of microbial communities | ||
Microbial communities form complex ecosystems that provide beneficial services to humans in a variety of contexts, such as food fermentation, crop protection, bioprocessing or health and well-being. The complexity of microbial interactions makes it difficult to decipher the drivers of community dynamics and functions. Building digital twins of microbial communities could provide insights into their functioning, and strategies for improving the services they provide. In this talk, I will present genome-based models of microbial communities that predict functions and dynamics, and thus represent good candidates for digital twins. However, they induce a high numerical load, especially when coupled with PDE models of microbial populations. A surrogate modeling strategy will be used to provide fast approximations of the genome-based model, in order to overcome this difficulty. | ||
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| Sara Merino Aceituno (Universität Wien) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Wed, 17. Jul 24, 9:30 |
| Stability of equilibria in collective motion and phase transitions | ||
In this talk, I will review some questions that arise around the classical Vicsek model - which is a model for collective dynamics where agents move at a constant speed while trying to adopt the averaged orientation of their neighbours, up to some noise. I will discuss the emergence of bifurcations leading to disordered and ordered motion, depending on the local density of the agents. This is a very interesting phenomenon: it showcases how two completely different observed behaviours can appear simultaneously from agents that interact following the same rules. | ||
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| Tommaso Tenna (Université Côte D’Azur) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Tue, 16. Jul 24, 14:40 |
| Bridging Scales: Advancements in Hybrid Multiscale Modeling and Simulation for Cell Dynamics (PART 2) | ||
The adoption of hybrid models for self-organization dynamics allows to provide an accurate description of cell motion in tissues or organs. From a numerical point of view, the proposed approach may have drawbacks in terms of computational cost, if the number of cells involved significantly increases. In this perspective, the idea is to introduce a fully macroscopic mathematical model, in which cells are treated as a continuous cellular density. Starting from a class of hybrid ODE-PDE models, a new pressureless nonlocal Euler-type model with chemotaxis has been rigorously derived in [1], under the assumption of monokinetic initial data. Outside the monokinetic case, a numerical study has been performed in the one-dimensional case [2]. In this talk I will present some advancements in the numerical approximation of this model in the multidimensional case, to understand the role of different effects in the dynamics. Finally, parameter estimation of the macroscopic model is performed, in order to find the optimal parameters and to provide realistic numerical simulations. I will show different scenarios, comparing the nonlocal Euler-type model with chemotaxis models existing in the literature. This talk is based on an ongoing work with Marta Menci and Roberto Natalini. | ||
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| Marta Menci (Università Campus Bio-Medico di Roma) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Tue, 16. Jul 24, 13:30 |
| Bridging Scales: Advancements in Hybrid Multiscale Modeling and Simulation for Cell Dynamics (PART 1 | ||
The study of collective dynamics is attracting the interest of different research fields, both due to their wide range of applications and to their ability to model self-organization. The emergence of global patterns from local interactions can be easily observed in flock of birds, schools of fish, human crowds, but also cells exhibit collective behaviors in different biological processes characterizing the human body (e.g. in embryogenesis, wound healing, immune response, tumor growth). The main feature of collective cells migration is that the emergent behavior is also driven by chemical stimuli, and not only by mechanical interactions. In this talk I will present a general class of hybrid ODE-PDE models, gathering the advantages of multiscale descriptions. In this context, cells are modeled as discrete entities and their dynamics is given described by a system of second-order ODEs, while the chemical signal influencing the motion is modelled as a continuous signal solving a diffusive equation. The particular coupling of the two scales raises some issues that have been analytically investigated over the last years. Concerning applications, I will present recent advancements on a hybrid mathematical model inspired by Cancer-on-chip experiments, where tumor cells are treated with chemotherapy drug and secrete chemical signals in the environment, thus stimulating immune response. | ||
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| Florence Hubert (Aix-Marseille Université) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Tue, 16. Jul 24, 11:20 |
| Some mathematical model of cell migration | ||
Cell migration is a complex biological phenomenon playing an important role in many processes such as embryogenesis, but also in the development of pathologies such as cancer. The main driver of the motility is the actin network, the dynamics of which is regulated by many proteins. Mathematical models have been developped in the last decades to better understand this complexity. One of the difficulty leads on the representation of this moving domain. Several approaches have been proposed: Lagrangian Markers Cells [Edelstein-Kechet et al.(2011)], Level-set methods [Tesson et al.(2020)] or phase fields models [Ziebert-Aronson (2011)]. We propose in this talk to illustrate these methods with two biological issues. In the first one, we will model the impact of the microtubules on the process using the level set method. In the second one, we will use phase field models to explain atypical cases of adhesive haptotaxis [Luo et al (2020)], [Seveau Phd (2022)]. | ||
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| Claudia Wytrzens (Universität Wien) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Tue, 16. Jul 24, 10:40 |
| Modelling Volume Exclusion Interactions of Particles via Anisotropic Repulsion Potentials | ||
Volume exclusion interactions play a key role in many biological systems. In particular, it seems to be the key to explaining spontaneous alignment of anisotropic particles, for example, alignment of myxobacteria or fibers in a network. Most individual-based models impose this type of alignment in their equations. Here we do not wish to impose this type of alignment, but to investigate how it might emerge from volume exclusion interactions. To carry this out, volume exclusion interactions will be modelled via a soft anisotropic repulsion potential (which are vastly used in the literature of liquid crystals). We will present an individual-based model based on this potential and derive the corresponding kinetic and macroscopic equations. This approach allows us to understand how alignment emerges from volume exclusion and how it also affects not only the orientation of the particles, but also their positions. | ||
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| Datong Zhou (Penn-State University) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Tue, 16. Jul 24, 9:30 |
| Mean-field models of neural networks with generic heterogeneous connections and integrate-and-fire-type dynamics. | ||
We investigate the mean-field limits of large-scale networks of interacting biological neurons, represented by the so-called integrate-and-fire models. However, we do not assume any prior structure on the network but consider instead any connection weights that obey certain types of mean-field scaling. When the networks are dense, we are able to achieve a limit that resembles the widely recognized form of mean-field limit, through a graphon limit that tracks the role of individual neurons in the network. When the networks are potentially sparse, mathematically interpreting the role of individual neurons becomes increasingly difficult. Instead, we introduce novel statistical notions that directly describe the large-scale dynamics of networks. This is a joint work with P.-E. Jabin and V. Schmutz. | ||
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| Nicola Torres (Universidad di Granada) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Mon, 15. Jul 24, 16:10 |
| A qualitative analysis of an A-Beta-monomer model with inflammation processes for Alzheimer's disease | ||
We introduce and study a new model for the progression of Alzheimer's disease incorporating the interactions of A_beta-monomers, oligomers, microglial cells and interleukins with neurons through different mechanisms such as protein polymerization, inflammation processes and neural stress reactions. In order to understand the complete interactions between these elements, we study a spatially-homogeneous simplified model that allows to determine the effect of key parameters such as degradation rates in the asymptotic behavior of the system and the stability of equilibriums. We observe that inflammation appears to be a crucial factor in the initiation and progression of Alzheimer's disease through a phenomenon of hysteresis, which means that there exists a critical threshold of initial concentration of interleukins that determines if the disease persists or not in the long term. These results give perspectives on possible anti-inflammatory treatments that could be applied to mitigate the progression of Alzheimer's disease. We also present numerical simulations that allow to observe the effect of initial inflammation and spatial dependence. | ||
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| Thierry Goudon (Université Côte d’Azur) | WPI, OMP 1, Seminar Room 08.135 | Mon, 15. Jul 24, 15:00 |
| A PDE model for the interactiuon between tumor growth and immune response. | ||
We propose a PDE system intended to describe the earliest stages of the interactions between immune cells and tumor growth. The model is structured in size and space, and it takes into account the migration of the tumor antigen-specific cytotoxic effector cells towards the tumor micro-environment by a chemotactic mechanism. Remarkably, the model exhibits a possible control of the tumor growth by the immune response; nevertheless, the control is not complete in the sense that the asymptotic equilibrium states keep residual tumors and activated immune cells. We will discuss the mathematical modeling, numerical investigation and a few results on the analysis of the system. | ||
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| Alain Aspect | Festsaal TU Wien, Karlsplatz 1030 Wien | Fri, 21. Jun 24, 14:30 |
| 26th Pauli Colloquium "From Einstein and Bell to quantum technologies: entanglement in action" | ||
As pointed out by Einstein, and confirmed by the violation of Bell’s inequalities, entanglement of separated particles is an extraordinary feature of quantum mechanics, suggesting some kind of non- locality. It is now used in quantum technologies. After recalling what are Bell’s inequalities and their experimental tests, I will show how the notion of non-locality provides fruitful intuitions for some quantum communication methods. | ||
| Fernando Casas | WPI, OMP 1, Seminar Room 08.135 | Tue, 27. Feb 24, 10:00 |
| Symmetric-conjugate splitting methods for evolution equations of parabolic type | ||
In this talk I will provide a short introduction to a class of operator splitting methods with complex coefficients which possess a special symmetry, the so-called symmetric-conjugate methods, and analyze their application for the time integration of linear evolution problems. Including complex coefficients with non-negative real parts permits the design of favorable high-order schemes that remain stable in the context of parabolic problems. This sets aside the second-order barrier for standard splitting methods with real coefficients as well as the fourth-order barrier for modified splitting methods involving double commutators. Relevant applications include nonreversible systems and ground state computations for Schr{\"o}dinger equations based on the imaginary time propagation method. | ||
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| Sergio Blanes | WPI, OMP 1, Seminar Room 08.135 | Mon, 26. Feb 24, 10:00 |
| Splitting methods with complex coefficients for the numerical integration of quantum systems | ||
The evolution of most quantum systems is modeled by differential equation in the complex space. However, in general, the equations are numerically solved using integrators with real coefficients. To consider complex coefficients usually does not make the schemes computationally more costly and can provide more accurate results. In this talk, we explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schrödinger equation. There are pros (high accuracy and not to increase the cost) and cons (instability and loose of qualitative properties) when using complex coefficients. However, there is a class of methods with complex coefficients with a particular symmetry that keep most pros while avoid most cons. This class of integrators are stable and are conjugate to unitary methods for sufficiently small step sizes. These are promising methods that we will explore: we build new methods and we analyse their performance on several examples. This is joint work with Joakim Bernier, Fernando Casas and Alejandro Escorihuela. | ||
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| Yu Zhang (MMM Univ. Wien and Macau Univ. Science & Technology) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Tue, 16. Jan 24, 14:30 |
| Numerical Methods for Hydrodynamic Simulations and Linear Stability Analysis | ||
In this presentation, three projects are sketched: 1) F-Plane Approximation for Solar Simulation: We introduced the f-plane approximation into the ANTARES code and ran 3-D solar simulation with and without rotation, attempting to analyze how much influence rotation would have on the convection structures. 2) Linear Stability Analysis of an Incompressible Fluid with Vertical Shear in F-plane: Shear instability and GSF instability are two possible sources of extra mixing in stars to explain the differences between theoretical stellar evolution models and observations. We consider an incompressible fluid with vertical shear in f-plane and try to find out what really happens when shear instabilities coexist with GSF instabilities. 3) The Stability Analysis of Polar Cyclones on Saturn and Jupiter: The long-lived cyclones in the polar regions of Jupiter and Saturn have been explored for a long time. We aim to explain the number and location of Jupiter’s circumpolar cyclones and the absence of those on Saturn by linear stability analysis. This is ongoing joint work with O. Koch, F. Kupka and N.J. Mauser. | ||
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| Inmaculada Higueras (Public Univ. of Navarra) | WPI Seminar Room, 8th floor, Fak.Math. OMP1 | Tue, 16. Jan 24, 13:45 |
| IMplicti-EXplicit time stepping methods for some problems in astrophysics | ||
We consider equations of motion associated to a model in astrophysics. The PDE are firstly semi-discretized in space and subsequently integrated in time by IMplicit-EXplicit (IMEX) Runge-Kutta methods constructed to preserve different stability properties. For some simple examples, as well as for the problem of double-diffusive convection, it can be demonstrated that they provide a significant computational advantage over other methods from the literature. Ongoing work continues with the study of implementation issues as well as with the study and construction of robust IMEX schemes for some other problems in astrophysics. This is joint work with O. Koch and F. Kupka. | ||
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| Peter Korn | SkyLounge, 12th floor, Oskar-Morgenstern-Platz 1, 1090 | Fri, 3. Nov 23, 10:45 |
| PDE dynamics in numerical ultra-high-resolution climate modelling | ||
We discuss some aspects of the effort to produce a "digital twin" of the earth climate. The status of ultra-high-resolution numerical climate modelling and recent computational achievements are discussed. Mathematical challenges and opportunities arise when numerical models aim to represent an increasing number of turbulent scales. These challenges comprise the PDE of atmosphere and ocean dynamics, their numerical discretization and the modelling of (still) unresolved scales. This is part of the research of the DFG Forschungsgruppe FOR 5528: Mathematical Study of Geophysical Flow Models: Analysis and Computation. | ||
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| Vittorio Canuto | HS11, 2nd floor, Oskar-Morgenstern-Platz 1, 1090 Wien | Thu, 31. Aug 23, 15:00 |
| My Life as a Scientist: 50+ Years at NASA-GISS | ||
I take the audience on a scientific journey from the physics of neutron stars to cosmology and further on to turbulence and its role for oceaongraphy and climate modeling. Scientific highlights on this journey include an exact equation of state for neutron stars, results on cosmology, and a general turbulence model which has guided the modeling of transport processes in oceanography which is needed in climatology. From short encounters to longterm collaborations famous physicists are part of this story, including P.A.M. Dirac, W. Heisenberg, I. Rabi, J.A. Wheeler and many others. | ||
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| Damian Fabbian | WPI, OMP 1, Seminar Room 08.135 | Thu, 31. Aug 23, 10:10 |
| Stellar Atmospheres & Activity | ||
The atmospheres of most stars have at least some level of magnetic activity. This is modulated by variability, which manifests itself as varying magnetic strength across the stellar surface and in time as well as in the form of different magnetic behaviour of different stars. This is moreover intertwined with all the other physical effects occurring in the atmospheres of stars, in particular convection, radiative transfer and turbulence. In the case of the Sun, magnetic fields are known to be ubiquitous, at an average level of roughly 1 hG across its surface, which - inter alia - has an impact on its inferred temperature stratification and chemical abundance. It is especially interesting to understand solar magnetism, for example its main magnetic cycle, also in comparison to other stars, given the Sun's driving influence on life on Earth and as the base energy input for terrestrial climate. Knowledge of stellar activity is also crucial for improved exoplanet detection and characterisation. Our team is focussing on different aspects of stellar atmosphere physics, from the viewpoint of numerical (magneto-)hydrodynamic simulations. Recent examples include the production of models for stars of spectral type F to A, and the study of hard turbulence as possible driver of synchronised swaying atmospheric motions akin to the still unexplained effect of solar supergranulation. | ||
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| Petri Käpylä | WPI, OMP 1, Seminar Room 08.135 | Thu, 31. Aug 23, 9:30 |
| Convective scale, overshooting, and subadiabatic layers in deep stellar convection zones - Insights from 3D LES | ||
The overall understanding of solar and stellar convection has been questioned during the last decade or so with helioseismic results suggesting that the convective amplitudes at large horizontal scales in the Sun might be much lower than indicated by current simulations or mixing length estimates. A manifestation of this ``convective conundrum'' is that global simulations struggle to reproduce a solar-like differential rotation with a fast equator and slow poles with nominally solar parameters. A major contributor to this is that giant cell convection, with characteristic length scale comparable to the depth of the convection zone, is excited in simulations but appears to be much weaker in the Sun. A possible solution to this conundrum is that a large fraction of the solar convection zone is in fact stably stratified due to plumes originating near the surface and piercing the whole convection zone, such that giant cells are not excited. Non-rotating numerical simulations lend support to such non-local scenario of convection and lead to sizeable Schwarzschild-stable, yet convecting, layers in deep convection zones. Another possibility is that convection is rotationally constrained such that horizontal extent of convection cells is significantly reduced. New results from hydrodynamic rotating Cartesian convection simulations are presented that seek to capture the rotationally constrained convection near the base of the solar convection zone. The current results indicate that in models corresponding to the deep parts of the solar convection zone, the subadiabatic and overshoot layers are somewhat shallower than in the non-rotating case. Furthermore, these simulations suggest that deep convection in the Sun is not strongly rotationally constrained and that rotational suppression of large scale flows is weak. | ||
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| Teresa Braun | WPI, OMP 1, Seminar Room 08.135 | Wed, 30. Aug 23, 15:50 |
| Applying the Kuhfuss Convection Theory to Convective Envelopes | ||
In 1D stellar evolution models, the process of convection is often described using the mixing length theory (MLT). However, MLT does not account for the non-locality of convection, and an ad hoc implementation of overshooting is needed. The Kuhfuss theory is one of the theories that attempts to derive a more complete picture of turbulent convection. In this theory, non-locality is not implemented artificially, but is included in the theory. Both versions of the Kuhfuss theory, the 1-equation model as well as the 3-equation model, are implemented in the stellar evolution code GARSTEC and have already been tested on convective cores on the main sequence before (Ahlborn et al. 2022). Following these promising results for convection in stellar cores, we tested the Kuhfuss theory for convective envelopes. We applied the 1-equation model of the Kuhfuss convection theory to a stellar model calibrated to the Sun. Using helioseismic measurements of quantities of the convective envelope and interior structure, we quantified the differences and improvements from the Kuhfuss theory compared to MLT. We furthermore followed the evolution of stars to the red giant branch to study the influence of the Kuhfuss theory on the location of the red giant branch bump, which is known to be sensitive to the description and depth of convective overshooting. In the future, these cases will also be studied using the full 3-equation Kuhfuss model. | ||
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| Felix Ahlborn | WPI, OMP 1, Seminar Room 08.135 | Wed, 30. Aug 23, 14:40 |
| Non-local convection models in stellar evolution | ||
Observations of stars with convectively burning cores have shown that the size of these cores is substantially underestimated. The increase of the convective core size, known as overshooting, has profound effects on the stellar structure and evolution, e.g. affecting age estimates, luminosities or nucleosynthetic yields of stars. Here, we applied a turbulent convection theory to model the evolution of intermediate and high-mass stars. We predict the emergence of an overshooting zone and modifications to the thermal stratification. The application of a turbulent convection theory is a crucial step towards a more realistic description of convection in stellar models. The predictions of the turbulent convection model may be tested against a variety of different observations, e.g. spectroscopic observations of massive stars, asteroseismic observations or observations of detached binary systems. Finally, the predictions of the turbulent convection model can be compared to hydrodynamic simulations of turbulent convection. | ||
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| Günter Houdek | WPI, OMP 1, Seminar Room 08.135 | Wed, 30. Aug 23, 14:00 |
| Stellar convection and pulsation mode physics | ||
In this presentation I shall provide an overview of our current understanding of modelling energy exchange between stellar convection and oscillations in stars supporting solar-type oscillations. Stellar calculations, adopting a 1D, non-local, time-dependent convection model, are calibrated against seismic observations and 3D-simulation results. These stellar models are tested against data from the Sun and from Kepler main-sequence stars. This provides insight into the physical processes that determine energy transport in the outer stellar layers and to a better understanding of the so-called surface effects of pulsation frequencies. | ||
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| Gábor Kovács | WPI, OMP 1, Seminar Room 08.135 | Wed, 30. Aug 23, 11:20 |
| Convection and turbulence in classical variable stars: achievements and recent progress | ||
While all of the stars change their brightness during their lifetimes, there are many among them that do this on a human timescale (from less than a day to years) due to external or internal reasons. We call those stars classical variables, which exhibit a strong, stable radial pulsation with periods from 0.3-100 days. In these cases, the outer envelope of the star periodically expands and shrinks due to an effect tied to hydrogen and helium ionisations called the kappa mechanism. They are important to astronomers because their period is proportional to their average brightness, making them perfect distance indicators. Since the first electronic computers became available, astronomers have applied them to model the structure and dynamics of these (and every other) types of stars. The first attempts neglected convection and turbulence, considering only radiative energy transport. However, it soon turned out that we could not adequately describe pulsation without convection. Moreover, the different improved forms of static mixing length theory were also inadequate. Hence, massive research was started to create a time-dependent theory that can describe convection correctly in a one-dimensional approximation. These efforts revealed some hidden features of the phenomena but could not answer all of the questions raised. Since convection and non-radial pulsation are genuinely multi-dimensional phenomena, multi-D models seem inevitable, but this approach requires high computational performance, which was not available decades ago. Today, though we have better equipment, numerical modelling of turbulent convection in stars is still a great challenge due to the many magnitudes of scale it involves, especially in classical pulsators. In this talk, I highlight some of the achievements of this journey and show the recent developments and future aspects of turbulent RHD modelling in classical pulsating stars. | ||
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| Herbert Muthsam | WPI, OMP 1, Seminar Room 08.135 | Wed, 30. Aug 23, 10:10 |
| From turbulent to laminar: multidimensional simulations of solar granulation and pulsating stars | ||
We speak about numerical issues and results regarding the simulation of solar granulation flows and the pulsation-convection interaction in Cepheids in 3D and 2D, respectively. | ||
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| Friedrich Kupka | WPI, OMP 1, Seminar Room 08.135 | Wed, 30. Aug 23, 9:30 |
| A turbulent context | ||
In intention of this talk is to show how research on a rather specific topics from stellar astrophysics, the study of atmospheres of A-type stars, has led myself to numerous collaborations with researchers working in other fields such as meteorology, oceanography, numerical mathematics, and high preformance computing. To explain "turbulence" in the context of solar and stellar astrophysics, a short introduction into simulations of solar granulation will be given (much more details will follow in Herbert Muthsam's talk) followed by how turbulent convection is detected and modelled in A-type stars. Various modelling approaches have been used in this context: mixing lenth theory, two-point closure models, Reynolds stress models, and numerical simulations. The latter lead to the necessity to develop improved time integration methods which have first been probed in studies of semi-convection (diffusive convection). Studies in meteorology inspired new models for higher order moments required for Reynolds stress models. Finally, some result on the modelling of convective overshooting is presented which has been inspired by work that will be discussed in detail in other talks during the workshop (by Felix Ahlborn, Teresa Braun, Petri Käpylä). | ||
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| Rupert Klein | HS11, 2nd floor, Oskar-Morgenstern-Platz 1, 1090 Wien | Tue, 29. Aug 23, 15:40 |
| "Mathematical modelling in geophysical fluid dynamics" | ||
Three examples from geophysical fluid dynamics will showcase mathematical modelling as the "art of judicious simplification": The computational prediction of two seasonal to decadal phenomona, the "quasi-biennial oscillation" (QBO) and the "El Niño Southern Oscillation" (ENSO) became possible only after theoreticians had captured their essential causal structures in convincing reduced mathematical models. With our own research, we aim to similarly untangle the mechanisms behind the "rapid intensification" (RI) of tropical storms during their transition to hurricane strength. | ||
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| Dmitrii Mironov | HS11, 2nd floor, Oskar-Morgenstern-Platz 1, 1090 Wien | Tue, 29. Aug 23, 14:25 |
| Some Possibly Useful Thoughts on Modelling Turbulence in Operational Meteorology | ||
Turbulence closure models (parameterization schemes) currently used in numerical models of the atmosphere are discussed. The focus is on truncated one-equation turbulence kinetic energy (TKE) closure schemes that are arguably the present-day draft horses of operational meteorology, e.g., numerical weather prediction. Advantages and shortcomings of one-equation TKE schemes are outlined in the context of various operational constraints. A TKE scalar variance (TKESV) closure scheme is considered in some detail. The TKESV scheme carries transport equations (with due regard for the time-rate-of-change and third-order transport terms) for both the TKE and the variances and covariance of scalar quantities (e.g., temperature and humidity) that characterize turbulence potential energy. It is argued that the TKESV scheme has considerable advantages over the TKE scheme in terms of the essential physics but it can still meet severe operational requirements. Careful consideration is given to a number of tricky parameterization issues, including the pressure-scrambling effects in the Reynolds-stress and scalar-flux equations and the influence of clouds on turbulent mixing. An assumed PDF (probability distribution function) closure approach is briefly outlined. Finally, realizability of turbulence closures is considered within a more general framework of the problem of moments of the probability theory. | ||
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| Carsten Eden | HS11, 2nd floor, Oskar-Morgenstern-Platz 1, 1090 Wien | Tue, 29. Aug 23, 13:40 |
| "Eddies, waves and turbulence in the ocean" | ||
The three principal dynamical regimes of the atmosphere and the ocean are: i) small-scale turbulence down to the smallest space and time scales ii) internal gravity waves over a wide range of spatial scales iii) geostrophically balanced eddying motion at the largest space and time scales. All regimes are of turbulent character and need parameterisations in ocean components of climate models because of the lack of coarse grid resolution. A few aspects of closures for gravity wave turbulence are presented and closures for eddies in the ocean are discussed. | ||
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| Maurizio Salaris | HS11, 2nd floor, Oskar-Morgenstern-Platz 1, 1090 Wien | Tue, 29. Aug 23, 10:55 |
| Stellar evolution anf turbulent convection | ||
Stellar evolution models provide the foundation of several methods applied to study the evolutionary properties of stars and stellar populations, both Galactic and extragalactic. The accuracy of the results obtained with these techniques is tied to the accuracy of the stellar models, and in this context the correct treatment of turbulent convection is crucial. Unfortunately, the modelling of turbulent convection in stellar evolution computations is still affected by sizable uncertainties. The aim of this talk is to highlight the effect of turbulent convection on the most important stellar model predictions in the context of the study of stellar systems like star clusters and galaxies, and the (simple) prescriptions we currently use (out of necessity). | ||
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| Bérengère Dubrulle | HS11, 2nd floor, Oskar-Morgenstern-Platz 1, 1090 Wien | Tue, 29. Aug 23, 9:35 |
| “Irreversibility and Singularities in Turbulence" | ||
In a viscous fluid, the energy dissipation is the signature of the breaking of the time-reversal symmetry (hereafter TSB) t->-t, u-> -u, where u is the velocity. This symmetry of the Navier-Stokes equations is explicitly broken by viscosity. Yet, in the limit of large Reynolds numbers, when flow becomes turbulent, the non-dimensional energy dissipation per unit mass becomes independent of the viscosity, meaning that the time-reversal symmetry is spontaneously broken. Natural open questions related to such observation are: what is the mechanism of this spontaneous symmetry breaking? Can we associate the resulting time irreversibility to dynamical processes occurring in the flow? Can we devise tools to locally measure this time irreversibility? In this talk, I first show that the TSB is indeed akin to a spontaneous phase transition in the Reversible Navier-Stokes equations, a modification of the Navier-Stokes equation suggested by G. Gallavotti to ensure energy conservation and relevance of statistical physics interpretation. I then discuss a mechanism of the TSB in Navier-Stokes was first suggested by L. Onsager in 1949, in which quasi-singularities or singularities create a non-viscous dissipation. I exhibit the tools to track these quasi-singularities. I show how the application of these tools to velocity measurements in a turbulent swirling flow allows to detect Eulerian and Lagrangian signatures of irreversibility. This enables me to evidence the structures that are responsible for irreversibility and associate them with peculiar properties of the local velocity field or trajectories. | ||
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| Anna Marciniak-Czochra | WPI, OMP 1, Seminar Room 08.135 | Tue, 8. Aug 23, 14:00 |
| Transcriptomics-structured population models: From data to models and model-based data analysis | ||
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| Johnny Ottesen | WPI, OMP 1, Seminar Room 08.135 | Tue, 8. Aug 23, 11:15 |
| A Mathematical Modeling Approach to Clonal Architecture of Hematopoietic Cancers and its Impact on Stem Cell Dynamics, Disease Progression and Treatment Efficiency | ||
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| Doron Levy | WPI, OMP 1, Seminar Room 08.135 | Tue, 8. Aug 23, 10:00 |
| Mathematical Models for Immunotherapy | ||
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| Michael Bergmann | WPI, OMP 1, Seminar Room 08.135 | Tue, 8. Aug 23, 9:15 |
| Short Term Primary Tumor Culture to Understand the Response to Therapy in Colorectal Cancer | ||
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| Walter Berger | WPI, OMP 1, Seminar Room 08.135 | Mon, 7. Aug 23, 16:50 |
| Unusual Mode of Action for Usual Pharmacon | ||
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| Peter Roth | WPI, OMP 1, Seminar Room 08.135 | Mon, 7. Aug 23, 15:30 |
| Computational Medicine: Computer Science in Veterinary Medicine | ||
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| Benoît Perthame | WPI, OMP 1, Seminar Room 08.135 | Mon, 7. Aug 23, 14:15 |
| Analysis of Mechanical Models of Living Tissues and Free Boundary Problems | ||
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| Morten Andersen | WPI, OMP 1, Seminar Room 08.135 | Mon, 7. Aug 23, 13:30 |
| Blood Cancer (MPN) Progression and Treatments Clarified by Mathematical Modeling | ||
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| Luca Gerardo-Giorda | WPI, OMP 1, Seminar Room 08.135 | Mon, 7. Aug 23, 11:15 |
| Digital Twins in Computational Medicine | ||
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| Thomas Stiehl | WPI, OMP 1, Seminar Room 08.135 | Mon, 7. Aug 23, 10:00 |
| Mechanistic modeling of stem cell dynamics during inflammation, aging and cancer | ||
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| Francois Rincon & David Hosking | WPI, OMP 1, Seminar Room 08.135 | Fri, 4. Aug 23, 10:00 |
| Summary | ||
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| Claude Bardos & Nicolas Besse | WPI, OMP 1, Seminar Room 08.135 | Thu, 3. Aug 23, 16:15 |
| Homogeneous approximations for solutions of the Vlasov equation from quasilinear to Balescu-Lenard equation | ||
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| Archie Bott | WPI, OMP 1, Seminar Room 08.135 | Thu, 3. Aug 23, 10:45 |
| Firehose-induced collisionality | ||
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| Robbie Ewart | WPI, OMP 1, Seminar Room 08.135 | Thu, 3. Aug 23, 10:00 |
| TBA | ||
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| Nuno Loureiro | WPI, OMP 1, Seminar Room 08.135 | Wed, 2. Aug 23, 16:15 |
| Ruminations on reconnection | ||
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| Anatoly Spitkovsky | WPI, OMP 1, Seminar Room 08.135 | Wed, 2. Aug 23, 10:45 |
| 1) Recovering phase-space structures in particle simulations 2) Particle diffusion in large-amplitude waves near shocks | ||
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| Tunde Fulop | WPI, OMP 1, Seminar Room 08.135 | Wed, 2. Aug 23, 10:00 |
| Seeding an avalanche: which snowflake is most responsible | ||
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| Steve Cowley | WPI, OMP 1, Seminar Room 08.135 | Tue, 1. Aug 23, 17:00 |
| Magnetic reconnection from a different perspective | ||
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| Patrick Reichherzer | WPI, OMP 1, Seminar Room 08.135 | Tue, 1. Aug 23, 10:45 |
| Micromirrors mediating multiscale motions in magnetised megastructures | ||
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| Martin Lemoine | WPI, OMP 1, Seminar Room 08.135 | Tue, 1. Aug 23, 10:45 |
| Discussion on on particle acceleration in turbulent environments | ||
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| Philipp Kempski | WPI, OMP 1, Seminar Room 08.135 | Tue, 1. Aug 23, 10:00 |
| Towards a new theory of cosmic ray transport | ||
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| Bruno Despres | WPI, OMP 1, Seminar Room 08.135 | Mon, 31. Jul 23, 16:15 |
| 1) Scattering theory and plasma physics (Linear Landau Damping revisited, others, and extension to non homogeneous case) 2) Design of moment methods for numerical magnetized plasmas (with 3D calculation) | ||
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| Stephen Majeski | WPI, OMP 1, Seminar Room 08.135 | Mon, 31. Jul 23, 10:45 |
| Wave interactions and turbulence in collisionless, high-beta plasmas | ||
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| Alex Velberg | WPI, OMP 1, Seminar Room 08.135 | Mon, 31. Jul 23, 10:00 |
| Resistive-kink-induced turbulence in magnetic flux ropes | ||
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| Matthew Kunz | WPI, OMP 1, Seminar Room 08.135 | Fri, 28. Jul 23, 10:45 |
| Week 1 summary | ||
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| David Hosking | WPI, OMP 1, Seminar Room 08.135 | Fri, 28. Jul 23, 10:00 |
| Metastable MHD atmospheres and their relaxation | ||
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| Ian Abel | WPI, OMP 1, Seminar Room 08.135 | Thu, 27. Jul 23, 16:15 |
| Stability of centrifugal mirrors | ||
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| Georgia Acton | WPI, OMP 1, Seminar Room 08.135 | Thu, 27. Jul 23, 10:45 |
| TBC | ||
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| Hanne Thienpondt | WPI, OMP 1, Seminar Room 08.135 | Thu, 27. Jul 23, 10:00 |
| Turbulence prevents core particle depletion in stellarators | ||
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| Felix Parra Diaz | WPI, OMP 1, Seminar Room 08.135 | Wed, 26. Jul 23, 17:00 |
| Ideal MHD equilibria around stellarator rational flux surfaces | ||
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| Toby Adkins | WPI, OMP 1, Seminar Room 08.135 | Wed, 26. Jul 23, 11:30 |
| Do we really need the torus? Lessons learned from the humble slab (latest news on q scaling and thermo-Alfvenic instability in a GK torus). | ||
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| Palmen Ivanov | WPI, OMP 1, Seminar Room 08.135 | Wed, 26. Jul 23, 10:45 |
| Effects of flow shear in models of ITG and ETG turbulence | ||
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| Richard Nies | WPI, OMP 1, Seminar Room 08.135 | Wed, 26. Jul 23, 10:00 |
| Radial magnetic drift effects on critical balance and secondary instability | ||
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| Per Helander | WPI, OMP 1, Seminar Room 08.135 | Tue, 25. Jul 23, 16:15 |
| Upper bounds on gyrokinetic instabilities | ||
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| Romain Meyrand | WPI, OMP 1, Seminar Room 08.135 | Tue, 25. Jul 23, 10:45 |
| Reflection-driven turbulence beyond the Alfven surface | ||
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| Vinicius Duarte | WPI, OMP 1, Seminar Room 08.135 | Tue, 25. Jul 23, 10:00 |
| Formulation of a self-consistent reduced transport theory for discrete near-threshold modes | ||
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| Ben Chandran | WPI, OMP 1, Seminar Room 08.135 | Mon, 24. Jul 23, 16:15 |
| MTMs | ||
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| Silvia Trinczek | WPI, OMP 1, Seminar Room 08.135 | Mon, 24. Jul 23, 10:45 |
| Neoclassical transport in strong-gradient regions | ||
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| Thomas Foster | WPI, OMP 1, Seminar Room 08.135 | Mon, 24. Jul 23, 10:00 |
| Particles orbits near rational flux surfaces in stellarators | ||
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| Peter Schmelcher | HS 11 Fak. Math. OMP1, Uni Wien | Fri, 21. Jul 23, 14:15 |
| Impurities in highly imbalanced ultracold mixtures: Controlled transport and counterflow dynamics | ||
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| Ofir Alon | HS 11 Fak. Math. OMP1, Uni Wien | Fri, 21. Jul 23, 14:00 |
| How accurate the MCTDHB wavefunction is: Lessons from numerics, analytics, and examples | ||
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| Eric Fischer | HS 11 Fak. Math. OMP1, Uni Wien | Fri, 21. Jul 23, 11:15 |
| How Chemistry and Physics Meet in Optical Infrared Cavities: Application of the MCTDH Method to Vibrational Strong Coupling Models | ||
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| Jiajun Ren: | HS 11 Fak. Math. OMP1, Uni Wien | Fri, 21. Jul 23, 10:00 |
| Tensor Network Methods for Electron-Phonon Problems | ||
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| David Mendive-Tapia | HS 11 Fak. Math. OMP1, Uni Wien | Fri, 21. Jul 23, 9:15 |
| Finding optimal multi-layer trees through graph theory | ||
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| Graham Worth | HS 11 Fak. Math. OMP1, Uni Wien | Thu, 20. Jul 23, 16:00 |
| New Applications Using ML-MCTDH: Gaussian basis sets and Density Matrices | ||
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| Örs Legeza | HS 11 Fak. Math. OMP1, Uni Wien | Thu, 20. Jul 23, 14:45 |
| Simulation of long time and Lindbladian evolution via massively parallel hybrid CPU-GPU based tensor network state algorithms | ||
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| Micheline Soley | HS 11 Fak. Math. OMP1, Uni Wien | Thu, 20. Jul 23, 14:00 |
| Tensor Trains and Quantum Computing for Highly Multidimensional Molecular Simulations | ||
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| Tucker Carrington | HS 11 Fak. Math. OMP1, Uni Wien | Thu, 20. Jul 23, 11:15 |
| Obviating the need for as many points as basis functions when using collocation with MCTDH to do efficient and accurate quantum dynamics on a general PES | ||
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| Haobin Wang | HS 11 Fak. Math. OMP1, Uni Wien | Thu, 20. Jul 23, 10:00 |
| ML-MCTDH simulation in the interaction picture | ||
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| Roman Ellerbrock | HS 11 Fak. Math. OMP1, Uni Wien | Thu, 20. Jul 23, 9:15 |
| Quantum Circuit simulations with Tree Tensor Network States | ||
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| Sudip Sasmal | HS 11 Fak. Math. OMP1, Uni Wien | Wed, 19. Jul 23, 16:45 |
| Compact sum-of-products form of the molecular electronic Hamiltonian and its application within the MCTDH method | ||
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| Markus Schröder | HS 11 Fak. Math. OMP1, Uni Wien | Wed, 19. Jul 23, 16:00 |
| Compact representation of operators in sum-of-products form | ||
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| Daniel Pelaez | HS 11 Fak. Math. OMP1, Uni Wien | Wed, 19. Jul 23, 14:45 |
| Towards high-dimensional analytical sum-of-products representations | ||
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| Irene Burghardt | HS 11 Fak. Math. OMP1, Uni Wien | Wed, 19. Jul 23, 14:00 |
| Multiconfigurational quantum dynamics with multiplicative neural network potentials | ||
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| Uli Schollwöck | HS 11 Fak. Math. OMP1, Uni Wien | Wed, 19. Jul 23, 12:00 |
| Dynamics of singlet fission in covalently linked tetracene dimers using tensor network states | ||
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| Pierre-Nicholas Roy | HS 11 Fak. Math. OMP1, Uni Wien | Wed, 19. Jul 23, 10:00 |
| Quantum Critical Molecular assemblies: from matrix product states to path integrals | ||
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| Nina Glaser | HS 11 Fak. Math. OMP1, Uni Wien | Wed, 19. Jul 23, 9:15 |
| Large-scale anharmonic vibrational calculations with the DMRG algorithm | ||
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| Benedikt Kloss | HS 11 Fak. Math. OMP1, Uni Wien | Tue, 18. Jul 23, 16:45 |
| Subspace expansions: Schemes to dynamically adapt the approximation rank or bond dimension | ||
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| Christian Lubich | HS 11 Fak. Math. OMP1, Uni Wien | Tue, 18. Jul 23, 16:00 |
| Time integration of tree tensor networks | ||
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| Uwe Manthe | HS 11 Fak. Math. OMP1, Uni Wien | Tue, 18. Jul 23, 14:45 |
| Developments in the non-hierarchical multi-layer MCTDH approach | ||
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| Henrik R. Larsson | HS 11 Fak. Math. OMP1, Uni Wien | Tue, 18. Jul 23, 14:00 |
| Introduction to MCTDH and Tensor Network States | ||
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| Shi Jin (Inst. Natural Sciences - Shanghai Jiao Tong Univ.) | WPI Seminar room | Tue, 7. Feb 23, 14:30 |
| Consensus-based High Dimensional Global Non-convex Optimization in Machine Learning | ||
We introduce a stochastic interacting particle consensus system for global optimization of high dimensional non-convex functions. This algorithm does not use gradient of the function thus is suitable for non-smooth functions. We prove, for fully discrete systems, that under dimension-independent conditions on the parameters, with suitable initial data, the algorithms converge to the neighborhood of the global minimum almost surely. We also introduce an Adaptive Moment Estimation (ADAM) based version to significantly improve its performance in high-space dimension. | ||
| Note: External webpage: http://old.ins.sjtu.edu.cn/faculty/jinshi | ||
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| Nana Liu (INS – U. Michigan - Shanghai Jiao Tong Univ.) | WPI Seminar room | Tue, 31. Jan 23, 12:00 |
| Quantum simulation of partial differential equations via Schrödingerisation | ||
In this talk, I’ll introduce a simple new way – called „Schrödingerisation“ – to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the „warped phase transformation“, any linear partial differential equation can be recast into a system of Schrödinger’s equations – in real time — in a straightforward way. This can be seen directly on the level of the dynamical equations without more sophisticated methods. This approach is not only applicable to PDEs for classical problems but also those for quantum problems – like the preparation of quantum ground states, Gibbs states and the simulation of quantum states in random media in the semiclassical limit. | ||
| Note: External webpage: www.nanaliu.weebly.com | ||
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| Rupert Klein (FU Berlin) | Hörsaal 2 ”Eduard Suess” 2A122, 1 st floor UZA II, “Geozentrum”, Josef-Holaubek Platz 2, 1090 Wien | Mon, 12. Dec 22, 15:30 |
| Mathematics, a key to Climate Research | ||
Abstract: Mathematics in climate research is often thought to be mainly a provider of techniques for solving, e.g., the atmosphere and ocean flow equations. Three examples elucidate that its role is much broader and deeper: 1) Climate modelers often employ reduced forms of “the flow equations” for efficiency. Mathematical analysis helps assessing the regimes of validity of such models and defining conditions under which they can be solved robustly. 2) Climate is defined as “weather statistics”, and climate research investigates its change in time in our “single realization of Earth” with all its complexity. The required reliable notions of time dependent statistics for sparse data in high dimensions, however, remain to be established. Recent math- ematical research offers advanced data analysis techniques that could be “game changing” in this respect. 3) Climate research, economy, and the social sciences are to generate a scientific basis for informed political decision making. Subtle misunderstandings often hamper systematic progress in this area. Mathematical for- malization can help structuring discussions and bridging language barriers in interdisciplinary research. | ||
| Note: Click here for further information | ||
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| Jannis Körner (TU Wien) | WPI, OMP 1, Seminar Room 08.135 | Thu, 20. Oct 22, 15:30 |
| WKB scheme for the 1D stationary Schrödinger equation in the highly oscillating regime | ||
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| Erik Wahlen (U. Lund) | WPI, OMP 1, Seminar Room 08.135 | Thu, 20. Oct 22, 14:00 |
| Large amplitude solitary waves for the Whitham equation | ||
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| Ken McLaughlin (Tulane) | WPI, OMP 1, Seminar Room 08.135 | Thu, 20. Oct 22, 10:45 |
| Analysis of soliton interactions and random matrix theory | ||
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| Peter Perry (U. Kentucky) | WPI, OMP 1, Seminar Room 08.135 | Thu, 20. Oct 22, 9:15 |
| Towards Inverse Scattering for the intermediate long wave equation | ||
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| Douglas Svensson (NTNU) | WPI, OMP 1, Seminar Room 08.135 | Wed, 19. Oct 22, 15:30 |
| Asymmetric traveling waves for the gravity -capillary Whitahm equation | ||
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| Nikola Stoilov (U. Bourgogne) | WPI, OMP 1, Seminar Room 08.135 | Wed, 19. Oct 22, 14:00 |
| Numerical studies of the Zakharov-Kuznetsov family of equations | ||
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| Anton Arnold (TU Wien) | WPI, OMP 1, Seminar Room 08.135 | Wed, 19. Oct 22, 10:45 |
| All relative entropies for the Fokker-Planck equation | ||
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| Benoit Grebert (U. Nantes) | WPI, OMP 1, Seminar Room 08.135 | Wed, 19. Oct 22, 9:15 |
| Dynamics of Hamiltonian PDEs at low regularity | ||
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| Jiao He (U. Paris-Saclay) | WPI, OMP 1, Seminar Room 08.135 | Tue, 18. Oct 22, 15:30 |
| Some work in progress on integrability of the Kadomtsev-Petviashvili-II equation | ||
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| Petar Topalov (Northeastern U. College of Science) | WPI, OMP 1, Seminar Room 08.135 | Tue, 18. Oct 22, 14:00 |
| Spatially quasi-periodic solutions of the Euler equation | ||
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| Patrick Gerard (U. Paris-Saclay) | WPI, OMP 1, Seminar Room 08.135 | Tue, 18. Oct 22, 10:45 |
| Doubly periodic solutions of the Benjamin-Ono equation | ||
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| Christian Klein (U. Bourgogne) | WPI, OMP 1, Seminar Room 08.135 | Tue, 18. Oct 22, 9:15 |
| Complex geometric optics for the Davey-Stewartson-II equation | ||
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| Jakob Möller (U. Wien) | WPI, OMP 1, Seminar Room 08.135 | Mon, 17. Oct 22, 16:45 |
| Semiclassical limit of Pauli-Poisswell by WKB and Wigner methods | ||
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| Rémi Carles (CNRS Rennes) | WPI, OMP 1, Seminar Room 08.135 | Mon, 17. Oct 22, 15:45 |
| Time dependent Hartree approximation in quantum dynamics | ||
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| Jean-Claude Saut (U. Paris-Saclay) | WPI, OMP 1, Seminar Room 08.135 | Mon, 17. Oct 22, 14:30 |
| Old and new on Boussinesq systems | ||
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| Christian Lubich (U. Tübingen) | HS13, 2nd floor Fak Math Oskar Morgensternplatz 1 | Tue, 27. Sep 22, 14:00 |
| Time integration of tree tensor networks | ||
I first report on recent numerical experiments with time-dependent tree tensor network algorithms for the approximation of quantum spin systems. I will then describe the basics in the design of time integration methods that are robust to the usual presence of small singular values, that have good structure-preserving properties (norm, energy conservation or dissipation), and that allow for rank (= bond dimension) adaptivity and also have some parallelism. This discussion of basic concepts will be done for the smallest possible type of tensor network differential equations, namely low-rank matrix differential equations. Once this simplest case is understood, there is a systematic path to the extension of the integrators and their favourable properties to general tree tensor networks. This talk is based on joint work with many colleagues and former and present students, among which I wish to single out Othmar Koch for the first mathematical work on dynamical low-rank approximation (DLRA) in 2007, Ivan Oseledets for jointly finding the first robust DLRA integrator (the projector-splitting integrator) in 2014, Gianluca Ceruti for jointly finding the Basis Update & Galerkin (BUG) integrators in 2021, and him and Hanna Walach and Dominik Sulz for the recent systematic extension from low-rank matrices to general tree tensor networks. | ||
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| Christian Kühnlein | Wed, 17. Aug 22, 16:00 | |
| Developing a performance-portable finite-volume model for numerical weather prediction) | ||
| Note: (remote) | ||
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| Rupert Klein | Wed, 17. Aug 22, 15:00 | |
| Aspects of the BK19 scheme: seamlessness & the Euler equations in two almost linear steps | ||
| Note: (in presence) | ||
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| Joachim Schöberl | Wed, 17. Aug 22, 14:00 | |
| Simulation of Moist Air by Discontinuous Galerkin Methods within NGSolve | ||
| Note: (in presence) | ||
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| Gottfried Hastermann | Tue, 16. Aug 22, 17:15 | |
| Analysis of the cell-vertex finite volume method for pseudo-incompressible divergence constraints on quadrilateral and cuboid meshes | ||
| Note: (in presence) | ||
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| Felix Jochum | Tue, 16. Aug 22, 16:15 | |
| Implementing terrain-following coordinates into a semi-implicit pseudo-incompressible flow solver | ||
| Note: (in presence) | ||
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| Ray Chew | Tue, 16. Aug 22, 14:30 | |
| Balanced data assimilation with a blended numerical model: Acoustic imbalances | ||
| Note: (in presence) | ||
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| Piotr Smolarkiewicz | Mon, 15. Aug 22, 17:15 | |
| A suite of Richardson preconditioners for semi-implicit all-scale atmospheric models | ||
| Note: (remote) | ||
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| Joanna Szmelter | Mon, 15. Aug 22, 16:15 | |
| Preconditioning elliptic operators in high-performance all-scale atmospheric models on unstructured meshes | ||
| Note: with M. Gillard (Loughborough University) & F. Cocetta (Centro Euro-Mediterraneo Sui Cambiamenti Climatici) (in presence) | ||
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| Tommaso Benacchio | Mon, 15. Aug 22, 14:30 | |
| A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics | ||
| Note: (remote) | ||
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| Nicolas Besse | Mon, 20. Dec 21, 15:30 | |
| Trying to prove quasilinear theory in plasma physics | ||
The aim of quasilinear theory is to explain relaxation or saturation of kinetic instabilities governed by the Vlasov-Poisson (VP) equation, by showing that in fact the Hamiltonian dynamics of VP can be approximated by a diffusion equation in velocity for the space-average distribution function. | ||
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| Ivan Moyano | Mon, 20. Dec 21, 15:00 | |
| Unique continuation, Carleman estimates and propagation of smallness with applications in observability | ||
Based on a series of works in collaboration with Gilles Lebeau and Nicolas Burq -Propagation of smallness and control for heat equations (with Nicolas Burq, to appear in JEMS), -Spectral Inequalities for the Schrödinger operator (with Gilles Lebeau). -Propagation of smallness and spectral estimates (with Nicolas Burq) And the recent advances in propagation of smallness introduced by Logonuv and Malinnikova. A. Logunov and E. Malinnikova. Quantitative propagation of smallness for solutions of elliptic equations. Preprint, Arxiv, (arXiv:1711.10076), 2017 A. Logunov. Nodal sets of Laplace eigenfunctions : polynomial upper estimates of the Hausdorff measure. Ann. of Math. (2), 187(1):221–239, 2018. | ||
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| Jakob Möller | Mon, 20. Dec 21, 12:30 | |
| The Pauli-Poisson equation and its cassical limit | ||
The Pauli-Poisson equation is a semi-relativistic description of electrons under the influence of a given linear (strong) magnetic field and a self-consistent electric potential computed from the Poisson equation in 3 space dimensions. It is a system of two magnetic Schrödinger type equations for the two components of the spinor, coupled by the additional Stern-Gerlach term of magnetic field and spin represented by the Pauli matrices. On the other hand the Pauli-Poiswell equation includes the self-consistent description of the magnetic field by coupling it via a three Poisson equations with the Pauli current as source term to the Pauli equation. The Pauli-Poiswell equation offers a fully self-consistent description of spin-1/2-particles in the semi-relativistic regime. We introduce the equations and study the semiclassical limit of Pauli-Poisson towards a semi-relativistic Vlasov equation with Lorentz force coupled to the Poisson equation. We use Wigner transform methods and a mixed state formulation, extending the work of Lions-Paul and Markowich-Mauser on the semiclassical limit of the Schrödinger-Poisson equation. We also present a result on global weak solutions of the Pauli-Poiswell equation. | ||
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| Francois Golse | Mon, 20. Dec 21, 12:00 | |
| From N-Body Schrödinger to Euler-Poisson | ||
This talk presents a joint mean-field and classical limit by which the Euler-Poisson system is rigorously derived from the N-body Schrödinger equation with Coulomb interaction in space dimension 3. One of the key ingredients in this derivation is a remarkable inequality for the Coulomb potential which has been obtained by S. Serfaty in 2020 (Duke Math. J.). 2) | ||
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| Didier Pilod | Fri, 26. Nov 21, 10:30 | |
| Unconditional uniqueness for the Benjamin-Ono equation POSTPONED | ||
We study the unconditional uniqueness of solutions to the Benjamin-Ono equation with initial data in Hs, both on the real line and on the torus. We use the gauge transformation of Tao and two iterations of normal form reductions via integration by parts in time. By employing a refined Strichartz estimate we establish the result below the regularity threshold s = 1/6. As a by-product of our proof, we also obtain a nonlinear smoothing property on the gauge variable at the same level of regularity. This talk is based on a joint work with Razvan Mosincat (University of Bergen). | ||
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| Ola Maehlen | Fri, 26. Nov 21, 9:15 | |
| One-sided Hölder regularity of global weak solutions of negative order dis- persive equations | ||
The majority of dispersive equations in one space-dimension can be realized as dispersive perturbations of the Burgers equation ut + uux = Lux, where L is a local or nonlocal symmetric operator. For negative order dispersion, the Burg- ers’ nonlinearity dominates and classical solutions break down due to shock-formation/wave- breaking. Using hyperbolic techniques we establish global existence and uniqueness of entropy solutions, with L2 initial data, for a family of negative order dispersive equations, but our main focus will be on a new generalization of the classical Oleïnik estimate for Burgers equation. We obtain one sided Hölder regularity for the solutions, which in turn controls their height and provides a novel bound of the lifespan of classical solutions based on their initial skewness. This is joint work with Jun Xue (NTNU). | ||
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| Nikola Stoilov | Thu, 25. Nov 21, 10:45 | |
| Numerical study of Davey-Stewartson -I I systems | ||
An efficient high precision hybrid numerical approach for integrable Davey-Stewartson (DS) I equations for trivial boundary conditions at infinity is presented for Schwartz class initial data. The code is used for a detailed numerical study of DS I solutions in this class. Localized stationary solutions are constructed and shown to be unstable against dispersion and blow-up. A finite-time blow-up of initial data in the Schwartz class of smooth rapidly decreasing functions is discussed. | ||
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| Anton Arnold | Thu, 25. Nov 21, 9:15 | |
| Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium | ||
We are concerned with finding Fokker-Planck equations in whole space with the fastest exponential decay towards a given equilibrium. For a prescribed, anisotropic Gaussian we determine a non-symmetric Fokker-Planck equation with linear drift that shows the highest exponential decay rate for the convergence of its solutions towards equilibrium. At the same time it has to allow for a decay estimate with a multiplicative constant arbitrary close to its infimum. This infimum is 1, corresponding to the high-rotational limit in the Fokker-Planck drift. Such an optimal Fokker-planck equation is constructed explicitly with a diffusion matrix of rank one, hence being hypocoercive. The proof is based on the recent result that the L2- projector norms of the Fokker-Planck equation and of its drift-ODE coincide. Finally we give an outlook onto using Fokker-Planck equation with t-dependent coefficients. This talk is based on a joint work with Beatrice Signorello. | ||
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| Goeksu Oruk | Wed, 24. Nov 21, 15:15 | |
| A Numerical Approach for the Spectral Stability of Periodic Travelling Wave Solutions to the Fractional Benjamin-Bona-Mahony Equation | ||
Currently, the studies on periodic travelling waves of the nonlinear dispersive equations are becoming very popular. In this study we investigate the spectral stability of the periodic waves for the fractional Benjamin-Bona-Mahony (fBBM) equation, numerically. For the numerical generation of periodic travelling wave solutions we use an iteration method which is based on a modification of Petviashvili algorithm. This is a joint work with S. Amaral, H. Borluk, G.M. Muslu and F. Natali. | ||
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| Christian Klein | Wed, 24. Nov 21, 14:00 | |
| Hybrid approaches to Davey-Stewartson II systems | ||
We present a detailed numerical study of solutions to Davey-Stewartson (DS) II systems, nonlocal non-linear Schrödinger equations in two spatial dimensions. A possible blow-up of solutions is studied, a conjecture for a self-similar blow-up is formulated. In the integrable cases, numerical and hybrid approaches for the inverse scattering are presented. | ||
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| Thomas Kappeler | Wed, 24. Nov 21, 10:45 | |
| Normal form coordinates for the Benjamin-Ono equation having ex- pansions in terms of pseudo-differential operators | ||
Using the Birkhoff map of the Benjamin-Ono equation as a starting point, we deform it near an arbitrary compact family of finite dimensional tori, invariant under the Benjamin-Ono flow, so that the following main properties hold: (i) When restricted to the family of finite dimensional tori, the transformation coincides with the Birkhoff map. (ii) Up to a remainder term, which is smoothing to any given order, it is a pseudo-differential operator of order 0, with principal part given by the Fourier transform, modified by a phase factor. (iii) The transformation is canonical and the pullback of the Benjamin-Ono Hamiltonian by it is in normal form up to order three. Such coordinates are a key ingredient for studying the stability of finite gap solutions of arbitrary size of the Benjamin-Ono equation under small, quasi-linear, momentum preserving perturbations. This is joint work with Riccardo Montalto. | ||
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| Patrick Gérard | Wed, 24. Nov 21, 9:15 | |
| High frequency approximation of solutions of the Benjamin-Ono equation on the torus | ||
For solutions of the Benjamin-Ono equation with periodic boundary conditions, I will discuss the link in the high frequency regime between the nonlinear Fourier transform inherited from the integrable structure, and a gauge transform introduced by T. Tao in 2004 in the context of the low regularity initial value problem. As an application, we will get optimal high frequency approximations of solutions. This talk is based on a recent joint work with T. Kappeler and P. Topalov. | ||
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| Jean-Claude Saut | Tue, 23. Nov 21, 14:30 | |
| New and old on the Intermediate Long Wave equation | ||
We survey new and old results on the Intermediate Long Wave (ILW) equation from modeling, PDE and integrability aspects. | ||
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| Golinski, Tomasz | OMP 1, HS 11 | Fri, 20. Aug 21, 16:30 |
| Restricted Grassmannian and integrable systems around it | ||
The talk deals with the restricted Grassmannian which is a Hilbert manifold and related Banach Lie-Poisson spaces. One of the integrable systems related to this setup is of course the KdV equation. Using Magri method it is also possible to define another infinite hierarchy of differential equations on a certain central extension of a Banach Lie-Poisson space. Using integral of motions it is possible to write down solutions in particular cases. | ||
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| Slizewska, Aneta | OMP 1, HS 11 | Fri, 20. Aug 21, 15:00 |
| Fibre-wise linear Poisson structures related to W-algebras | ||
see external webpage | ||
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| Nahari, Hadi | OMP 1, HS 11 | Fri, 20. Aug 21, 14:00 |
| Morita equivalence of singular Riemannian foliations and I-Poisson geometry | ||
We define the notion of Morita equivalence for singular Riemannian foliations (SRFs) such that the underlying singular foliations are Hausdorff-Morita equivalent as recently introduced by Garmendia and Zambon. We then define a functor from SRFs to the category of I-Poisson manifolds, where the objects are Poisson manifolds together with appropriate ideals and morphisms are defined as a particular relaxation of Poisson maps. We show that Morita equivalent SRFs are mapped to I-Poisson manifolds with isomorphic Poisson algebra of smooth functions on the symplectically reduced spaces. This is joint work in progress with T. Strobl. | ||
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| Seol, Seokbong | OMP 1, HS 11 | Fri, 20. Aug 21, 13:30 |
| Formal exponential map of differential graded manifolds | ||
Exponential maps arise naturally in Lie theory and in the context of smooth manifolds endowed with affine connections. The Poincaré--Birkhoff--Witt isomorphism and the complete symbols of differential operators are related to these classical exponential maps through their infinite-order jets. The construction of (jets of) exponential maps can be extended to differential graded (dg) manifolds. As a consequence, the space of vector fields of any dg manifold inherits an L-infinity algebra structure, which is related to the Atiyah class of the dg manifold. Specializing this construction to the dg manifold arising from a foliation of a smooth manifold, one obtains an L-infinity structure on the de Rham complex of the foliation. In particular, a complex manifold can be regarded as a sort of `complexified' foliation. It turns out that the induced L-infinity structure is quasi-isomorphic to the L-infinity structure associated to the Atiyah class of the holomorphic tangent bundle on the Dolbeault complex first discovered by Kapranov. This is a joint work with Mathieu Stiénon and Ping Xu. | ||
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| Visman, Cornelia ((Univ. de Vest din Timisoara) / Haller Stefan (Univ. Wien) | OMP 1, HS 11 | Fri, 20. Aug 21, 11:30 |
| Infinite dimensional Grassmannians and flag manifolds | ||
see external webpage | ||
| Note: Minicourse (4) | ||
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| Beltita, Daniel (Inst.of Mathematics | OMP 1, HS 11 | Fri, 20. Aug 21, 10:00 |
| Poisson geometrical aspects of von Neumann algebras | ||
We plan to discuss certain genuine Poisson geometrical structures that arise in the theory of operator algebras on Hilbert spaces. Lecture 1 should be a gentle introduction to the basic notions on operator algebras that are needed later, with emphasis on the so-called standard form of von Neumann algebras that goes back to the PhD thesis of of U. Haagerup (1973). In Lecture 2, the focus is on the Poisson bracket carried by the predual of any von Neumann algebra, which turns out to admit smooth symplectic leaves, just as in the case of finite-dimensional Poisson manifolds. This lecture is partly based on joint work with T.S. Ratiu (2005). Finally, in Lecture 3, the geometric structures underlying the standard representations are pointed out, thereby presenting infinite-dimensional versions of presymplectic groupoids. This lecture is based on joint work with A. Odzijewicz (2019). | ||
| Note: Minicourse (3) | ||
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| Preston, Stephen (Brooklyn College) | OMP 1, HS 11 | Thu, 19. Aug 21, 16:30 |
| Breakdown of the mu-Camassa-Holm equation | ||
see external webpage | ||
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| Zambon, Marco (KU Leuven) | OMP 1, HS 11 | Thu, 19. Aug 21, 15:00 |
| Singular subalgebroids and their integrations | ||
see external webpage | ||
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| Kadiyan, Lory (Max Planck Institut, Bonn) | OMP 1, HS 11 | Thu, 19. Aug 21, 14:00 |
| The Lie algebroids of diffeological groupoids | ||
see external webpage | ||
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| Villatoro, Joel (KU Leuven) | OMP 1, HS 11 | Thu, 19. Aug 21, 13:30 |
| Paths in Lie-Rinehart algebras | ||
In this talk I will discuss how one can construct an infinite dimensional space of paths associated to a sheaf of Lie-Rinehart algebras. We will briefly examine some of the topological properties of this path space and how it can be used to construct a diffeological groupoid which appears to integrate the underlying sheaf. We will also take a look at some motivating examples for studying sheaves of Lie-Rinehart algebras over manifolds. | ||
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| Garmendia, Alfonso (Univ. Potsdam) | OMP 1, HS 11 | Thu, 19. Aug 21, 12:00 |
| Path Integration: The fundamental groupoid of a singular foliation | ||
In this talk I will present the diffeological space of paths along a singular foliation and its groupoid structure. I will also show how to construct the fundamental groupoid of a singular foliation from its diffeological space of paths. This is a presentation of the joint work with Joel Villatoro entitled "Integration of singular foliations via paths" and to be published on IMRN. | ||
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| Visman, Cornelia ((Univ. de Vest din Timisoara) / Haller Stefan (Univ. Wien) | OMP 1, HS 11 | Thu, 19. Aug 21, 10:45 |
| Infinite dimensional Grassmannians and flag manifolds | ||
see external webpage | ||
| Note: Minicourse (3) | ||
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| Blohmann, Christian (Max-Planck-Institut f. Mathematik, Bonn) | OMP 1, HS 11 | Thu, 19. Aug 21, 9:30 |
| Diffeological groupoids | ||
Diffeological groupoids appear in many areas of mathematics, such as infinite-dimensional Lie theory, classical field theory, deformation theory, and moduli spaces. The category of diffeological spaces, however, is too general and does not have a good differential calculus, which would be needed for a Lie theory of diffeological groupoids. I will introduce the notion of elastic diffeological spaces and show that these form a subcategory with an abstract tangent structure in the sense of Rosicky. The tangent structure yields a Cartan calculus consisting of vector fields, differential forms, the de Rham differential, inner derivatives, and Lie derivatives, satisfying the usual relations. Surprisingly, all diffeological groups are elastic. I then introduce the notion of diffeological Lie algebroids and show that the invariant vector fields of an elastic diffeological groupoid form a diffeological Lie algebroid. As application, I will revisit a diffeological groupoid that arises in lorentzian geometry whose diffeological Lie algebroid encodes the Poisson brackets of the Gauss-Codazzi constraint functions. | ||
| Note: Minicourse (3) | ||
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| Visman, Cornelia (Univ. de Vest din Timisoara) / Haller Stefan (Univ. Wien) | OMP 1, HS 11 | Wed, 18. Aug 21, 12:00 |
| Infinite dimensional Grassmannians and flag manifolds | ||
see external webpage | ||
| Note: Minicourse (2) | ||
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| Blohmann, Christian (Max-Planck-Institut f. Mathematik, Bonn) | OMP 1, HS 11 | Wed, 18. Aug 21, 10:45 |
| Diffeological groupoids | ||
Diffeological groupoids appear in many areas of mathematics, such as infinite-dimensional Lie theory, classical field theory, deformation theory, and moduli spaces. The category of diffeological spaces, however, is too general and does not have a good differential calculus, which would be needed for a Lie theory of diffeological groupoids. I will introduce the notion of elastic diffeological spaces and show that these form a subcategory with an abstract tangent structure in the sense of Rosicky. The tangent structure yields a Cartan calculus consisting of vector fields, differential forms, the de Rham differential, inner derivatives, and Lie derivatives, satisfying the usual relations. Surprisingly, all diffeological groups are elastic. I then introduce the notion of diffeological Lie algebroids and show that the invariant vector fields of an elastic diffeological groupoid form a diffeological Lie algebroid. As application, I will revisit a diffeological groupoid that arises in lorentzian geometry whose diffeological Lie algebroid encodes the Poisson brackets of the Gauss-Codazzi constraint functions. | ||
| Note: Minicourse (2) | ||
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| Beltita, Daniel (Inst.of Mathematics | Wed, 18. Aug 21, 9:30 | |
| Poisson geometrical aspects of von Neumann algebras | ||
We plan to discuss certain genuine Poisson geometrical structures that arise in the theory of operator algebras on Hilbert spaces. Lecture 1 should be a gentle introduction to the basic notions on operator algebras that are needed later, with emphasis on the so-called standard form of von Neumann algebras that goes back to the PhD thesis of of U. Haagerup (1973). In Lecture 2, the focus is on the Poisson bracket carried by the predual of any von Neumann algebra, which turns out to admit smooth symplectic leaves, just as in the case of finite-dimensional Poisson manifolds. This lecture is partly based on joint work with T.S. Ratiu (2005). Finally, in Lecture 3, the geometric structures underlying the standard representations are pointed out, thereby presenting infinite-dimensional versions of presymplectic groupoids. This lecture is based on joint work with A. Odzijewicz (2019). | ||
| Note: Minicourse (2) | ||
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| Diez, Tobias (TU Delft) | OMP 1, HS 11 | Tue, 17. Aug 21, 16:30 |
| A journey through the infinite lands of symplectic geometry | ||
I will discuss different aspects of infinite-dimensional symplectic geometry. Why is it interesting and what are important applications? What are the common technical issues in the infinite-dimensional setting and how to overcome them? In particular, I will explain how the Marle-Guillemin-Sternberg local normal form and symplectic reduction work in infinite dimensions. | ||
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| Janssens, Bas (TU Delft) | OMP 1, HS 11 | Tue, 17. Aug 21, 15:00 |
| Localization for positive energy representations of gauge groups | ||
see external webpage | ||
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| Ryvkin, Leonid (Univ. Göttingen) | Tue, 17. Aug 21, 14:00 | |
| Extensions for the Poisson algebra of a symplectic manifold | ||
see external webpage | ||
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| Miaskiwskyi, Lukas | OMP 1, HS 11 | Tue, 17. Aug 21, 13:30 |
| Continuous Lie Algebra Homology of Gauge Algebras | ||
Quantizations of infinitesimal gauge symmetries are classified in terms of the continuous Lie algebra cohomology group of gauge algebras in degree 2. For gauge bundles with semisimple fibers, this space was calculated by Janssens-Wockel (2013), their method relying heavily on the low degree of the cohomology group. In this talk, we extend these results to homology in higher degree. To this end, we review some homological algebra for topological chain complexes and use it to lift the well-known Loday-Quillen-Tsygan-Theorem (1983, 1984) from a statement in algebraic Lie algebra homology to one that takes topological data into account. For globally trivial gauge algebras whose fibres are classical Lie algebras, this calculates a certain stable part of continuous homology. A similar description was given by Feigin (1988), but lacking a detailed proof. Finally, we use the results for trivial bundles to construct a Gelfand Fuks-like local-to-global spectral sequence from which homological information about nontrivial gauge algebras can be extracted. If time permits, we discuss obstructions to a full understanding of this spectral sequence. This talk is based on joint work with Bas Janssens. | ||
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| Khavkine, Igor (Akad. ved Ceske republiky, Prague) | OMP 1, HS 11 | Tue, 17. Aug 21, 12:00 |
| The geometry of analytic structures | ||
Analytic structure on a manifold (adapted to a specific analytic atlas) is a special type of G-structure of infinite order. I will report on work in progress that aims to answer the following questions: What is an almost analytic structure? What are obstructions to integrability? Does formal integrability imply integrability? What natural geometric objects define corresponding analytic structures? | ||
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| Visman, Cornelia (Univ. de Vest din Timisoara) / Haller Stefan (Univ. Wien) | Tue, 17. Aug 21, 10:45 | |
| Infinite dimensional Grassmannians and flag manifolds | ||
see external homepage | ||
| Note: Minicourse (1) | ||
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| Beltita, Daniel (Inst.of Mathematics | OMP 1, HS 11 | Tue, 17. Aug 21, 9:30 |
| Poisson geometrical aspects of von Neumann algebras | ||
We plan to discuss certain genuine Poisson geometrical structures that arise in the theory of operator algebras on Hilbert spaces. Lecture 1 should be a gentle introduction to the basic notions on operator algebras that are needed later, with emphasis on the so-called standard form of von Neumann algebras that goes back to the PhD thesis of of U. Haagerup (1973). In Lecture 2, the focus is on the Poisson bracket carried by the predual of any von Neumann algebra, which turns out to admit smooth symplectic leaves, just as in the case of finite-dimensional Poisson manifolds. This lecture is partly based on joint work with T.S. Ratiu (2005). Finally, in Lecture 3, the geometric structures underlying the standard representations are pointed out, thereby presenting infinite-dimensional versions of presymplectic groupoids. This lecture is based on joint work with A. Odzijewicz (2019). | ||
| Note: Minicourse (1) | ||
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| Larotonda, Gabriel (Univ. de Buenos Aires) | OMP 1, HS 11 | Mon, 16. Aug 21, 16:30 |
| Hamiltonian actions of compact Lie groups and their induced geometry | ||
see external webpage | ||
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| Marcut, Ioan (Radboud Univ., Nijmegen) | OMP 1, HS 11 | Mon, 16. Aug 21, 15:00 |
| Rigidity of solutions to PDEs with symmetry | ||
Local normal form theorems in differential geometry are often the manifestation of rigidity of the structure in normal form. For example, the existence of local Darboux coordinates in symplectic geometry follows from the fact that, locally, the standard symplectic structure has no deformations. After introducing closed pseudogroups and their associated sheaf of Lie algebras, I will discuss a general local rigidity result for solutions to PDE’s under the action of a closed pseudogroup of symmetries. The result is of the form: “infinitesimal tame rigidity” implies “tame rigidity”; it is in the smooth setting, and the proof uses the Nash-Moser fast convergence method. Several classical theorems fit in our setting: e.g. the Newlander-Nirenberg theorem in complex geometry, Conn’s theorem in Poisson geometry. This is a joint work with Roy Wang. | ||
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| Zeiser, Florian (Max-Planck-Institut für Mathematik, Bonn) | OMP 1, HS 11 | Mon, 16. Aug 21, 14:00 |
| Poisson linearization using the Nash-Moser method | ||
In this talk we outline how one can use the Nash-Moser method to prove Poisson linearization results of compact semisimple Lie algebras. We use Conn's idea to prove a more general linearization result. | ||
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| Angulo, Camilo (Univ. Federal Fluminense) | OMP 1, HS 11 | Mon, 16. Aug 21, 13:30 |
| Gray stability for contact groupoids | ||
A Jacobi structure is a Lie bracket on the sections of a line bundle. These brackets encode time-dependent mechanics in the same way Poisson brackets encode mechanics. Contact groupoids are finite-dimensional models for the "integrations" of these infinite-dimensional Lie algebras. In this talk, we explain how, under a certain compactness hypothesis, one can adapt the argument of Gray-Moser to these multiplicative contact structures and point out some applications. | ||
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| Blohmann, Christian (Max-Planck-Institut f. Mathematik, Bonn) | OMP 1, HS 11 | Mon, 16. Aug 21, 11:30 |
| Diffeological groupoids | ||
Diffeological groupoids appear in many areas of mathematics, such as infinite-dimensional Lie theory, classical field theory, deformation theory, and moduli spaces. The category of diffeological spaces, however, is too general and does not have a good differential calculus, which would be needed for a Lie theory of diffeological groupoids. I will introduce the notion of elastic diffeological spaces and show that these form a subcategory with an abstract tangent structure in the sense of Rosicky. The tangent structure yields a Cartan calculus consisting of vector fields, differential forms, the de Rham differential, inner derivatives, and Lie derivatives, satisfying the usual relations. Surprisingly, all diffeological groups are elastic. I then introduce the notion of diffeological Lie algebroids and show that the invariant vector fields of an elastic diffeological groupoid form a diffeological Lie algebroid. As application, I will revisit a diffeological groupoid that arises in lorentzian geometry whose diffeological Lie algebroid encodes the Poisson brackets of the Gauss-Codazzi constraint functions. | ||
| Note: Minicourse (1) | ||
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| Schmeding, Alexander (Univ. of Bergen) | OMP 1, HS 11 | Mon, 16. Aug 21, 10:00 |
| Connecting finite, infinite-dimensional and higher differential geometry | ||
Infinite-dimensional differential geometry is often viewed as a fairly arcane subject with little connection to geometric questions arising in (finite-dimensional) applications. The aim of this talk is to show that this impression could not be further from the truth. We will take a scenic tour to a multitude of examples, connecting finite, infinite-dimensional and higher geometry. While some of these are well known classics such as Euler-Arnold theory for partial differential equations, also new results with surprising applications (such as in rough path integration theory) will be presented. As this talk is intended as a gentle introduction to these topics, no prior knowledge of infinite-dimensional geometry will be necessary. | ||
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| Cornelius Rampf (Obs Nice) | Fri, 21. Feb 20, 15:00 | |
| Singularities in cosmological Vlasov-Poisson and quantum picture | ||
The evolution of cold dark matter (CDM) is governed by the cosmological Vlasov–Poisson equations. As it is well-known, the gravitational collapse of CDM leads to infinite-density caustics that seed the primordial dark-matter halos in the cosmic large-scale structure. Focusing on the one-dimensional case, I report a landscape of so far unknown singularities in the particle acceleration that emerge after the first crossing of particle trajectories. These singular features may be regulated by assuming a finite temperature for dark matter, which, to some extend, simplifies the numerical computation but complicates the theoretical modelling. Alternatively, singular features are naturally tamed in semiclassical, Schrödinger-like descriptions for the large-scale structure which I will discuss as well. | ||
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| Sebastian Erne (VCQ Wien) | Fri, 21. Feb 20, 14:30 | |
| Analog simulators for early universe cosmology: from false vacuum decay to reheating | ||
Designing effective field theories in a laboratory setup has gained increasing attention over the last years and lies at the heart of analog-gravity experiments. Probing the validity of these effective models constitutes an essential step towards (quantum) simulators of otherwise inaccessible systems. Focusing on its applications for early universe cosmological problems, I report on the opportunities, validation, and limitations of analog classical and quantum simulators for (Quantum) Field Theory in curved and time-dependent spacetimes, in particular to cosmic inflation. As specific examples, I will discuss applications of single and multi-component quantum fluids and classical two-fluid systems in strong gradient magnetic fields. | ||
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| Robin Kaiser (INLPH Nice) | Fri, 21. Feb 20, 11:45 | |
| Photon –Atom Interactions: from cold atoms to astrophysics | ||
Atomic physics experiments, based on hot vapors or laser-cooled atomic samples, may be useful to simulate some astrophysical problems, where radiation pressure, radiative transport or light amplification are involved. I will present some ongoing experimental efforts in Nice and discuss spontaneous self-organisation with light-induced long-range forces. | ||
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| Oliver Hahn (Obs Nice) | Fri, 21. Feb 20, 11:15 | |
| Cosmological Structure Formation: Numerics and Theory, State of the Art and Open Problems | ||
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| Tiziano Dalmonte (Aix-Marseille University) | WPI, OMP 1, Seminar Room 08.135 | Wed, 13. Nov 19, 15:00 |
| Countermodel construction via optimal hypersequent calculi for non-normal modal logics (joint work with Björn Lellmann, Nicola Olivetti, and Elaine Pimentel) | ||
We develop semantically-oriented calculi for the cube of non-normal modal logics and some deontic extensions. The calculi manipulate hypersequents and have a simple semantic interpretation. Their main feature is that they allow for direct countermodel extraction. Moreover they provide an optimal decision procedure for the respective logics. They also enjoy standard proof-theoretical properties, such as a syntactical proof of cut-admissibility. | ||
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| Bjoern Lellmann (TU Wien) | WPI, OMP 1, Seminar Room 08.135 | Wed, 13. Nov 19, 14:15 |
| Nested sequents and countermodels for monotone modal logic | ||
In this talk I will present a nested sequent system for a combination of (non-normal) monotone modal logic M and normal modal logic K. The system is fully internal, can be used for proof search, and is suitable for countermodel construction. I will also consider some deontic extensions and present a prototype implementation. | ||
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| Guido Governatori (Data61, Brisbane) | WPI, OMP 1, Seminar Room 08.135 | Wed, 13. Nov 19, 9:30 |
| Combining Modalities and Substructural conclusions with non-monotonic reasoning using Defeasible Logic. | ||
Defeasible Logic is a simple practical computationally oriented (sceptical) non-monotonic formalism that proved (i) to be flexible to capture different facets of non-monotonic reasoning and (ii) to be extensible. The logic is based on a constructive proof theory. We are going to show to use the proof theory to extend the logic with modalities, and to capture some aspects of substructural logic. We also show how to use some of these features to address some paradoxes of deontic logic. | ||
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| Tim Lyon (TU Wien) | WPI, OMP 1, Seminar Room 08.135 | Tue, 12. Nov 19, 16:45 |
| On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems | ||
In this talk we look at how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. As a consequence of the extraction process, each nested calculus inherits favorable proof-theoretic properties from its associated labelled calculus. | ||
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| Roman Kuznets (TU Wien) | WPI, OMP 1, Seminar Room 08.135 | Tue, 12. Nov 19, 16:00 |
| Translating Quantitative Semantic Bounds into Nested Sequents | ||
As follows from their name, tree-hypersequents (also known as nested sequents) were created to represent the tree structure of underlying Kripke models. While this approach works well on modal and intermediate logics complete w.r.t. many types of tree-like frames, it is not directly suited to encode quantitative restrictions on these frames, e.g., bounded depth and/or bounded number of children per node. In order to capture these restrictions, we add the injectivity condition to nested sequents requiring different sequent nodes to correspond to distinct worlds in the underlying Kripke model. The downside is the loss of the formula interpretation. On the plus side, we show how the injective nested sequents can be used to constructively prove the Craig interpolation property for all interpolable intermediate logics strictly between the intuitionistic and classical propositional logics that are complete with respect to tree-like models, i.e., Smetanich logic (also known as the logic of here and there), the greatest semiconstructive logic, logic BD_2 of bounded depth 2, and Gödel logic. For the last one, we obtain a stronger form of interpolation called Lyndon interpolation. | ||
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| Luigi Santocanale (Aix-Marseille University) | WPI, OMP 1, Seminar Room 08.135 | Tue, 12. Nov 19, 12:15 |
| Residuated lattices of join-continuous endofunctions of chains, ... and the Fibonacci numbers. | ||
I shall expose recent advances on exploring the equaltional theories of the residuated lattices Q(C) made of join-continuous endofunctions of a complete chain C. On one side, when investating congruences, we observed that the number of idempotents in the residuated lattice Q({0,1,...,n}) is the 2n+1-th Fibonacci number. Our proof yields a combinatorial interpretation of results due to Howie and Laradji-Umar. If C is a finite chain or the interval [0,1] of the reals, Q(C) is an involutive residuated lattice. Generalizing this fact, we shall present the following result : for a complete lattice L, the residuated lattice Q(L) of join-continuous endofunctions of L is involutive if and only of L is a completely distributive lattice. Thus, the step from ILL to MALL requires, for those residuated lattices, also a classical structure on the additives. It also holds that Q(L) is an involutive mix residuated lattice if and only if L is a complete chain. | ||
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| Kees van Berkel (TU Wien) | WPI, OMP 1, Seminar Room 08.13 | Tue, 12. Nov 19, 11:30 |
| Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for (Deontic) STIT Logics (joint work with Tim Lyon) | ||
The logic of STIT (`seeing to it that') is an agency logic for reasoning about agents that make choices at certain moments in time. This class of modal logics has received considerable attention in the past decades with formal application in epistemic-, legal-, and deontic reasoning. Furthermore, in relation to the increasing development of autonomous systems assisting and interacting with humans, the need for automated normative reasoning with STIT logics has been stressed in the literature. Our present research addresses this issue. In this talk we will set out the concrete aims of our STIT project and discuss some of the results obtained so far. We will first provide an introduction to the logic of STIT and discuss our recently proposed Temporal Deontic extension STIT. Second, we provide labelled sequent calculi for the class of multi-agent STIT logic with limited choice axioms and show how these calculi can be refined with the use of propagation rules, enabling us to reduce the structure of sequents and to make the proofs more compact. For the class of refined calculi we obtain automated proof-search and counter-model extraction. We will conclude by discussing some open problems. | ||
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| Sara Negri (University of Helsinki) | WPI, OMP 1, Seminar Room 08.135 | Tue, 12. Nov 19, 10:00 |
| Proof analysis for the logics of agency: the deliberative STIT (joint work with Edi Pavlovic) | ||
TBA | ||
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| Timo Lang (TU Wien) | WPI, OMP 1, Seminar Room 08.135 | Mon, 11. Nov 19, 15:45 |
| Bounded sequent calculi via hypersequents (joint work with A.Ciabattoni and R.Ramanayake) | ||
Many substructural, intermediate and modal logics have found cut-free presentations in the hypersequent calculus. We demonstrate that for many such logics, this cut-freeness at the level of hypersequents also implies completeness with respect to a sequent system where only cuts of a certain shape are allowed. The restriction on the cuts thus obtained is often strong enough to allow for proofs of metalogical properties such as decidability, or embeddability into a weaker base logic. Our method also allows for a new proof of the fact that the modal logic S5 has a sequent calculus in which only analytic cuts are needed. | ||
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| Daniel Mery (LORIA - Université de Lorraine) | WPI, OMP 1, Seminar Room 08.135 | Mon, 11. Nov 19, 14:30 |
| Relating Labelled and Label-Free Bunched Calculi in BI Logic (joint work with Didier Galmiche) | ||
In this talk we discuss proof translations between labelled and label-free calculi for the logic of Bunched Implications (BI). We first consider the bunched sequent calculus LBI and define a labelled sequent calculus, called GBI, in which labels and constraints reflect the properties of a specifically tailored Kripke resource semantics of BI with two total resource composition operators and explicit internalization of inconsistency. After showing the soundness of GBI wrt our specific Kripke frames, we show how to translate any LBI-proof into a GBI-proof. Building on the properties of that translation we devise a tree property that every LBI-translated GBI-proof enjoys. We finally show that any GBI-proof enjoying this tree property (and not only LBI-translated ones) can systematically be translated to an LBI-proof. | ||
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| Francesca Gulisano (Scuola Normale Superiore, Pisa) | WPI, OMP 1, Seminar Room 08.135 | Mon, 11. Nov 19, 11:45 |
| Resolving conflicting obligations in Mimamsa: a sequent-based approach | ||
Over the course of more than two millennia, the philosophical school of Mimamsa has thoroughly discussed and analyzed the prescriptive portion of the Vedas, the sacred texts of Hinduism, in order to make sense of it as a consistent corpus of rules. We present a formalization of the deontic system applied by Mimamsa authors for resolving conflicts between normative statements by giving preference to the more specific ones. Finally, we show how to use the resulting system to provide a better understanding of these philosophical texts. | ||
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| Dominique Larchey-Wendling (LORIA - CNRS) | WPI, OMP 1, Seminar Room 08.135 | Mon, 11. Nov 19, 11:00 |
| Hilbert's Tenth Problem in Coq (joint work with Yannick Forster) | ||
We formalise the undecidability of solvability of Diophantine equations, i.e. polynomial equations over natural numbers, in Coq's constructive type theory. To do so, we give the first full mechanisation of the Davis-Putnam-Robinson-Matiyasevich theorem, stating that every recursively enumerable problem - in our case by a Minsky machine - is Diophantine. We obtain an elegant and comprehensible proof by using a synthetic approach to computability and by introducing Conway's FRACTRAN language as intermediate layer. | ||
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| Matthias Baaz (TU Wien) | WPI, OMP 1, Seminar Room 08.135 | Mon, 11. Nov 19, 9:40 |
| Note on Globally Sound Analytic Calculi for Quantifier Macros (joint work with Anela Lolic) | ||
This paper focuses on a globally sound but possibly locally unsound analytic sequent calculus for the quantifier macro Q. It is demonstrated that no locally sound analytic representation exists. | ||
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| Seiji Miyashita (University of Tokyo) | WPI, OMP 1, Seminar Room 08.135 | Mon, 14. Oct 19, 12:30 |
| Atomistic study on thermal and dynamical properties of Nd-magnet | ||
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| Harald Oezelt (Donau-Universität Krems) | WPI, OMP 1, Seminar Room 08.135 | Mon, 14. Oct 19, 12:00 |
| Renormalization of the intrinsic magnetic propertiesfor stochastic micromagnetics | ||
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| Alexander Kovacs (Donau-Universität Krems) | WPI, OMP 1, Seminar Room 08.135 | Mon, 14. Oct 19, 11:30 |
| Classification and optimization of a magnet's microstructure | ||
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| Thomas Schrefl (Donau-Universität Krems) | WPI, OMP 1, Seminar Room 08.135 | Mon, 14. Oct 19, 11:00 |
| Permanent magnet design - results from the European NOVAMAG project | ||
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| Markus Gusenbauer (Donau-Universität Krems) | WPI, OMP 1, Seminar Room 08.135 | Mon, 14. Oct 19, 10:30 |
| From electron microscopy to machine learningbased coercivity models | ||
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| Lukas Exl (Universität Wien) | WPI, OMP 1, Seminar Room 08.135 | Mon, 14. Oct 19, 10:00 |
| Machine Learning and Dimensionality Reduction for Computational Micromagnetism | ||
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| Johann Fischbacher (Donau-Universität Krems) | WPI, OMP 1, Seminar Room 08.135 | Mon, 14. Oct 19, 9:30 |
| Surface Anisotropies in Permanent magnets | ||
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| Joackim Bernier (ENS Rennes) | WPI, OMP 1, Seminar Room 08.135 | Fri, 4. Oct 19, 10:30 |
| Long time behavior of the Solutions of NLW on the d-dimensional torus | ||
I will present a new normal form transformation decomposing the dynamics of some nonlinear Hamiltonian systems into low and high frequencies with weak interactions. While the low part of the dynamics can be put under classical Birkhoff normal form, the high modes evolves according to a time dependent linear Hamiltonian system. We then control the global dynamics by using poly- nomial growth estimates for high modes and the preservation of Sobolev norms for the low modes. We will see how this procedure allows us to prove that, for almost any mass, small and smooth solutions of the nonlinear wave equation on Td of high Sobolev indices are stable up to arbitrary long times with respect to the size of the initial data. This is a joint work with Erwan Faou and Benoit Grebert. | ||
| Thomas Alazard (ENS Paris-Saclay) | WPI, OMP 1, Seminar Room 08.135 | Fri, 4. Oct 19, 9:00 |
| Entropies and Lyapounov functionals for the Hele-Shaw equation | ||
This lecture is devoted to the study of the Hele-Shaw equation, based on a joint work with Nicolas Meunier and Didier Smets. We introduce an approach inspired by the water-wave theory. Starting from a reduction to the boundary, introducing the Dirichlet to Neumann operator and exploiting various cancel- lations, we exhibit parabolic evolution equations for the horizontal and vertical traces of the velocity on the free surface. This allows to quasi-linearize the equa- tions in a very simple way. By combining these exact identities with convexity inequalities, we prove the existence of hidden Lyapounov functions of different natures. We also deduce from these identities and previous works on the water wave problem a simple proof of the well-posedness of the Cauchy problem. | ||
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| Corentin Audiard (UPMC Paris) | WPI, OMP 1, Seminar Room 08.135 | Thu, 3. Oct 19, 11:30 |
| Lifespan of solutions of the Euler-Korteweg System | ||
The Euler-Korteweg system is a dispersive perturbation of the usual compress- ible Euler equations that includes the effect of capillary forces. For small ir- rotational initial data, global well-posedness is known to hold in dimension at least three. In this talk we discuss the case of small initial data with non zero vorticity, where the dispersive system becomes a coupled dispersive-transport system. The main result is that the time of existence only depends on the size of the initial vorticity. | ||
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| Guillaume Ferriere (ENS Paris-Saclay) | WPI, OMP 1, Seminar Room 08.135 | Thu, 3. Oct 19, 10:30 |
| Multi-Solitons for the logarithmic Schroedinger equation | ||
In this presentation, we consider the nonlinear Schr¨odinger equation with loga- rithmic nonlinearity (logNLS in short). We mostly focus on the focusing case which presents a very special Gaussian stationary solution, called Gausson, which is orbitally stable. In fact, more generally, it has been shown that every Gaussian data remains Gaussian through the flow of logNLS, and this feature gives rise to (almost) periodic solutions in the focusing case, called breathers. The main result of this talk addresses the existence of multi-solitons, i.e. solu- tions to logNLS which behaves like the sum of several solitons (i.e. Gaussons here) for large times, in dimension 1. This kind of result is rather usual for dispersive equations with polynomial-like nonlinearity, and our proof is directly inspired from the usual proof with energy techniques. The main difficulty is the fact that the energy cannot be linearized as one would want, at least not ev- erywhere. Furthermore, some new and surprising features appear in this result: the convergence is in H1 and (H1) with a rate faster than exponential, and there is no need for a large enough relative speed (non-zero is sufficient). | ||
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| Miguel Rodrigues (U. Rennes) | WPI, OMP 1, Seminar Room 08.135 | Thu, 3. Oct 19, 9:00 |
| Harmonic and solitary wave limits of periodic traveling waves. | ||
In a series of papers with Sylvie Benzoni-Gavage (and, depending on papers, Pascal Noble or Colin Mietka), we have studied both co-periodic stability and modulation systems for periodic traveling waves of a rather large class of Hamil- tonian partial differential equations that includes quasilinear generalizations of the Korteweg–de Vries equation and dispersive perturbations of the Euler equa- tions for compressible fluids, either in Lagrangian or in Eulerian coordinates. All characterizations are derived in terms of the Hessian matrix of the action integral of profile equations, a finite-dimensional object. In the present talk, with this in mind, we shall discuss the consequences of the recently obtained expansions of this matrix in two asymptotic regimes, namely the zero-amplitude and the zero-wavelength limits. | ||
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| Valeria Banica (LJLL Paris) | WPI, OMP 1, Seminar Room 08.135 | Wed, 2. Oct 19, 11:30 |
| On the energy of critical Solutions of the binormal flow | ||
The binormal flow is a model for the dynamics of a vortex filament in a 3-D in- viscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism, and the 1-D cubic Schr¨odinger equation. We consider a class of solutions at the critical level of regularity that generate singularities in finite time. One of our main results presented in this talk is to prove the existence of a natural energy associated to these solutions. This energy remains constant except at the time of the formation of the singularity when it has a jump discontinuity. When interpreting this conservation law in the framework of fluid mechanics, it involves the amplitude of the Fourier modes of the variation of the direction of the vorticity. This is a joint work with Luis Vega. | ||
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| Ricardo Barros (U. Loughborough) | WPI, OMP 1, Seminar Room 08.135 | Wed, 2. Oct 19, 10:30 |
| Effect of variation in density on the stability of bilinear shear currents with a free surface | ||
The linear stability of homogenous shear flows between two rigid walls is a clas- sical problem that goes back to Rayleigh (1880). Among other things, Rayleigh was able to show that a shear flow with no inflection points is linearly stable. The generalisation of this stability criterion to the free-surface setting is not straightforward and was established much later by Yih (1971) (under certain restrictions) and, more recently, Hur & Lin (2008). In the case when a shear flow with a free surface is modelled by constant vorticity layers, no stability criterion is known. As a first step in this direction we consider the stability analysis of a bilinear shear current and establish a criterion for the stability of the flow. The effect of density stratification on the stability of the flow will also be investigated. | ||
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| Vincent Duchene (U. Rennes) | WPI, OMP 1, Seminar Room 08.135 | Wed, 2. Oct 19, 9:00 |
| On the Favrie-Gavrilyuk approximation to the Serre-Green-Naghdi system. | ||
The Serre-Green-Naghdi system is a fully nonlinear and weakly dispersive model for the propagation of surface gravity waves. It enjoys many good theoretical properties, including a robust well-posedness theory for the initial-value prob- lem, and a Hamiltonian structure. It is however not so suitable for practical use, as standard numerical strategies involve the costly inversion of an elliptic operator at each time step. N. Favrie and S. Gavrilyuk proposed a novel strat- egy for efficiently producing approximate solutions, by introducing a “relaxed” first-order quasilinear system of balance laws, depending on additional unknows and a free parameter. The claim is that in the singular limit when the param- eter goes to infinity, solutions of the relaxed system approach solutions of the Serre-Green-Naghdi system. We will discuss a rigorous analysis. It differs from standard results due to the presence of an additional parameter (describing the shallowness of the flow) and order-zero source terms which become dominant when the shallowness parameter goes to zero. | ||
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| Anton Arnold (TU Wien) | WPI, OMP 1, Seminar Room 08.135 | Tue, 1. Oct 19, 11:30 |
| Short- and long-time behavior in (hypo)coercive ODE-systems and Fokker-Planck equations. | ||
| Thomas Kappeler (U. Zurich) | WPI, OMP 1, Seminar Room 08.135 | Tue, 1. Oct 19, 10:30 |
| On Birkhoff coordinates of the Benjamin Ono equation on the torus and applications to solutions with negative Sobolev regularity. Part 2. | ||
| Patrick Gérard (U. Paris-Sud) | WPI, OMP 1, Seminar Room 08.135 | Tue, 1. Oct 19, 9:00 |
| On Birkhoff coordinates of the Benjamin Ono equation on the torus and applications to solutions with negative Sobolev regularity. Part 1. | ||
This is a jointwork with Thomas Kappeler. Using the Lax pair structure for the Benjamin-Ono equation with periodic boundary conditions, we construct a global system of Birkhoff coordinates on the phase space of real valued square integrable functions with average 0 on the torus, including a characterisation of finite gap potentials. Among consequences, we infer almost periodicity of all trajectories, identification of traveling waves and construction of periodic in time solutions with low regularity. | ||
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| Christian Klein (U. Bourgogne) | WPI, OMP 1, Seminar Room 08.135 | Mon, 30. Sep 19, 17:00 |
| Multi-domain spectral methods for dispersive PDEs. | ||
We discuss numerical methods to construct solutions to nonlinear dispersive PDEs on the whole real line, and this for initial data which are slowly decreasing towards infinity or just bounded there. As an example we discuss the transverse stability of the Peregrine solution in the 2d nonlinear Schrodinger equation. | ||
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| Nikola Stoilov (U. Bourgogne) | WPI, OMP 1, Seminar Room 08.135 | Mon, 30. Sep 19, 15:30 |
| Numerical study of the Davey-Stewartson equation | ||
In this work we will look at the focusing Davey-Stewartson equation from two different angles, using advanced numerical tools. As a nonlinear dispersive PDE and a generalisation of the non-linear Schr¨odinger equation, DS possesses solutions that develop a singularity in finite time. We numerically study the long time behaviour and potential blow-up of solutions to the focusing Davey-Stewartson II equation for various initial data and propose a conjecture describing the blow up rate and solution profiles near the singularity. Secondly, DS is an integrable system and can be studied as an inverse scat- tering problem. Both the forward and inverse scattering transformation in this case are reduced to a d-bar system which plays the role that Riemann-Hilbert problems play in one dimensional problems. We will present numerical solutions for Schwartzian and compactly supported potentials. Further, to complement numerics, we will discuss analytical considerations to handle asymptotic be- haviour. In all studied cases we use spectral methods and achieve machine pre- cision. Based on joint works with Christian Klein and Ken McLaughlin | ||
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| Rémi Carles (CNRS) | WPI, OMP 1, Seminar Room 08.135 | Mon, 30. Sep 19, 14:30 |
| Turbulent effects through quasi-rectification | ||
This is a joint work with Christophe Cheverry. We study high frequency so- lutions of nonlinear hyperbolic equations for time scales at which dispersive and nonlinear effects can be present in the leading term of the solution, on a model stemming from strongly magnetized plasmas or nuclear magnetic reso- nance experiments. We show how the produced waves can accumulate during long times to produce constructive and destructive interferences which, in the above contexts, are part of turbulent effects. | ||
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| Khedher, Asma (U. Amsterdam) | WPI, OMP 1, Seminar Room 08.135 | Thu, 5. Sep 19, 16:30 |
| Semimartingale characterstics in Hilbert space | ||
TBA | ||
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| Eisenberg, Paul (U. Liverpool) | WPI, OMP 1, Seminar Room 08.135 | Thu, 5. Sep 19, 16:00 |
| Abstract polynomial processes | ||
TBA | ||
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| Detering, Nils (Santa Barbara, California) | WPI, OMP 1, Seminar Room 08.135 | Thu, 5. Sep 19, 15:30 |
| Directed Chain Stochastic Differential Equations | ||
TBA | ||
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| Cuchiero, Christa (U. Wien) | WPI, OMP 1, Seminar Room 08.135 | Thu, 5. Sep 19, 14:30 |
| Infinite dimensional polynomial processes and applications to rough volatility modeling (Part II) | ||
TBA | ||
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| Svaluto-Ferro, Sara (U. Wien) | WPI, OMP 1, Seminar Room 08.135 | Thu, 5. Sep 19, 14:00 |
| Infinite dimensional polynomial processes and applications to rough volatility modeling (Part I) | ||
TBA | ||
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| Bergmann, Michael (Med. Uni Vienna) | OMP 1, Sky Lounge (12th floor) | Fri, 2. Aug 19, 15:45 |
| Interplay of Therapy and Tumor Microenvironment in Human Colorectal Cancer | ||
Advances in tumor immunology now calls for a novel understanding of the immunological consequence of standard cancer therapy. At the same time the expression of proteins mediating immunogenic cell death should have a positive predictive and prognostic impact. This molecular understanding of the disease will allow a more rational design of immunomodulating drugs and standard therapy. Murine models clearly indicate that irradiation induced DNA damage can stimulates the innate and adaptive immune system. However, there is little evidence that irradiation leads to apiscopal effects in the clinic. We here show that neoadjuvant irradiation applied in rectal cancer patients induces the polarization of tumor associated M2-like macrophages to an M1-like phenotype in surgical resection specimen. Ex vivo primary cultures and organotypic assays were used to better dissect this re-polarization. Using exvivo cultures we further show that the shift of irradiation-induced macrophage polarization could be mediated by exosomes. Those data clearly indicate that radiotherapy induced DNA damage using 25 Gy actively stimulates the innate immune system. This pro-inflammatory effect of radiotherapy might now be complemented by immunomodulating drugs modulating the adaptive part of the immune system. In contrast, when analyzing the prognostic and predictive impact of spontaneous DNA damage and associated pathways in colorectal liver metastases we demonstrate that DNA damage had a strong negative impact on response to neoadjuvant applied chemotherapy but also on disease free and overall survival. Spontaneous DNA damage was not associated with an induction of the innate immune response in this setting and inversely correlated with infiltrates of CD8+ or CD45RO+ cells. This calls for a more detailed understanding of spontaneous DNA damage induced pathways in colorectal liver metastases as their blockade might enhance prognoses. | ||
| Menche, Jörg (CeMM Vienna) | OMP 1, Sky Lounge (12th floor) | Fri, 2. Aug 19, 14:40 |
| From Protein-Protein to Drug-Drug Interactions | ||
From protein interactions to signal transduction, from metabolism to the nervous system: Virtually all processes in health and disease rely on the careful orchestration of a large number of diverse individual components ranging from molecules to cells and entire organs. Networks provide a powerful framework for describing and understanding these complex systems in a wholistic fashion. They offer a unique combination of a highly intuitive, qualitative description, and a plethora of analytical, quantitative tools. In my presentation, I will introduce three ongoing projects of my group, each highlighting a different aspect of how network science can help us understand the pathobiological processes of human disease: First, I will sketch out how protein-protein interaction networks can be understood as maps to investigate relationships between diseases. Second, I will discuss how drug-drug interaction networks can be used to identify basic principles of the cellular response to multiple perturbations. Lastly, I will present our vision of a virtual reality platform for the next generation of network-based data integration and exploration. | ||
| Peurichard, Diane (INRIA) | OMP 1, Sky Lounge (12th floor) | Fri, 2. Aug 19, 14:00 |
| Modelling Adhesion-Independent Cell Migration: How Cells Can Cross Biological Barriers | ||
One of the most important cellular behaviors is cell crawling migration. It is observed in many cellular systems both in culture and in vivo, and involved in many essential physiological or pathological processes (wound healing, embryonic development, cancer metastasis etc). As in the last decade adhesion-independent migration has been observed in confining environement and has emerged as a possibly common migration mode, we propose a simplified 2D model for focal adhesion-free cell migration: A cell is modeled through its membrane represented as a set of connected springs which undergo internal pressure forces. The renewal of the actin network is modelled by creation/suppression of springs in the membrane, and we suppose that a cell generates internal counter-forces compensating mass displacement due to membrane renewal. Numerical simulations show that these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for cell motility in confined environment. | ||
| Komorowski, Michal (Polish Academy of Sciences) | OMP 1, Sky Lounge (12th floor) | Fri, 2. Aug 19, 11:20 |
| Making Sense of Signaling Complexity | ||
An engineer designing a communication system would use few distinct signaling components while ensuring that the output of each component is highly accurate. However, natural evolution came up with a different solution: cells have many interconnected, cross- reactive components that individually produce noisy signals. Why? In the talk, I will present the perspective of mathematical information-theory at the two intriguing properties of cellular signaling pathways: noisiness and cross-talk. Specifically, I will discuss their (i) evolutionary origins; (ii) implications for interpretation of single cell data; and (iii) consequences for the design of therapeutic interventions in signaling. | ||
| Hecht, Sophie (Imperial College London) | OMP 1, Sky Lounge (12th floor) | Fri, 2. Aug 19, 10:40 |
| An Individual-Based Model for Inter-Kinetic Nuclear Movement | ||
Understanding how tissues develop and regulate their growth is crucial in biology. Both proliferation and regulation of cells growth are fundamental for the development of healthy tissue in animals and plants, as well as for the progression of tumours. In pseudostratified epithelia, the organisation of the nuclei and their movement inside the tissue influence the final architecture of the tissue and impact growth. In particular, nuclei move along the apical/basal axis during the inter-kinetic phases of the cell cycle. This movement is called the inter-kinetic nuclear movement. Because pseudostratified epithelia have a high density of nuclei, their movement is likely to be influenced by the crowing inside the tissue. We developed an Individual-based model for the interkinetic nuclear movement in pseudostratified epithelia based in a minimisation framework. The model focuses is placed on the nuclei and their deformation. We study the influence of crowding the specific case of the Imaginal Disc of Drosophila and tuned the model with biological data. We then show that the crowding increases the cell cycle duration, resulting in the slow down of growth. | ||
| Cordero, Francesca (U. Turin) | OMP 1, Sky Lounge (12th floor) | Fri, 2. Aug 19, 10:20 |
| Multiscale models to investigate IntraTumor Heterogeneity | ||
In cancer research most efforts are devoted on the decipher of the IntraTumoral Heterogeneity (ITH). In ITH the action of the evolutionary forces of mutation and selection are essential to determinant the tumor progression, diagnosis and treatment. ITH gives rise to cancer cell populations with distinct genotypic and metabolic characteristics contributing to the failure of cure, by initiating phenotypic diversity and enabling more aggressive and drug resistant clones. I will present multi-scale models of cancer linking the tumor growth to the intracellullar signalling and metabolic events to genomic profiles. The models consider several heterogenous omics data (metabolomics, proteomics, transcriptomics, genomics) to investigate the ITH associated with different genomic and metabolic traits. | ||
| Berger, Walter (Med. Uni Wien) | OMP 1, Sky Lounge (12th floor) | Fri, 2. Aug 19, 9:40 |
| Contribution of Immune Mechanisms to the Anticancer Activity of Platinum Drugs | ||
Currently, immunotherapy with checkpoint inhibitor antibodies is revolutionizing clinical oncology even allowing cure of highly aggressive cancer types like melanoma and lung cancer. However, response to these immunotherapies is restricted to patient subgroups and currently conclusive predictive biomarkers are not available. Classically, anticancer metal drugs are considered to target predominantly nucleic acids, hence killing cancer cells by inducing genomic damage and apoptotic cell death. However, during the last years it became clear that metal drugs are not pure cytotoxic agents, but might also strongly interact with the fidelity of anticancer immune responses. Central underlying mechanisms include upregulation of cancer cell immunogenicity or depletion of regulatory immune cell compartments1. As one example, we have found that an intraperitoneal colon cancer model can be cured when combining oxaliplatin with bacterial ghosts as adjuvants2. Bacterial ghosts are empty envelopes of gram-negative bacteria with a distinct immune-stimulatory potential. In contrast, oxaliplatin alone only retarded tumor growth. Interestingly, animals cured by this immunochemotherapy approach were vaccinated against the original cancer cells making regrowth of the tumor graft impossible. As this vaccination effect was entirely depending on the presence of activated T cells, induction of an immunogenic cell death by oxaliplatin supported by innate immune activation via the adjuvant can be anticipated. This hypothesis was proven be induction of endoplasmic reticulum (ER) stress, calreticulin cell surface exposure, as well as HMGB1 and ATP release be the combination-treated cancer cells. A platinum(IV) prodrug of oxaliplatin targeted for tumor-specific activation based on albumin binding was able to cure CT26 murine colon cancer even without additional adjuvant in immunocompetent but not severe combined immunodeficient (SCID) mice3. The question arises whether mathematical modelling of at least parts of the complex interplay between DNA damage and immune activation by anticancer platinum drugs would be conceivable. | ||
| Lorenzi, Tommaso (University of St. Andrews) | OMP 1, Sky Lounge (12th floor) | Fri, 2. Aug 19, 9:00 |
| Dissecting the Evolutionary Dynamics of Cancer Cell Populations in Fluctuating Environments | ||
A number of studies have demonstrated that the disordered process of angiogenesis occurring in malignant tumours produces stochastic variations in blood flow leading to cycles of perfusion, cessation of flow, and then re-perfusion. This produces corresponding fluctuations in environmental conditions that include the concentration of nutrients, such as oxygen and glucose. In order to support a deeper understanding of the adaptive role of spontaneous phenotypic variations in cancer cell populations exposed to fluctuating environments, we consider a system of non-local partial differential equations modelling the evolutionary dynamics of two competing populations in the presence of periodically oscillating nutrient levels. Exploiting the analytical tractability of our model, we study the long-time behaviour of the solutions to obtain a detailed mathematical depiction of evolutionary dynamics. Our analytical results formalise the idea that when nutrient levels experience small and slow periodic oscillations, and thus environmental conditions are relatively stable, it is evolutionarily more efficient to rarely undergo spontaneous phenotypic variations. Conversely, under relatively large and fast periodic oscillations in the nutrient levels, which lead to alternating cycles of starvation and nutrient abundance, higher rates of spontaneous phenotypic variations can confer a competitive advantage, as they may allow for a quicker adaptation to changeable environmental conditions. In the latter case, our results indicate that higher levels of phenotypic heterogeneity are to be expected compared to those observed in slowly fluctuating environments. Finally, our results suggest that bet-hedging evolutionary strategies, whereby cancer cells switch between antithetical phenotypic states, can naturally emerge in the presence of relatively large and fast nutrient fluctuations leading to drastic environmental changes. | ||
| Eder, Thomas (Vetmed Uni Wien) | OMP 1, Sky Lounge (12th floor) | Thu, 1. Aug 19, 15:45 |
| Benchmarking Differential ChIP-Seq Tools | ||
Chromatin immunoprecipitation followed by sequencing (ChIP-seq) is widely used in the global investigation of protein-DNA interactions. One of its main applications is the analysis of differential chromatin binding patterns of the proteins of interest in varying biological states. While various algorithms can be used to quantitatively compare ChIP-seq datasets, different computational tools apply different normalization strategies, which can strongly influence the results of the analyses. Applying inappropriate normalization can lead to erroneous outcomes, and the performance of different tools can strongly depend on the nature of the investigated dataset. Therefore it is hard to choose the most appropriate differential ChIP-seq tool. To overcome this limitation, we systematically assessed available tools for differential ChIP-seq analysis to provide recommendations which tools to use for different biological scenarios and data types. We created standardized reference datasets by in-silico simulation of ChIP-seq data to represent different biological scenarios, including global reduction of genomic regions in one sample versus the other, but also up- and down-regulation of equal proportions of genomic regions in both samples. We used these scenarios to evaluate the performance of 24 computational tools for differential ChIP-seq analysis. We found enormous differences in precision and recall across differential ChIP-seq analysis tools. The performance was strongly dependent on the sizes and shapes of simulated peaks as well as on the regulation scenario. We are currently extending these findings to publicly available and unpublished experimental ChIP-seq datasets. Our analysis provides unbiased recommendations which tools to use for particular biological scenarios. The application of appropriate analysis tools will greatly improve the outcomes of ChIP-seq studies, and will thus contribute to improved identification of molecular mechanisms. | ||
| Szakacs, Gergely (Med. Uni Wien) | OMP 1, Sky Lounge (12th floor) | Thu, 1. Aug 19, 14:40 |
| Treasure Hunting in the NCI60 Anticancer Drug Screen Database | ||
Molecular descriptor (2D) and three dimensional (3D) shape based similarity methods are widely used in ligand based virtual drug design. In the present study pairwise structure comparisons among a set of 4858 DTP compounds tested in the NCI60 tumor cell line anticancer drug screen were computed using chemical hashed fingerprints and 3D molecule shapes to calculate 2D and 3D similarities, respectively. Additionally, pairwise biological activity similarities were calculated by correlating the 60 element vectors of pGI50 values corresponding to the cytotoxicity of the compounds across the NCI60 panel. Subsequently, we compared the power of 2D and 3D structural similarity metrics to predict the toxicity pattern of compounds. We found that while the positive predictive value and sensitivity of 3D and molecular descriptor based approaches to predict biological activity are similar, a subset of molecule pairs yielded contradictory results. By simultaneously requiring similarity of biological activities and 3D shapes, and dissimilarity of molecular descriptor based comparisons, we identify pairs of scaffold hopping candidates displaying characteristic core structural changes such as heteroatom/heterocycle change and ring closure. Attempts to discover scaffold hopping candidates of mitoxantrone recovered known Topoisomerase II (Top2) inhibitors, and also predicted new, previously unknown chemotypes possessing in vitro Top2 inhibitory activity. | ||
| Saut, Olivier (CNRS, INRIA Monc Bordeaux) | OMP 1, Sky Lounge (12th floor) | Thu, 1. Aug 19, 14:00 |
| Early Evaluation of Cancer Treatment Using Modeling and AI | ||
The main goal of this talk is to present examples of how mathematical modeling and AI may help clinicians following the evolution of cancer. The first example uses machine learning to evaluate the efficacy of neoadjuvant chemotherapy of softtissue sarcoma. Standard of care for advanced stages (grade 3) is the following: neoadjuvant chemotherapy (6 cycles), curative surgery and then adjuvant radiotherapy. Unfortunately, for some patients, chemotherapy does not improve the situation. In clinical routine, two MR exams are performed on patients: one before the chemotherapy and one after two cycles. Using a retrospective study of more than 60 patients from Institut Bergonié, we investigate whether the differences between these two exams may be correlated with response to chemotherapy. For this matter a radiomics approach is used with novel handcrafted features specific to the disease. On the cohort, the results we obtain are better than state of the art. In the second example, we try to evaluate the efficacy of tyrosine kinase inhibitors (TKI) for patients with EGFR mutated Non-Small Cell Lung Carcinoma. Patients almost always end up relapsing. Our goal is to analyze if an insight on this relapse may be obtained from the early response to treatment. We built a mathematical model — based on a set of PDE - of the response to TKI. This model is personalized for each patient of a retrospective cohort from Institut Bergonié. For the patient-specific model, we compute a novel marker that we show to be correlated with risk of relapse. Finally, a new data assimilation technique will be presented that is able to recover patient-specific parameters of a PDE model of growth of brain metastases. It may be used to predict the evolution of these metastases. | ||
| Pils, Dietmar (Med. Uni Wien) | OMP 1, Sky Lounge (12th floor) | Thu, 1. Aug 19, 11:40 |
| Network Analysis for Hypothesis Generation, Target Definition, and (Multiomics) Data Integration | ||
In high grade serous ovarian cancer patients with peritoneal involvement have an unfavorable outcome and would benefit from targeted therapies. In the last years we comprehensively described two types of peritoneal tumor spreading, miliary, with many millet sized tumor nodules in the peritoneal cavity, and non-miliary, with few larger and exophytically growing tumors. The former showed significant shorter survival, therefore we aimed to find a druggable target against miliary peritoneal metastasizing. We constructed a planar – scale free and small world – co-association gene expression network from RNAsequencing data using mutual information as the association measure, defined sub-clusters with multiscale clustering, and searched for sub-clusters with hub genes up-regulated in miliary tumors. A subcluster of 38 genes and Nectin 4 as hub-gene was among the highest significant up-regulated sub-clusters. Using the genes of this sub-cluster for a gene signature we validated the impact on survival with six publicly available expression datasets. Protein expression and impact on survival of Nectin 4 was validated via immunohistochemistry and correlated to other omics and medium-dimensional data. Results were condensed to a network and used for biological interpretation of the impact of Nectin 4 on peritoneal ovarian cancer metastasizing. An anti-Nectin 4 antibody with a linked antineoplastic drug – already used in clinical trials for cancer treatment – could be a promising candidate for a targeted therapy in patients with miliary peritoneal involvement. | ||
| Bunimovich, Svetlana (Ariel University) | OMP 1, Sky Lounge (12th floor) | Thu, 1. Aug 19, 11:00 |
| Mathematical Model of CRC Lung Metastases Growth Patterns | ||
Colorectal cancer (CRC) is one of the most common causes of cancer-related mortality worldwide. Most cases of deaths result from metastases, assumed to be shed, in many cases, before disease detection. Providing reliable predictions of the metastases' growth pattern may help planning treatment. Available mathematical tumor growth models rely mainly on primary tumor data, and rarely relate to metastases growth. The aim of this talk was to explore CRC lung metastases growth patterns. We used data of a metastatic CRC patient, for whom ten lung metastases were measured while untreated by seven serial computed tomography (CT) scans, during almost three years. Three mathematical growth models – Exponential, logistic and Gompertzian – were fitted to the actual measurements. Goodness of fit of each of the models to actual growth was estimated using different scores. Factors affecting growth pattern were explored: size, location and primary tumor resection. Exponential growth model demonstrated good fit to data of all metastases. Logistic and Gompertzian growth models, in most cases, were overfitted and hence unreliable. Metastases inception time, calculated by backwards extrapolation of the fitted growth models, was 8-19 years before primary tumor diagnosis date. Three out of ten metastases demonstrated enhanced growth rate shortly after primary tumor resection. Our unique data provide evidence that exponential growth of CRC lung metastases is a legitimate approximation, and encourage focusing research on short-term effects of surgery on metastases growth rate. | ||
| Tolios, Alexander (Med.Uni Wien) | OMP 1, Sky Lounge (12th floor) | Thu, 1. Aug 19, 9:50 |
| Predicting Healthy and Cancerous Tissue Samples by Applying Predictive Modeling Techniques on Epigenetic Markers | ||
DNA methylation is known to have a major impact on the protein biosynthesis of tissues. Those epigenetic modifications could theoretically also be used for tissue classification. In this study we hypothesized that machine learning algorithms could be applied to distinguish between different tissue samples. | ||
| Delitala, Marcello (Politechnico Torino) | OMP 1, Sky Lounge (12th floor) | Thu, 1. Aug 19, 9:10 |
| Combination Therapies and Drug Resistance in Heterogeneous Tumoral Populations | ||
How combination therapies can reduce the emergence of cancer resistance? Can we exploit intratumoral competition to modify the effectiveness of anti-cancer treatments? Bearing these questions in mind, we present a mathematical model of cancer-immune competition under therapies. The model consists of a system of differential equations for the dynamics of two cancer clones and T-cells. Comparisons with experimental data and clinical protocols have been performed. In silico experiments confirm that the selection of proper infusion schedules plays a key role in the success of anti-cancer therapies. The outcomes of protocols of chemotherapy and immunotherapy (separately and in combination) differing in doses and timing of the treatments are analyzed. In particular, we highlight how exploiting the competition between cancer populations seems to be an effective recipe to limit the insurgence of resistant populations. In some cases, combination of low doses therapies could yield a substantial control of the total tumor population without imposing a massive selective pressure that would suppress the sensitive clones leaving unchecked the clonal types resistant to therapies. | ||
| Hao Wu (Tsinghua Univ.) | WPI, OMP 1, Seminar Room 08.135 | Mon, 22. Jul 19, 12:00 |
| The focus computing method | ||
In this study, we propose a novel direct numerical method with computational cost to simulate the wave equation in the seismic inverse problem. It based on the fact that the computation of the entire wave filed may not be necessary here. Thus, we only need to evaluate the wave equation around the waveform of interest and the computational cost is significantly saved here. | ||
| Sebastian Erne (Nottingham) | WPI Seminarroom | Tue, 9. Jul 19, 11:30 |
| Analog cosmology in classical and quantum fluids | ||
The dynamics of the early universe and black holes are deeply linked to the interplay between general relativity and quantum fields. The essential physical processes occur in situations that are hard to observe and impossible to experiment with: when gravitational interactions are strong and/or when quantum effects are important. Analog (quantum) simulators, utilising the analogy between the dynamics of perturbations in classical or quantum fluids and relativistic fields in a curved space-time metric, enable us to study these processes in controlled laboratory setups. I will give an introduction to the current questions, opportunities, and challenges concerning analog simulations in the context of early universe cosmology, focusing, in particular, on cosmic inflation. It is our current understanding that, during inflation, quantum fluctuations are stretched to cosmic scales during the rapid expansion of space-time, yielding the seed for the large scale structure formation in our universe. Analog simulations give direct experimental access to the field dynamics in these extreme conditions, enabling us to study the underlying processes, like mode-freezing, particle creation, quantum-classical transition, and signature changes in the space-time metric, in detail. | ||
| Edriss S. Titi, U. Texas | WPI, OMP 1, Seminar Room 08.135 | Mon, 17. Dec 18, 10:00 |
| TBA | ||
TBA | ||
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| Peter Constantin, U. Princeton | WPI Seminarr Room | Sun, 16. Dec 18, 16:00 |
| TBA | ||
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| Piotr Gwiazda, Polish Academy of Science | WPI, OMP 1, Seminar Room 08.135 | Sun, 16. Dec 18, 14:30 |
| On the Extension of Onsager's Conjecture for General Conservation Laws | ||
The aim of this talk is to extend and prove the Onsager conjecture for a class of conservation laws that possess generalized entropy. One of the main findings of this work is the "universality" of the Onsager exponent, larger than 1/3, concerning the regularity of the solutions - space of Hölder continuous functions with the above exponent, that guarantees the conservation of the generalized entropy; regardless of the structure of the genuine nonlinearity in the underlying system. | ||
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| Agnieska Swierczewka-Gwiazda, U. Warsaw | WPI, OMP 1, Seminar Room 08.135 | Sun, 16. Dec 18, 11:00 |
| Measure-valued - strong uniqueness for general conservation laws | ||
In the last years measure-valued solutions started to be considered as a relevant notion of solutions if they satisfy the so-called measure-valued - strong uniqueness principle. This means that they coincide with a strong solution emanating from the same initial data if this strong solution exists. Following result of Yann Brenier, Camillo De Lellis and Laszlo Szekelyhidi Jr. for incompresible Euler equation, this property has been examined for many systems of mathematical physics, including incompressible and compressible Euler system, compressible Navier-Stokes system, polyconvex elastodynamics et al. In my talk I will concentrate on results concerning general conservation laws. Our goal is to provide a unified framework for general systems, that would cover the most interesting cases of systems. Following earlier common result with Eduard Feireisl, Piotr Gwiazda and Emil Wiedemann for compresible Navier-Stokes system, we develop the concept of dissipative measure-valued solution to general hyperbolic systems. The talk is based on joint results with Piotr Gwiazda and Ondrej Kreml. | ||
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| Francois Golse, X Paris | WPI, OMP 1, Seminar Room 08.135 | Sun, 16. Dec 18, 10:00 |
| Derivation of Models for the Dynamics of Sprays/Aerosols | ||
This talk proposes a derivation of the Vlasov-Navier-Stokes system used in the modeling of "thin" aerosol flows from a system of Boltzmann equations for a binary gas mixture involving the propellant gas and the dispersed phase in the aerosol. This derivation is formal, in the sense of the program for deriving fluid dynamic limits of the Boltzmann equation laid out in [C. Bardos - F. Golse - C.D. Levermore: J. Stat. Phys. 63 (1991), 323-344]. | ||
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| Vlad Vicol, U. Princeton | WPI, OMP 1, Seminar Room 08.135 | Sat, 15. Dec 18, 16:00 |
| Convex integration on thin sets | ||
I will discuss the construction of wild weak solutions to the Navier-Stokes equation which are smooth on the complement of a thin set of times (with Haursdorff dimension strictly less than 1). This is based on joint work with T. Buckmaster and M. Colombo. | ||
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| Emil Wiedemann; U. Hannover | WPI, OMP 1, Seminar Room 08.135 | Sat, 15. Dec 18, 11:00 |
| The viscosity limit with boundaries and interfaces: some remarks | ||
It is a notorious and classical problem whether Leray solutions of the Navier-Stokes equations converge to a solution of the Euler equations, as viscosity tends to zero. The problem is only well-understood in the case that the Euler solution is smooth and there are no physical boundaries. If one (or both) of these requirements are violated, the problem is still largely open. We discuss two specific situations: First, we prove a version of Onsager's conjecture in bounded domains that gives rise to a statement on the viscosity limit and the absence of anomalous dissipation (joint work with C. Bardos and E. S. Titi). Secondly, we discuss the viscosity limit problem for the (non-smooth) shear flow, also departing from work with Bardos and Titi; we investigate in particular the question what happens when the initial data is not exactly fixed along the viscosity sequence (in progress). | ||
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| Marco Sammartino, U. Palermo | WPI, OMP 1, Seminar Room 08.135 | Sat, 15. Dec 18, 10:00 |
| 2D analytic solutions of Euler equations with concentrated vorticity | ||
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| Peter Constantin, U. Princeton | OMP 1, Lecture Room 5 (Ground floor) | Fri, 14. Dec 18, 16:00 |
| Remarks on some mathematical problems in hydrodynamics | ||
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| Tim Langen, U. Stuttgart | WPI, OMP 1, Seminar Room 08.135 | Wed, 31. Oct 18, 12:15 |
| "Dipolar Gases - From Magnetic Atoms to Molecules" | ||
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| Ilaria Perugia, U. Wien | WPI, OMP 1, Seminar Room 08.135 | Fri, 5. Oct 18, 10:00 |
| Trefftz finite element methods | ||
Over the last years, finite element methods based on operator-adapted approximating spaces have been developed in order to better reproduce physical properties of the analytical solutions, and to enhance stability and approximation properties. They are based on incorporating a priori knowledge about the problem into the local approximating spaces, by using trial and/or test spaces locally spanned by functions belonging to the kernel of the differential operator (Trefftz spaces). These methods are particularly popular for wave problems in frequency domain. Here, the use of oscillating basis functions allows to improve the accuracy vs. computational cost, with respect to standard polynomial finite element methods, and breaks the strong requirements on number of degrees of freedom per wavelength to ensure stability. In this talk, the basic principles of Trefftz finite element methods for time-harmonic wave problems will be presented. Trefftz methods differ from each other by the way interelement continuity conditions are imposed. We will focus on discontinuous Galerkin approaches, where the approximating spaces are made of completely discontinuous Trefftz spaces, and on the recent virtual element framework. | ||
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| Nikola Stoilov, U. Bourgogne | WPI, OMP 1, Seminar Room 08.135 | Fri, 5. Oct 18, 9:00 |
| Electric Impedance Tomography | ||
Electric Impedance Tomography (EIT) is a medical imaging technique that uses the response to voltage difference applied outside the body to reconstruct tissue conductivity. As different organs have different impedance, this technique makes it possible to produce images of the body without exposing the patient to potentially harmful radiation. In mathematical terms, EIT is what is a nonlinear inverse problem, whereby data inside a given domain is recovered from data on its boundary. Such problems also belong to the area of Integrable Systems, which deals with nonlinear problems for which analytic solutions can be found, thus providing us with a mathematical framework for reconstructing images from the electrical information created by EIT. I will discuss the design of numerical algorithms based on spectral collocation methods that address D-bar problems found in both integrable systems and medical imaging. Successfully implementing these methods in EIT on modern computing architectures should allow us to achieve images with much higher resolutions at reduced processing times. | ||
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| Didier Pilod, U. Bergen | WPI, OMP 1, Seminar Room 08.135 | Thu, 4. Oct 18, 14:00 |
| Well-posedness for some dispersive perturbations of Burger’s equation | ||
We show that the Cauchy problem associated to a class of dispersive perturbations of Burgers' equations containing the low dispersion Benjamin-Ono equation $$ \partial_tu-D_x^{\alpha}\partial_xu+u\partial_xu=0 \, ,$$ with $0<\alpha \le 1$, is locally well-posed in $H^s(\mathbb R)$ for $s>s_\alpha: = \frac 32-\frac {5\alpha} 4$. As a consequence, we obtain global well-posedness in the energy space $H^{\frac{\alpha}2}(\mathbb R)$ as soon as $\frac\alpha 2> s_\alpha$, i.e. $\alpha>\frac67$. | ||
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| Thomas Kappeler, U. Zürich | WPI, OMP 1, Seminar Room 08.135 | Thu, 4. Oct 18, 11:00 |
| Normal form coordinates for the KdV equation having expansions in terms of pseudodifferential operators | ||
Complex normal coordinates for integrable PDEs on the torus can be viewed as 'nonlinear Fourier coefficients'. Based on previous work we construct near an arbitrary finite gap potential a real analytic, 'nonlinear Fourier transform' for the KdV equation having the following two main properties: (1) Up to a remainder term, which is smoothing to any given order, it is a pseudodifferential operator of order 0 with principal part given by the Fourier transform. (2) It is canonical and the pullback of the KdV Hamiltonian is in normal form up to order three. Furthermore, the corresponding Hamiltonian vector field admits an expansion in terms of a paradifferential operator. Such coordinates are a key ingredient for studying the stability of finite gap solutions, i.e., periodic multisolitons, of the KdV equation under small, quasi-linear perturbations. This is joint work with Riccardo Montalto. | ||
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| Patrick Gérard, U. Paris-Sud | WPI, OMP 1, Seminar Room 08.135 | Thu, 4. Oct 18, 9:30 |
| Growth of Sobolev norms for a weakly damped Szegö equation | ||
The Szegö equation is an integrable model for lack of dispersion on the circle. An important feature of this model is the existence of a residual set --- in the Baire sense--- of initial data leading to unbounded trajectories in high Sobolev norms. It is therefore natural to study the effect of a weak damping on such a system. In this talk I will discuss the damping of the lowest Fourier mode, which has the specificity of saving part of the integrable structure. Somewhat surprinsingly, we shall show that such a weak damping leads to a wider set of unbounded trajectories in high Sobolev norms. This is a jointwork in collaboration with Sandrine Grellier. | ||
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| Peter Perry, U. Kentucky | WPI, OMP 1, Seminar Room 08.135 | Wed, 3. Oct 18, 14:00 |
| Soliton Resolution for the Derivative Nonlinear Schr"{o}dinger Equation | ||
This talk reports on joint work with Robert Jenkins, Jiaqi Liu, and Catherine Sulem. The derivative nonlinear Schr\"{o}dinger equation (DNLS) is a completely integrable, dispersive nonlinear equation in one space dimension that arises in the study of circularly polarized Alfv\'{e}n waves in plasmas, and admits soliton solutions. In 1978, Kaup and Newell showed that the DNLS is completely integrable, and in the 1980's, J.-H. Lee used the Beals-Coifman approach to inverse scattering to solve the DNLS. In the work to be described, drawing on recent advances in the Riemann-Hilbert formulation of inverse scattering due to Dieng-McLaughlin (2008) and Borghese-Jenkins-McLaughlin (2017), we use the inverse scattering formalism to show that, for a spectrally determined generic set of initial data, the solution decomposes into the sum of 1-soliton solutions with calculable phase shifts plus radiation. | ||
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| Derchyi Wu, Academia Sinica | WPI, OMP 1, Seminar Room 08.135 | Wed, 3. Oct 18, 11:00 |
| The Direct Problem of perturbed Kadomtsev-Petviashvili II 1-line solitons | ||
Boiti-Pempinelli-Pogrebkov's inverse scattering theories on the KPII equation provide an integrable approach to solve the Cauchy Problem and the stability problem of the KPII equation for perturbed multisoliton solutions. In this talk, we will present rigorous analysis for the direct scattering theory of perturbed KPII one line solitons, the simplest case in Boiti-Pempinelli-Pogrebkov's theories. Namely, for generic small perturbation of the one line soliton, the existence of the eigenfunction is proved by establishing uniform estimates of the Green function and the Cauchy integral equation for the eigenfunction is justified by nonuniform estimates of the spectral transform. Difficulties and outlooks for the inverse problem will be discussed as well. | ||
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| Anton Arnold, TU Wien | WPI, OMP 1, Seminar Room 08.135 | Wed, 3. Oct 18, 9:30 |
| A hybrid WKB-based method for Schrödinger scattering problems in the semi-classical limit | ||
We are concerned with 1D scattering problems related to quantum transport in (tunneling) diodes. The problem includes both oscillatory and evanescent regimes, partly including turning points. We shall discuss the efficient numerical integration of ODEs of the form epsilon^2 u" + a(x) u = 0 for 0 < epsilon << 1 on coarse grids, but still yielding accurate solutions. In particular we study the numerical coupling of the highly oscillatory regime (i.e. for given a(x) > 0 ) with evanescent regions (i.e. for a(x) < 0 ). In the oscillatory case we use a marching method that is based on an analytic WKB-preprocessing of the equation. And in the evanescent case we use a FEM with WKB-ansatz functions. We present a full convergence analysis of the coupled method, showing that the error is uniform in epsilon and second order w.r.t. h, when h = O(epsilon^1/2). We illustrate the results with numerical examples for scattering problems for a quantum-tunnelling structure. The main challenge when including a turning point is that the solution gets unbounded there as epsilon -> 0. Still one can obtain epsilon-uniform convergence, when h = O(epsilon^7/12). | ||
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| Christian Klein, U. Bourgogne | WPI, OMP 1, Seminar Room 08.135 | Tue, 2. Oct 18, 11:00 |
| Numerical study of blow-up in dispersive PDEs | ||
We study numerically the stability of solitons and a possible blow-up of solutions in dispersive PDEs of the family of Kortweg-de Vries and nonlinear Schr\"odinger equations. The biow-up mechanism in the $L^2$ critical and supercritical case is studied. | ||
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| Jean-Claude Saut, ICP & U. Paris Sud | WPI, OMP 1, Seminar Room 08.135 | Tue, 2. Oct 18, 9:30 |
| On KP type equations | ||
After recalling the known results on the KP I and KP II equations, we survey some open problems on the KP equations, both from the PDE and IST aspects, and also on some relevant KP type equations. | ||
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| Parra Diaz, Felix (U.Oxford) | WPI, OMP 1, Seminar Room 08.135 | Fri, 3. Aug 18, 10:00 |
| TBA | ||
TBA | ||
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| Milanese, Lucio (MIT) | WPI, OMP 1, Seminar Room 08.135 | Thu, 2. Aug 18, 16:00 |
| Electron-temperature-gradient-driven inverse cascade of energy | ||
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| White, Ryan (MIT) | WPI, OMP 1, Seminar Room 08.135 | Thu, 2. Aug 18, 10:00 |
| Anomalous resistivity and reconnection in an evolving current profile | ||
TBA | ||
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| Abel, Ian (U. Maryland) | WPI, OMP 1, Seminar Room 08.135 | Wed, 1. Aug 18, 16:00 |
| The simplest possible pedestal? | ||
TBA | ||
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| Parker, Jeff (LLNL) | WPI, OMP 1, Seminar Room 08.135 | Wed, 1. Aug 18, 10:00 |
| Multiple-timescale global GK turbulence and transport simulations for tokamaks | ||
TBA | ||
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| Dodin, Ilya (U. Princeton) | WPI, OMP 1, Seminar Room 08.135 | Tue, 31. Jul 18, 10:00 |
| Inhomogeneous drift-wave turbulence as an effective quantum plasma | ||
TBA | ||
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| Hardman, Michael (U. Oxford) | WPI, OMP 1, Seminar Room 08.135 | Mon, 30. Jul 18, 10:45 |
| A scale separated framework for studying cross scale interactions in plasma turbulence | ||
TBA | ||
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| Maeyama, Shinya (U. Nagoya) | WPI, OMP 1, Seminar Room 08.135 | Mon, 30. Jul 18, 10:00 |
| Effects of sub-ion-scale structures on cross-scale interactions in Tokamak plasma turbulence | ||
TBA | ||
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| Schekochihin, Alex (U. Oxford) | WPI, OMP 1, Seminar Room 08.135 | Fri, 27. Jul 18, 10:45 |
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1. Ion vs. electron heating in astro-GK turbulence (theory with Kawazura & Barnes) 2. Some interesting nuggets in MHD turbulence theory 3. Fluidisation of kinetic density turbulence (with Meyrand & Dorland) | ||
TBA | ||
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| Loureiro, Nuno (MIT) | WPI, OMP 1, Seminar Room 08.135 | Fri, 27. Jul 18, 10:00 |
| Turbulence in pair plasmas | ||
TBA | ||
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| Werner, Greg (UC Boulder) | WPI, OMP 1, Seminar Room 08.135 | Thu, 26. Jul 18, 16:45 |
| 1. Relativistic reconnection: heating and nothermal particle acceleration in pair and electron-ion plasmas 2. Relativistic reconnection with external inverse Compton cooling | ||
TBA | ||
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| Uzdensky, Dmitri (UC Boulder) | WPI, OMP 1, Seminar Room 08.135 | Thu, 26. Jul 18, 16:00 |
| 1. Relativistic nonthermal particle acceleration in magnetic reconnection 2. Ion vs. electron heating in relativistic collisionless turbulence | ||
TBA | ||
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| Stone, James (U. Princeton) | WPI, OMP 1, Seminar Room 08.135 | Thu, 26. Jul 18, 10:45 |
| Statistics of current sheets in MRI turbulence | ||
TBA | ||
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| Kunz, Matthew (U. Princeton) | WPI, OMP 1, Seminar Room 08.135 | Thu, 26. Jul 18, 10:00 |
| 1. Sound waves in high-beta plasma 2. Mirror-mediated magnetic reconnection | ||
TBA | ||
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| Bott, Archie (U. Oxford) | WPI, OMP 1, Seminar Room 08.135 | Wed, 25. Jul 18, 10:45 |
| New plasma dynamo experiments on OMEGA | ||
TBA | ||
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| St-Onge, Denis (U. Princeton) | WPI, OMP 1, Seminar Room 08.135 | Wed, 25. Jul 18, 10:00 |
| Plasma dynamo: latest results | ||
TBA | ||
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| Beloborodov, Andrei (U. Columbia) | WPI, OMP 1, Seminar Room 08.135 | Tue, 24. Jul 18, 16:45 |
| Radiative reconnection | ||
TBA | ||
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| Spitkovsky, Anatoly (U. Princeton) | WPI, OMP 1, Seminar Room 08.135 | Tue, 24. Jul 18, 16:00 |
| 1. Electron heating in shocks 2. Relativistic reconnection with pair production | ||
TBA | ||
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| Chandran, Ben (U. New Hampshire) | WPI, OMP 1, Seminar Room 08.135 | Tue, 24. Jul 18, 10:45 |
| Parametric instability, inverse cascade, and the 1/f spectrum of solar-wind turbulence | ||
TBA | ||
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| Arzamasskiy, Lev (U. Princeton) | WPI, OMP 1, Seminar Room 08.135 | Tue, 24. Jul 18, 10:00 |
| Hybrid-kinetic simulations of driven solar-wind turbulence: spectral anisotropy, perpendicular ion heating and non-thermal features in distribution function | ||
TBA | ||
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| Sironi, Lorenzo (U. Columbia) | WPI, OMP 1, Seminar Room 08.135 | Mon, 23. Jul 18, 16:45 |
| Electron heating in shocks and reconnection | ||
TBA | ||
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| Kawazura, Yohei (U. Oxford) | WPI, OMP 1, Seminar Room 08.135 | Mon, 23. Jul 18, 16:00 |
| Ion vs. electron heating in astro-GK turbulence (simulations) | ||
TBA | ||
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| Cerri, Silvio (U. Princeton) | WPI, OMP 1, Seminar Room 08.135 | Mon, 23. Jul 18, 10:45 |
| 3D hybrid-kinetic turbulence and phase-space cascades in a beta=1 plasma | ||
TBA | ||
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| Groselj, Daniel (IPP Garching) | WPI, OMP 1, Seminar Room 08.135 | Mon, 23. Jul 18, 10:00 |
| Kinetic turbulence in astrophysical plasmas: waves and/or structures? | ||
TBA | ||
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| Levy, Doron (U. Maryland) | Sat, 21. Jul 18, 16:25 | |
| Closing Remarks | ||
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| Lorz, Alexander (KAUST) | Sat, 21. Jul 18, 15:45 | |
| Mathematics meets oncology: from Adaptive evolution to Zebrafish | ||
In this talk, I focus on current biological problems and on how to use mathematical modeling to analyze a variety of pressing questions arising from oncology, developmental pattern formation and population ecology. I first discuss novel mathematical models for cancer growth dynamics and heterogeneity. These studies rely on evolutionary principles and shed light on 3D hepatic tumor dynamics, spatial heterogeneity and tumor invasion, and single cancer cell responses to antimitotic therapies. We also develop mathematical models that quantitatively demonstrate how the interplay between non-genetic instability, stress-induced adaptation, and selection leads to the transient and reversible phenotypic evolution of cancer cell populations exposed to therapy. Finally, we study control techniques for optimal therapeutic administration. | ||
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| Kefurt, Ronald (Med. Uni Vienna) | Sat, 21. Jul 18, 14:40 | |
| TBA | ||
TBA | ||
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| Kicheva, Anna (IST Austria) | Sat, 21. Jul 18, 14:00 | |
| Coordination of progenitor specification and growth in the developing spinal cord | ||
As the spinal cord grows during embryonic development, an elaborate pattern of molecularly distinct neuronal precursor cells forms along the DV axis. This pattern depends both on the dynamics of a morphogen-regulated gene regulatory network, and on tissue growth. We study how these processes are coordinated. Our data revealed that during mouse and chick development the gene expression pattern changes but does not scale with the overall tissue size. These changes in the pattern are sequentially controlled by distinct mechanisms. Initially, neural progenitors integrate signaling from opposing morphogen gradients to determine their identity by using a mechanism equivalent to maximum likelihood decoding. This strategy allows accurate assignment of position along the patterning axis and can account for the observed precision and shifts of pattern. During the subsequent developmental phase, cell-type specific regulation of differentiation rate, but not proliferation, elaborates the pattern. | ||
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| Gevertz, Jana (New Jersey College) | Sat, 21. Jul 18, 11:20 | |
| Identifying robust optimal cancer treatment protocols from small experimental | ||
Mathematical models of biological systems are often validated by fitting the model to the average of an (often small) experimental dataset. Here we ask the question of whether predictions made from a model fit to the average of a dataset are actually applicable in samples that deviate from the average. We will explore this in the context of a murine model of melanoma treated with oncolytic viruses and dendritic cell injections. We have hierarchically developed a system of ordinary different equations to describe the average of this experimental data, and optimized treatment subject to clinical constraints. Using a virtual population method, we explore the robustness of treatment response to the predicted optimal protocol; that is, we quantify the extent to which the optimal treatment protocol elicits the same qualitative response in virtual populations that deviate from the average. We find that our predicted optimal is not robust and in fact is potentially a dangerous protocol for a fraction of the virtual populations. However, if we consider a different drug dose than used in the experiments, we are able to identify an optimal protocol that elicits a robust anti-tumor response across virtual populations. | ||
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| Cordero, Francesca (U. Turin) | Sat, 21. Jul 18, 10:40 | |
| Multiscale models to investigate IntraTumor Heterogeneity | ||
In cancer research most efforts are devoted on the decipher of the IntraTumoral Heterogeneity (ITH). In ITH the action of the evolutionary forces of mutation and selection are essential to determinant the tumor progression, diagnosis and treatment. ITH gives rise to cancer cell populations with distinct genotypic and metabolic characteristics contributing to the failure of cure, by initiating phenotypic diversity and enabling more aggressive and drug resistant clones. I will present multi-scale models of cancer linking the tumor growth to the intracellullar signalling and metabolic events to genomic profiles. The models consider several heterogenous omics data (metabolomics, proteomics, transcriptomics, genomics) to investigate the ITH associated with different genomic and metabolic traits. | ||
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| Klingmüller, Ursula (U. Heidelberg) | Sat, 21. Jul 18, 9:40 | |
| Model-based optimization of personalized anemia treatment in chronic diseases | ||
Anemia associated with chronic diseases is the second most prevalent anemia in the world after anemia caused by iron deficiency. Advanced stages of diseases such as chronic kidney disease (CKD) and cancer coincide with a high prevalence of severe anemia that results in fatigue, reduced quality of life and decreased treatment responses in patients. Two therapeutic options are available to manage anemia: blood transfusion and treatment with erythropoiesis stimulating agents (ESAs) in combination with iron supplementation. However, adverse events and increased risk of mortality have been reported for blood transfusions and ESAs. Decisions on the clinical treatment should be based on the specific benefit-to-risk ratio of each patient, which is complicated to assess due to the heterogeneity of the patients, the lack of prognostic markers and the dynamics of comorbidities associated with the diseases. We developed a multiscale mathematical model that links mechanistic insights at the cellular scale to response at the body level to guide clinical decisions based on the prediction of the response to the available therapeutic options. The mathematical model stratifies patients based on the estimation of two patient specific dynamic parameters. These parameters are estimated by the mathematical model based on the time-course of the haemoglobin (Hb) values, CRP, iron values and scheduled chemotherapy in each patient. These two patient specific parameters reflect the anaemic status of the patient as well as the capability to respond to treatment with ESAs. The model is capable to propose optimized personalized interventions for anaemia management in lung cancer and CKD patients. | ||
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| Clairambault, Jean (INRIA) | Sat, 21. Jul 18, 9:00 | |
| Evolutionary viewpoint on drug resistance in cancer cell populations with perspectives in therapeutic control, and open general questions on cancer with respect to evolution | ||
To tackle the question of drug resistance in cancer, I will present an adaptive dynamic framework to represent the evolution in phenotype of cell populations, that allows to follow the instantaneous distribution and asymptotic behaviour of drug resistance phenotype(s) in the cell population. Such phenotypes evolve under drug pressure towards either established or transient, possibly reversible, drug tolerance, a behaviour taken into account by the models we design to allow for therapeutic control. Optimal control strategies describing the combination of different categories of drugs on specified cell functional targets (thus far cytotoxics, that act on death terms, and cytostatics, that act on proliferation terms) are proposed, aiming at minimising a tumour cell population while limiting both unwanted toxic side effects on healthy cell populations and occurrence of drug resistance in cancer cell populations. The models used for these representations, their asymptotic properties and their theoretical therapeutic control are integro-differential (non-local Lotka-Volterra-like) or PDE models (reaction-diffusion models with or without advection). Finally, I will present some transdisciplinary challenges of cancer modelling that should concern mathematicians, cell biologists, evolutionary biologists and oncologists, aiming to go beyond the present state of the art in the treatments of cancer. | ||
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| Nenning, Karl Heinz (Med. Uni Vienna) | Fri, 20. Jul 18, 16:25 | |
| The changing global functional connectivity structure in patients with glioblastoma | ||
Glioblastoma may have wide-spread effects on the cortical organization and cognitive function since even focal lesions impact the brains’ functional network architecture. Currently, our understanding of the interaction between tumor lesions and their impact on the functional connectome is limited. Hence, we used 3 Tesla resting-state functional magnetic resonance imaging to evaluate the functional connectivity structure of 15 patients with glioblastoma. We further tracked the functional characteristics of six patients over time using bimonthly follow-up examinations. We found changes in resting-state networks to be highly symmetric and mirrored by changes in the cerebellum. Patients shared a pattern of network deterioration after surgery, with subsequent recovery at the first follow-up examination. Additionally, we showed that glioblastoma has a global effect on the functional connectivity structure of the individual patient, which might serve as sensitive early marker of tumor recurrence. Of note, local tumor recurrence coincided with network deterioration before structural changes were apparent upon imaging. In summary, our results demonstrate how the functional connectome is affected by focal lesions, and that it might be exploited as an early predictor of local tumor recurrence. This renders the individual patient’s functional connectome a promising novel biomarker for the longitudinal patient follow-up in order to support early informed treatment decisions. | ||
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| Seoane Sepúlveda, Jesús M. (U. Rey Juan Carlos) | Fri, 20. Jul 18, 15:45 | |
| Dynamics of tumor and immune cell aggregates | ||
In this talk we present our work on the dynamics of tumor and immune cell interactions [1-4]. A hybrid probabilistic cellular automaton model describing the spatio-temporal evolution of tumor growth and its interaction with the cell-mediated immune response is developed. The model parameters are adjusted to an ordinary differential equation model, which has been previously validated [1] with in vivo experiments and chromium release assays. The cellular automaton is used to perform in silico experiments which, together with mathematical analyses, allow us to characterize the rate at which a tumor is lysed by a population of cytotoxic immune cells [2-3]. Finally, the transient and asymptotic dynamics of the cell-mediated immune response to tumor growth is considered [4]. The cellular automaton model is used to investigate and discuss the capacity of the cytotoxic cells to sustain long periods of tumor mass dormancy, as commonly observed in recurrent metastatic disease. This is a joint work with Alvaro G. López and Miguel A. F. Sanjuán. | ||
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| Mayerhöfer, Marius (Med. Uni Wien) | Fri, 20. Jul 18, 14:40 | |
| Novel trends in cancer imaging: from hybrid techniques to radiomics | ||
Cancer imaging has undergone major paradigm shifts within the last decade. Hybrid imaging techniques, and in particular, PET/CT (positron emission tomography / computed tomography) with the glucose analogue radiotracer [18F]FDG is now an integral part of the management guidelines for patients with different cancers, with a particular emphasis on the early detection of treatment effects on the tumor. Novel PET radiotracers that are specific for certain types of cancer – such as [68Ga]PSMA for prostate cancer – are currently being evaluated in clinical trials. Notably, though visual image interpretation is still the clinical standard, there is now a trend towards the use of quantitative data extracted from diagnostic images. The recently introduced PET/MRI (magnetic resonance imaging) is of particular interest in that regard, because it offers information on tissue properties such as cell density and blood flow in addition to the metabolic information provided by PET. The combination of quantitative parameters extracted from MRI and PET may not only improve non-invasive, image-based characterization of tumor heterogeneity, but may also improve evaluation of the effects of novel types of treatment. This multi-parametric approach also provides an ideal basis for radiomics – i.e., computer-assisted image analysis, and based on it, recognition of mathematical image patterns that are related to tumor characteristics. This novel approach to image interpretation, which is aided by advanced techniques such as artificial neural networks, has the potential to contribute significantly to the success of precision medicine, and the welfare of patients. | ||
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| Peurichard, Diane (INRIA) | Fri, 20. Jul 18, 14:00 | |
| A multi-scale approach for models of tumor growth: from short-range repulsion to Hele-Shaw problems | ||
In this talk, we investigate the link between multi-scale models for tumor growth. We start from a microscopic model where cells are modelled as 2D spheres undergoing short range repulsion and cell division. We derive the associated macroscopic dynamics leading to a porous media type equation. As the macroscopic equation obtained through usual derivation method fails at providing the correct qualitative behavior, we propose a modified version of the macroscopic equation introducing a density threshold for the repulsion. We numerically validate the new formulation by comparing the solutions of the micro- and macro- dynamics. Moreover, we study the asymptotic behavior of the dynamics as the repulsion between cells becomes singular (leading to non-overlapping constraints in the microscopic model). We show formally that such asymptotic limit leads to a Hele-Shaw type problem for the macroscopic dynamics. The numerical simulations reveal an excellent agreement between the micro- and macro- descriptions, validating the formal derivation of the macroscopic model. The macroscopic model derived here therefore enables to overcome the problem of large computational time raised by the microscopic model, but stays closely linked to the microscopic dynamics. | ||
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| Benzekry, Sebastien (INRIA) | Fri, 20. Jul 18, 11:40 | |
| Mathematical modeling and prediction of clinical metastasis | ||
In the majority of cancers, secondary tumors (metastases) and associated complications are the main cause of death. To design the best therapy for a given patient, one of the major current challenge is to estimate, at diagnosis, the eventual burden of invisible metastases and the future time of emergence of these, as well as their growth speed. In this talk, I will present the current state of research efforts towards the establishment of a predictive computational tool for this aim. I will first shortly present the model used, which is based on a physiologically-structured partial differential equation for the time dynamics of the population of metastases, combined to a nonlinear mixed-effects model for statistical representation of the parameters’ distribution in the population. Then, I will show results about the descriptive power of the model on data from clinically relevant ortho-surgical animal models of metastasis (breast and kidney tumors). The main part of my talk will further be devoted to the translation of this modeling approach toward the clinical reality. Using clinical imaging data of brain metastasis from non-small cell lung cancer, several biological processes will be investigated to establish a minimal and biologically realistic model able to describe the data. Integration of this model into a biostatistical approach for individualized prediction of the model’s parameters from data only available at diagnosis will also be discussed. Together, these results represent a step forward towards the integration of mathematical modeling as a predictive tool for personalized medicine in oncology. | ||
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| Grebien, Florian (LBI Cancer Research) | Fri, 20. Jul 18, 11:00 | |
| Identification of actionable nodes in cancer-specific protein networks | ||
Oncogenes perturb molecular mechanisms to drive neoplastic initiation and progression. Chromosomal rearrangements are frequent events in cancer, and can result in the expression of fusion proteins. Fusion proteins represent neomorphic protein variants with aberrant activities and are often drivers of oncogenesis. Acute myeloid leukemia (AML) is an aggressive cancer of the white blood cell lineage that is associated with poor prognosis. While AML features a particular high prevalence of fusion proteins, it is largely unknown how the majority of AML fusion proteins rewire the molecular machinery of normal blood cells to induce leukemia. We hypothesize that oncogenic mechanisms of AML fusion proteins are hard-wired in specific networks of physical, genetic and epigenetic interactions with key effector proteins. Functional exploration of these networks by systematic comparative approaches will provide new insights into cellular processes that depend on critical effector proteins among these networks. The goal of our research is a comprehensive systems-level investigation of oncogenic mechanisms employed by AML fusion proteins. We have established a robust experimental pipeline for the rapid characterization of fusion oncoproteins in a multilayered, global fashion. We use modern genetic tools to generate advanced cell and animal models for tunable expression of AML fusion proteins. Fusion protein-dependent changes in cellular topologies are charted by proteomic and transcriptomic approaches. In parallel, genome-scale loss-of function CRISPR/Cas9 screening is used to identify critical effectors of leukemogenesis. High-confidence candidates are validated using a wide array of different approaches, including studies in primary patient-derived leukemia cells. Results from this pipeline provide evidence for its robust validity, but also for its translational impact, strongly implying that this approach will contribute to an improved understanding of oncogenesis. | ||
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| Bergmann, Michael (Med. Uni Vienna) | Fri, 20. Jul 18, 9:50 | |
| Understanding and modulation of the immune infiltrate in solid tumors | ||
TBA | ||
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| Maini, Philip (U. Oxford) | Fri, 20. Jul 18, 9:10 | |
| Mathematical modelling of angiogenesis | ||
Angiogenesis is the process by which the body generates new blood vessels. This occurs in the context of wound healing where, of course, it is beneficial to the body. However, it can also occur in cancer where it can enhance delivery of nutrients to the cancer and enable cancer cells to infiltrate the blood system and metastasize to vital organs, leading to the often fatal secondary tumours. Understanding this process is a challenge for both experimentalists and theoreticians. I will review some recent work we have done on this problem which includes generating a new partial differential equation model for the so-called ``snail-trail'' movement of blood vessel cells to the tumour (Pillay et al, 2017), by developing a continuuum model of the process from a discrete description. I will then present a computational multiscale model for a key experimental assay that is used by experimentalists to measure the efficacy of anti-angiogenesis drugs and use it to make predictions (Grogan et al, 2018; 2017). | ||
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| Mauser, Norbert J. (WPI Director) | Fri, 20. Jul 18, 9:00 | |
| Opening Remarks | ||
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| Schmidt, Thorsten (U. Freiburg) | Wed, 4. Jul 18, 11:00 | |
| Affine processes under parameter uncertainty | ||
We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call non-linear affine processes. This is done as follows: given a set $Theta$ of parameters for the process, we construct a corresponding non-linear expectation on the path space of continuous processes. By a general dynamic programming principle we link this non-linear expectation to a variational form of the Kolmogorov equation, where the generator of a single affine process is replaced by the supremum over all corresponding generators of affine processes with parameters in $Theta$. This non-linear affine process yields a tractable model for Knightian uncertainty, especially for modelling interest rates under ambiguity. We then develop an appropriate Ito-formula, the respective term-structure equations and study the non-linear versions of the Vasicek and the Cox-Ingersoll-Ross (CIR) model. Thereafter we introduce the non-linear Vasicek-CIR model. This model is particularly suitable for modelling interest rates when one does not want to restrict the state space a priori and hence the approach solves this modelling issue arising with negative interest rates. Joint work with Tolulope Fadina and Ariel Neufeld. | ||
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| Peyre, Remi (U. Lorraine) | Wed, 4. Jul 18, 10:00 | |
| Where stochastic processes, fractal dimensions, numerical computations and quasi-stationary distributions meet | ||
In a joint work with Walter Schachermayer (still in progress), we investigate the optimal strategy of an economic agent trading a fractional asset in presence of transaction costs. A fascinating conjecture by us asserts that, contrary to the Bronwnian case, such an optimal trading would be fully discrete, only involving countably many trading times. What we can already prove is that only certain specific times, which we call "potential trading times", may involve trading, regardless of the agent's porfolio (this shall be explained more in detail). An idea towards our conjecture (though unsuccessful yet) would be to bound above the fractal dimension of the set of potential trading times. The nice point with this approach is that, contrary to the optimal strategy, this fractal dimension can be computed numerically: the goal of my talk will be to explain how one can do so. The method I propose involves quasi-stationary distributions, that is, killed Markov processes conditioned by long-time survival: which is rather surprising, as this concept has a priori nothing to do with fractal dimension ... | ||
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| Pulido, Sergio (ENSIIE France) | Wed, 4. Jul 18, 9:00 | |
| Affine Volterra processes | ||
Motivated by recent advances in rough volatility modeling, we introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classica affine diffusions constitute a special case, but affine Volterra processes are neither semimartingales, nor Markov processes in general. Nonetheless, their Fourier-Laplace functionals admit exponential-affine representations in terms of solutions of associated deterministic integral equations, extending the well-known Riccati equations for classical affine diffusions. Our findings generalize and clarify recent results in the literature on rough volatility. | ||
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| Glau, Kathrin (Queen Mary U. London) | Tue, 3. Jul 18, 17:30 | |
| A new approach for American option pricing: The Dynamic Chebyshev method | ||
We introduce a new method to price American options based on Chebyshev interpolation. The key advantage of this approach is that it allows to shift the model-dependent computations into an offline phase prior to the time-stepping. This leads to a highly efficient online phase. The model-dependent part can be solved with any computational method such as solving a PDE, using Fourier integration or Monte Carlo simulation. | ||
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| Liu, Chong (ETH Zürich) | Tue, 3. Jul 18, 17:00 | |
| Cadlag rough paths | ||
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| Teichmann, Josef (ETH Zürich) | Tue, 3. Jul 18, 16:30 | |
| Machine Learning and regularity structures | ||
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| Khosrawi, Wahid (U. Freiburg) | Tue, 3. Jul 18, 16:00 | |
| A homotopic view on machine learning with applications to SLV calibration | ||
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| Escobar,Daniela (U. Wien) | Tue, 3. Jul 18, 15:30 | |
| The distortion premium principle: properties, identification and robustness | ||
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| Tangpi, Ludovic (U. Wien) | Tue, 3. Jul 18, 15:00 | |
| New limit theorems for Wiener process and applications | ||
We will discuss non-exponential versions of well known limit theorems, specialising on the case of Brownian motion. The proofs will partially rely on the theory of BSDEs and their convex dual formulations, and an application to (stochastic) optimal transport will be provided. | ||
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| Rogers, Chris (U. Cambridge) | Tue, 3. Jul 18, 11:00 | |
| Economics: science or sudoku? | ||
When we are ill, most of us would prefer to receive treatment that was supported by scientific evidence, rather than anecdotal tradition or superstition. When a nation's economy is ill, policy-makers turn to economists for advice, but how well is their advice supported by evidence? This talk critiques the value of economic theory in practice, and tries to suggest ways of increasing the practical relevance of the subject. | ||
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| Jentzen, Arnulf (ETH Zürich) | Tue, 3. Jul 18, 10:00 | |
| Stochastic approximation algorithms for high-dimensional PDEs | ||
Partial differential equations (PDEs) are among the most universal tools used in modelling problems in nature and man-made complex systems. For example, stochastic PDEs are a fundamental ingredient in models for nonlinear filtering problems in chemical engineering and weather forecasting, deterministic Schroedinger PDEs describe the wave function in a quantum physical system, deterministic Hamiltonian-Jacobi-Bellman PDEs are employed in operations research to describe optimal control problems where companys aim to minimise their costs, and deterministic Black-Scholes-type PDEs are also highly employed in portfolio optimization models as well as in state-of-the-art pricing and hedging models for financial derivatives. The PDEs appearing in such models are often high-dimensional as the number of dimensions, roughly speaking, corresponds to the number of all involved interacting substances, particles, resources, agents, or assets in the model. For instance, in the case of the above mentioned financial engineering models the dimensionality of the PDE often corresponds to the number of financial assets in the involved hedging portfolio. Such PDEs can typically not be solved explicitly and it is one of the most challenging tasks in applied mathematics to develop approximation algorithms which are able to approximatively compute solutions of high-dimensional PDEs. Nearly all approximation algorithms for PDEs in the literature suffer from the so-called "curse of dimensionality" in the sense that the number of required computational operations of the approximation algorithm to achieve a given approximation accuracy grows exponentially in the dimension of the considered PDE. With such algorithms it is impossible to approximatively compute solutions of high-dimensional PDEs even when the fastest currently available computers are used. In this talk we introduce of a class of new stochastic approximation algorithms for high-dimensional nonlinear PDEs. We prove that these algorithms do indeed overcome the curse of dimensionality in the case of a general class of semilinear parabolic PDEs and we thereby prove, for the first time, that a general semilinear parabolic PDE with a nonlinearity depending on the PDE solutiothe approximation algorithm to achieve a given approximation accuracy grows exponentially in the dimension of the considered PDE. | ||
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| Kardaras, Kostas (London School of Economics) | Tue, 3. Jul 18, 9:00 | |
| Equilibrium in thin security markets under restricted participation | ||
A market of financial securities with restricted participation is considered. Agents are heterogeneous in beliefs, risk tolerance and endowments, and may not have access to the trade of all securities. The market is assumed thin: agents may influence the market and strategically trade against their price impacts. Existence and uniqueness of the equilibrium is shown, and an efficient algorithm is provided to numerically obtain the equilibrium prices and allocations given market’s inputs. (Based on joint work with M. Anthropelos.) | ||
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| Svaluto-Ferro, Sara (U. Wien) | Mon, 2. Jul 18, 17:30 | |
| Generators of probability-valued jump-diffusions | ||
Probability-valued jump-diffusions provide useful approximations of large stochastic systems in finance, such as large sets of equity returns, or particle systems with mean-field interaction. The dynamics of a probability-valued jump-diffusion is governed by an integro-differential operator of Levy type, expressed using a notion of derivative that is well-known from the superprocesses literature. General and easy-to-use existence criteria for probability-valued jump-diffusions are derived using new optimality conditions for functions of probability arguments. In general, we consider the space of probability measures as endowed with the topology of weak convergence. For jump-diffusions taking value on a specific subset of the probability measures, it can however be useful to work with a stronger notion of convergence. Think for instance at the well-known Wasserstein spaces. This change of topology permits to include in the theory a larger class of generators, and hence, a larger class of probability-valued jump-diffusions. We derive general and easy-to-use existence criteria for jump-diffusions valued in those spaces. | ||
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| Harms, Philipp (U. Freiburg) | Mon, 2. Jul 18, 17:00 | |
| Cylindrical Wiener Processes | ||
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| Reppen, Max (ETH Zürich) | Mon, 2. Jul 18, 16:30 | |
| Discrete dividends in continuous time | ||
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| Zeineddine, Raghid (U. Freiburg) | Mon, 2. Jul 18, 16:00 | |
| Variable Annuities in hybrid financial market | ||
In this talk I will explain what is a Variable Annuities (VA) contract and how we can find the pricing formula of VA when the financial market is hybrid in the sense introduced by Eberlein. | ||
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| Jamneshan, Asgar (ETH Zürich) | Mon, 2. Jul 18, 15:30 | |
| On the structure of measure preserving dynamical systems and extensions of disintegration of measure | ||
TBA | ||
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| Birghila, Corina (U. Wien) | Mon, 2. Jul 18, 15:00 | |
| Optimal insurance contract under ambiguity. Applications in extreme events. | ||
Insurance contracts are efficient risk management techniques to operate and reduce losses. However, very often, the underlying probability model for losses - on the basis of which premium is computed - is not completely known. Furthermore, in the case of extreme climatic events, the lack of data increases the epistemic uncertainty of the model. In this talk we propose a method to incorporate ambiguity into the design of an optimal insurance contract. Due to coverage limitations in this market, we focus on the limited stop-loss contract, given by $I(x)=min(max(x-d_1),d_2)$, with deductible $d_1$ and cap $d_2$. Therefore, we formulate an optimization problem for finding the optimal balance between the contract parameters that minimize some risk functional of the final wealth. To compensate for possible model misspecification, the optimal decision is taken with respect to a set of non-parametric models. The ambiguity set is built using a modified version of the well-known Wasserstein distance, which results to be more sensitive to deviations in the tail of distributions. The optimization problem is solved using a distributionally robust optimization setup. We examine the dependence of the objective function as well as the deductible and cap levels of the insurance contract on the tolerance level change. Numerical simulations illustrate the procedure. | ||
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| Fontana, Claudio (U. Paris VII); Gümbel, Sandrine (U. Freiburg) | Mon, 2. Jul 18, 11:00 | |
| Term structure models for multiple curves with stochastic discontinuities | ||
In this talk, we propose a novel approach to the modelling of multiple yield curves. Adopting the HJM philosophy, we model term structures of forward rate agreements (FRA) and OIS bonds. Our approach embeds most of the existing approaches and additionally allows for stochastic discontinuities. In particular, this last feature has an important motivation in interest rate markets, which are affected by political events and decisions occurring at predictable times. We study absence of arbitrage using results from the recent literature on large financial markets and discuss special cases and examples. This talk is based on joint work with Zorana Grbac, Sandrine Gümbel and Thorsten Schmidt. | ||
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| Schachermayer, Walter (U. Wien) | Mon, 2. Jul 18, 10:00 | |
| TBA | ||
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| Rainer, Catherine (U. Brest) | Mon, 2. Jul 18, 9:00 | |
| On continuous time games with asymmetric information | ||
I'll try in this talk to present the main ideas on zero-sum continuous time games where one of the two players has some private information (for instance when only one player observes a Brownian motion): how to formalize these games, the associated Hamilton-Jacobi-Isaacs-equation and the analyse of the optimal revelation in terms of an optimization problem over a set of martingales. In a second time I'll present the last developments in this area. | ||
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| Ollett, Andrew (U. Chicago) | Seminar Room Zemanek, TU Wien, Favoritenstrasse 9-11, 1040 Wien | Wed, 13. Jun 18, 15:00 |
| Different Deontic Concepts in Mimamsa | ||
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| Cummins, Patrick (Cornell University) | Seminar Room Zemanek, TU Wien, Favoritenstrasse 9-11, 1040 Wien | Wed, 13. Jun 18, 14:00 |
| Obligation as Linguistic Category in Prabhakara's Hermeneutics of Deontology | ||
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| Guhe, Eberhard (U. Fudan) | Seminar Room Zemanek, TU Wien, Favoritenstrasse 9-11, 1040 Wien | Wed, 13. Jun 18, 10:00 |
| Ross's Paradox and the Navya-Nyaya Interpretation of Injunctions | ||
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| Patil, Parimal (U. Harvard) | Seminar Room Zemanek, TU Wien, Favoritenstrasse 9-11, 1040 Wien | Wed, 13. Jun 18, 9:00 |
| The Cognition of Commands in Navya-Nyaya | ||
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| Parent, Xavier (U. Luxembourg) | Seminar Room Zemanek, TU Wien, Favoritenstrasse 9-11, 1040 Wien | Tue, 12. Jun 18, 16:30 |
| A Rule-Based Deontic Reasoner | ||
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| Modgil, Sanjay (King's College London) | Seminar Room Zemanek, TU Wien, Favoritenstrasse 9-11, 1040 Wien | Tue, 12. Jun 18, 15:00 |
| Logic, Dialogue and Moral Reasoning | ||
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| Brick, David (U. Yale) | Seminar Room Zemanek, TU Wien, Favoritenstrasse 9-11, 1040 Wien | Tue, 12. Jun 18, 14:00 |
| Arguments Regarding Sati from Classical Hindu Law | ||
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| McCrea, Lawrence (U. Cornell) | Seminar Room Zemanek, TU Wien, Favoritenstrasse 9-11, 1040 Wien | Tue, 12. Jun 18, 10:00 |
| Contextual Factors in the Interpretation of Prohibitions | ||
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| Gabbay, Dov (King's College London) | Seminar Room Zemanek, TU Wien, Favoritenstrasse 9-11, 1040 Wien | Tue, 12. Jun 18, 9:00 |
| Principles of Talmudic Logic - Sample Export to Modern AI | ||
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| Sartor, Giovanni (U. Bologna) | Seminar Room Zemanek, TU Wien, Favoritenstrasse 9-11, 1040 Wien | Mon, 11. Jun 18, 17:00 |
| Defeasible Legal Argumentation | ||
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| Baaz, Matthias (TU Wien) | Seminar Room Zemanek, TU Wien, Favoritenstrasse 9-11, 1040 Wien | Mon, 11. Jun 18, 15:45 |
| Logical Aspects of Legal Reasoning | ||
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| Katsaounis, Theodoros (U. FORTH c/o KAUST) | WPI, OMP 1, Seminar Room 08.135 | Fri, 25. May 18, 10:00 |
| TBA | ||
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| Skordis, Constantinos (CEICO) | WPI, OMP 1, Seminar Room 08.135 | Thu, 24. May 18, 14:30 |
| TBA | ||
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| Zhao, Xiaofei (U. Rennes1) | WPI, OMP 1, Seminar Room 08.135 | Thu, 24. May 18, 10:00 |
| TBA | ||
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| Zhang, Yong (WPI c/o U. Wien) | WPI, OMP 1, Seminar Room 08.135 | Thu, 24. May 18, 9:30 |
| TBA | ||
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| Uhlemann, Cora (DAMTP Cambridge) | WPI, OMP 1, Seminar Room 08.135 | Wed, 23. May 18, 16:00 |
| TBA | ||
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| Rampf, Cornelius (U. Heidelberg) | WPI, OMP 1, Seminar Room 08.135 | Wed, 23. May 18, 15:00 |
| TBA | ||
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| Gosenca, Mateja (U.Sussex) | WPI, OMP 1, Seminar Room 08.135 | Wed, 23. May 18, 10:30 |
| TBA | ||
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| Athanassoulis, Agis (U. Dundee) | WPI, OMP 1, Seminar Room 08.135 | Wed, 23. May 18, 10:00 |
| TBA | ||
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| Kopp, Michael | WPI, OMP 1, Seminar Room 08.135 | Tue, 22. May 18, 14:30 |
| TBA | ||
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| Hahn, Oliver (Observatoire Nice) | WPI, OMP 1, Seminar Room 08.135 | Tue, 22. May 18, 14:00 |
| TBA | ||
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| Mauser, Norbert J. (WPI c/o U.Wien) | WPI, OMP 1, Seminar Room 08.135 | Tue, 22. May 18, 13:30 |
| TBA | ||
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| David Muraki (Simon Fraser Univ, BC) | WPI, OMP 1, Seminar Room 08.135 | Mon, 7. May 18, 15:00 |
| Mysterious Holes in the Sky & A Theory for the Motion of Cloud Edges | ||
A holepunch cloud is a curious and rare atmospheric feature where an aircraft, descending or ascending through a thin cloud layer, leaves behind a growing circular hole of clear air. Observed since the early days of aviation, only in 2011 was this holepunch phenomenon simulated in a full-physics numerical weather model. Although the initiation process has long been explained by ice crystal formation, the continued growth of the hole, even up to an hour after its birth, remained a bit of a fluid dynamical mystery. We begin by excluding some of the ``obvious" reasons by tweaking the physics in the numerical simulations (fake weather!). We then attribute the expansion of the hole to the presence of an expanding wavefront. The leading edge of this wave is a front of phase change, where cloudy air is continually evaporated and so expands the hole. Our explanation has led us towards the development of a more general theory for an understanding of how atmospheric waves can evolve the shape of clouds. This work is in collaboration with R Rotunno (NCAR), H Morrison (NCAR), R Walsh (SFU) and H Lynn (SFU). | ||
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| Bouin, Emeric (U. Paris-Dauphine) | OMP 1, Sky Lounge (12th floor) | Fri, 20. Apr 18, 14:50 |
| Hypocoercivity without confinement | ||
In this talk, we will present some recent results on decay to zero for linear kinetic models with weak or without space confinement. Joint with Mouhot, Mischler, Dolbeault, Schmeiser. | ||
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| Peter Markowich (WPI c/o U. Wien & KAUST) | OMP 1, Sky Lounge (12th floor) | Fri, 20. Apr 18, 14:00 |
| Discrete and continuum modeling of biological network formation | ||
Motivated by recent papers describing rules for natural network formation in discrete settings, we propose an elliptic-parabolic system of partial differential equations. The model describes the pressure field due to Darcy’s type equation and the dynamics of the conductance network under pressure force effects with a diffusion rate representing randomness in the material structure. After a short overview of the principles of discrete network modeling, we show how to derive the corresponding macroscopic (continuum) description. The highly unusual structure of the resulting PDE system induces several interesting challenges for its mathematical analysis. We give a short overview of the tools and tricks that can be used to overcome them. In particular, we present results regarding the existence of weak solutions of the system, based on recent results on elliptic regularity theory. Moreover, we study the structure and stability properties of steady states that play a central role to understand the pattern capacity of the system. We present results of systematic numerical simulations of the system that provide further insights into the properties of the network-type solutions. | ||
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| Cuesta, Carlotta (U. Basque Country) | OMP 1, Sky Lounge (12th floor) | Fri, 20. Apr 18, 11:25 |
| Some aspects of a non-local regularisation of scalar conversation laws | ||
We consider a regularisation of a scalar conservation law where the viscous term is a Caputo type fractional derivative of order between 1 and 2. We shall first focus on some recent results on the study travelling wave solutions of the Korteweg-de Vries-Burgers equation with such non-local viscous term, the third order one being local and linear. This model equation arises in the analysis of a shallow water flow by performing formal asymptotic expansions associated to the triple-deck regularisation (which is an extension of classical boundary layer theory). We show rigorously the existence of these waves in the case of a genuinely non-linear flux and for the case of a non genuinely non-linear one, we give results on the existence of the waves that do not satisfy the entropy condition. We shall also discuss the vanishing viscosity limit when the third order term is not present. | ||
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| Raoul, Gael (X Palaiseau) | OMP 1, Sky Lounge (12th floor) | Fri, 20. Apr 18, 10:05 |
| Wasserstein estimates and macroscopic limits in a model from ecology | ||
We are interested in evolutionary biology models for sexual populations. The sexual reproductions are modelled through the so-called Infinitesimal Model, which is similar to an inelastic Boltzmann operator. This kinetic operator is then combined to selection and spatial dispersion operators. In this talk, we will show how the Wasserstein estimates that appear naturally for the kinetic operator can be combined to estimates on the other operators to study the qualitative properties of the solutions. In particular, this approach allows us to recover a well-known (in populations genetics) macroscopic model. | ||
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| Mouhot, Clement (U. Cambridge) | OMP 1, Sky Lounge (12th floor) | Fri, 20. Apr 18, 9:15 |
| De Giorgi-Nash-Moser and H"ormander theories: new interplays | ||
We report on recent results and a new line of research at the crossroad of two major theories in the analysis of partial differential equations: the tools developed for studying elliptic or parabolic equations with rough coefficients on the one hand (De Giorgi, Nash, Moser, Krylov, Safonov), and the theory of hypoellipticity (H\"ormander) on the other hand. We discuss recent results about hypoelliptic equations of kinetic type with rough coefficients. We then discuss applications to the Boltzmann and Landau equations and present a program of research about the regularity for these equations, with some open questions. | ||
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| Doumic, Marie (WPI & INRIA) | OMP 1, Sky Lounge (12th floor) | Thu, 19. Apr 18, 17:00 |
| Some entropy-based results for linear and non-linear aggregation-fragmentation equations | ||
Entropy-based methods, and in particular the so-called "generalised relative entropy" inequalities, have been developed and successfully applied to structured population equations, and in particular to aggregation-fragmentation problems, over the last two decades. In this talk, we study how entropy methods have been recently extended to measure solutions [1] as well as to the convergence towards a periodic limit [2]. We also investigate the long-time dynamics of a family of nonlinear nucleation-aggregation equations, for which specific entropy functionals may be built [3]. Ref: [1] Thomasz Debiec, Marie Doumic, Piotr Gwizada, Emil Wiedemann, Relative entropy method for measure solutions of a structured population model, 2018 [2] Etienne Bernard, Marie Doumic, Pierre Gabriel, Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts, 2016 [3] Juan Calvo, Marie Doumic, Benot Perthame, Long-time asymptotics for polymerization models, 2017 | ||
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| Manhart, Angelika (NYU Courant) | OMP 1, Sky Lounge (12th floor) | Thu, 19. Apr 18, 16:10 |
| Traveling Waves in Cell Populations | ||
Transport-reaction equations are abundant in the description of movement of motile organisms. In this talk I will focus on a system of coupled transport-reaction equations that arises from an age-structuring of a species of turning individuals. The highlight consists of the explicit construction and characterization of counter-propagating traveling waves, patterns which have been observed in bacterial colonies, e.g. in earth-dwelling myxobacteria. Fascinatingly, while the wave profiles do not change, the wave composition does and the fractions of reversible and non-reversible bacteria form waves traveling in the opposite direction. Stability analysis reveals conditions for wave formation as well as for pulsating-in-time spatially constant solutions. | ||
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| Oelz, Dietmar (U. Queensland) | OMP 1, Sky Lounge (12th floor) | Thu, 19. Apr 18, 14:50 |
| Microtubule dynamics, kinesin-1 sliding and dynein action drive growth of cell processes | ||
Intracellular transport is driven by molecular motors which pull cargo vesicles along cytoskeletal filaments. In a collaborative study combining experiments and Brownian Dynamics simulations we investigate cellular morphogenesis of neuron cells, namely establishment and growth of axons and dendrites, which is both driven by kinesin and dynein motors. We find that the growth of cellular processes depends critically on dynamical instability, i.e. alternating growing and shrinking, of microtubule fibres. | ||
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| Small, Victor J. (IMBA) | OMP 1, Sky Lounge (12th floor) | Thu, 19. Apr 18, 14:00 |
| Moving cells and pathogens with actin: from structure to mathematical models | ||
Cell movement plays an essential role in diverse processes, not least during embryonic development and wound repair. Armies of mobile immune cells are likewise engaged in the defence of the body against invading pathogens. Cell movement has been a popular playground for mathematicians and there has been no shortage of theoretical models of how cells extend a thin sheet, a so-called “lamellipodium” at the cell front to initiate migration. Our recent application of electron tomography in studies of migrating cells provided the first complete structure of the branched actin networks that make up lamellipodia. These findings coincided with the timely collaboration with the group of Christian Schmeiser and the subsequent development of a realistic mathematical simulation of the actin-mediated protrusion process. Actin-based protrusion is also used by certain viruses, which usurp the motile machinery of cells to spread their infection. These viruses move in cells by generating a comet tail of actin at their rear. Using again electron tomography we were able to determine, for the first time, the structural organization of actin comet tails. This structural information was then utilized in collaboration with the Schmeiser group to develop a new, more realistic mathematical model of pathogen propulsion. In conclusion, the fortuitous and timely interest of Christian Schmeiser in the cytoskeleton resulted in a productive and fruitful, inter-disciplinary collaboration. | ||
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| Gasser, Ingenuin (U. Hamburg) | OMP 1, Sky Lounge (12th floor) | Thu, 19. Apr 18, 11:25 |
| A few examples of alternative energy power stations: modelling, simulation and optimisation | ||
We discuss power stations based on solar thermal energy, on condensation and on pressure retarded osmosis. In all cases we aim to consider the complete power station and to optimize the net power output. This is done with respect to system parameters and also in the operational phase. Mathematically this relies on fluid dynamical models with a special emphasis on energy, its production mechanisms and the related energy losses. | ||
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| Nouri, Anne (U. Marseille) | OMP 1, Sky Lounge (12th floor) | Thu, 19. Apr 18, 10:05 |
| Bose condensates in interaction with excitations. Two-component space-dependent models close to equilibrium | ||
We consider models for Bose gases in the so-called 'high-temperature range' below the temperature where Bose-Einstein condensation sets in. The first model is of non-linear two-component type and vanishing force term, consisting of a kinetic equation with periodic boundary conditions for the distribution function of a gas of excitations interacting with a Bose condensate, which is described by the Gross-Pitaevskii equation. Results on well-posedness and long time behavior are proved in a Sobolev space setting close to equilibrium. The second model has a non-vanishing force term and is linearized around a space-homogenous equilibrium. | ||
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| Calvez, Vincent (ENS Lyon) | OMP 1, Sky Lounge (12th floor) | Thu, 19. Apr 18, 9:15 |
| Equilibria in quantitative genetic models | ||
I will describe recent results obtained in the asymptotic analysis of quantitative genetic models. I will focus on the adaptation of a population to a moving fitness optimum. Our methodology is able to handle age-structured populations, either reproducing in an asexual way or with a sexual mode of reproduction (namely Fisher's infinitesimal model). | ||
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| Burger, Martin (WWU Münster) | OMP 1, Sky Lounge (12th floor) | Wed, 18. Apr 18, 16:15 |
| “Propagation of gradient flow structures from microscopic to macroscopic models” | ||
In this talk we will discuss the propagation of gradient flow structures from microscopic models in statistical mechanics such as overdamped particle dynamics or interacting particle systems on lattices to macroscopic partial differential equations. The key insight is that microscopic models can be formulated as linear Markov chains in high-dimensional spaces, e.g. via Liouville equations, for which recent work by Maas, Mielke and others has provided a rather complete picture. The propagation to macroscopic models is then carried out - at least formally - by constructing a metric structure on an associated infinite hierarchy of equations, resembling the BBGKY hierarchy in kinetic theory, and studying mean-field or other limits in this setup. | ||
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| Zubelli, Jorge (IMPIA) | OMP 1, Sky Lounge (12th floor) | Wed, 18. Apr 18, 14:50 |
| A Non-intrusive Stratified Resampler for Regression Monte Carlo with Applications to Reaction-Diffusion Equations | ||
Stochastic dynamic programming equations are classic equations arising in the resolution of nonlinear evolution equations, like in stochastic control. In this talk we address a technique to solve certain dynamic programming equations associated to a given Markov chain $X$, using a regression-based Monte Carlo algorithm. More specifically, we assume that the model for $X$ is not known in full detail and only a root sample $X^1,\dots,X^M$ of such process is available. By a stratification of the space and a suitable choice of a probability measure, we design a new resampling scheme that allows to compute local regressions (on basis functions) in each stratum. The combination of the stratification and the resampling allows to compute the solution to the dynamic programming equation (possibly in large dimension) using only a relatively small set of root paths. To assess the accuracy of the algorithm, we establish non-asymptotic error estimates in L2 of the chosen measure. Our numerical experiments illustrate the good performance, even with as low as 20 to 40 root paths. This talk is based on joint work with Emmanuel Gobet and Gang Liu (E. Polytechnique, Paris) published in SIAM J. Numer. Anal., 56(1), 50?77. 2018. | ||
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| Ascher, Uri (U. British Columbia) | OMP 1, Sky Lounge (12th floor) | Wed, 18. Apr 18, 14:00 |
| Numerical Methods in Visual Computing: what we can learn from each other | ||
Visual computing is a wide area that includes computer graphics and image processing, where the "eyeball-norm" rules. I will briefly discuss two case studies involving numerical methods and analysis applied to this area. The first case study involves motion simulation and calibration of soft objects such as plants, skin, and cloth. The governing elastodynamics PDE system, discretized in space already at the variational level using co-rotated FEM, leads to a large, expensive to assemble, dynamical system in time, where the damped motion may mask highly oscillatory stiff-ness. An exponential differencing method will be described, in search for more quantitative computations. The second case study involves some image processing problems where there is a premium for local approaches that do not necessarily use underlying PDEs. I will demonstrate and discuss. | ||
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| Poelchau, Michael (U. Freiburg) | Maria-Theresien-Platz, 1010 Vienna, Lecture Hall of Natural History Museum | Wed, 11. Apr 18, 11:45 |
| Shooting into Stone - What we learned from the MEMIN Project | ||
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| Alac, Ruken (U. Sydney) | Maria-Theresien-Platz, 1010 Vienna, Lecture Hall of Natural History Museum | Wed, 11. Apr 18, 11:30 |
| Modeling of Pantasma impact crater using Badlands software with Monte Carlo method | ||
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| Rae, Auriol (Imperial College London) | Maria-Theresien-Platz, 1010 Vienna, Lecture Hall of Natural History Museum | Wed, 11. Apr 18, 11:15 |
| Combining observations of shock metamorphism with numerical Impact simulations: Insights into complex crater formation | ||
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| Collins, Gareth (Imperial College London) | Maria-Theresien-Platz, 1010 Vienna, Lecture Hall of Natural History Museum | Wed, 11. Apr 18, 10:55 |
| A brief introduction to numerical Impact modelling | ||
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| Goderis, Steven (U. Brussel) | Maria-Theresien-Platz, 1010 Vienna, Lecture Hall of Natural History Museum | Wed, 11. Apr 18, 10:10 |
| Recent advances in tracing meteoritic contributions to the Earth's crust | ||
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| Deutsch, Alex (U. Münster) | Maria-Theresien-Platz, 1010 Vienna, Lecture Hall of Natural History Museum | Wed, 11. Apr 18, 9:55 |
| A simple cooking recipe for dating impact events | ||
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| Pittarello, Lidia (U. Wien) | Maria-Theresien-Platz, 1010 Vienna, Lecture Hall of Natural History Museum | Wed, 11. Apr 18, 9:40 |
| Shock metamorphic effects in a common Mineral: shocked plagioclase in nature and experiments | ||
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| Fritz, Jörg (Saalbau Weltraum Projekt) | Maria-Theresien-Platz, 1010 Vienna, Lecture Hall of Natural History Museum | Wed, 11. Apr 18, 9:25 |
| Shock metamorphism of meteorites: A record of Impact cratering events in the planetary system | ||
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| Timo Lang | OMP 1, Sky Lounge (12th floor) | Wed, 28. Feb 18, 17:10 |
| Remarks on the Exponential Rules in Linear Logic | ||
Abstract | ||
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| Kaustuv Chaudhuri, Leonardo Lima and Giselle Reis | OMP 1, Sky Lounge (12th floor) | Wed, 28. Feb 18, 16:45 |
| Formalized Meta-theory of Sequent Calculi for Substructural Logics | ||
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| Giuseppe Greco, Fei Liang and Alessandra Palmigiano | OMP 1, Sky Lounge (12th floor) | Wed, 28. Feb 18, 16:20 |
| Measurable Kleene Algebras and Structural Control | ||
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| Carlos Olarte, Kaustuv Chaudhuri, Joelle Despeyroux and Elaine Pimentel | OMP 1, Sky Lounge (12th floor) | Wed, 28. Feb 18, 15:15 |
| Hybrid Linear Logic, Revisited | ||
Abstract | ||
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| Elaine Pimentel | OMP 1, Sky Lounge (12th floor) | Wed, 28. Feb 18, 14:20 |
| A unified view of modal and substructural logics | ||
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| Samuel Balco, Giuseppe Greco, Alexander Kurz, M. Andrew Moshier, Alessandra Palmigiano and Apostolos Tzimoulis | OMP 1, Sky Lounge (12th floor) | Wed, 28. Feb 18, 12:15 |
| Proper Display Calculus for First-order Logic | ||
Abstract | ||
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| Matthias Baaz | OMP 1, Sky Lounge (12th floor) | Wed, 28. Feb 18, 11:45 |
| Fast Cut-elimination for Intuitionistic Logic | ||
Abstract | ||
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| Marianna Girlando, Sara Negri and Nicola Olivetti | OMP 1, Sky Lounge (12th floor) | Wed, 28. Feb 18, 11:25 |
| Internal and Labelled Sequent Calculi: An Equivalence Result for Conditional Logic V | ||
Abstract | ||
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| Andrea Aler Tubella and Alessio Guglielmi | OMP 1, Sky Lounge (12th floor) | Wed, 28. Feb 18, 11:00 |
| Subatomic Proof Systems | ||
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| Lutz Straßburger | OMP 1, Sky Lounge (12th floor) | Wed, 28. Feb 18, 9:55 |
| On the Normalization of Combinatorial Proofs for Classical and Intuitionistic Logic | ||
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| Alwen Tiu | OMP 1, Sky Lounge (12th floor) | Wed, 28. Feb 18, 9:00 |
| A proof theory for dual nominal quantifiers | ||
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| Nissim Francez and Michael Kaminski | OMP 1, Sky Lounge (12th floor) | Tue, 27. Feb 18, 16:45 |
| Structural Rules for Multi-valued Logics | ||
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| Arnon Avron | OMP 1, Sky Lounge (12th floor) | Tue, 27. Feb 18, 16:20 |
| Purely Relevant Logics with Contraction and Its Converse | ||
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| Luca Tranchini and Gianluigi Bellin | OMP 1, Sky Lounge (12th floor) | Tue, 27. Feb 18, 15:55 |
| A Refutation Calculus for Intuitionistic Logic | ||
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| Luigi Santocanale and Maria Joâo Gouveia | OMP 1, Sky Lounge (12th floor) | Tue, 27. Feb 18, 14:50 |
| Mix ⋆ - Autonomous Quantales and the Continuous Weak Bruhat Order | ||
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| Michele Pra Baldi, Stefano Bonzio and Tommaso Moraschini | OMP 1, Sky Lounge (12th floor) | Tue, 27. Feb 18, 14:25 |
| Logics of Variable Inclusion | ||
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| Petr Cintula, José Gil-Férez, Tommaso Moraschini and Francesco Paoli | OMP 1, Sky Lounge (12th floor) | Tue, 27. Feb 18, 14:00 |
| An Abstract Approach to Consequence Relations II | ||
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| Stefano Bonzio, Andrea Loi and Luisa Peruzzi | OMP 1, Sky Lounge (12th floor) | Tue, 27. Feb 18, 11:50 |
| Dualities for Plonka Sums of Algebras | ||
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| Stefano Aguzzoli, Matteo Bianchi and Diego Valota | OMP 1, Sky Lounge (12th floor) | Tue, 27. Feb 18, 11:25 |
| The Classification of All the Subvarieties of DNMG | ||
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| Nick Galatos and Adam Pøenosil | OMP 1, Sky Lounge (12th floor) | Tue, 27. Feb 18, 11:00 |
| On an Equivalence between Integral and Involutive Residuated Structures | ||
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| José Gil-Férez, Peter Jipsen, George Metcalfe and Constantine Tsinakis | OMP 1, Sky Lounge (12th floor) | Tue, 27. Feb 18, 9:55 |
| The Amalgamation Property for Semilinear Commutative Idempotent Residuated Lattices | ||
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| Francesco Paoli | OMP 1, Sky Lounge (12th floor) | Tue, 27. Feb 18, 9:00 |
| The Archimedean Property: New Horizons and Perspectives Joint work with Antonio Ledda and Constantine Tsinakis | ||
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| Federico Aschieri, Agata Ciabattoni and Francesco A. Genco | OMP 1, Sky Lounge (12th floor) | Mon, 26. Feb 18, 17:20 |
| Logic-based Concurrent ë-Calculi | ||
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| Giuseppe Primiero | OMP 1, Sky Lounge (12th floor) | Mon, 26. Feb 18, 16:55 |
| A Substructural Modal Type Theory to Handle Mobility Failures in Distributed Computing | ||
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| Matteo Maffei | OMP 1, Sky Lounge (12th floor) | Mon, 26. Feb 18, 16:00 |
| Security and Privacy by Typing in Cryptographic Systems | ||
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| Jorge A. Pérez | OMP 1, Sky Lounge (12th floor) | Mon, 26. Feb 18, 14:45 |
| The Challenge of Typed Expressiveness in Concurrency | ||
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| Philip Wadler | OMP 1, Sky Lounge (12th floor) | Mon, 26. Feb 18, 14:00 |
| Propositions as Sessions | ||
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| Vijay D'Silva, Alessandra Palmigiano, Apostolos Tzimoulis and Caterina Urban | OMP 1, Sky Lounge (12th floor) | Mon, 26. Feb 18, 11:50 |
| A proof-theoretic approach to abstract interpretation | ||
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| Larchey-Wendling; Dominique | OMP 1, Sky Lounge (12th floor) | Mon, 26. Feb 18, 11:25 |
| Mechanising Undecidability Results in Coq: Elementary Linear Logic and Boolean BI | ||
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| Ramanayake, Revantha | OMP 1, Sky Lounge (12th floor) | Mon, 26. Feb 18, 11:00 |
| Syntactic Decidability and Complexity Upper Bound for the Logic of Bunched Implication BI | ||
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| Galmiche, Didier, Kimmel, Pierre, Pym, David | OMP 1, Sky Lounge (12th floor) | Mon, 26. Feb 18, 9:55 |
| An Epistemic Resource Logic Based on Boolean BI | ||
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| Pym, David | OMP 1, Sky Lounge (12th floor) | Mon, 26. Feb 18, 9:00 |
| Logic as a modelling technology: resource semantics, systems modelling, and security | ||
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| Fritz R.S. Diorico (TU Wien) | WPI, OMP 1, Seminar Room 08.135 | Fri, 23. Feb 18, 10:00 |
| Articial Gauge Fields in Quantum Systems | ||
In this talk, I will present an overview/review of progress in articial gauge fields in quantum systems. I will start with the underlying first principles with the seminal paper of Berry, the Berry or Geometric phase. Following a few month after its publication Wilczek and Zee concluded with Berry's results, that non-Abelian gauges fields can naturally emerge from the adiabatic development of simple quantum systems. I will mainly focus on how ultracold atomic systems can be prepared such that a mapping to a ultracold atoms behaving like charged particles in a magnetic field. The induced gauge field whether abelian or non-Abelian introduces a space dependent coupling between the dressed states of the ultracold atoms. This provides motivation for extending MCTDH-X to tackle quantum systems with artificial gauge fields where the spatial dynamics of the dressed states or pseudo-spins can be studied in great detail. This could open up interesting physics that could potentially be observed in the experiment. | ||
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| Fernández–Pacheco, Amalio (Cavendish Lab, Cambridge) | Ernst-Mach-HS, 2. Stock Fak. Physik, Strudlhofgasse 4/Boltzmanngasse 5 | Mon, 29. Jan 18, 16:00 |
| "Investigation of three-dimensional magnetic nanostructures for applications in spintronics" | ||
In this talk, I will show our recent work on 3D magnetic nanostructures for applications in spintronics. We are developing 3D nano-printing methods based on focused electron beams [2]. In particular, we have achieved great control over the growth of 3D magnetic nanowires for domain wall studies [3]. Advanced magnetic microscopy experiments reveal the magnetic state and magnetisation reversal mechanism of the wires, dominated by their geometry and metallic composition [4]. Recent results also show how controllable domain wall motion along the whole space becomes now possible [5]. This has been realised by development of new methods for 3D nano-printing and magneto-optical detection of 3D nanostructures. During the talk, I will discuss novel methodologies to characterise 3D nanomagnets, including magneto-optical, electron and X-ray microscopy. I will also highlight key challenges and opportunities of 3D nanomagnetism. | ||
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| Golse, Francois (CNRS X Palaiseau) | WPI, OMP 1, Seminar Room 08.135 | Fri, 22. Dec 17, 14:30 |
| From quantum N-body problem to Vlasov via „optimal transport“ | ||
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| Germain, Pierre (NYU Courant) | WPI, OMP 1, Seminar Room 08.135 | Fri, 22. Dec 17, 10:00 |
| Recent mathematical progress on weak turbulence” | ||
I will present two recent rigorous results on weak turbulence: the first one is on the local well-posedness of the kinetic wave equation (with A. Ionescu and M.-B. Tran). And the second one on the derivation of the kinetic wave equation from the nonlinear Schrodinger equation (work in progress, with T. Buckmaster, Z. Hani, and J. Shatah). | ||
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| Uhlemann, Cora (U. Cambridge) | WPI, OMP 1, Seminar Room 08.135 | Thu, 21. Dec 17, 15:00 |
| Finding closure - what Schrödinger-Poisson can teach us about cumulant hierarchies | ||
Since dark matter almost exclusively interacts gravitationally, the dynamics of its phase space distribution is described by Vlasov-Poisson. One key property of Vlasov-Poisson is that it corresponds to an infinite tower of coupled equations for its cumulants. Hence, determining the time-evolution of dark matter density and velocity demands solving the full cumulant hierarchy. While the perfect pressureless fluid model is the only consistent truncation, it cannot describe the dynamics in the multi-streaming regime. Given this inadequacy of truncations for the cumulant hierarchy, I suggest to take a closer look at closure schemes that rely on recurrence. To this end, I will introduce Schrödinger-Poisson as theoretically motivated and phenomenologically viable approximation to Vlasov-Poisson. I will show how Schrödinger-Poisson generates cumulants at all orders consistently and hence can serve as inspirational example for finding closure schemes. | ||
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| Diamond, Patrick (UC San Diego) | WPI, OMP 1, Seminar Room 08.135 | Thu, 21. Dec 17, 9:30 |
| Quasi-Geostrophic Fluids and Vlasov Plasmas: Parallels and Intersections | ||
This talk explores connections and contrasts between the nonlinear dynamics of two prototypical systems in plasmas and fluids. The first is the quasi-geostrophic fluid, which evolves by conservative advection of potential vorticity. The QG system is the minimal model for large-scale atmospheric waves and the jet stream (zonal flow). The second is the Vlasov–Poisson system, in which the Vlasov equation describes the conservative advection of a phase space density. Many interesting connections between these two systems already have been noted. This talk will expand the list and suggest directions for future cross-fertilization . | ||
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| Gürcan, Özgür (U. PMC Paris) | WPI, OMP 1, Seminar Room 08.135 | Wed, 20. Dec 17, 14:30 |
| Dynamics of a shell model of bounced averaged gyrokinetic Vlasov Equation | ||
Development of a shell model for a bounced averaged gyrokinetic Vlasov equation is presented. First, the linear dynamics is compared with a linear solver based on solving the linear dispersion relation numerically. Then the nonlinear dynamics is studied by analyzing the wave-number spectrum of quadratic conserved quantities. The resulting spectra seems to show a cascade spectrum at high k and predator-prey like oscillations in low k. Future perspectives including a logarithmically discretized three dimensional version of the model, which is 2D in space and 1D in energy, is discussed. | ||
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| Brenier, Yann (CNRS X Palaiseau): | WPI, OMP 1, Seminar Room 08.135 | Wed, 20. Dec 17, 9:30 |
| On the MAK reconstruction method for the early universe | ||
I will report on some very recent progress made on the MAK method for the numerical reconstruction of the early universe (in particular by Bruno Lévy and Jean-David Benamou), based either on the geometric algorithm of Mérigot for the Monge-Ampère equation or on the entropic regularization method (going back to Schrödinger in the 30s) for the optimal mass transport problem with quadratic cost. | ||
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| Lesur, Maxime (U. Lorraine) | WPI, OMP 1, Seminar Room 08.135 | Tue, 19. Dec 17, 14:30 |
| Plasma turbulence and transport dominated by nonlinear kinetic effects | ||
In hot plasmas, collisions are so rare that microscopic vortex-like structures develop in the phase-space of the particle distribution: coupling both real space and velocity (or energy) space. In this work, we focus on magnetic confinement fusion plasmas (in toroidal geometry). We base our approach on a reduced kinetic model [1, 2], akin to the Vlasov-Poisson model. Our numerical simulations indicate the nonlinear self-organisation, within the turbulence, of fine-scale velocity-space (or energy-space) structures, which can drive most of the macroscopic radial transport in some regimes. | ||
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| Nguyen, Toan (U. Pennsylvania) | WPI, OMP 1, Seminar Room 08.135 | Tue, 19. Dec 17, 9:30 |
| Long-time estimates for Vlasov-Maxwell in the non-relativistic limit | ||
I will present a joint work with D. Han-Kwan and F. Rousset on establishing long time estimates for Vlasov-Maxwell systems near stable homogeneous equilibria, which are valid for times of an arbitrarily large polynomial order of the speed of light in the non-relativistic limit. | ||
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| Colombi, Stephane (I.Astrophysique Paris) | WPI, OMP 1, Seminar Room 08.135 | Mon, 18. Dec 17, 15:30 |
| Phase-space structure of dark matter proto-halos: pre- and -post-collapse regimes | ||
During this talk I'll discuss the formation of primordial dark matter halos from smooth initial conditions. To simplify furthermore the context, we shall consider structures seeded by 3 sine waves of various amplitudes. Phase-space evolution of these objects will be studied from the computational point of view, by using a state of the art Vlasov solver, and the theoretical point of view, by comparing the numerical results to predictions of Lagrangian perturbation theory. While these latter are in principle only calculable prior to collapse, extension to multi-streaming regime will be discussed, with actual implementation in the 1D cosmological case of "post-collapse" Lagrangian perturbation theory. | ||
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| Rampf, Cornelius (U. Heidelberg) | WPI, OMP 1, Seminar Room 08.135 | Mon, 18. Dec 17, 14:00 |
| Shell-crossing in quasi-one-dimensional flow | ||
Blow-up of solutions for the cosmological fluid equations, often dubbed shell-crossing or orbit crossing, denotes the breakdown of the single-stream regime of the cold-dark-matter fluid. At this instant, the velocity becomes multi-valued and the density singular. Shell-crossing is well understood in one dimension (1D), but not in higher dimensions. This talk is about quasi-one-dimensional (Q1D) flow that depends on all three coordinates but differs only slightly from a strictly 1D flow, thereby allowing a perturbative treatment of shell-crossing using the Euler-Poisson equations written in Lagrangian coordinates. The signature of shell-crossing is then just the vanishing of the Jacobian of the Lagrangian map, a regular perturbation problem. In essence the problem of the first shell-crossing, which is highly singular in Eulerian coordinates, has been desingularized by switching to Lagrangian coordinates, and can then be handled by perturbation theory. All-order recursion relations are obtained for the time-Taylor coefficients of the displacement field, and it is shown that the Taylor series has an infinite radius of convergence. This allows the determination of the time and location of the first shell-crossing, which is generically shown to be taking place earlier than for the unperturbed 1D flow. The time variable used for these statements is not the cosmic time t but the linear growth time $tau sim t^{2/3}$. For simplicity, calculations are restricted to an Einstein-de Sitter universe in the Newtonian approximation, and tailored initial data are used. However it is straightforward to relax these limitations, if needed. | ||
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| Ivanovici, Oana (CNRS Nice) | WPI, OMP 1, Seminar Room 08.135 | Wed, 25. Oct 17, 16:30 |
| Dispersion estimates for the wave equation outside a strictly convex obstacle in 3D | ||
We consider the linear wave equation outside a compact, strictly convex obstacle in R^3 with smooth boundary and we show that the linear wave flow satisfies the dispersive estimates as in R^3 (which is not necessarily the case in higher dimensions). | ||
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| Banica, Valeria (U.Evry) | WPI, OMP 1, Seminar Room 08.135 | Wed, 25. Oct 17, 15:00 |
| 1-D cubic NLS with several Diracs as initial data and consequences | ||
We solve the cubic nonlinear Schrödinger equation on $mathbb R$ with initial data a sum of Diracs. Then we describe some consequences for a class of singular solutions of the binormal flow, that is used as a model for the vortex filaments dynamics in 3-D fluids and superfluids. This is a joint work with Luis Vega. | ||
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| Collot, Charles (U.Nice) | WPI, OMP 1, Seminar Room 08.135 | Wed, 25. Oct 17, 10:30 |
| Shock formation for Burgers equation with transversal viscosity | ||
This talk is about singularity formation for solutions to $$ (*) partial_{t}u+upa_x u-pa_{yy}u=0, (x,y) in mathbb R^2 $$ which is a simplified model of Prandtl's boundary layer equation. Note that it reduces to Burgers equation for $y$-independent solutions $u(t,x,y)=v(t,x)$. We will first recast the well-known shock formation theory for Burgers equation using the framework of self-similar blow-up. This will provide us with an analytic framework to study the effect of the transversal viscosity. The main result (still work in progress) is the construction and precise description of singular solutions to $(*)$. This is joint work with T.E. Ghoul and N. Masmoudi. | ||
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| Zaag, Hatem (U.Paris 13) | WPI, OMP 1, Seminar Room 08.135 | Wed, 25. Oct 17, 9:00 |
| Blow-up solutions for two non-variational semilinear parabolic systems | ||
We consider two non-variational semilinear parabolic systems, with different diffusion constants between the two components. The reaction terms are of power type in the first system. They are of exponential type in the second. Using a formal approach, we derive blow-up profiles for those systems. Then, linearizing around those profiles, we give the rigorous proof, which relies on the two-step classical method: (i) the reduction of the problem to a finite-dimensional one, then, (ii) the proof of the latter thanks to Brouwer's lemma. In comparison with the standard semilinear heat equation, several technical problems arise here, and new ideas are needed to overcome them. This is a joint work with T. Ghoul and V.T. Nguyen from NYU Abu Dhabi. | ||
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| Lan, Yang (U.Basel) | WPI, OMP 1, Seminar Room 08.135 | Tue, 24. Oct 17, 16:30 |
| On asymptotic dynamics for $L^2$-critical gKdV with saturated perturbations | ||
We consider the $L^2$ critical gKdV equation with a saturated perturbation. In this case, all $H^1$ solution are global in time. Our goal is to classify the asymptotic dynamics for solutions with initial data near the ground state. Together with a suitable decay assumption, there are only three possibilities: (i) the solution converges asymptotically to a solitary wave, whose $H^1$ norm is of size $gamma^{-2/(q-1)}$, as $gammarightarrow0$; (ii) the solution is always in a small neighborhood of the modulated family of solitary waves, but blows down at $+infty$; (iii) the solution leaves any small neighborhood of the modulated family of the solitary waves. This extends the result of classification of the rigidity dynamics near the ground state for the unperturbed $L^2$ critical gKdV (corresponding to $gamma=0$) by Martel, Merle and Rapha"el. It also provides a way to consider the continuation properties after blow-up time for $L^2$ -crtitical gKdV equations. | ||
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| Merle, Frank (IHES & U. Cergy Pontoise) | WPI, OMP 1, Seminar Room 08.135 | Tue, 24. Oct 17, 15:00 |
| Different notion of nondispersive solutions for hyperbolic problems | ||
We will see various notion of nondispersive solution in the case of the energy criticl wave equation and applications. | ||
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| Munoz, Claudio (U. Chile Santiago) | WPI, OMP 1, Seminar Room 08.135 | Tue, 24. Oct 17, 10:30 |
| Local decay estimates for nonlinear equations in the energy space | ||
In this talk we will discuss some recent improvements on well-known decay estimates for nonlinear dispersive and wave equations in 1D with supercritical decay, or no decay at all. Using Virial estimates, we will get local decay where standard dispersive techniques are not available yet. These are joint works with M.-A. Alejo, M. Kowalczyk, Y. Martel, F. Poblete, and J.-C. Pozo. | ||
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| Lenzman, Enno (U.Basel) | WPI, OMP 1, Seminar Room 08.135 | Tue, 24. Oct 17, 9:00 |
| Energy-Critical Half-Wave Maps: Solitons and Lax Pair Structure | ||
We discuss some essential features of solitons for the energy-critical half-wave maps equation. Furthermore, we will present a Lax pair structure and explain its applications to understanding the dynamics. The talk is based on joint work with P. Gérard (Orsay) and A. Schikorra (Pittsburgh). | ||
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| Visciglia, Nicola (U.Pisa) | WPI, OMP 1, Seminar Room 08.135 | Mon, 23. Oct 17, 16:30 |
| Large data scattering for gKdV | ||
By combining the Kenig-Merle approach with a suitable inequality proved by Tao we deduce that solutions to gKdV, in the L^2-supercitical regime, scatter to free waves for large times. | ||
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| Vega, Luis (BCA Bilbao) | WPI, OMP 1, Seminar Room 08.135 | Mon, 23. Oct 17, 15:30 |
| Selfsimilar solutions of the Binormal Flow: a new approach | ||
I shall present some recent results obtained with F. de la Hoz about the selfsimilar solutions of the Binormal Flow, also known as the Vortex Filament Equation. Some connections with the transfer of energy in the case when the filament is a regular polygon will be also made. | ||
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| Szeftel, Jeremie (UMPC Paris) | WPI, OMP 1, Seminar Room 08.135 | Mon, 23. Oct 17, 14:00 |
| The nonlinear stability of Schwarzschild | ||
I will discuss a joint work with Sergiu Klainerman on the stability of Schwarzschild as a solution to the Einstein vacuum equations with initial data subject to a certain symmetry class. | ||
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| Michael Kniely | Seminar Room 08.135 | Wed, 18. Oct 17, 0:00 |
| On two problems in the field of semiconductor materials and photovoltaics | ||
The first part of the talk is concerned with a semiconductor model including trapped states in an intermediate energy band. We will introduce a reaction-drift-diffusion system and employ the entropy approach in order to obtain an entropy-entropy production (EEP) inequality. In particular, we shall focus on the derivation of the EEP-inequality. Exponential convergence to the equilibrium is then a consequence of this EEP-estimate. An interesting feature of our results is the fact that the EEP-constant, and hence the convergence rate, is independent of the average lifetime of an electron in a trapped state. In the second part of the talk, we will investigate a material design problem in the context of photovoltaics. We employ a quantum-mechanical model for a prescribed distribution of positive charges and the corresponding density of negative charges. By a light-induced excitation, the electronic system may end up in an excited state possessing a different electronic structure. Our goal is to maximize the resulting spatial charge transfer as a function of the underlying nuclear charge distribution. A general existence proof regarding an optimal nuclear density as well as numerical results for a chain of atoms will be presented. | ||
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| Saut, Jean-Claude | WPI, OMP 1, Seminar Room 08.135 | Fri, 22. Sep 17, 9:30 |
| Existence of solitary waves for internal waves in two-layers systems | ||
We establish the existence of solitary waves for two classes of two-layers systems modeling the propagation of internal waves. More precisely we consider the Boussinesq-Full dispersion system and the Intermediate Long Wave (ILW) system together with its Benjamin-Ono (B0) limit. This is work in progress with Jaime Angulo Pava (USP) | ||
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| Barros, Ricardo | WPI, OMP 1, Seminar Room 08.135 | Thu, 21. Sep 17, 14:30 |
| Large amplitude internal waves in three-layer flows | ||
Large amplitude internal waves in a three-layer flow confined between two rigid walls will be examined in this talk. The mathematical model under consideration arises as a particular case of the multi-layer model proposed by Choi (2000) and is an extension of the two-layer MCC (Miyata-Choi-Camassa) model. The model can be derived without imposing any smallness assumption on the wave amplitudes and is well-suited to describe internal waves within a strongly nonlinear regime. We will investigate its solitary-wave solutions and unveil some of their properties by carrying out a critical point analysis of the underlying dynamical system. | ||
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| Klein, Christian | WPI, OMP 1, Seminar Room 08.135 | Thu, 21. Sep 17, 11:00 |
| Numerical study of PDEs with nonlocal dispersion | ||
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| Haspot, Boris | WPI, OMP 1, Seminar Room 08.135 | Thu, 21. Sep 17, 9:30 |
| Global well-posedness of the Euler-Korteweg system for small irrotational data | ||
The Euler-Korteweg equations are a modification of the Euler equations that takes into account capillary effects. In the general case they form a quasi-linear system that can be recast as a degenerate Schr ̈odinger type equation. Local well-posedness (in subcritical Sobolev spaces) was obtained by Benzoni-Danchin-Descombes in any space dimension, however, except in some special case (semi-linear with particular pressure) no global well- posedness is known. We prove here that under a natural stability condition on the pressure, global well-posedness holds in dimension d ¡Ý 3 for small irrotational initial data. The proof is based on a modified energy estimate, standard dispersive properties if d ¡Ý 5, and a careful study of the nonlinear structure of the quadratic terms in dimension 3 and 4 involving the theory of space time resonance. | ||
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| Rousset, Frederic | WPI, OMP 1, Seminar Room 08.135 | Wed, 20. Sep 17, 15:30 |
| Large time behavior of asymptotic models for water-waves | ||
We will discuss modified scattering properties, for small Solutions and/or in the vicinity of a solitary waves for model dispersive equations in dimension one. We will mainly focus on the modified Korteweg de Vries equation and the cubic Nonlinear Schrodinger equation with potential. Joint works with P. Germain and F. Pusateri. | ||
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| Iguchi, Tatsuo | WPI, OMP 1, Seminar Room 08.135 | Wed, 20. Sep 17, 14:00 |
| Isobe-Kakinuma model for water waves as a higher order shallow water approximation | ||
We justify rigorously an Isobe-Kakinuma model for water waves as a higher order shallow water approximation in the case of a flat bottom. It is known that the full water wave equations are approximated by the shallow water equations with an error of order $delta^2$, where $delta$ is a small nondimensional parameter defined as the ratio of the typical wavelength to the mean depth. The Green-Naghdi equations are known as higher order approximate equations to the water wave equations with an error of order $delta^4$. In this talk I report that the Isobe-Kakinuma model is a much higher approximation to the water wave equations with an error of order $delta^6$. | ||
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| Burtea, Cosmin | WPI, OMP 1, Seminar Room 08.135 | Wed, 20. Sep 17, 11:00 |
| Long time existence results for the abcd Bousssinesq systems | ||
In this talk we will review some long time existence results for the abcd-Boussinesq systems. We will discuss both the Sobolev and the nonlocalized, bore-type initial data cases. The main idea in order to get a priori estimates is to symmetrize the family of systems of equations verified by the frequencies of magnitude 2^{j} of the unknowns for each j¡Ý0. For the bore-type case, an additional decomposition of the initial data into low-high frequencies is needed in order to tackle the infinite-energy aspect of these kind of data. | ||
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| Groves, Mark | WPI, OMP 1, Seminar Room 08.135 | Wed, 20. Sep 17, 9:30 |
| Fully localised solitary gravity-capillary water waves (joint work with B. Buffoni and E. Wahlén) | ||
We consider the classical gravity-capillary water-wave problem in its usual formulation as a three-dimensional free-boundary problem for the Euler equations for a perfect fluid. A solitary wave is a solution representing a wave which moves in a fixed direction with constant speed and without change of shape; it is fully localised if its profile decays to the undisturbed state of the water in every horizontal direction. The existence of fully localised solitary waves has been predicted on the basis of simpler model equations, namely the Kadomtsev-Petviashvili (KP) equation in the case of strong surface tension and the Davey-Stewartson (DS) system in the case of weak surface tension. In this talk we confirm the existence of such waves as solutions to the full water-wave problem and give rigorous justification for the use of the model equations. | ||
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| Duchêne, Vincent | WPI, OMP 1, Seminar Room 08.135 | Tue, 19. Sep 17, 14:30 |
| A full dispersion model for the propagation of long gravity waves | ||
We will motivate and study a model for the propagation of surface gravity waves, which can be viewed as a fully nonlinear bi-directional Whitham equation. This model belongs to a family of systems of Green-Naghdi type with modified frequency dispersion. We will discuss the well-posedness of such systems, as well as the existence of solitary waves. The talk will be based on a work in collaboration with Samer Israwi and Raafat Talhouk (Beirut) and another in collaboration with Dag Nilsson and Erik Wahlén (Lund) | ||
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| Ehrnstrom, Mats | WPI, OMP 1, Seminar Room 08.135 | Tue, 19. Sep 17, 11:00 |
| Small-amplitude solitary waves for the full-dispersion Kadomtsev-Petviashvili equation | ||
Using constrained minimisation and a decomposition in Fourier space, we prove that the Kadomtsev-Petviashvili (KPI) equation modified with the exact dispersion relation from the gravity-capillary water-wave problem admits a family of small solitary solutions, approximating these of the standard KPI equation. The KPI equation, as well as its fully dispersive counterpart, describes gravity-capillary waves with strong surface tension. This is joint work with Mark Groves, Saarbrücken | ||
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| Lannes, David | WPI, OMP 1, Seminar Room 08.135 | Tue, 19. Sep 17, 9:30 |
| The shoreline problem for the nonlinear shallow water and Green-Naghdi equations | ||
The nonlinear shallow water equations and the Green-Naghdi equations are the most commonly used models to describe coastal flows. A natural question is therefore to investigate their behavior at the shoreline, i.e. when the water depth vanishes. For the nonlinear shallow water equations, this problem is closely related to the vacuum problem for compressible Euler equations, recently solved by Jang-Masmoudi and Coutand-Shkoller. For the Green-Naghdi equation, the analysis is of a different nature due to the presence of linear and nonlinear dispersive terms. We will show in this talk how to address this problem. | ||
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| Jie Gao | HS 1 | Fri, 8. Sep 17, 9:00 |
| New challenges in distributed sensing, processing and query of spatial data | ||
The vision of networked sensors in a ubiquitous manner has motivated the development of new algorithms on distributed sensing, processing and query of spatially and temporally separated data in the past 15 years. As smart sensing continues to spread in everyday living space, new challenges in the frontier of data privacy emerge. In this talk I would like to discuss new problems and solutions on distributed sensing and processing of location and trajectory data, which protect personally sensitive information. | ||
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| Daniel Delling | HS 1 | Thu, 7. Sep 17, 13:30 |
| Route planning in Transportation Networks - from Research to practice | ||
The last 15 years have seen astonishing progress in the performance of shortest path algorithms for transportation networks. In particular, for road networks, modern algorithms can be up to seven orders of magnitude faster than standard solutions. Since these algorithms enable several new applications, many of them have found their way into systems serving hundreds of millions of users every day. This talk highlights key techniques, discusses their impact on the industry, and provides an outlook on upcoming challenges. | ||
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| Kurk Pruhs | HS 1 | Thu, 7. Sep 17, 9:00 |
| The Itinerant List Update Problem | ||
I will introduce a variation of the online List Update Problem, which we call the Itinerant List Update Problem (ILU). The main difference between ILU and the standard list update problem is that in ILU the read head is not required to return to a home position between accesses. The motivation for considering ILU arises from track management within Domain Wall Memory (DWM), a promising new memory technology. I will explain DWM technology, discuss how ILU differs algorithmically from the standard list update problem, and explain what we know about the offline and online versions of ILU. This is joint work with Neil Olver, Kevin Schewior, Rene Sitters and Leen Stougie. | ||
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| David Mount | HS 1 | Wed, 6. Sep 17, 13:30 |
| Approximation algorithms for geometric proximity problems | ||
I will present an overview of recent developments in the design of efficient approximation algorithms for geometric proximity problems. These include polytope membership, nearest neighbor searching, Euclidean minimum spanning trees, low-complexity polytope approximation, and coresets. I will discuss how new sampling techniques arising from classical concepts such as Delone sets, Macbeath regions, and the Hilbert geometry have led to a number of new results, which are simple, general, implementable, and provably close to optimal. | ||
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| Fabrizio Grandoni | Wed, 6. Sep 17, 9:00 | |
| A measure and conquer approach for the analysis of exact algorithms | ||
Branch-and-reduce is one of the most common techniques to design exact (exponential-time) algorithms for NP-hard problems. The basic idea is to branch on a collection of “smaller” subproblems which are solved recursively. The traditional way to upper bound the running time of such algorithms is to lower bound the decrease of the “size” of each subproblem with respect to the original one. Here the size of a subproblem is traditionally measured according to the target parameter in terms of which one wishes to express the final running time (e.g., the number of nodes or edges in the input graph, the number of clauses in a CNF formula, etc.). The basic idea behind the Measure and Conquer technique is to use a non-standard measure of subproblems size, in order to implicitly exploit configurations where an “expensive” branching step leads to a “simpler” collection of subproblems. A smartly designed measure can lead to a dramatic reduction of the running time bound (without changing the algorithm!). In this talk I will illustrate Measure and Conquer with a few examples coming from my past work on this topic and from some more recent developments. | ||
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| Babak Falsafi | HS 1 | Tue, 5. Sep 17, 13:30 |
| The clouds have taken over, but algorithms are here to save the day | ||
Cloud providers are building infrastructure at unprecedented speeds. We have witnessed the emergence of data-centric information technology in almost every aspect of our life from commerce, healthcare, entertainment, governance to scientific discovery. The demand for processing, communicating and storing data has grown faster than conventional growth in digital platforms. Meanwhile the conventional silicon technologies we have relied on for the past several decades leading to the exponential growth in IT have slowed down. In light of this increase in demand on data-centric IT and the diminishing returns in platform scalability, our future increasingly relies on algorithms to save the day and enable a continued growth in IT. In this talk, I will motivate the grand challenges in scaling digital platforms and data-centric technologies, then present opportunities for hand-in-hand collaboration of algorithms and platforms. | ||
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| David Woodruff | HS 1 | Mon, 4. Sep 17, 13:30 |
| Sketching for geometric problems | ||
I will give an overview of the technique of sketching, or randomized data dimensionality reduction, and its applications to fundamental geometric problems such as projection (regression) onto flats and more general objects, as well as low rank approximation and clustering applications. | ||
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| Alexander Lorz (KAUST and Université Pierre et Marie Curie) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Sat, 29. Jul 17, 16:20 |
| Mathematics meets oncology: from Adaptive evolution to Zebrafish | ||
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| James Greene (Rutgers University) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Sat, 29. Jul 17, 15:40 |
| The role of induced drug resistance in cancer chemotherapy | ||
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| Lisa Gabler (Medical University, Vienna) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Sat, 29. Jul 17, 15:10 |
| Co-expression network-based identification of molecular subtypes in cancer | ||
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| John King (University of Nottingham) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Sat, 29. Jul 17, 14:10 |
| Mathematical modeling of biological tissue growth | ||
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| Dominik Wodarz (University of California, Irvine) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Sat, 29. Jul 17, 13:30 |
| Oncolytic virus therapy: Dynamics of virus spread at low infection multiplicities | ||
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| Min Tang (Shanghai Jiao Tong University) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Sat, 29. Jul 17, 11:10 |
| The role of intracellular pathways on the E.coli population dynamics | ||
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| Maria Lukácová-Medvidová (University of Mainz) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Sat, 29. Jul 17, 10:30 |
| Mathematical and numerical modelling of cancer invasion | ||
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| Dana-Adriana Botesteanu (University of Maryland) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Sat, 29. Jul 17, 9:40 |
| Modeling cancer cell growth dynamics in vitro in response to antimitotics | ||
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| Christoph Bock (Center for Molecular Medicine, Vienna) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Sat, 29. Jul 17, 9:00 |
| Bioinformatics for personalized medicine: Looking beyond the genome | ||
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| Bernhard Englinger (Medical University, Vienna) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Fri, 28. Jul 17, 17:00 |
| Mathematical models to predict intracellular drug distribution – Do they work? | ||
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| Michael Breitenbach (University of Salzburg) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Fri, 28. Jul 17, 16:10 |
| The human NADPH oxidase, Nox4, its S. cerevisiae ortholog, Yno1, and its role in regulating the actin cytoskeleton | ||
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| Natalia Komarova (University of California, Irvine) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Fri, 28. Jul 17, 15:30 |
| Stochastic Calculus of Stem Cells | ||
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| Thomas Mohr (Medical University, Vienna) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Fri, 28. Jul 17, 14:40 |
| Deciphering gene co-expression networks in tumor endothelium | ||
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| Michael Speicher (Medical University, Graz) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Fri, 28. Jul 17, 14:00 |
| Inferring expressed genes by whole-genome sequencing of plasma DNA | ||
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| Heyrim Cho (University of Maryland) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Fri, 28. Jul 17, 11:30 |
| Modeling the chemotherapy-induced selection of drug-resistant traits during tumor growth | ||
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| Anna Marciniak-Czochra (University of Heidelberg) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Fri, 28. Jul 17, 10:50 |
| Mathematical Modeling of Clonal Dynamics in Acute Leukemias | ||
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| Michael Medvedev (Kansas) | WPI, OMP 1, Seminar Room 08.135 | Fri, 28. Jul 17, 10:00 |
| Quasi-nonlinear theory of the Weibel instability | ||
Astrophysical and high-energy-density laboratory plasmas often have large-amplitude, sub-Larmor-scale electromagnetic fluctuations excited by various kinetic-streaming or anisotropy-driven instabilities. The Weibel (or the filamentation) instability is particularly important because it can rapidly generate strong magnetic fields, even in the absence of seed fields. Particles propagating in collisionless plasmas with such small-scale magnetic fields undergo stochastic deflections similar to Coulomb collisions, with the magnetic pitch-angle diffusion coefficient representing the effective "collision" frequency. We show that this effect of the plasma "quasi-collisionality" can strongly affect the growth rate and evolution of the Weibel instability in the deeply nonlinear regime. This result is especially important for understanding cosmic-ray-driven turbulence in an upstream region of a collisionless shock of a gamma-ray burst or a supernova. We demonstrate that the quasi-collisions caused by the fields generated in the upstream suppress the instability slightly but can never shut it down completely. This confirms the assumptions made in the self-similar model of the collisionless foreshock. | ||
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| Michael Bergmann (Medical University, Vienna) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Fri, 28. Jul 17, 9:50 |
| The understanding of the DNA damage response in solid tumors and the development of oncolytic influenza viruses | ||
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| Benoit Perthame (Université Pierre et Marie Curie) | HS 13, 2nd floor of Fak.Mathematik Uni Wien | Fri, 28. Jul 17, 9:10 |
| Modeling of living tissues and free boundary asymptotics | ||
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| Denis St-Onge (Princeton) | WPI, OMP 1, Seminar Room 08.135 | Thu, 27. Jul 17, 16:00 |
| Plasma dynamo | ||
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| Dmitri Uzdensky (UC Boulder) | WPI, OMP 1, Seminar Room 08.135 | Thu, 27. Jul 17, 10:30 |
| Nonthermal particle acceleration in relativistic collisionless magnetic reconnection | ||
As a fundamental process converting magnetic to plasma energy in high-energy astrophysical plasmas, relativistic magnetic reconnection is a leading explanation for the acceleration of particles to the ultrarelativistic energies necessary to power nonthermal emission (especially X-rays and gamma-rays) in pulsar magnetospheres and pulsar wind nebulae, coronae and jets of accreting black holes, and gamma-ray bursts. An important objective of plasma astrophysics is therefore the characterization of nonthermal particle acceleration (NTPA) effected by reconnection. Reconnection-powered NTPA has been demonstrated over a wide range of physical conditions using large two-dimensional (2D) kinetic simulations. However, its robustness in realistic 3D reconnection -- in particular, whether the 3D relativistic drift-kink instability (RDKI) disrupts NTPA -- has not been systematically investigated, although pioneering 3D simulations have observed NTPA in isolated cases. Here we present the first comprehensive study of NTPA in 3D relativistic reconnection in collisionless electron-positron plasmas, characterizing NTPA as the strength of 3D effects is varied systematically via the length in the third dimension and the strength of the guide magnetic field. We find that, while the RDKI prominently perturbs 3D reconnecting current sheets, it does not suppress particle acceleration, even for zero guide field; fully 3D reconnection robustly and efficiently produces nonthermal power-law particle spectra closely resembling those obtained in 2D. This finding provides strong support for reconnection as the key mechanism powering high-energy flares in various astrophysical systems. We also show that strong guide fields significantly inhibit NTPA, slowing reconnection and limiting the energy available for plasma energization, yielding steeper and shorter power-law spectra. | ||
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| Vladimir Zhdankin (UC Boulder) | WPI, OMP 1, Seminar Room 08.135 | Thu, 27. Jul 17, 10:00 |
| Particle acceleration in relativistic kinetic turbulence | ||
We present results from particle-in-cell simulations of driven turbulence in magnetized, collisionless, and relativistic pair plasmas. We find that the fluctuations are consistent with the classical k −5/3 ¡Ñ magnetic energy spectrum at fluid scales and a steeper k −4 ¡Ñ spectrum at sub-Larmor scales, where k¡Ñ is the wave vector perpendicular to the mean field. We demonstrate the development of a nonthermal, power-law particle energy distribution f(E)¡E−¥á, with an index ¥á that decreases with increasing magnetization and increases with an increasing system size (relative to the characteristic Larmor radius). Our simulations indicate that turbulence can be a viable source of energetic particles in high-energy astrophysical systems, such as pulsar wind nebulae, if scalings asymptotically become insensitive to the system size. | ||
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| Jonathan Squire (Caltech) | WPI, OMP 1, Seminar Room 08.135 | Wed, 26. Jul 17, 16:00 |
| Resonant instabilities: dust-gas coupling and others? | ||
It is shown that grains streaming through a fluid are generically unstable if their velocity, projected along some direction, matches the phase velocity of a fluid wave. This can occur whenever grains stream faster than a fluid wave. The wave itself can be quite general--sound waves, magnetosonic waves, epicyclic oscillations, and Brunt-V\"ais\"al\"a oscillations each generate instabilities, for example. A simple expression for this "resonant drag instability" (RDI) growth rate is derived. This expression (i) illustrates why such instabilities are so virulent and generic, and (ii) allows for simple analytic computation of RDI growth rates and properties for different fluid systems. As examples, we introduce several new instabilities, which could see application across a variety of astrophysical systems from protoplanetary disks to galactic outflows. | ||
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| Archie Bott (Oxford) | WPI, OMP 1, Seminar Room 08.135 | Wed, 26. Jul 17, 10:00 |
| When are plasmas collisional? | ||
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| Nuno Loureiro (MIT) | WPI, OMP 1, Seminar Room 08.135 | Tue, 25. Jul 17, 16:00 |
| Fully-kinetic versus reduced-kinetic modelling of collisionless plasma turbulence Pulsed-power driven magnetic reconnection experiments | ||
We report the results of a direct comparison between different kinetic models of collisionless plasma turbulence in two spatial dimensions. The models considered include a first principles fully-kinetic (FK) description, two widely used reduced models [gyrokinetic (GK) and hybrid-kinetic (HK) with fluid electrons], and a novel reduced gyrokinetic approach (KREHM). Two different ion beta (â i ) regimes are considered: 0.1 and 0.5. For â i =0.5 , good agreement between the GK and FK models is found at scales ranging from the ion to the electron gyroradius, thus providing firm evidence for a kinetic Alfv'en cascade scenario. In the same range, the HK model produces shallower spectral slopes, presumably due to the lack of electron Landau damping. For â i =0.1 , a detailed analysis of spectral ratios reveals a slight disagreement between the GK and FK descriptions at kinetic scales, even though kinetic Alfv'en fluctuations likely still play a significant role. The discrepancy can be traced back to scales above the ion gyroradius, where the FK and HK results seem to suggest the presence of fast magnetosonic and ion Bernstein modes in both plasma beta regimes, but with a more notable deviation from GK in the low-beta case. The identified practical limits and strengths of reduced-kinetic approximations, compared here against the fully-kinetic model on a case-by-case basis, may provide valuable insight into the main kinetic effects at play in turbulent collisionless plasmas, such as the solar wind. | ||
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| Francois Rincon (Toulouse) | WPI, OMP 1, Seminar Room 08.135 | Tue, 25. Jul 17, 10:00 |
| Some thoughts on theoretical problems and appoaches in dynamo theory | ||
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| Nuno Loureiro (MIT) | WPI, OMP 1, Seminar Room 08.135 | Mon, 24. Jul 17, 16:45 |
| MHD turbulence + magnetic reconnection | ||
The current understanding of magnetohydrodynamic (MHD) turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheetlike structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale ¥ë¡LS −4/7L, where SL is the outer-scale (L) Lundquist number and ¥ë is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the subinertial, reconnection interval of MHD turbulence, with the estimated scaling of the Fourier energy spectrum E(k¡Ñ)¡ðk−5/2¡Ñ, where k¡Ñ is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas (Pm), where the reconnection scale is found to be ¥ë/L¡S−4/7LPm−2/7. | ||
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| Alex Schekochihin (Oxford) | WPI, OMP 1, Seminar Room 08.135 | Mon, 24. Jul 17, 16:00 |
| MHD turbulence in 2017: end of the road? ++kinetic extensions | ||
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| Yohei Kawazura (Oxford) | WPI, OMP 1, Seminar Room 08.135 | Mon, 24. Jul 17, 10:30 |
| Hybrid GK-isothermal electrons code + ion heating calculations | ||
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| Lev Arzamasskiy (Princeton) | WPI, OMP 1, Seminar Room 08.135 | Mon, 24. Jul 17, 10:00 |
| Hybrid-kinetic simulations of solar wind turbulence | ||
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| David Hatch (UT Austin) | WPI, OMP 1, Seminar Room 08.135 | Thu, 20. Jul 17, 16:00 |
| Flow Shear Suppression of Pedestal Turbulence--A First Principles Theoretical Framework | ||
A combined analytic and computational gyrokinetic approach is developed to address the question of the scaling of pedestal turbulent transport with arbitrary levels of E×B shear. Due to strong gradients and shaping in the pedestal, the instabilities of interest are not curvature-driven like the core instabilities. By extensive numerical (gyrokinetic) simulations, it is demonstrated that pedestal modes respond to shear suppression very much like the predictions of a basic analytic decorrelation theory. The quantitative agreement between the two provides us with a new dependable, first principles (physics based) theoretical framework to predict the efficacy of shear suppression in burning plasmas that lie in a low-shear regime not accessed by present experiments. | ||
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| Denis St-Onge (Princeton) | WPI, OMP 1, Seminar Room 08.135 | Wed, 19. Jul 17, 16:30 |
| The Dimits Shift in a One-Field Fluid Model | ||
The two-dimensional Terry-Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth-Hinton states. This phenomena persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. Analytic progress on the truncated system is reported, focused on determining the growth rates of zonal flows and calculating the upper bound of the Dimits shift. The results for the truncated system are then used to estimate the Dimits shift of the fully nonlinear system. A new understanding is thus developed on the fundamental nature of the Dimits shift, both on its operation and its eventual termination. | ||
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| Justin Ball (EPFLausanne) | WPI, OMP 1, Seminar Room 08.135 | Wed, 19. Jul 17, 10:00 |
| Optimized up-down asymmetry to drive fast intrinsic rotation in tokamaks | ||
Breaking the up-down symmetry of the tokamak poloidal cross-section can significantly increase the spontaneous rotation due to turbulent momentum transport. In this work, we optimize the shape of flux surfaces with both tilted elongation and tilted triangularity in order to maximize this drive of intrinsic rotation. Nonlinear gyrokinetic simulations demonstrate that adding optimally-tilted triangularity can double the momentum transport of a tilted elliptical shape. This work indicates that tilting the elongation and triangularity in an ITER-like device can reduce the energy transport and drive intrinsic rotation with an Alfv\'{e}n Mach number on the order of 1% . This rotation is four times larger than the rotation expected in ITER and is sufficient to stabilize MHD instabilities. It is shown that this optimal shape can be created using the shaping coils of several experiments. | ||
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| Alessandro Geraldini (Oxford) | WPI, OMP 1, Seminar Room 08.135 | Tue, 18. Jul 17, 16:00 |
| Gyrokinetic treatment of a grazing angle magnetic presheath | ||
We develop a gyrokinetic treatment for ions in the magnetic presheath, close to the plasma-wall boundary. We focus on magnetic presheaths with a small magnetic field to wall angle, $\alpha \ll 1$ (in radians). Characteristic lengths perpendicular to the wall in such a magnetic presheath scale with the typical ion Larmor orbit size, ${\rho }_{{\rm{i}}}$. The smallest scale length associated with variations parallel to the wall is taken to be across the magnetic field, and ordered $l={\rho }_{{\rm{i}}}/\delta $, where $\delta \ll 1$ is assumed. The scale lengths along the magnetic field line are assumed so long that variations associated with this direction are neglected. These orderings are consistent with what we expect close to the divertor target of a tokamak. We allow for a strong component of the electric field ${\bf{E}}$ in the direction normal to the electron repelling wall, with strong variation in the same direction. The large change of the electric field over an ion Larmor radius distorts the orbit so that it is not circular. We solve for the lowest order orbits by identifying coordinates, which consist of constants of integration, an adiabatic invariant and a gyrophase, associated with periodic ion motion in the system with $\alpha =\delta =0$. By using these new coordinates as variables in the limit $\alpha \sim \delta \ll 1$, we obtain a generalised ion gyrokinetic equation. We find another quantity that is conserved to first order and use this to simplify the gyrokinetic equation, solving it in the case of a collisionless magnetic presheath. Assuming a Boltzmann response for the electrons, a form of the quasineutrality equation that exploits the change of variables is derived. The gyrokinetic and quasineutrality equations give the ion distribution function and electrostatic potential in the magnetic presheath if the entrance boundary condition is specified. | ||
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| Silvia Espinosa (MIT) | WPI, OMP 1, Seminar Room 08.135 | Tue, 18. Jul 17, 10:00 |
| Pedestal radial flux measuring method to prevent impurity accumulation | ||
The use of high-z wall materials attempts to shift the fusion challenge from heat handling to impurity removal. We demonstrate that not only the impurity density in-out asymmetry but also the poloidal flow has a major impact on the radial impurity flux direction. This realization provides the first method of measuring the flux from available diagnostics, without the need of a computationally demanding kinetic calculation of the full bulk ion response. Moreover, it affords insight into optimal tokamak operation to avoid impurity accumulation while allowing free fueling. | ||
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| Iván Calvo (CIEMAT) | WPI, OMP 1, Seminar Room 08.135 | Mon, 17. Jul 17, 16:00 |
| The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity | ||
In general, the orbit-averaged radial magnetic drift of trapped particles in stellarators is non-zero due to the three-dimensional nature of the magnetic field. Stellarators in which the orbit-averaged radial magnetic drift vanishes are called omnigeneous, and they exhibit neoclassical transport levels comparable to those of axisymmetric tokamaks. However, the effect of deviations from omnigeneity cannot be neglected in practice, and it is more deleterious at small collisionalities. For sufficiently low collision frequencies (below the values that define the $1/nu $ regime), the components of the drifts tangential to the flux surface become relevant. This article focuses on the study of such collisionality regimes in stellarators close to omnigeneity when the gradient of the non-omnigeneous perturbation is small. First, it is proven that closeness to omnigeneity is required to actually preserve radial locality in the drift-kinetic equation for collisionalities below the $1/nu $ regime. Then, using the derived radially local equation, it is shown that neoclassical transport is determined by two layers located at different regions of phase space. One of the layers corresponds to the so-called $sqrt{nu }$ regime and the other to the so-called superbanana-plateau regime. The importance of the superbanana-plateau layer for the calculation of the tangential electric field is emphasized, as well as the relevance of the latter for neoclassical transport in the collisionality regimes considered in this paper. In particular, the role of the tangential electric field is essential for the emergence of a new subregime of superbanana-plateau transport when the radial electric field is small. A formula for the ion energy flux that includes the $sqrt{nu }$ regime and the superbanana-plateau regime is given. The energy flux scales with the square of the size of the deviation from omnigeneity. Finally, it is explained why below a certain collisionality value the formulation presented in this article ceases to be valid. | ||
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| Elizabeth Paul (Maryland) | WPI, OMP 1, Seminar Room 08.135 | Mon, 17. Jul 17, 10:00 |
| Rotation and Neoclassical Ripple Transport in ITER | ||
Neoclassical transport in the presence of non-axisymmetric magnetic fields causes a toroidal torque known as neoclassical toroidal viscosity (NTV). The toroidal symmetry of ITER will be broken by the finite number of toroidal field coils and by test blanket modules (TBMs). The addition of ferritic inserts (FIs) will decrease the magnitude of the toroidal field ripple. 3D magnetic equilibria in the presence of toroidal field ripple and ferromagnetic structures are calculated for an ITER steady-state scenario using the Variational Moments Equilibrium Code (VMEC). Neoclassical transport quantities in the presence of these error fields are calculated using the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver (SFINCS). These calculations fully account for E r , flux surface shaping, multiple species, magnitude of ripple, and collisionality rather than applying approximate analytic NTV formulae. As NTV is a complicated nonlinear function of E r , we study its behavior over a plausible range of E r . We estimate the toroidal flow, and hence E r , using a semi-analytic turbulent intrinsic rotation model and NUBEAM calculations of neutral beam torque. The NTV torque due to TF ripple without ferritic components is found to be comparable in magnitude to the turbulent and NBI torques, though their radial profiles differ. The NTV from the |n|=18 ripple dominates that from lower n perturbations of the TBMs. With the inclusion of FIs, the magnitude of NTV torque is reduced by about 75% near the edge. We present comparisons of several models of tangential magnetic drifts on superbanana-plateau transport at small E r , and we consider the scaling of calculated NTV torque with ripple magnitude. | ||
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| Nina Lange (University of Sussex, UK) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Thu, 6. Jul 17, 15:45 |
| Risk premia in forward freight agreements | ||
We investigate the risk premium in cash settled forward contracts on the Baltic Exchange Indices – the so-called Forward Freight Agreements – in the dry bulk shipping markets. We estimate multiple spot price models using Markov Chain Monte Carlo. Using a structure-preserving measure change, we then calibrate the risk premium of traded FFA contracts. Finally we link the risk premium to explanatory variables like e.g., oil prices, demand and supply for shipping and the state of the global economy. Joint work with Jonas Lager and Nikos Nomikos. | ||
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| Iben Cathrine Simonsen (University of Oslo, Norway) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Thu, 6. Jul 17, 15:15 |
| The Heston stochastic volatility model in Hilbert space | ||
We extend the Heston stochastic volatility model to a Hilbert space framework. The stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein-Uhlenbeck process with itself. We compute the dynam- ics of this process under certain conditions, and project it down to the real line to compare it with the one-dimensional Heston variance process. The stochastic volatility process is defined by a Cholesky decomposition of the variance process. We define another Hilbert-valued Ornstein-Uhlenbeck process with Wiener noise perturbed by this stochastic volatility, and compute the characteristic functional of this process. Joint work with Fred Espen Benth. | ||
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| Troels Sønderby Christensen (NEAS and University of Aal- borg, Denmark) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Thu, 6. Jul 17, 14:45 |
| Stabilizing revenue using wind power futures - an empirical study of the German market | ||
The newly introduced wind power futures on the European Energy Exchange have brought interesting opportunities for energy market players in Germany. In this paper, we analyze the benefits of wind power futures in the context of both the buyer’s and the seller’s side. From the buyer’s side, we con- sider gas-fired power plants. To increase the competitiveness of such plants, we propose a simple yet powerful spot-based trading strategy taking advantage of wind power futures. The purpose of the trading strategy is two-fold: 1) increase the revenue of running the gas-fired power plant, and 2) minimize the variance of the revenue generated from the strategy using wind power futures. To fa- cilitate optimal hedging decisions, we employ ARMA-GARCH models for the marginal behavior of electricity price, gas price, and wind power production, and a mixed vine copula for the dependency between the variables. We find that significant benefits can be achieved by employing a spot-trading strategy as opposed to a strategy acting in the forward market (conditional on the for- ward spark spread being positive). More importantly, using wind power futures reduces the variance of the spot-trading strategy significantly. From the seller’s side, we have the wind mill owners who are facing a quite volatile revenue due to their exposure to joint price and volumetric risk, which they wish to minimize. By performing a similar analysis as in the case of the gas-fired power plants, we again find that wind power futures are beneficial. Joint work with Anca Pircalabu. | ||
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| Rüdiger Kiesel (University of Duisburg-Essen, Germany) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Thu, 6. Jul 17, 14:00 |
| Empirics and analytics for intraday power markets | ||
We will give an introduction to short-term electricity markets. We will start with the relation of day-ahead and intraday prices on the EPEX for deliveries in Germany/Austria. In the sequel we will focus on analyzing the intraday market. We will discuss empirical properties of intraday power markets and point out development in recent years. Furthermore, we study the optimal liquidation problem for traders in intraday power markets. | ||
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| Jan Palczewski (University of Leeds, UK) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Thu, 6. Jul 17, 11:15 |
| Regress-later Monte Carlo for optimal inventory control with applications in energy | ||
We develop a Monte-Carlo based numerical method for solving discrete- time stochastic optimal control problems with inventory. These are optimal control problems in which the control affects only a deterministically evolving inventory process on a compact state space while the random underlying pro- cess manifests itself through the objective functional. We propose a Regress Later modification of the traditional Regression Monte Carlo which allows to decouple inventory levels in two successive time steps and to include in the basis functions of the regression the dependence on the inventory levels. We develop a backward construction of trajectories for the inventory which enables us to use policy iteration of Longstaff-Schwartz type avoiding nested simulations.Our al- gorithm improves on the grid discretisation procedure largely used in literature and practice, and on the recently proposed control randomisation by Kharroubi et al. (2014). We validate our approach on two numerical examples: one is a benchmark problem of energy arbitrage used to compare different methods available in literature, the other is a high-dimensional problem of the manage- ment of a battery with the purpose of assisting the operations of a wind turbine in providing electricity to a group of buildings in a cost effective way. Joint work with Alessandro Balata. | ||
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| Dylan Possamai (University of Paris-Dauphine, France) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Thu, 6. Jul 17, 10:15 |
| Volatility demand management for electricity: a moral hazard approach | ||
In this work, we propose a model of electricity demand management through a principal-agent problem, allowing to obtain almost explicit optimal compensations for the consumer. We then illustrate our findings through several numerical experiments, putting the emphasis on the practical implementation of the contracts. (Joint work with Rene Aid and Nizar Touzi). | ||
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| Delphine Lautier (University of Paris-Dauphine, France) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Thu, 6. Jul 17, 9:00 |
| Equilibrium relations between the spot and futures markets for commodi- ties: an infinite horizon model | ||
We give new insights into the theory of the dynamic behavior of com- modity prices with an infinite horizon rational expectations equilibrium model for spot and futures commodity prices. Numerical simulations of the model emphasize the heterogeneity that exists in the behavior of commodity prices by showing the link between the physical characteristics of a market and some stylized facts of commodity futures prices. They show the impact of storage costs on both the variability of the basis and on the Samuelson effect. Finally, the simulations of the model show that an increase in the speculative activity on commodity futures markets has an overall positive effect on risk premia. However, not all of the agents benefit from it. | ||
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| Erik Hove Karlsen (University of Oslo, Norway) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Wed, 5. Jul 17, 15:45 |
| Approximation of Volterra type processes | ||
In this paper we find an approximation to a non-semimartingale Volterra-type process by semimartingales, and furthermore, in the setting of gen- eralized Lebesgue-Stieltjes integration, we find an approximation to the pathwise stochastic integral with this non-semimartingale process as noise. A link to the Itˆo integral and an algorithm for numerical simulation are presented. Joint work with Giulia Di Nunno. | ||
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| Anca Pircalabu (NEAS and University of Aalborg, Denmark) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Wed, 5. Jul 17, 15:15 |
| A regime-switching copula approach to modeling day-ahead prices in coupled electricity markets | ||
The recent price coupling of many European electricity markets has triggered a fundamental change in the interaction of day-ahead prices, challeng- ing additionally the modeling of the joint behavior of prices in interconnected markets. We propose a regime-switching AR-GARCH copula to model pairs of day-ahead electricity prices in coupled European markets. While capturing key stylized facts empirically substantiated in the literature, this model easily allows us to 1) deviate from the assumption of normal margins and 2) include a more detailed description of the dependence between prices. We base our empirical study on four pairs of prices, namely Germany-France, Germany- Netherlands, Netherlands-Belgium and Germany-Western Denmark. We find that the marginal dynamics are better described by the flexible skew t distribu- tion than the benchmark normal distribution. Also, we find significant evidence of tail dependence in all pairs of interconnected areas we consider. As appli- cations of the proposed empirical model, we consider the pricing of financial transmission rights and the forecasting of tail quantiles. In both applications, we highlight the effects of the distributional assumptions for the margins and the tail dependence. Joint work with Fred Espen Benth. | ||
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| Tiziano Vargiolu (University of Padova, Italy) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Wed, 5. Jul 17, 14:00 |
| Capacity markets and the pricing of reliability options | ||
The growing penetration of non-programmable renewable sources, like solar and wind, introduced in the latest years market uncertainties in the quan- tity of electricity produced, which can possibly originate price spikes. Capacity markets have exactly the purpose of providing new potential capacity when that present in the market is already allocated and there is a sudden drop in supply (due for example to unexpected adverse weather events). In this talk we will present the different capacity remuneration mechanisms, and analyze in more detail the so-called reliability option, which is a call option sold by producers to transmit system operators. This option has the important advantage of shaving possible price peaks, but its correct pricing require non-trivial techniques. | ||
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| Roberto Baviera (Politecnico di Milano, Italy) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Wed, 5. Jul 17, 11:15 |
| Stop-loss and leverage in optimal statistical arbitrage with an application to energy market | ||
In this paper we develop a statistical arbitrage trading strategy with two key elements in high frequency trading: stop-loss and leverage. We con- sider, as in Bertram (2009), a mean-reverting process for the security price with proportional transaction costs; we show how to introduce stop-loss and lever- age in an optimal trading strategy. We focus on repeated strategies using a self-financing portfolio. For every given stop-loss level we derive analytically the optimal investment strategy consisting of optimal leverage and market en- try/exit levels. First we show that the optimal strategy a la Bertram depends on the probabilities to reach entry/exit levels, on average First-Passage-Times and on average First-Exit-Times from an interval. Then, when the underlying log- price follows an Ornstein-Uhlenbeck process, we deduce analytical expressions for average First-Exit-Times and we write the long-run return of the strategy as an elementary function of the stop-loss. Finally we describe how to apply the strategy to a generic continuous mean-reverting process. Following industry practice of pairs trading we consider two examples of pairs in the energy futures’ market. We report in detail the analysis for two spreads on Heating-Oil and Gas-Oil futures in a year and a half sample of half-hour market prices. Joint work with Tommaso Santagostino Baldi. | ||
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| Noor ’Adilah Ibrahim (University of Oslo, Norway) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Wed, 5. Jul 17, 10:45 |
| Stochastic modelling of photovoltaic power generation | ||
In recent years, renewable energy has gained importance in producing power in many markets. The aim of this article is to model photovoltaic (PV) production for three transmission operators in Germany. PV power can only be generated during sun hours and the cloud cover will determine its overall production. Therefore, we propose a model that takes into account the sun intensity as a seasonal function. We model the deseasonalized data by an au- toregressive process to capture the stochastic dynamics in the data. We present two applications based on our suggested model. First, we build a relationship between electricity spot prices and PV production where the higher the volume of PV production, the lower the power prices. As a further application, we discuss virtual power plant derivatives and energy quanto options. Joint work with Fred Espen Benth. | ||
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| Carlo Sgarra (Politecnico di Milano, Italy) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Wed, 5. Jul 17, 10:15 |
| A Branching Process Approach to Power Markets | ||
Energy markets, and in particular, electricity markets, exhibit very peculiar features. The historical series of both futures and spot prices include seasonality, mean-reversion, spikes and small fluctuations. After the pioneer- ing paper by Schwartz, where an Ornstein-Uhlenbeck dynamics is assumed to describe the spot price behavior, several different approaches have been inves- tigated in order to describe the price evolution. A comprehensive presentation of the literature until 2008 is offered in the book by Benth, Saltyte-Benth and Koekebakker [8]. High frequency trading, on the other hand, introduced some new features in commodity prices dynamics: in the paper by Filimonov, Bic- chetti, Maystre and Sornette [11] evidence is shown of endogeneity and struc- tural regime shift, and in order to quantify this level the branching ratio is adopted as a measure of this endogenous impact and a Hawkes processes dy- namics is assumed as a reasonable modeling framework taking into account the self-exciting properties [1]. The purpose of the present paper is to pro- pose a new modeling framework including all the above mentioned features, still keeping a high level of tractability. The model considered allows to obtain the most common derivatives prices in closed or semi-closed form. Here with semi-closed we mean that the Laplace transform of the derivative price admits an explicit expression. The models we are going to introduce can describe the prices dynamics in two different forms, that can be proved to be equivalent: the first is a representation based on random fields, the second is based on Continuous Branching Processes with Immigration (CBI in the following). The idea of adopting a random fields framework for power prices description is not new: O.E. Barndorff-Nielsen, F.E. Benth and A. Veraart introduced the Ambit Fields to this end, showing how this approach can provide a very flexible and still tractable setting for derivatives pricing [2], [3]. A model based on CBI has been proposed recently by Y. Jiao, C. Ma and S. Scotti in view of short interest rate modeling, and in that paper it was shown that, with a suitable choice of the L´evy process driving the CBI dynamics, the model can offer a significant extension of the popular CIR model [12]. The model we propose extends in different ways some relevant models al- ready available in the literature. It belongs to the class of arithmetic models (following the classification proposed by F.E. Benth, J. Salthythe-Benth and S. Koekebakker), and the driving processes are L´evy processes with positive jumps, i.e. subordinators, so it extends the model proposed by F.E. Benth, J. Kallsen and T. Meyer-Brandis [6] by formulating the dynamics via a random field ap- proach, which allows to include some self-exciting features. On the other hand, the random field approach highlights some similarities with the Ambit Field- based models introduced by O.E. Barnorff-Nielsen, F.E. Benth and A. Veraart [3]; the main difference between the model proposed in this paper and the Ambit Field-based models consists in the character of the extra dimension appearing in the random field adopted: while in the Ambit Field setting the parameter of this dimension is a time parameter, in the present setting this will be a pa- rameter of space type. This main difference will be reflected moreover in the integration domain of the integrals defining the dynamics. The features of our modeling approach just outlined, allow to introduce the so- called self-exciting properties in a simple and natural way and, although the pricing formulas for basic contracts like forward will exhibit very small changes with respect to those obtained for the previous models, the present model will exhibit a substantially different risk premium term structure. The presentation will be organized as follows: in Section 2 we’ll introduce the market model we are going to consider, while in Section 3 we shall discuss the relations between our model and the CBI processes. In Section 4 we’ll present some closed formulas for Futures and Option prices when the underlying dynamics is assumed to be given by the model introduced. Section 5 includes a theoretical analysis of the jumps behavior and the self-exciting property. In Section 6 we’ll provide some suggestions about estimation methods for the same model. In this last section, in particular, we are going to highlight the main issues and to propose a theoretical statistical approach. In particular, we are going to derive the maximum likelihood estimator for the parameters of the intensity process. By following the ideas presented in [7] and in [13], the first step to perform will be to de-seasonalise the data. The second step, definitely less trivial, is to split the components Y1 and Y2 emerging from the data. This issue is well analyzed in [7] and [13] and their approach is directly applicable to our framework. Then, we first focus on the process Y1, sometimes called the base signal. Following [7], we look for the ergodic distribution of Y1 fitting the data. By recalling that the ergodic distribution of a CIR diffusion is of Gamma type [10], our model is in agreement with the previous literature (see subsection 5.4.2 in[7]) and we obtain the estimated parameters values for the driving processes. Joint work with Ying Jiao, Chunhua Ma and Simone Scotti. References [1] Bacry, E., Mastromatteo, J. and Muzy, J.-F. Hawkes Processes in Finance, PREPRINT (2015). [2] Barndorff-Nielsen, O.E., Benth, F.E. and Veraart, A. (2013): Modelling en- ergy spot prices by volatility modulated L´evy driven Volterra processes, Bernoulli, 19, 803-845. [3] Barndorff-Nielsen, O.E., Benth, F.E. and Veraart, A. (2014): Modelling Electricity Futures by Ambit Fields, Advances in Applied Probability, 46 (3), 719-745. [4] Barndorff-Nielsen, O.E. and Shephard, N. (2000): Modelling by L´evy Pro- cesses for Financial Econometrics, in L´evy Processes Theory and Applications, eds. Barndorff- Nielsen, Mikosch and Resnick, Boston, Birkhauser. [5] Benth F. E., Cartea A. and Kiesel R. (2008): Pricing forward contracts in power markets by the certainty equivalence principle: explaining the sign of the market risk premium, Journal of Banking and Finance, 32, 2006-2021. [6] Benth, F. E., Kallsen J. and Meyer-Brandis T. (2007): A Non-Gaussian Ornstein- Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing, Appl. Math. Finance, 14(2), 153-169. [7] Benth, F. E., Kiesel, R. and Nazarova A. (2012): A critical empirical study of three electricity price models, Energy Economics, 34, 1589-1616. [8] Benth, F. E., Salthyte-Benth J. and Koekebakker S. (2008): Stochastic Mod- elling of Electricity and Related Markets , World Scientific, Singapore. [9] Benth, F. E. and Sgarra C. (2012): The Risk Premium and the Esscher Transform in Power Markets, Stoch. Anal. Appl., 30(1), 20-43. [10] Cox, J., Ingersoll, J. and Ross, S. (1985): A theory of the term structure of interest rate. Econometrica 53, 385-408. [11] Filimonov, V., Bicchetti, D., Maystre, N., Sornette, D. (2015):Quantifica- tion of the High Level of Endogeneity and Structural Regime Shifts in Com- modity Markets, preprint. [12] Jiao, Y., Ma, C., Scotti, S. (2016): Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling, preprint, hal-01275397v2. [13] Meyer-Brandis, T. and Tankov, P. (2008): Multi-factor jump-diffusion mod- els of electricity prices. International Journal of Theoretical and Applied Fi- nance, 11(5), 503-528. | ||
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| John Moriarty (Queen Mary University, London, UK) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Wed, 5. Jul 17, 9:00 |
| Energy imbalance market call options and the valuation of storage | ||
The use of energy storage to balance electric grids is increasing and, with it, the importance of operational optimisation from the twin viewpoints of cost and system stability. In this paper we assess the real option value of balancing reserve provided by an energy-limited storage unit. The contractual arrangement is a series of American-style call options in an energy imbalance market (EIM), physically covered and delivered by the store, and purchased by the power system operator. We take the EIM price as a general regular one- dimensional diffusion and impose natural economic conditions on the option parameters. In this framework we derive the operational strategy of the storage operator by solving two timing problems: when to purchase energy to load the store (to provide physical cover for the option) and when to sell the option to the system operator. We give necessary and sufficient conditions for the finiteness and positivity of the value function – the total discounted cash flows generated by operation of the storage unit. We also provide a straightforward procedure for the numerical evaluation of the optimal operational strategy (EIM prices at which power should be purchased) and the value function. This is illustrated with an operational and economic analysis using data from the German Amprion EIM. (Joint work with Jan Palczewsk (University of Leeds)). | ||
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| Marco Piccirilli (University of Padova, Italy) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Tue, 4. Jul 17, 15:45 |
| Additive energy forward curves in a Heath-Jarrow-Morton framework | ||
In energy markets forward contracts can be of two types: in our ter- minology, forwards and swaps. Who sells a swap contract commits to deliver over a certain period, for instance, power, while by forward we mean the classi- cal financial agreement settled on a maturity date. Our purpose is to design a Heath-Jarrow-Morton framework for an additive, mean-reverting, multidimen- sional market consisting of forward contracts of any maturity date or delivery period. The main assumption is that forward prices can be represented as affine functions of a universal source of randomness. In a Brownian setting, we are able to completely characterize the models which do not allow for arbitrage opportunities. We study the possibility of introducing more general L´evy com- ponents either driving the dynamics of prices or in the context of a stochastic volatility model. Joint work with Fred Espen Benth and Tiziano Vargiolu. | ||
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| Rune Hjorth Nielsen (NEAS and University of Aalborg, Denmark) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Tue, 4. Jul 17, 15:15 |
| Simulations of short term power prices: capturing the intraday structure of the German power day-ahead auction | ||
This presentation is on the simulation of the hour-based German day-ahead power auction, where I apply vector autoregressive (VAR) models, in order to capture the effects of the market infrastructure of the day-ahead auction. This approach ensures that the correct intraday correlation structure is simulated, which will be important for valuing assets with production timing issues (e.g. pumped storages and batteries), thereby creating a more suitable simulation alternative to classic Brownian motion based stochastic simulation for these flexible assets. In order to handle the large dimensionality of the data created by the VAR approach, lasso and elasticnet shrinkages are applied, as well as their adaptive versions. The assessment of these methods is done by performing a classic forecast quality assessment, combined with an evaluation of the (often asymptotic) simulation relevant properties of each model. After estimating the model parameters, simulation from the fitted model is carried out using a block bootstrap. Sanity checks of the appropriateness of the forecasting approach are presented, highlighting both the advantages of the model and the points where future work is necessary. | ||
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| Ana Busic (INRIA Paris, France) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Tue, 4. Jul 17, 14:00 |
| Distributed demand control in power grids and ODEs for Markov decision processes | ||
Renewable energy sources such as wind and solar have a high degree of unpredictability and time variation. As a result, balancing supply and demand in real time is becoming ever more challenging and the power grids need greater flexibility on many levels. The proposed approach addresses this challenge by harnessing the inherent flexibility in demand of many types of loads. We develop a distributed control theory and algorithms for automated demand dispatch, which can be used by grid operators as ancillary service to regulate demand- supply balance. The proposed approach uses local control solutions that a) take into account local measurements, constraints, and preferences, and b) lead to a controllable input-output model for the aggregate dynamics. The local control problem can be defined by a family of Markov decision processes, parameterized by a weighting factor that appears in the one-step reward function. This talk introduces a new methodology for solving an entire family of MDPs. In our application to demand control, the focus will be on a family of average-cost optimal control models in which the one-step reward function is defined by Kullback-Leibler divergence with respect to nominal dynamics. The proposed ODE methodology can be seen as a generalization of the linearly solvable MDP framework of Todorov to the case with exogenous disturbances, such as weather or customer behavior. | ||
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| Matteo Basei (University of Paris-Diderot, France) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Tue, 4. Jul 17, 11:15 |
| The coordination of centralised and distributed generation | ||
This paper analyses the interaction between centralised carbon emis- sive technologies and distributed intermittent non-emissive technologies. In our model, there is a representative consumer who can satisfy her electricity demand by investing in distributed generation (solar panels) and by buying power to a centralised firm at a price he set up. Distributed generation is intermittent and induces an externality cost to the consumer. The firm provides non-random electricity generation subject to carbon price and to transmission costs. The objective of the consumer is to satisfy her demand while minimising investment costs, payment to the firm and intermittency cost. The objective of the firm is to satisfy consumer’s residual demand while minimising investment costs, de- mand deviation costs and maximising payment from the consumer. Investment decisions are formulated as McKean-Vlasov control problems with stochastic coefficients. We provide explicit, model-free solutions to the optimal decision problems faced by each player, the solution of the Pareto optimum and the Stackelberg equilibrium where the firm is the leader. We find that, from the social planner point of view, carbon price or transmission costs are necessary to justify a positive share of distributed capacity in the long-term, whatever the re- spective investment costs of both technologies are. The Stackelberg equilibrium is far from the Pareto equilibrium, leading to a much larger share of distributed energy and to a much higher price for centralised energy. Joint work with Rene Aid, Imen Ben Tahar and Huyen Pham | ||
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| Gabriele D’Amore (Sapienza University of Rome, Italy) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Tue, 4. Jul 17, 10:45 |
| Predictability information criterion for selecting stochastic pricing models | ||
Pricing models of derivative instruments usually fail to provide reli- able results when risks rise and financial crises occur. More advanced stochastic pricing models try to improve the fitting results adding risk factors and/or pa- rameters to the models, incurring the risk of overfitted results. Drawing on these observations, it is proposed a generalisation of the Akaike information criterion suitable to evaluate forecasting power of alternative stochastic pricing models for any fixed arbitrary forecasting time-horizon. The Predictability Informa- tion Criterion (PIC) differs from the classical criteria for evaluating statistical models as it assumes that the random variable to study can ( or cannot) be par- tially predictable, which makes it particularly suitable for studying stochastic pricing models coherently with the semimartingale definition of the price pro- cess. On the basis of this assumption the criterion measures and compares the uncertainty of the predictions of two different alternative models when prices are (or are not) predictable. We conclude with a focus on Crude Oil market by comparing GBM and OU stochastic processes that are generally used for modeling West Texas Intermediate (WTI) oil spot price returns in derivative pricing models. | ||
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| Michael Coulon (University of Sussex, UK) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Tue, 4. Jul 17, 10:15 |
| Spread option implied correlation and the optimal choice of strike con- vention | ||
By means of Malliavin Calculus we construct an optimal linear strike convention for exchange options under stochastic volatility models. This convention allows us to minimize the difference between the model and implied correlations between the two underlying assets in the spread. Moreover, we show that this optimal convention does not depend on the specific stochastic volatility model. Numerical examples are given. Joint work with Elisa Alos. | ||
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| Nadia Oudjane (EDF, France) | Oskar-Morgenstern-Platz 1, Lecture Room 13, 2nd floor | Tue, 4. Jul 17, 9:00 |
| Advanced numerical methods for nonlinear PDEs and perspectives of applications for energy management control problems | ||
With the emergence of renewable energies (as wind or solar genera- tion), local generation systems are rapidly multiplying integrating renewables, batteries or more conventional plants (such as gas turbines or hydro plants). The impact of random factors (such as demand, energy prices, wind, luminosity etc.) on the management of such local generation systems are significant. Hence, an important issue is to be able to manage efficiently such microgrids in presence of uncertainties. Mathematically, the related optimization problem can be stated in terms of a stochastic control problem which can be reduced to a nonlinear Partial Differential Equation (PDE), known as Hamilton-Jacobi-Bellman (HJB) equation. The presentation focuses on recent forward numerical schemes based on generalized Fokker-Planck representations for nonlinear PDEs in high space dimension. In the specific case of mass conservative PDEs, it is well known that the solution can be probabilistically represented as the marginal densities of a Markov diffusion nonlinear in the sense of Mckean. Then one can design forward interacting particle schemes to approximate numerically the PDEs solu- tion. We present some extensions of this kind of representation and interacting particle scheme associated to a large class of PDEs including the case when they are non-conservative, non integrable with various kind of nonlinearities. (Joint work with Anthony Le Cavil, (HSBC, Paris) and Francesco Russo, (ENSTA ParisTech) | ||
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| Blakie Blair | WPI, OMP 1, Seminar Room 08.135 | Fri, 23. Jun 17, 11:00 |
| Self-bound droplets of a dipolar Bose-Einstein condensate | ||
Recent experiments with Bose-Einstein condensates of dysprosium [1] and erbium [2] atoms have observed the formation of droplets that can preserve their form, even in the absence of any external confinement [3]. These droplets occur when the long-ranged dipole-dipole interaction between the atoms dominates over the short-ranged contact interaction. In this regime meanfield theory predicts that the condensate is unstable to collapse, however the Lee-Huang-Yang corrections to the meanfield energy [3] can stabilize the system as one or many finite sized droplets. I will discuss our current understanding of these droplets, and introduce a new type of nonlinear Schrodinger equation used to describe their equilibrium and dynamical properties. | ||
| Note: Click here for further information | ||
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| Yong Zhang | WPI, OMP 1, Seminar Room 08.135 | Thu, 22. Jun 17, 14:00 |
| “Numerical methods/analysis for Schrödinger equations and micro-magnetism” | ||
We present some mathematical methods occurring in the modeling and simulation of Nonlinear Schrödinger equations and nonlocal potentials. We focus on Gross-Pitaevskii equations describing Bose Einstein Condensates and stray field calculations in micro-magnetism. | ||
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| François Golse | WPI, OMP 1, Seminar Room 08.135 | Thu, 22. Jun 17, 10:00 |
| A convergence rate estimate for the semiclassical limit with Lipschitz continuous force field | ||
We propose an explicit bound for the convergence rate in the semiclassical limit for the Schrödinger equation which holds for potentials with Lipschitz continuous gradient. This bound is based on an analogue of the Wasserstein metric used in optimal transportation, adapted to measuring the distance between a quantum and a classical density. | ||
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| Olivier Pinaud (Colorado State University) | WPI, OMP 1, Seminar Room 08.135 | Wed, 21. Jun 17, 14:00 |
| Waves in random media and applications | ||
We will review some results concerning uncertainties in the derivation of kinetic equations from wave propagation in random media, that is modeled by a wave or a Schroedinger equation. Kinetic equations usually describe quadratic quantities in the wavefield such as the energy or wave-wave correlations, and can be used to solve some imaging problems in complex media. | ||
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| Shi Jin (University of Wisconsin-Madison and Shanghai Jiao Tong University) | WPI, OMP 1, Seminar Room 08.135 | Wed, 21. Jun 17, 10:00 |
| Semiclassical computational methods for oscillatory and uncertain quantum dynamics with band-crossings | ||
Band-crossing is a quantum dynamical behavior that contributes to important physics and chemistry phenomena such as quantum tunneling, Berry connection, charge transfer, chemical reaction etc. In this talk, we will discuss some recent works in developing semiclassical methods for band-crossing in surface hopping. For such systems we will also introduce an nonlinear geometric optics method based "asymptotic-preserving" method that is accurate uniformly for all wave numbers, including the problem with random uncertain band gaps. | ||
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| Mohammed Lemou | WPI, OMP 1, Seminar Room 08.135 | Tue, 20. Jun 17, 15:30 |
| "Averaging techniques and application to numerical methods for highly oscillatory Vlasov and Klein-Gordon models" | ||
A brief description of averaging theory for highly-oscillatory problems will be first presented with an emphasis on the so-called classical and stroboscopic averaging methods. Then I will present two general strategies to construct efficient numerical schemes for a class of highly oscillatory PDEs: the so-obtained numerical schemes have a uniform accuracy with respect to the frequency. Two applications will be considered: the Vlasov kinetic equation with strong magnetic field and the Klein-Gordon equation in the non-relativistic regime. | ||
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| Olof Runborg (Mathematik Institution, Stockholm) | WPI, OMP 1, Seminar Room 08.135 | Tue, 20. Jun 17, 10:00 |
| Uncertainty Quantification for High Frequency Wave Propagation | ||
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest (QoI) related to the solution $u^\varepsilon$ and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. In the talk we will discuss how the rate of convergence for the stochastic collocation and the complexity of evaluating the QoI depend on the short wavelength $\varepsilon$. We find in particular that QoIs based on local averages of $\vert u^\varepsilon\vert ^2$ can give fast convergence rates, despite the fact that $u^\varepsilon$ is highly oscillatory in both physical and stochastic space. | ||
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| Cuesta Carlota | WPI, OMP 1, Seminar Room 08.135 | Mon, 19. Jun 17, 15:00 |
| Analysis of travelling waves in a nonlocal Korteweg-de Vries-Burgers equation arising in a two-layer shallow-water model | ||
We study travelling wave solutions of a Korteweg-de Vries-Burgers equation with a non-local diffusion term. This model equation arises in the analysis of a shallow water flow by performing formal asymptotic expansions associated to the triple-deck regularisation (which is an extension of classical boundary layer theory). The resulting non-local operator is of fractional differential type with order between 1 and 2. Travelling wave solutions are typically analysed in relation to shock formation in the full shallow water problem. We show rigorously the existence of these waves in the case of a quadratic nonlinearity. The travelling wave problem for the classical KdV-Burgers equation is usually analysed via a phase-plane analysis, which is not applicable here due to the presence of the non-local diffusion operator. Instead, we apply fractional calculus results available in the literature and a Lyapunov functional. In addition we discuss the monotonicity of the waves in terms of a control parameter and prove their dynamic stability in case they are monotone. We also discuss some partial results concerning the existence of travelling waves in the case of a cubic nonlinearity. This existence problem and the monotonicity of the waves in the quadratic case for a small dispersion term in relation with the diffusive one are still open problems, for this reason we have also developed numerical schemes in order to support our conjectures. We will discuss in a second part of the talk, a pseudo-spectral method that approximates the initial value problem. The basic idea is, using an algebraic map, to transform the whole real line into a bounded interval where we can apply a Fourier expansion. Special attention is given to the correct computation of the fractional derivative in this setting. Interestingly, there is a connection of the mapping method to fractional calculus, that we will also mention. | ||
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| Jinkai Li | WPI, OMP 1, Seminar Room 08.135 | Fri, 16. Jun 17, 11:00 |
| Some mathematical analyses on two dynamical models for atmosphere with moisture (with Sabine Hittmeir, Rupert Klein, Edriss S. Titi) | ||
In this talk, we will present some recent mathematical results, mainly the global wellposedness and convergence of the relaxation limit, on two kinds of dynamical models for the atmosphere with moisture. In the rst part of this talk, which is a joint work with Edriss S. Titi [1], we will consider a tropical atmosphere model introduced by Frierson, Majda, and Pauluis (Commum. Math. Sci. 2004); for this model, we will present the global well-posedness of strong solutions and the strong convergence of the relaxation limit, as the relaxation time " tends to zero. It will be shown that, for both the nite-time and instantaneous-relaxation systems, the H1 regularities on the initial data are sucient for both the global existence and uniqueness of strong solutions, but slightly more regularities than H1 are required for both the continuous dependence and strong convergence of the relaxation limit. In the second part of this talk, which is a joint work with Sabine Hittmeir, Rupert Klein, and Edriss S. Titi [2], we will consider a moisture model for warm clouds used by Klein and Majda (Theor. Comput. Fluid Dyn. 2006), where the phase changes are allowed, and we will present the global well-posedness of this system. [1] Jinkai Li; Edriss S. Titi: A tropical atmosphere model with moisture: global well- posedness and relaxation limit, Nonlinearity, 29 (2016), 2674{2714. [2] Sabine Hittmeir; Rupert Klein; Jinkai Li; Edriss S. Titi: Global well-posedness for passively transported nonlinear moisture dynamics with phase changes, arXiv:1610.00060 | ||
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| Manuel Baumgartner | WPI, OMP 1, Seminar Room 08.135 | Fri, 16. Jun 17, 10:00 |
| Diffusional Growth in Clouds (with Peter Spichtinger) | ||
Di usional growth is the most important growth mechanism for newly formed cloud droplets and ice crystals. Non-linear di usion equations control the transport of water vapor towards the cloud particles. Although the solution of these di usion equations is circumvented in numerical cloud models, it remains computationally expensive to include the details of di usional growth due to severe timestep restrictions. Moreover, as soon as ice crystals are present in a cloud consisting mostly of cloud droplets, the Wegener- Bergeron-Findeisen process becomes active and the ice crystals grow at the expense of the cloud droplets. In the rst part of the talk, we discuss the aspect of locality of the Wegener-Bergeron- Findeisen process, i.e. an ice crystal does only a ect its immediate vicinity. Its presence decouples the di usional growth behavior of nearby droplets from environmental conditions. We show some simulation results and a possible way to include locality in the context of bulk-microphysics. The second part considers the case of a liquid cloud. In the context of numerical models, the microphysical details of the di usional growth and the timestep restrictions are e ectively avoided through the technique of saturation adjustment. We will show some of these techniques and analyze an air parcel model containing activation of new droplets using asymptotics. | ||
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| Matthias Hieber | WPI, OMP 1, Seminar Room 08.135 | Fri, 16. Jun 17, 9:00 |
| Thermodynamical Consistent Modeling and Analysis of Heat-Conducting Fluids | ||
In this talk, we derive and discuss thermodynamically consistent models for heat-conduction fluids. Our approach is based on the entropy principle. | ||
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| Annette Muller | WPI, OMP 1, Seminar Room 08.135 | Thu, 15. Jun 17, 15:30 |
| The DSI as an indicator for diabatic processes across the scales | ||
In atmospheric ows, the Dynamic State Index (DSI) indicates local deviations from a steady wind solution. This steady wind solution is based on the primitive equations under adiabatic and inviscid conditions. Hence, from theoretical point of view, atmospheric dynamics is regarded relative to a solution derived from uid mechanic's rst principles. Thus, this parameter provides a tool to capture diabatic processes. The DSI can be designed for di erent uid mechanical models on distinguished scales, we will introduce a DSIQG for the quasi-geostrophic ow, a DSIRo for the Rossby model and DSImois that is based on the equations of motions including moisture processes. | ||
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| Wojciech W. Grabowski | WPI, OMP 1, Seminar Room 08.135 | Thu, 15. Jun 17, 14:00 |
| Modeling condensation in cloud-scale models | ||
Condensation of water vapor to form and grow cloud droplets is the most fundamental process of cloud and precipitation formation. It drives cloud dynamics through the release of latent heat and determines the strength of convective updrafts. Cloud-scale models simulate condensation by applying two drastically di erent methods. The rst one is the bulk condensation where condensation/evaporation is assumed to always maintain saturated conditions. The second approach involves prediction of the in-cloud super- or sub-saturation and can be used in models that predict not only condensate mass but also relevant features of the droplet size distribution (e.g., models with the 2-moment microphysics or with the bin microphysics). This presentation will address the question whether the di erence between the two approaches has a noticeable impact on convective dynamics. Model simulations with the bin microphysics for shallow non-precipitating convection and with the double-moment bulk microphysics for deep convection will be discussed to document the di erences in cloud eld simulations applying the two methodologies. For the shallow convection, the di erences in cloud eld simulated with bulk and bin schemes come not from small di erences in the condensation, but from more signi cant di erences in the evaporation of cloud water near cloud edges as a result of entrainment and mixing. For the deep convection, results show a signi cant dynamical impact of nite supersaturations and a strong microphysical e ect associated with upper-tropospheric anvils. Implications of these results for modeling convective dynamics will be discussed and a possible intermediate modeling methodology will be suggested. | ||
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| Piotr Smolarkiewicz | WPI, OMP 1, Seminar Room 08.135 | Thu, 15. Jun 17, 11:00 |
| Finite-volume integrators for cloud-resolving simulations of global atmospheric flows | ||
This work extends to moist-precipitating dynamics a recently documented high-performance nite-volume integrators for simulating global all-scale atmospheric ows (doi:10.1016/j.jcp. 2016.03.015). A key objective of the current development is a seamless coupling of the conservation laws for moist variables engendered by cloud physics with the semi-implicit, non-oscillatory forward-in-time integrators already proven for dry dynamics. The representation of the water substance and the associated processes in weather and climate models can vary widely in formulation details and complexity levels. The adopted representation assumes a canonical warm-rain" bulk microphysics parametrisation, recognised for its minimal physical intricacy while accounting for the essential mathematical complexity of cloud-resolving models. A key feature of the presented numerical approach is global conservation of the water substance to machine precision | implied by the local conservativeness and positivity preservation of the numerics | for all water species including water vapour, cloud water, and precipitation. The moist formulation assumes the compressible Euler equations as default, but includes reduced anelastic equations as an option. The theoretical considerations are illustrated with a benchmark simulation of a tornadic thunderstorm on a reduced size planet, supported with a series of numerical experiments addressing the accuracy of the associated water budget. | ||
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| Rupert Klein | WPI, OMP 1, Seminar Room 08.135 | Thu, 15. Jun 17, 10:00 |
| The role of multiscale convection in hurricane intensi cation | ||
Paeschke et al (2012) showed analytically how non-axisymmetric external diabatic forcing of a tilted vortex in dry air can amplify or attenuated the ow depending on the relative orientation of vortex tilt and the "heating dipole". Here we include a bulk moist microphysics closure and describe how boundary layer processes and multiscale deep moist convection can interact to produce this e ect self-consistently. | ||
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| Tom Dörffel | WPI, OMP 1, Seminar Room 08.135 | Thu, 15. Jun 17, 9:00 |
| Intensification of atmospheric vortices through asymmetric diabatic heating (with Ariane Papke, Rupert Klein) | ||
The dynamics of atmospheric vortices such as tropical storms, hurricanes and mid-latitude cyclones is driven by a variety of interacting scales. [1] developed an asymptotic theory for the dynamics of strongly tilted atmospheric vortices in the gradient-wind regime, embedded into a synoptic-scale geostrophic background eld. One central outcome of the theory is the evolution equation for the nearly axisymmetric primary circulation. It predicts that Fourier-mode 1 of asymmetric diabatic heating/ cooling patterns can spin up or spin down a vortex depending on the relative arrangement of the heating dipole relative to the vortex tilt. Based on this methodology further investigations led to the conclusion that this theory is generalizable to Rossby numbers of order 1 and higher, i.e. cyclostrophic balance. Accompaning the asymptotics numerical experiments are conducted to test the theory within an anelastic model [2]. In this talk we present the latest results showing consistency of numerical simulations and theoretical predictions. [1] E. Paschke, P. Marschalik, A. Z. Owinoh and R. Klein, Motion and structure of at- mospheric mesoscale baroclinic vortices: dry air and weak environmental shear, J. Fluid Mech. 701: 137{170, (2012) [2] J. M. Prusa, P. K. Smolarkiewicz and A. A. Wyszogrodzki, EULAG, a computational model for multiscale ows, Comput. Fluids 37: 1193{1207 (2008) | ||
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| Boualem Khouider | WPI, OMP 1, Seminar Room 08.135 | Wed, 14. Jun 17, 17:00 |
| A zonally symmetric model for the monsoon-Hadley circulation with stochastic convective forcing | ||
Idealized models of reduced complexity are important tools to understand key processes underlying a complex system. In climate science in particular, they are important for helping the community improve our ability to predict the e ect of climate change on the earth system. Climate models are large computer codes based on the discretization of the uid dynamics equations on grids of horizontal resolution in the order of 100 km, whereas unresolved processes are handled by subgrid models. For instance, simple models are routinely used to help understand the interactions between small-scale processes due to atmospheric moist convection and large-scale circulation patterns. Here, a zonally symmetric model for the monsoon circulation is presented and solved numerically. The model is based on the Galerkin projection of the primitive equations of atmospheric synoptic dynamics onto the rst modes of vertical structure to represent free tropospheric circulation and is coupled to a bulk atmospheric boundary layer (ABL) model. The model carries bulk equations for water vapor in both the free troposphere and the ABL, while the processes of convection and precipitation are represented through a stochastic model for clouds. The model equations are coupled through advective nonlinearities, and the resulting system is not conservative and not necessarily hyperbolic. This makes the design of a numerical method for the solution of this system particularly dicult. We develop a numerical scheme based on the operator time-splitting strategy, which decomposes the system into three pieces: a conservative part and two purely advective parts, each of which is solved iteratively using an appropriate method. The conservative system is solved via a central scheme, which does not require hyperbolicity since it avoids the Riemann problem by design. One of the advective parts is a hyperbolic diagonal matrix, which is easily handled by classical methods for hyperbolic equations, while the other advective part is a nilpotent matrix, which is solved via the method of lines. Validation tests using a synthetic exact solution are presented, and formal second-order convergence under grid re nement is demonstrated. Moreover, the model is tested under realistic monsoon conditions, and the ability of the model to simulate key features of the monsoon circulation is illustrated in two distinct parameter regimes. This is joint work with Michale De La Chevrotiare. | ||
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| Olivier Pauluis | WPI, OMP 1, Seminar Room 08.135 | Wed, 14. Jun 17, 16:00 |
| Thermodynamic analysis of atmospheric motions | ||
In this talk, I will show how to extract thermodynamic cycles from high resolution simulations of atmospheric ows. On the one hand, thermodynamic processes are typically analyzed in terms of the behavior of individual parcel trajectories. On the other hand, most atmospheric ows are associated with in nitely many turbulent lagrangian trajectories. The Mean Air Flow As Lagrangian Dynamics Approximation (MAFALDA) has been recently developed to address this problem. It MAFALDA, the ow is rst averaged in isentropic coordinates, typically pressure and equivalent potential temperature, and the mean ow is then treated as a set of thermodynamic cycles. This o er a systematic procedure to analyze the thermodynamic transformation in atmospheric ows, which is applied here to compare the thermodynamics behavior of convection and hurricanes. | ||
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| Sam Stechmann | WPI, OMP 1, Seminar Room 08.135 | Wed, 14. Jun 17, 15:00 |
| Precipitating Quasi-Geostrophic Equations and Minimal Cloud Mi- crophysics | ||
Two simpli ed models are presented for precipitating atmospheric dynamics. First, a minimal version of cloud microphysics is presented. The time scales of all microphysical processes are assumed to be fast, and the resulting microphysics has only one parameter, the terminal velocity of falling rain drops. It is shown that, despite its simplicity, this minimal microphysics scheme can reproduce distinct canonical modes of convective organization (scattered convection and a squall line) under appropriate environmental conditions. This suggests that the essential physical processes underlying moist convection are simply phase changes and falling rain drops. Second, a precipitating version of the quasi-geostrophic (QG) equations is presented. The precipitating QG (PQG) equations include phase changes between water vapor and liquid water, which arise as Heaviside nonlinearities in the new PQG PDEs. Finally, we present an initial application of the PQG equations, in a linearized setting that can be solved analytically, to understanding meridional moisture transport by baroclinic eddies. | ||
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| Didier Bresch | WPI, OMP 1, Seminar Room 08.135 | Tue, 13. Jun 17, 14:00 |
| Mathematical analysis of relevant compressible geophysical models | ||
In this talk, we talk about mathematical results related to compressible uid systems with applications to geophysical flows. We focus on pressure laws, viscosity e ects, bi-fluid flows description. Some singular limits are also discussed. | ||
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| Didier Bresch | WPI, OMP 1, Seminar Room 08.135 | Tue, 13. Jun 17, 11:00 |
| Mathematical analysis of relevant compressible geophysical models | ||
In this talk, we talk about mathematical results related to compressible uid systems with applications to geophysical flows. We focus on pressure laws, viscosity e ects, bi-fluid flows description. Some singular limits are also discussed. | ||
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| Olivier Pauluis | WPI, OMP 1, Seminar Room 08.135 | Tue, 13. Jun 17, 9:00 |
| Tutorial 2: Thermodynamic cycles and heat engines | ||
The atmosphere can be describe as a heat engine that continuously generates kinetic energy by transporting energy from a warm source, i.e. the Earth surface, to a cold sink, i.e the colder troposphere. However, the ability of the atmosphere to generate kinetic energy is strongly reduced by the hydrological cycle. We will analyze how the impacts of moist processes can be a quanti ed in terms of a Gibbs penalty associated with the evaporation of water in unsaturated air and its removal as liquid water. | ||
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| Rupert Klein (FU Berlin) | Oskar-Morgenstern-Platz 1, Hörsaal 4, ground floor. | Mon, 12. Jun 17, 17:00 |
| How Mathematics helps structuring climate discussions | ||
Mathematics in climate research is often thought to be mainly a provider of techniques for solving the continuum mechanical equations for the ows of the atmosphere and oceans, for the motion and evolution of Earth's ice masses, and the like. Three examples will elucidate that there is a much wider range of opportunities. Climate modellers often employ reduced forms of "the continuum mechanical equations" to eciently address their research questions of interest. The rst example discusses how mathematical analysis can provide systematic guidelines for the regime of applicability of such reduced model equations. Meteorologists de ne "climate", in a narrow sense, as "the statistical description in terms of the mean and variability of relevant quantities over a period of time" (World Meteorological Society, http://www.wmo.int; see the website for a broader sense de nition). Now, climate researchers are most interested in changes of the climate over time, and yet there is no unique, well-de ned notion of "time dependent statistics". In fact, there are restrictive conditions which data from time series need to satisfy for classical statistical methods to be applicable. The second example describes recent developments of analysis techniques for time series with non-trivial temporal trends. Modern climate research has joined forces with economy and the social sciences to generate a scienti c basis for informed political decisions in the face of global climate change. One major type of problems hampering progress of the related interdisciplinary research consists of often subtle language barriers. The third example describes how mathematical formalization of the notion of "vulnerability" has helped structuring related interdisciplinary research e orts. | ||
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| Didier Bresch | WPI, OMP 1, Seminar Room 08.135 | Mon, 12. Jun 17, 15:45 |
| Mathematical analysis of relevant compressible geophysical models | ||
In this talk, we talk about mathematical results related to compressible uid systems with applications to geophysical flows. We focus on pressure laws, viscosity e ects, bi-fluid flows description. Some singular limits are also discussed. | ||
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| Olivier Pauluis | WPI, OMP 1, Seminar Room 08.135 | Mon, 12. Jun 17, 14:05 |
| Tutorial 1: Thermodynamic properties of cloudy air | ||
In this tutorial, I will review the thermodynamic properties cloudy air and how they are typically treated in numerical models. This will include the concepts of saturation, equation of state for moist air, moist entropy and potential temperature of many kinds. We will then discuss the implications for buoyancy and convective processes. | ||
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| Human Rezaei (Inra Jouy-en-Josas, France) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 8. Jun 17, 15:20 |
| Prion quasi-species and molecular basis of auto-perpetuation of Prion structural information. | ||
Davy Martin1, Joan Torrent i Mas1, Stéphanie Prigent1, Mathieu Mezache2, Marie Doumic-Jauffret2, Vincent Béringue1 and Human Rezaei1* 1. National Institute for Agricultural Research (INRA), Pathological Macro-assemblies and Prion Pathology group (MAP2), UR892, Virologie Immunologie Moléculaires, Jouy-en-Josas, 78350-F, France 2. Sorbonne Universités, Inria, UPMC Univ Paris 06, Lab. J.L. Lions UMR CNRS 7598, Paris, France The prion phenomenon is based on autonomous structural information propagation towards single or multiple protein conformational changes. Since this last decade the prion concept referring to the transmission of structural information has been extended to several regulation systems and pathologies including Alzheimer and Parkinson’s diseases. The unified theory in Prion replication implies structural information transference (SIT) from the prion to a non-prion conformer through a mechanism also called improperly, with regards to biophysical considerations “seeding” phenomenon. Therefore considering prion replication as a structural information transduction from a donor (i.e. template) to an acceptor (i.e. substrate) through a transduction interface a new questioning arises: what are molecular mechanisms of the auto-perpetuation of the Prion structural information and its faithfulness? Considering the Prion propagation as more or less faithful perpetuation of structural information, in the present work, we explored the concept of prion quasi-species (i.e. existence of prion heterogeneous assemblies) and highlighted the existence of prion network, which has an autopoietic behaviour (autoreplicative). Our observations strongly suggest that specific criteria in term of: protein structure, delayprocess and thermo-kinetics should be collated before a system become dissipative and autopoietic. | ||
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| Sara Merino-Aceituno (Imperial College, London, United Kingdom) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 8. Jun 17, 14:30 |
| A new flocking model through body attitude coordination | ||
We present a new model for multi-agent dynamics where each agent is described by its position and body attitude: agents travel at a constant speed in a given direction and their body can rotate around it adopting different configurations. Agents try to coordinate their body attitudes with the ones of their neighbours. This model is inspired by the Vicsek model. The goal of this talk will be to present this new flocking model, its relevance and the derivation of the macroscopic equations from the particle dynamics. In collaboration with Pierre Degond (Imperial College London) and Amic Frouvelle (Université Paris Dauphine). | ||
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| Alexander K. Buell (Institute of Physical Biology, University of Düsseldorf) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 8. Jun 17, 13:50 |
| Kinetic and thermodynamic analysis of peptide self-assembly | ||
In this talk I will discuss various aspects of the kinetics and thermodynamics of the self assembly of peptides into amyloid fibrils and crystals. I will present a theoretical framework that allows to determine free energy barriers and entropies from kinetic data of amyloid fibril growth [1,2]. I will contrast the kinetic behaviour of longer, amyloid forming sequences with that of aromatic dipeptides that form crystals, rather than amyloid fibrils [3,4]. Furthermore, I will present the phenomenon of autocatalytic secondary nucleation, whereby new amyloid fibrils nucleate on the surface of existing ones [5,6]. In particular, I will show how this phenomenon manifests itself in kinetic measurements of protein aggregation, and how biosensing can be used to explore its molecular origin [6,7]. [1] A. K. Buell, J. R. Blundell, C. M. Dobson, M. E. Welland, E. M. Terentjev, and T. P. Knowles, Phys. Rev. Lett. 104, 228101 (2010). [2] A. K. Buell, A. Dhulesia, D. A. White, T. P. J. Knowles, C. M. Dobson, and M. E. Welland, Angew. Chem. Int. Ed Engl. 51, 5247 (2012). [3] T. O. Mason, T. C. T. Michaels, A. Levin, E. Gazit, C. M. Dobson, A. K. Buell, and T. P. J. Knowles, J. Am. Chem. Soc. 138, 9589 (2016). [4] T. O. Mason, A. Levin, C. M. Dobson, E. Gazit, T. P.J. Knowles and A. K. Buell, JACS under revision, (n.d.). [5] A. K. Buell, C. Galvagnion, R. Gaspar, E. Sparr, M. Vendruscolo, T. P. J. Knowles, S. Linse, and C. M. Dobson, Proc. Natl. Acad. Sci. 111, 7671 (2014). [6] R. Gaspar, G. Meisl, A. K. Buell, L. Young, C. F. Kaminski, T. P. J. Knowles, E. Sparr, and S. Linse, Q. Rev. Biophys. 50, (2017). [7] A. Šariæ, A. K. Buell, G. Meisl, T. C. T. Michaels, C. M. Dobson, S. Linse, T. P. J. Knowles, and D. Frenkel, Nat. Phys. 12, 874 (2016). | ||
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| Yi Yin (Inria Paris and Univ. Pierre et Marie Curie, France) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 8. Jun 17, 12:00 |
| Automated quantification of amyloid fibrils morphological features based on image analysis of transmission electron microscopies | ||
Yi Yin*, 1, Stéphanie Prigent1, Joan Torrent, Dirk Drasdo1, Human Rezaei, and Marie Doumic1 1. INRIA Paris, and Sorbonne Universités UPMC Univ. Paris 6, Laboratoire Jacques-Louis Lions, Paris, France, * yi.yin@inria.fr Protein aggregation into fibrils is a key process in amyloid diseases and also in other biological processes. The quantification of fibrils’ morphology and molecular structures is urgently needed in understanding of the key mechanisms and properties of fibrils. In this study, we propose an automated image analysis procedure to extract and quantify fibril morphological features from transmission electron microscopy (TEM) images. Fibrils are segmented by a ‘maximum entropy’ thresholding method and then the ‘fast marching’ skeletonization is applied to detect the fibril centerlines. The individual information of each fibril is gathered based on the fibril segmentation and extracted centerline, including the length (following the curvature of the fibrils, which are rarely straight lines), the varying width along the length, the curvature, as well as the number, position and length of branches. The intricate overlapping and branching structures are identified based on the angles between fibril segments. The proposed method was tested on experiments on the prion protein (PrP), which also allows us to explain in detail the parameters needed for the image analysis. Our method has high estimation accuracy (e.g. width estimation as shown in the figure). The results from different mutants of the PrP protein fibrils showed the potential of the method in fibrils classification through a statistical analysis. Romain | ||
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| Frédéric Halgand (University Paris-Sud, France) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 8. Jun 17, 11:20 |
| Prion protein conformational landscape studied by mass spectrometry and ion mobility | ||
Guillaume van der Rest, Human, Rezaei, Frédéric Halgand, Université Paris Sud, Laboratoire de Chimie Physique Prion protein is involved in deadly neurodegenerative diseases. Its pathogenicity is linked to its structural conversion (a-helix to b-strand transition). However, recent studies suggest that prion protein can follow a plurality of conversion pathways which hints towards different conformers that might coexist in solution. We therefore decided to screen the ovine and human PrP monomers using ion mobility coupled to mass spectrometry following electrospray ionization. After a short presentation of ion mobility for studying ionized proteins in the gas phase, we will briefly discuss issues with the collision cross section calibration procedure that we have encountered when using travelling wave ion mobility. We will also discuss the development of an automated data extraction pipeline for which we developed a Python/Qt script base interface. Infusion of monomeric PrP solutions have shown that at least three PrP conformers are observed in the gas phase. PrP monomers are known to lead to the formation of oligomeric species in specific conditions (temperature, pH and buffer), which are not compatible with mass spectrometry. We have therefore developed a size-exclusion chromatography IMS-MS setup with the aim to study the oligomers produced in these conditions. The development of this SEC-IMS-MS methodology will be presented as well as its application for calibration with standard protein complexes. Although we did not achieve resolution of the large (O1 ~36-mer) oligomeric species, optimization of the experimental parameters led to the observation of the small (O3) oligomeric species. One key observation in this process was that the abundance of the gas phase monomeric conformers changed upon the oligomerization process. First results allow us to interpret this as an effect of monomer concentration on the ratio of conformers present in solution, which is observed only in specific buffer conditions. | ||
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| Magali Tournus (University of Marseille, France) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 8. Jun 17, 10:10 |
| Estimating the division rate and kernel in the fragmentation equation. | ||
We consider the pure fragmentation fragmentation equation and address the question of estimating the fragmentation parameters (division rate and fragmentation kernel) from measurements of the size distribution at various times. Under the assumption of a polynomial division rate and a self-similar fragmentation kernel, we use the well-known asymptotic behaviour of the solution to guarantee the well-posedness of our inverse problem and provide a representation formula for the fragmentation kernel. The tools used are the Mellin transform and the Wiener-Hopf method. Motivations for studying this problem and applications to amyloid fibril breakage will be described in the talk of W.F. Xue. | ||
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| Wei-Feng Xue (University of Kent at Canterbury, United Kingdom) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 8. Jun 17, 9:30 |
| Nano-scale properties of amyloid fibril fragments | ||
A number of devastating human disorders, for example Alzheimer's disease (AD), Hungtington's diseases, type 2 diabetes and transmissible spongiform encephalopathies (TSEs), are associated with the abnormal folding and assembly of proteins. The net result of this misfolding is the formation of large insoluble protein deposits and small toxic and transmissible protein particles in a state called amyloid. What are the molecular mechanisms that govern the amyloid fibrils’ potential to seed the formation of new aggregates, to propagate the amyloid state as prion particles, and to damage cells in amyloid-associated diseases? We have developed AFM imaging approaches that are capable of resolving the fibril particle concentrations, their length distributions, as well as their toxic and infective potential to cells. With these approaches, we have shown that the disease-associated properties of amyloid can be linked to small nano-sized amyloid particles created through the breakage of amyloid fibrils. The approaches we have developed offer new opportunities to determine, quantify, and predict the course and the consequences in amyloid assembly of cytotoxic, infectious as well as functional amyloid systems. | ||
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| Nicola Vettore, Institute of Physical Biology, University of Düsseldorf, Germany | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Wed, 7. Jun 17, 17:15 |
| Temperature dependence of amyloid fibril stability studied through equilibrium denaturation | ||
Nicola Vettore and Alexander K. Buell, Institute of Physical Biology, University of Düsseldorf Amyloid fibrils are thermodynamically very stable [1], but the origin of their enhanced stability with respect to the native state has not yet been elucidated in molecular detail. The high stabilities of amyloid fibrils render the study of their equilibrium behaviour challenging. One way to approach this issue, in direct analogy to the study of protein folding equilibria is denaturation with commonly used denaturants, such as GdmCl or Urea. A theoretical framework to extract from such measurements the free energy difference between the fibril state and the soluble state, based on Oosawa's linear polymerisation model, was proposed in [2]. Here we present experimental results of amyloid fibril equilibrium denaturation measured via capillary fluorescence over a wide range of temperatures. The data highlight how the influence of temperature seems of primary importance not only for the kinetics of fibril formation, but also for the thermodynamic stability of the fibrillar structures. We will also present our attempts to describe the temperature-dependence of fibril stability within a general thermodynamic framework. [1] A. J. Baldwin, T. P. J. Knowles, G. G. Tartaglia, A. W. Fitzpatrick, G. L. Devlin, S. L. Shammas, C. A. Waudby, M. F. Mossuto, S. Meehan, S. L. Gras, J. Christodoulou, S. J. Anthony-Cahill, P. D. Barker, M. Vendruscolo, and C. M. Dobson, J. Am. Chem. Soc. 133, 14160 (2011). [2] T. Narimoto, K. Sakurai, A. Okamoto, E. Chatani, M. Hoshino, K. Hasegawa, H. Naiki, and Y. Goto, FEBS Lett. 576, 313 (2004). | ||
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| Mathieu Mézache, Inria Paris and Univ. Pierre et Marie C, France | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Wed, 7. Jun 17, 17:15 |
| An oscillatory kinetic model for the Prion aggregation process. From Belousov-Zhabotinsky reaction to a Prion polymerisation/depolymerisation chemical system. | ||
We investigate the oscillatory behaviour of the PrP protein during the polymerization/depolymerization process. In order to modelize this oscillatory process, we study a simplified Belousov-Zhabotinsky reaction from a kinetic point of view. This simplified oscillatory system of chemical reactions allows us to introduce a modified Becker-Döring system where the trajectories oscillate. A key to have a closed oscillatory polymerization/depolymerization system is to consider different specices of polymers and monomers. We finally present several system where the numerical simulations show a more or less sustained oscillatory behaviour. | ||
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| Angélique Igel-Egalon, INRA Jouy-en-Josas, France | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Wed, 7. Jun 17, 17:15 |
| Depolymerization instead of fragmentation spreads the replication unit of prion assemblies | ||
Reine1, Charles-Adrien Richard1, Tina Knäpple1 Vincent Béringue1* and Human Rezaei1* 1: INRA, UR892, Virologie Immunologie Moléculaires, Jouy-en-Josas 78350, France *: Corresponding authors The prion phenomenon is based on autonomous structural information propagation towards single or multiple protein conformation changes. During this last decade the prion concept referring the transmission of structural information has been extended to several regulation systems and pathologies including Alzheimer and Parkinson’s diseases. Despite intensive investigation, the molecular basis of structural information transmission remains obscure. Templating (i.e. secondary nucleation as vector of structural information) has been proposed as origin of autocatalytic structural information perpetuation. However, the templating process does not consider the spreading process which consists in an exponential amplification of structural information. Active fibril fragmentation (AFF) constitutes a solution for exponential spreading and amplification of the structural information as strongly suggested in fungi prions (Shorter and Lindquist, Mol Cell, 2006). In the present work, we demonstrate that mammalian Prion assemblies (PrPSc) are constituted from an oligomeric elementary brick called suPrP. We show that in physiological conditions Prion assemblies are in equilibrium with suPrP. The existence of such equilibrium as simple depolymerization/condensation process is sufficient to spread the replicative unit through the release of suPrP, followed by its Brownian diffusion and condensation into PrPSc and discards the requirement of fragmentation for prion spreading. | ||
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| Marie Doumic (Inria Paris & Wolfgang Pauli Institute, France & Austria) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Wed, 7. Jun 17, 16:15 |
| Modelling protein polymerisation: results and open questions | ||
Mathematical modelling of protein polymerisation is a challenging topic, with wide applications, from actin filaments in myocytes (muscle tissues) to the so-called amyloid diseases (e.g. Alzheimer's, Parkinson's or Creuzfeldt-Jakob's diseases). In this talk, we will give an overview of recent results for both deterministic - where statistical mechanical fluctuations arising from intrinsic noise are negligible - and stochastic approaches, envisaged as giving complementary insights on the still largely mysterious intrinsic mechanisms of polymerisation. A data assimilation approach is developed in parallel of more specific methods for fragmentation estimation. The results we will present are partly joint work with A. Armiento, J. Calvo, S. Eugène, M. Escobedo, P. Moireau, B. Perthame, H. Rezaei, P. Robert, M. Tournus and W.F. Xue. | ||
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| Christian Schmeiser (University of Vienna and Wolfgang Pauli Institute, Austria) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Wed, 7. Jun 17, 14:10 |
| Homeostatic regulation of actin density at the leading edge of lamellipodia | ||
Some recent contributions to the modeling of the polymerization and depolymerization of actin filaments will be reviewed. Some results of the embedding of these models into the Filament Based Lamellipodium Model will be presented. | ||
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| Sascha Martens (Max F. Perutz Laboratories (MFPL), University of Vienna, Austria) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Wed, 7. Jun 17, 11:20 |
| Mechanism of p62-mediated protein aggregation in selective autophagy | ||
Autophagosomes are double membrane-bound organelles that are formed de novo during a process called autophagy. Autophagosomes mediate the bulk degradation of cytoplasmic material such as aggregated proteins, dysfunctional or surplus mitochondria and intracellular pathogens. Autophagy is conserved from yeast to human and has been shown to protect the organism from conditions such as starvation, neurodegeneration and infectious diseases. During autophagosome formation initially small membrane structures termed isolation membranes are formed. These isolation membranes expand and thereby gradually enclose cytoplasmic cargo. Finally, isolation membranes close to give rise to mature autophagosomes. After their formation autophagosomes fuse with lysosomes within which their inner membranes and the contents are degraded. Autophagy has the ability to selectively capture and subsequently degrade aggregated and ubiquitinated proteins. This is mediated by the p62 cargo receptor, which is required for the aggregation of these proteins into larger structures. These structures then serve as templates for autophagosome formation. I will present our results from a fully reconstituted system, which enabled us to dissect the interplay between p62 and ubiquitin positive proteins during protein aggregation in selective autophagy. | ||
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| Laurent Pujo-Menjouet (University of Lyon, France) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Wed, 7. Jun 17, 10:10 |
| Modelling prion dynamics: a fruitful collaboration between mathematicians and biologists | ||
In a previous work by Alvarez-Martinez et al. (2011), the authors pointed out some fallacies in the mainstream interpretation of the prion amyloid formation. It appeared necessary then to propose an original hypothesis able to reconcile the in vitro data with the predictions of a mathematical model describing the problem. The model presented here, has been developed accordingly with the hypothesis that an intermediate on-pathway leads to the conformation of the prion protein into an amyloid competent isoform thanks to a structure, called micelles, formed from hydrodynamic interaction. Experimental data have been compared to the prediction of our model leading to a new hypothesis for the formation of infectious prion amyloids. In the last part, we will introduce a new model describing another dangerous liaison: the interaction between prion proteins and Abeta peptides that may lead to Alzheimer’s disease. | ||
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| Cassandra Terry, MRC Prion, UCL Institute of Technology, London, United Kingdom | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Wed, 7. Jun 17, 9:30 |
| Structural characterisation of ex vivo mammalian prions. | ||
Cassandra Terrya Adam Wenborna Nathalie Grosa Jessica Sellsa Susan Joinera Laszlo L.P. Hosszua M. Howard Tattuma Silvia Panicob Daniel K. Clareb, John Collingea, Helen R. Saibilb and Jonathan D.F. Wadswortha* a, MRC Prion Unit and Department of Neurodegenerative Disease, UCL Institute of Neurology, Queen Square, London WC1N 3BG, UK b, Institute of Structural and Molecular Biology, Department of Biological Sciences, Birkbeck College, University of London, Malet Street, London WC1E 7HX, UK Prions cause lethal neurodegenerative diseases in mammals, including scrapie in sheep and goats, bovine spongiform encephalopathy (BSE) in cattle and Creutzfeldt–Jakob disease (CJD) in humans. Mammalian prions are hypothesised to be fibrillar or amyloid forms of prion protein (PrP) which self-propagate by means of seeded protein polymerisation but structures observed had not been definitively correlated with infectivity and the three-dimensional structure of prions remained unknown. We developed new methods to obtain pure preparations of intact prions from mouse brain1 and showed that pathogenic PrP is assembled into rod-like assemblies (PrP rods) that faithfully transmit prion strain-specific phenotypes when inoculated into mice. We have utilised the precision of cell culture prion infectivity assays to define the physical relationship between PrP rods and prion infectivity and used electron tomography to define their architecture. Our 3D analysis2 demonstrates that ex vivo infectious PrP rods from different strains observed have a common hierarchical assembly comprising twisted pairs of short fibres with repeating substructure which are markedly different to non-infectious PrP fibrils generated in vitro. References 1. A. Wenborn, C. Terry, N. Gros, S. Joiner, L. D’Castro, S. Panico, J. Sells, S. Cronier, J. Linehan, S. Brandner, H.R. Saibil, J. Collinge, J.D.F Wadsworth, Sci. Rep. A novel and rapid method for obtaining high titre intact prion strains from mammalian brain, 2015, 5, 10062. C. Terry, A. Wenborn, N. Gros, J. Sells, S. Joiner, L.L.P Hosszu, M.H. Tattum, S. Panico, D.K. Clare, J. Collinge, H.R. Saibil, J.D.F Wadsworth. Open Biology. Ex vivo mammalian prions are formed of paired double helical prion protein fibrils, 2016, 6, 160035. | ||
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| Romain Yvinec, INRA Tours, France | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Tue, 6. Jun 17, 16:50 |
| Time scales in a coagulation-fragmentation model} | ||
This work is motivated by protein aggregation phenomena in neurodegenerative diseases. A key observation of in-vitro spontaneous polymerization experiments of prion protein is the large variability of the so-called 'nucleation time', which is experimentally defined as the lag time before the polymerization of proteins truly starts (typically several hours in a 10-20 hours experiment). In this context, we study a stochastic version of a well-known nucleation model in physics, namely the Becker-Döring model [1]. In this model, aggregates may increase or decrease their size one-by-one, by capturing or shedding a single monomer particle. We will present numerical and analytical investigation of the nucleation time defined as a first passage time problem [2, 3]. Finally, we will present limit theorem techniques to study the link from the discrete size Becker-Döring model to a continuous size version (the Lifshitz-Slyozov model), which may be of importance to study large size aggregates formation. For general coefficients and initial data, we introduce a scaling parameter and show that the empirical measure associated to the Becker-Döring system converges in some sense to the Lifshitz-Slyozov equation when the scaling parameter goes to 0. When the aggregation is favorable, we derive a mean-field transport PDE limit together with an entrant boundary condition, leading to an effective reduced dynamical model [4]. When the aggregation is initially unfavorable, we shed light on metastable behavior and phase transition phenomena. [1] E. Hingant, R. Y., arXiv:1609.00697 (2016). [2] R. Y., M. R. D'Orsogna, and T. Chou. J. Chem. Phys., 137:244107, (2012). [3] R. Y., S. Bernard, E. Hingant, L. Pujo-Menjouet, J. Chem. Phys., 144(3):034106, (2016). [4] Julien Deschamps, Erwan Hingant, R.Y., arXiv:1605.08984 (2016). | ||
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| Vincent Béringue (Inra Jouy-en-Josas, France) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Tue, 6. Jun 17, 16:10 |
| Small prion assemblies are involved in prion replication | ||
Angélique Igel-Egalon1¶, Mohammed Moudjou1¶, Florent Laferrière1¶, Tina Knäpple1, Laetitia Herzog1, Fabienne Reine1, Hubert Laude1, Human Rezaei1*, Vincent Béringue1* 1VIM, INRA, Université Paris-Saclay, 78350 Jouy-en-Josas, France ¶Equal contributors, *Senior authorship Mammalian prions are proteinaceous pathogens responsible for fatal, neurodegenerative disorders in human and animals. They are formed of misfolded assemblies (PrPSc) of the host-encoded cellular prion protein (PrPC). In the infected species, prions replicate by seeding the conversion and polymerization of host PrPC. Distinct prion strains are recognized within the same host-species, exhibiting defined PrPSc biochemical properties and stereotyped biological traits. While strain information is encoded within the conformation of PrPSc assemblies, the storage of the structural information and the molecular requirements for self-perpetuation remain uncertain. In particular, the polymerization steps and its dynamic nature remains mostly hypothetical. It is widely believed that monomeric PrPC is constantly recruited within the forming aggregates allowing PrPSc fibril growth. Fibril fragmentation is supposed to provide further converting seeds, favouring prion exponential replication. Whether this proposed mechanism is versatile or strain-dependent remains to be determined, as is the real contribution of fragmentation. We have investigated this issue by analysing the dynamic of PrPSc assembling during cell-free prion amplification by protein misfolding cyclic amplification (PMCA). We show that: i) prion amplification occurs through preferential amplification of small oligomeric forms of PrPSc that can further assemble into larger aggregates; ii) disassembling rather than fragmentation sustains the self-perpetuation of the process, iii) different prion strains exhibit similar amplification dynamic. Thus, prion replication may proceed through an assembly/disassembly process. | ||
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| Klemens Fellner (University of Graz, Austria) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Tue, 6. Jun 17, 15:00 |
| Equilibration and Quasi-Steady-State Asymptotics of a Volume-Surface Reaction-Diffusion Model for Asymmetric Protein Localisation | ||
The protein Lgl (Lethal giant larvae) is part of a conserved protein complex, which is responsible for the asymmetric localisation of cell-fate determinants, for instance, in Drosophila SOP precursor cells. We formulate continuum models, which consider the phosphorylated and the unphosphorylated conformations of Lgl within the cell cytoplasm and on the cell cortex. After presenting illustrative numerical simulations, we prove first the equilibration of the underlying complex-balance volumesurface reaction-diffusion system and perform further a rigorous quasi-steady-state-approximation in a fast-reaction limit. | ||
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| John H Viles, Queen Mary, University of London, United Kingdom | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Tue, 6. Jun 17, 14:20 |
| Co-fibrillisation of truncated isoforms of Amyloid-â and ion-channel formation in Alzheimer’s Disease | ||
Amyloid-â peptide (Aâ) isoforms of different lengths and aggregation propensities coexist in vivo. These different isoforms are able to nucleate or frustrate the assembly of each other. Nterminal truncated Aâ(11-40) and Aâ(11-42) make up one fifth of plaque load yet nothing is known about their interaction with full-length Aâ(1-40/42). Here we show that in contrast to C-terminal truncated isoforms which do not co-fibrillise, deletions of ten residues from the N-terminus of Aâ have little impact on its ability to co-fibrillise with the full-length counterpart. As a consequence N-terminal truncated Aâ will accelerate fibre formation and co-assemble into short rod-shaped fibres with its full-length Aâ counterpart. Furthermore we show Cu2+ forms a very tight tetragonal complex with truncated Aâ(11-40) with a femtomolar affinity. These observations have implications for the assembly kinetics, morphology and toxicity of all Aâ isoforms. The process by which amyloid-â (Aâ) disrupts synaptic activity, and causes neuronal cell death in Alzheimer’s disease remains poorly understood. A potential mechanism of toxicity is in the ability of Aâ to form, membrane-spanning ion channels. However, there has been a mismatch between the channel forming properties of Aâ isoforms, 40 and 42 amino acids long, and their known relative pathogenicity. We observe ion channel formation by oligomeric Aâ42, but also show Aâ40 does not form ion channels in cellular membranes. This makes a strong link between ion channel formation and the pathology of Aâ isoforms. Molecules that block these ion channels may represent therapeutic targets. [1] Ion Channel Formation by Amyloid-â42 Oligomers but not Amyloid-â40 in Cellular Membranes DC Bode, MD Baker, JH Viles* (2017) J of Biol Chem 292, 1404-1413 [2] Truncated Amyloid-â (11-40/42) from Alzheimer's Disease Binds Copper2+ with a Femtomolar Affinity and Influences Fibre Assembly J D Barritt, J H. Viles* (2015) J of Biol Chem, 290, 27791-27802 [3] The Rapid Exchange of Zinc2+ Enables Trace Levels to Profoundly Influence Amyloid-â Misfolding and Dominates Assembly Outcomes in Cu2+/Zn2+ Mixtures C J Matheou, N D Younan, J H Viles* (2016) J Mol Biol 428, 2832-2846 | ||
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| Franca Hoffmann (University of Cambridge) | WPI, OMP 1, Seminar Room 08.135 | Fri, 12. May 17, 11:30 |
| Homogeneous functionals in the fair-competition regime | ||
We study interacting particles behaving according to a reaction-diffusion equation with non-linear diffusion and non-local attractive interaction. This class of equations has a very nice gradient flow structure that allows us to make links to homogeneous functionals and variations of well-known functional inequalities (Hardy-Littlewood-Sobolev inequality, logarithmic Sobolev inequality). Depending on the non-linearity of the diffusion, the choice of interaction potential and the dimensionality, we obtain different regimes. Our goal is to understand better the asymptotic behaviour of solutions in each of these regimes, starting with the fair-competition regime where attractive and repulsive forces are in balance. This is joint work with José A. Carrillo and Vincent Calvez. | ||
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| Sabine Hittmeir (Universität Wien) | WPI, OMP 1, Seminar Room 08.135 | Thu, 11. May 17, 16:15 |
| Cross diffusion models in chemotaxis and pedestrian dynamics | ||
The main feature of the two-dimensional Keller-Segel model is the blow-up behaviour of solutions for supercritical masses. We introduce a regularisation of the fully parabolic system by adding a cross-diffusion term to the equation for the chemical substance. This regularisation provides another helpful entropy dissipation term allowing to prove global existence of weak solutions for any initial mass. For the proof we first analyse an approximate problem obtained from a semi-discretisation and a carefully chosen regularisation by adding higher order derivatives. Compactness arguments are used to carry out the limit to the original system. A similar approach can be used to analyse a pedestrian dynamics model for two groups moving in opposite direction. The evolutionary equations are driven by cohesion and aversion and are formally derived from a 2d lattice based approach. Also numerical simulations illustrating lane formation will be presented. These methods are extended to a crossing pedestrian model, where we additionally analyse the stability of stationary states in the corresponding 1d model. | ||
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| Delphine Salort (UPMC Paris 6) | WPI, OMP 1, Seminar Room 08.135 | Thu, 11. May 17, 14:45 |
| Turing instabilities in reaction-diffusion with fast reaction | ||
In this talk, we consider some specific reaction-diffusion equations in order to understand the equivalence between asymptotic Turing instability of a steady state and backwardness of some parabolic equations or cross-diffusion equations in the formal limit of fat reaction terms. We will see that the structure of the studied equations involves some Lyapunov functions which leads to a priori estimates allowing to pass rigorously for the fast reaction terms in the case without Turing instabilities. | ||
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| Andrea Bondesan (Université Paris Descartes) | WPI, OMP 1, Seminar Room 08.135 | Thu, 11. May 17, 14:00 |
| A numerical scheme for the multi-species Boltzmann equation in the diffusion limit: well-posedness and main properties | ||
We consider the one-dimensional multi-species Boltzmann system of equations [2] in the diffusive scaling. Suppose that the Mach and the Knudsen numbers are of the same order of magnitude epsilon > 0 small enough. For each species i of the mixture, we define the macroscopic quantity of matter and flux as the moments 0 and 1 in velocity of the distribution functions f_i, solutions of the Boltzmann system associated to the scaling parameter epsilon. Using the moment method [4], we introduce a proper ansatz for each distribution function f_i in order to recover a Maxwell-Stefan diffusion limit-type as in [1]. In this way we build a suitable numerical scheme for the evolution of these macroscopic quantities in different regimes of the parameter epsilon. We prove some a priori estimates (mass conservation and nonnegativity) and well-posedness of the discrete problem. We also present numerical examples where we observe that the scheme shows an asymptotic preserving property similar to the one presented in [3]. This is a joint work with L. Boudin and B. Grec. References [1] L. Boudin, B. Grec and V. Pavan, The Maxwell-Stefan diffusion limit for a kinetic model of mixtures with general cross sections, Nonlinear Analysis: Theory, Methods and Applications, 2017. [2] L. Desvillettes, R. Monaco and F. Salvarani, A kinetic model allowing to obtain the energy law of polytropic gases in the presence of chemical reactions, Eur. J. Mech. B Fluids, 24(2005), 219-236. [3] S. Jin and Q. Li, A BGK-penalization-based asymptotic-preserving scheme for the multispecies Boltzmann equation, Numer. Methods Partial Differential Equations, 29(3), pp. 1056-1080, 2013. [4] C. D. Levermore, Moment closure hierarchies for kinetic theories, J. Statist. Phys., 83(5-6):1021-1065, 1996 | ||
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| Athmane Bakhta (École Nationale des Ponts et Chaussées) | WPI, OMP 1, Seminar Room 08.135 | Thu, 11. May 17, 11:30 |
| Cross-diffusion equations in a moving domain | ||
We show global-in-time existence of bounded weak solutions to systems of cross-diffusion equations in a one dimensional moving domain. These equations stem from the modelization of the evolution of the concentration of chemical species composing a crystalline solid during a physical vapor deposition process. To this aim, we use the so called boundedness-by-entropy technique developed in [1], [2] and [3] based on the formal gradient flow structure of the system. Moreover, we are interested in controlling the fluxes of the different atomic species during the process in order to reach a certain desired final profile of concentrations. This problem is formulated as an optimal control problem to which the existence of a solution is proven. In addition, an investigation of the long time behavior is presented in the case of constant positive external fluxes. Finally, some numerical results and comparison with actual experiments are presented. The material of this talk is a joint work with Virginie Ehrlacher. References [1] M.Burger, M.Di Francesco, J-F. Pietschmann and B. Schalke. Non linear cross diffusion with size exclusion. SIAM J. Math Anal 42 (2010). [2] A. Jüngel and Nicola Zamponi boundedness of weak solutions to cross-diffusion systems from population dynamics. arxiv:1404.6054v1 (2014). [3] A. Jüngel. The boundedness-by-entropy method for cross-diffusion systems. To appear in Nonlinearity, http://www.asc.tuwien.ac.at/ juengel/ (2015). | ||
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| Esther Daus (Université Paris 7 - Denis Diderot) | WPI, OMP 1, Seminar Room 08.135 | Thu, 11. May 17, 10:15 |
| Cross-diffusion systems and fast-reaction limit | ||
We investigate the rigorous fast-reaction limit from a reaction-cross-diffusion system with known entropy to a new class of cross-diffusion systems using entropy and duality estimates. Performing the fast-reaction limit leads to a limiting entropy of the limiting cross-diffusion system. In this way, we are able to obtain new entropies for new classes of cross-diffusion systems. This is a joint work with L. Desvillettes and A. Juengel. | ||
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| Thomas Lepoutre (INRIA) | WPI, OMP 1, Seminar Room 08.135 | Thu, 11. May 17, 9:30 |
| Entropy, duality and cross-diffusion | ||
In this talk, we will describe how to mix entropy structure and duality estimates in order to build global weak solutions to a class of cross-diffusion systems. | ||
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| Nicola Zamponi (TU Wien) | WPI, OMP 1, Seminar Room 08.135 | Wed, 10. May 17, 16:15 |
| Analysis of degenerate cross-diffusion population models with volume filling | ||
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk lattice model in the diffusion limit. Compared to previous results in the literature, the novelty is the combination of general degenerate diffusion and volume-filling effects. Conditions on the nonlinear diffusion coefficients are identified, which yield a formal gradient-flow or entropy structure. This structure allows for the proof of global-in-time existence of bounded weak solutions and the exponential convergence of the solutions to the constant steady state. The existence proof is based on an approximation argument, the entropy inequality, and new nonlinear Aubin-Lions compactness lemmas. The proof of the large-time behavior employs the entropy estimate and convex Sobolev inequalities. Moreover, under simplifying assumptions on the nonlinearities, the uniqueness of weak solutions is shown by using the H^{-1} method, the E-monotonicity technique of Gajewski, and the subadditivity of the Fisher information. | ||
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| Gianni Pagnini (BCAM) | WPI, OMP 1, Seminar Room 08.135 | Wed, 10. May 17, 14:45 |
| Stochastic processes for fractional kinetics with application to anomalous diffusion in living cells | ||
Fractional kinetics is derived from Gaussian processes when the medium where the diffusion takes place is characterized by a population of length-scales [1]. This approach is analogous to the generalized grey Brownian motion [2], and it can be used for modeling anomalous diffusion in complex media. In particular, the resulting stochastic process can show sub-diffusion with a behavior in qualitative agreement with single-particle tracking experiments in living cells, such as the ergodicity breaking, p variation, and aging. Moreover, for a proper distribution of the length-scales, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from nonfractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking [3]. References: [1] Pagnini G. and Paradisi P., A stochastic solution with Gaussian stationary increments of the symmetric space-time fractional diffusion equation. Fract. Cacl. Appl. Anal. 19, 408–440 (2016) [2] Mura A. and Pagnini G., Characterizations and simulations of a class of stochastic processes to model anomalous diffusion. J. Phys. A: Math. Theor. 41, 285003 (2008) [3] Molina–García D., Pham T. Minh, Paradisi P., Manzo C. and Pagnini G., Fractional kinetics emerging from ergodicity breaking in random media. Phys. Rev. E. 94, 052147 (2016) | ||
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| María José Cáceres (Universidad de Granada) | WPI, OMP 1, Seminar Room 08.135 | Wed, 10. May 17, 14:00 |
| Mesoscopic models for neural networks | ||
In this talk we present some PDE models which describe the activity of neural networks by means of the membrane potential. We focus on models based on nonlinear PDEs of Fokker-Planck type. We study the wide range of phenomena that appear in this kind of models: blow-up, asynchronous/synchronous solutions, instability/stability of the steady states ... | ||
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| Fellner Klemens (University of Graz) | WPI, OMP 1, Seminar Room 08.135 | Fri, 24. Mar 17, 15:10 |
| Regularity and Equilibration for spatially inhomogeneous coagulation-fragmentation models | ||
We consider results on discrete and continuous coagulation and coagulation-fragmentation models. For discrete models, we shall present some recent regularity results concerning smoothness of moments and absence of gelation. For the continuous Smoluchowski equation with constant rates, we shall prove exponential, resp. superlinear convergence to equlibrium. This are joint works with M. Breden, J.A. Canizo, J.A. Carrillo and L. Desvillettes. | ||
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| Cañizo José A. (University of Granada, Spain) | WPI, OMP 1, Seminar Room 08.135 | Fri, 24. Mar 17, 14:30 |
| Asymptotic behaviour of the Becker-Döring equations | ||
We will present some recent results on the long behaviour of the Becker-Döring equations, mainly involving subcritical solutions: speed of convergence to equilibrium (sometimes exponential, sometimes algebraic) and some new uniform bounds on moments. We will also comment on a continuous model that serves as an analogy of the discrete equations, that seems to exhibit a similar long-time behaviour. This talk is based on collaborations with J. Conlon, A. Einav, B. Lods and A. Schlichting. | ||
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| Salort Delphine (University Pierre & Marie Curie, Paris, France) | WPI, OMP 1, Seminar Room 08.135 | Fri, 24. Mar 17, 11:40 |
| Fragmentation Equations and Fokker-Planck equations in neuroscience | ||
In this talk, we present two types of linked partial differential equation models that describe the evolution of an interacting neural network and where neurons interact with one another through their common statistical distribution. We will show, according to the choice of EDP studied, what information can be obtained in terms of synchronization phenomena, qualitative and asymptotic properties of these solutions and what are the specific difficulties on each of these models. | ||
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| Banasiak Jacek (University of Pretoria, South Africa) | WPI, OMP 1, Seminar Room 08.135 | Fri, 24. Mar 17, 11:10 |
| Analytic fragmentation semigroups and discrete coagulation-fragmentation processes with growth | ||
In the talk we shall describe how the substochastic semigroup theory can be used to prove analyticity of a class of fragmentation semigroup. This result is applied to discrete fragmentation processes with growth to analyze their long time behaviour and to prove the existence of classical solutions to equations describing such processes combined with coagulation. | ||
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| Laurençot Philippe (Institut de Mathématiques de Toulouse, France) | WPI, OMP 1, Seminar Room 08.135 | Fri, 24. Mar 17, 10:10 |
| Self-similar solutions to coagulation-fragmentation equations | ||
When the coagulation kernel and the overall fragmentation rate are homogeneous of degree ë and ã > 0, respectively, there is a critical value ëc := ã + 1 which separates two different behaviours: all solutions are expected to be mass-conserving when ë < ëc while gelation is expected to take place when ë > ëc, provided the mass of the initial condition is large enough. The focus of this talk is the case ë = ëc for which we establish the existence of mass-conserving self-similar solutions. This is partly a joint work with Henry van Roessel (Edmonton). | ||
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| Niethammer Barbara (Institut for applied mathematics, Bonn, Germany) | WPI, OMP 1, Seminar Room 08.135 | Fri, 24. Mar 17, 9:30 |
| The coagulation equation: kernels with homogeneity one | ||
The question whether the long-time behaviour of solutions to Smoluchowski's coagulation equation is characterized by self-similar solutions has received a lot of interest within the last two decades. While this issue is by now well-understood for the three solvable cases, the theory for non-solvable kernels is much less developed. For kernels with homogeneity smaller than one existence results for self-similar solutions and some partial uniqueness results are available. In this talk I will report on some recent results on the borderline case of kernels with homogeneity of degree one. For so-called class II kernels we can prove the existence of a family of self-similar solutions. For class I, or diagonally dominant, kernels, it is known that self-similar solutions cannot exist. Formal arguments suggest that the long-time behaviour of solutions is, in suitable variables, to leading order the same as for the Burgers equation. However, in contrast to diffusive regularizations, we obtain phenomena such as instability of the constant solution or oscillatory traveling waves. (Joint work with Marco Bonacini, Michael Herrmann and Juan Velazquez) | ||
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| Gwiazda Piotr (Polish academy of sciences, Poland) | WPI, OMP 1, Seminar Room 08.135 | Thu, 23. Mar 17, 16:40 |
| Relative entropy method for measure solutions in mathematical biology | ||
In the last years there has appeared several applications of relative entropy method for strong measure-valued uniqueness of solutions in physical models (see: e.g. incompressible Euler equation [1], polyconvex elastodynamics [2], compressible Euler equation [3], compressible Navier-Stokes equation [4]). The topic of the talk will be application of similar techniques to structured population models. Preliminary result in this direction was obtain in [5]. The talk is based on the joint result with Marie Doumic-Jauffret and Emil Wiedemann. [1] Y. Brenier, C. De Lellis, and L. Sz´ekelyhidi, Jr. Weak-strong uniqueness for measure-valued solutions. Comm. Math. Phys., 305(2):351--361, 2011. [2] S. Demoulini, D.M.A. Stuart, and A.E. Tzavaras. Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics. Arch. Ration. Mech. Anal., 205(3):927--961, 2012. [3] P. Gwiazda, A. Œwierczewska-Gwiazda, and E. Wiedemann. Weak-strong uniqueness for measure-valued solutions of some compressible fluid models. Nonlinearity, 28(11):3873--3890, 2015. [4] E. Feireisl, P. Gwiazda, A. Œwierczewska-Gwiazda and E. Wiedemann Dissipative measure-valued solutions to the compressible Navier-Stokes system, Calc. Var. Partial Differential Equations 55 (2016), no. 6, 55--141 [5] P. Gwiazda, E. Wiedemann, Generalized Entropy Method for the Renewal Equation with Measure Data, to appear in Commun. Math. Sci., arXiv:1604.07657 | ||
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| Van Brunt Bruce (Massey university, New Zealand) | WPI, OMP 1, Seminar Room 08.135 | Thu, 23. Mar 17, 16:00 |
| Analytic solutions to certain equations from a cell division equation | ||
Click here for further information | ||
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| Haas Bénédicte (University of Paris XIII, France) | WPI, OMP 1, Seminar Room 08.135 | Thu, 23. Mar 17, 14:40 |
| The fragmentation equation with shattering | ||
We consider fragmentation equations with non-conservative solutions, some mass being lost to a dust of zero-mass particles as a consequence of an intensive splitting. Under assumptions of regular variation on the fragmentation rate, we describe the large time behavior of solutions. Our approach is based on probabilistic tools: the solutions to the fragmentation equations are constructed via non-increasing self-similar Markov processes that continuously reach 0 in finite time. We describe the asymptotic behavior of these processes conditioned on non-extinction and then deduced the asymptotics of solutions to the equation. | ||
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| Bertoin Jean (University of Zürich, Switzerland) | WPI, OMP 1, Seminar Room 08.135 | Thu, 23. Mar 17, 14:00 |
| A probabilistic approach to spectral analysis of growth-fragmentation equations (based on a joint work with Alex Watson, Manchester University) | ||
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach to the study of this asymptotic behaviour. We use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the spectral radius and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual. In special cases, we obtain exponential convergence. | ||
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| Gabriel Pierre (University of Versailles-Saint-Quentin, France) | WPI, OMP 1, Seminar Room 08.135 | Thu, 23. Mar 17, 11:10 |
| Long time behaviour of growth-fragmentation equations | ||
Growth-fragmentation equations can exhibit various asymptotic behaviours. In this talk we illustrate this diversity by working in suitable weighted L^p spaces which are associated to entropy functionals. We prove that, depending on the choice of the coefficients, the following behaviours can happen: uniform exponential convergence to the equilibrium, non-uniform convergence to the equilibrium, or convergence to periodic solutions. This is a joint work with Etienne Bernard and Marie Doumic. | ||
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| Mischler Stéphane (University Paris-Dauphine, France) | WPI, OMP 1, Seminar Room 08.135 | Thu, 23. Mar 17, 10:30 |
| Long time asymptotic of the solutions to the growth-fragmentation equation | ||
I will discuss the long time asymptotic of the solutions to the growthfragmentation equation, presenting several results and approaches. I will then focus on the spectral analysis and semigroup approach for which I will give some more details about the proof. | ||
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| Buszkowski Wojciech (Adam Mickiewicz University) | WPI, OMP 1, Seminar Room 08.135 | Wed, 15. Mar 17, 10:00 |
| Some open problems in substructural logics | ||
I will focus on several substructural logics, mainly conservative extensions of the Lambek calculus (associative and nonassociative, with and without constants) and point out some basic open problems. Examples: the lower bound of the complexity of the full nonassociative Lambek calculus, the decidability of Pratt's action logic, the decidability of the consequence relation for the nonassociative Lambek calculus with involutive negations, the decidability of the equational theory of lattice-ordered pregroups. I will briefly discuss what is known in these areas. | ||
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| Brotherston James (University College London) | WPI, OMP 1, Seminar Room 08.135 | Tue, 14. Mar 17, 10:00 |
| Biabduction (and Related Problems) in Array Separation Logic | ||
I describe array separation logic (ASL), a variant of separation logic in which the data structures are either pointers or arrays. This logic can be used, e.g., to give memory safety proofs of imperative array programs. The key to automatically inferring specifications is the so-called "biabduction" problem, given formulas A and B, find formulas X and Y such that A + X |= B + Y (and such that A + X is also satisfiable), where + is the well-known "separating conjunction" of separation logic. We give an NP decision procedure for this problem that produces solutions of reasonable quality, and we also show that the problem of finding a consistent solution is NP-hard. Along the way, we study satisfiability and entailment in our logic, giving decision procedures and complexity bounds for both problems. This is joint work with Nikos Gorogiannis (Middlesex) and Max Kanovich (UCL). | ||
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| Zhang Yong (WPI c/o Courant & NJIT) | WPI, OMP 1, Seminar Room 08.135 | Wed, 8. Mar 17, 13:45 |
| Analysis-based fast algorithms for convolution-type nonlocal potential in Nonlinear Schrödinger equation | ||
Convolution-type potential are common and important in many science and engineering fields. Efficient and accurate evaluation of such nonlocal potentials are essential in practical simulations.In this talk, I will focus on those arising from quantum physics/chemistry and lightning-shield protection, including Coulomb, dipolar and Yukawa potentials that are generated by isotropic and anisotropic smooth and fast-decaying density. The convolution kernel is usually singular or discontinuous at the origin and/or at the far field, and density might be anisotropic, which together present great challenges for numerics in both accuracy and efficiency. The state-of-art fast algorithms include Wavelet based Method(WavM), kernel truncation method(KTM), NonUniform-FFT based method(NUFFT) and Gaussian-Sumbased method(GSM). Gaussian-sum/exponential-sum approximation and kernel truncation technique, combined with finite Fourier series and Taylor expansion, finally lead to a O(NlogN) fast algorithm achieving spectral accuracy. Applications to NLSE are reviewed. | ||
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| Blanes Sergio (U. Politècnica de València) | WPI, OMP 1, Seminar Room 08.135 | Tue, 7. Mar 17, 17:15 |
| Time average on the numerical integration of non-autonomous differential equations | ||
Click here for further information | ||
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| Casas Fernando (U. Jaume I Castellón) | WPI, OMP 1, Seminar Room 08.135 | Tue, 7. Mar 17, 16:15 |
| Time dependent perturbation theory in matrix mechanics and time averaging | ||
Click here for further information | ||
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| Lode Axel (U. of Basel) | ATI; Stadionallee 2, 1020 Wien | Thu, 9. Feb 17, 11:00 |
| The multiconfigurational time-dependent Hartree method for indistinguishable particles -- overview and application to composite fragmentation of ultracold multicomponent bosons | ||
In this talk, I will review recent research and progress using the multiconfigurational time-dependent Hartree for indistinguishable particles method to obtain highly accurate solutions of the time-dependent many-body Schr"odinger equation for interacting, indistinguishable particles. As an example, I will focus on ultracold bosonic particles with internal degrees of freedom described by the multiconfigurational time-dependent Hartree for bosons method. For the groundstate of N=100 parabolically confined bosons with two internal states, fragmentation emerges as a function of the separation between the state-dependent minima of the two parabolic potentials: for small separations, the bosons occupy only one single-particle state while for larger separations, two single-particle states contribute macroscopically. The coherence of the system is maintained within each internal state of the atoms. Between the different internal states, however, correlations are built up and the coherence is lost for larger separations. This is a hallmark of a new kind of fragmentation -- "composite fragmentation" -- which is absent in bosons without internal structure. | ||
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| Golse François (Ecole polytechnique, Paris) | WPI, OMP 1, Seminar Room 08.135 | Fri, 16. Dec 16, 14:00 |
| Quantization of probability densities : a gradient flow approach | ||
Quantization of probability densities on the Euclidean space refers to the approximation of a probability measure that is absolutely continuous with respect to the Lebesgue measure by convex combination of Dirac measures. The quality of the approximation is measured in terms of a distance metrizing the weak convergence of probability measures, typically a Monge-Kantorovich (or Vasershtein) distance. The talk with describe a gradient flow approach to the quantization problem in the limit as the number of points goes to infinity. (Work in collaboration with E. Caglioti and M. Iacobelli). | ||
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| Ayi Nathalie (U.Nice & INRIA) | WPI, OMP 1, Seminar Room 08.135 | Fri, 16. Dec 16, 10:45 |
| From Newton's law to the linear Boltzmann equation without cut-off | ||
We provide a rigorous derivation of the linear Boltzmann equation without cut-off starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. The main difficulty in this context is that, due to the infinite range of the potential, a non-integrable singularity appears in the angular collision kernel, making no longer valid the single-use of Lanford's strategy. On this talk, I will present how a combination of Lanford's strategy, of tools developed recently by Bodineau, Gallagher and Saint-Raymond to study the collision process and of new duality arguments to study the additional terms associated with the infinite range interaction (leading to some explicit weak estimates) overcomes this difficulty. | ||
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| Jabin Pierre-Emmanuel (U. Maryland) | WPI, OMP 1, Seminar Room 08.135 | Fri, 16. Dec 16, 9:30 |
| Mean field limits for 1st order systems with bounded stream functions | ||
We consider a large systems of first order coupled equations. The system model the interaction ofdiffusive particles through a very rough force field, which can be the derivative of a bounded stream function. Through a new, modified law of large numbers, we are able to give quantitative estimates between any statistical marginal of the discrete solution and the mean field limit. We are also able to extend the method to cover the case of the 2d incompressible Navier-Stokes system in the vorticity formulation. | ||
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| Napiorkowski Marcin (IST, Austria) | WPI, OMP 1, Seminar Room 08.135 | Thu, 15. Dec 16, 15:15 |
| Norm approximation for many-body quantum dynamics | ||
Starting from the many-body Schroedinger equation for bosons, I will discuss the rigorous derivation of the Hartree equation for the condensate and the Bogoliubov equation for the excited particles. The effective equations allows us to construct an approximation for the many-body wave function in norm. This talk is based on joint works with Phan Thanh Nam. | ||
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| Saffirio Chiara (U. Zürich) | WPI, OMP 1, Seminar Room 08.135 | Thu, 15. Dec 16, 14:00 |
| Mean field evolution of fermions with Coulomb interaction | ||
We will consider the many-body evolution of initially confined fermions in a joint mean-field and semiclassical scaling, focusing on the case of Coulomb interaction. We will show that, for initial states close to Slater determinants and under some conditions on the solution of the time-dependent Hartree-Fock equation, the many-body evolution converges towards the Hartree-Fock dynamics. This is a joint work with M. Porta, S. Rademacher and B. Schlein. | ||
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| Pickl Peter (U. Munich) | WPI, OMP 1, Seminar Room 08.135 | Thu, 15. Dec 16, 11:00 |
| Microscopic Derivation of the Vlasov equation | ||
The rigorous derivation of the Vlasov equation from Newtonian mechanics of N Coulomb-interacting particles is still an open problem. In the talk I will present recent results, where an N-dependent cutoff is used to make the derivation possible. The cutoff is removed as the particle number goes to infinity. Our result holds for typical initial conditions, only. This is, however, not a technical assumption: one can in fact prove deviation from the Vlasov equation for special initial conditions for the system we consider. | ||
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| Bardos Claude (Lab. J.-L. Lions, Paris & WPI) & Mauser Norbert J. (WPI c/o U.Wien) | WPI, OMP 1, Seminar Room 08.135 | Thu, 15. Dec 16, 10:00 |
| Discussion of some open problems in many particle systems | ||
Discussion of history, methdods and open problems in mean field limits. | ||
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| Tournus Magali (École Centrale de Marseille) | Oskar-Morgenstern-Platz 1, Hörsaal 2, ground floor. | Wed, 23. Nov 16, 14:15 |
| Scalar conservation laws with heterogeneous flux in the BV framework | ||
We consider a scalar conservation law with a flux containing spatial heterogeneities of bounded variation, where the number of discontinuities may be infinite. We address the question of existence of an adapted entropy solution in the BV framework. A sufficient key condition guaranteeing existence is identified and new BV estimates are given. This provides the most general BV theory available. Moreover, we show with a counter-example that if this hypothesis is violated, the problem may be ill-posed in the BV framework. | ||
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| Bob Eisenberg (U. Rush Chicago) | WPI, OMP 1, Seminar Room 08.135 | Fri, 11. Nov 16, 11:00 |
| "Ions in Solutions and Channels: the plasma of life" | ||
All of biology occurs in ionic solutions that are plasmas in both the physical and biological meanings of the word. The composition of these ionic mixtures has profound effects on almost all biological functions, whether on the length scale of organs like the heart or brain, of the length scale of proteins, like enzymes and ion channels. Ion channels are proteins with a hole down their middle that conduct ions (spherical charges like Na+ , K+ , Ca2+ , and Clƒ{ with diameter ~ 0.2 nm) through a narrow tunnel of fixed charge (¡¥doping¡¦) with diameter ~ 0.6 nm. Ionic channels control the movement of electric charge and current across biological membranes and so play a role in biology as significant as the role of transistors in computers: almost every process in biology is controlled by channels, one way or the other. Ionic channels are manipulated with the powerful techniques of molecular biology in hundreds of laboratories. Atoms (and thus charges) can be substituted a few at a time and the location of every atom can be determined in favorable cases. Ionic channels are one of the few living systems of great importance whose natural biological function can be well described by a tractable set of equations. Ions can be studied as complex fluids in the tradition of physical science although classical treatments as simple fluids have proven inadequate and must be abandoned in my view. Ion channels can be studied by Poisson-Drift diffusion equations familiar in plasma and semiconductor physics ¡X called Poisson Nernst Planck or PNP in biology. Ions have finite size and so the Fermi distribution must be introduced to describe their filling of volume. The PNP-Fermi equations form an adequate model of current voltage relations in many types of channels under many conditions if extended to include correlations, and can even describe ¡¥chemical¡¦ phenomena like selectivity with some success. My collaborators and I have shown how the relevant equations can be derived (almost) from stochastic differential equations, and how they can be solved in inverse, variational, and direct problems using models that describe a wide range of biological situations with only a handful of parameters that do not change even when concentrations change by a factor of 107. Variational methods hold particular promise as a way to solve problems outstanding for more than a century because they describe interactions of ¡¥everything with everything¡¦ else that characterize ions crowded into channels. An opportunity exists to apply the well established methods of computational physics to a central problem of computational biology. The plasmas of biology can be analyzed like the plasmas of physics. | ||
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| Piotr Gwiazda (U. Warsaw) | Oskar-Morgenstern-Platz 1, Hörsaal 2, ground floor. | Wed, 9. Nov 16, 14:15 |
| "Mathematical scandal - Euler equations" | ||
In the recent years a significant attention has been directed again to Euler system, which was derived more than 250 years ago by Euler. The system describes the motion of an inviscid fluid. The main attention has been directed to incompressible fluids. Nevertheless, also the system of compressible fluids is an emerging topic, however still very far from a complete understanding. The classical results of Scheffer and Schnirelman pointed out the problem of non-uniqueness of distributional solutions to incompressible Euler system. However the crucial step appeared to be an application of methods arising from differential geometry, namely the celebrated theorem by Nash and Kuiper. This brought Camillo De Lellis and Laszlo Szekelyhidi Jr. in 2010 to the proof of existence of bounded nontrivial compactly supported in space and time solutions of the Euler equations (obviously not conserving physical energy!), basing on the Baire category method, which was highly non-standard kind of proof used in the theory of PDEs. Without a doubt this result is a first step towards the conjecture of Lars Onsager, who in his 1949 paper about the theory of turbulence asserted the existence of such solutions for any Hoelder exponent up to 1/3. As a result very much related to the Onsager conjecture one can find the result of P. Constantin, W. E and E. Titi for incompressible flow proving the energy conservation for any Hoelder exponent above 1/3. Our talk is based on several resent results joint with Eduard Feireisl and Emil Wiedemann and concerns various notions of solutions to compressible Euler equations and some systems of a similar structure. | ||
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| Vuk Milisic (U. Paris 13) | WPI, OMP 1, Seminar Room 08.135 | Fri, 21. Oct 16, 11:00 |
| "Mathematical modelling of cell adhesion Forces: From delay to fricition, from global to local existence" | ||
In this talk we present the starting mechanical model of the lamellipodial actin-cytoskeleton meshwork. The model is derived starting from the microscopic description of mechanical properties of filaments and cross-links and also of the life-cycle of cross-linker molecules. We introduce a simplified system of equations that accounts for adhesions created by a single point on which we apply a force. We present the non-dimensionalisation that led to a singular limit motivating our mathematical study. Then we explain the mathematical setting and results already published. In the last part we present the latest developments: we give results for the fully coupled system with unbounded non-linear off-rates. This leads to two possible regimes: under certain hypotheses on the data there is global existence, out of this range we are able to prove blow-up in finite time. | ||
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| Chris Rogers (U. Cambridge) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Fri, 23. Sep 16, 17:30 |
| "High-frequency data: why are we looking at this?" | ||
High-frequency financial data is certainly a `big data' problem, with all of the associated issues: what are the stylized facts of the data? what are we trying to do with the data? what are appropriate models? Industry approaches get the first two of these questions, but do badly on the third. Most academic studies do badly on all three. For example, it is a fairy tale that we can propose a time-invariant model for the evolution of high-frequency data, estimate the parameters of this model, and then apply the conclusions of an analysis that assumes that the paramters were known with certainty. In this talk, I will try to identify what we might want to do with high-frequency data, critique some existing research agendas, and illustrate a possible way of dealing with the problem of optimally liquidating a given position before a given time. | ||
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| Mark Podolskij (U. Aarhus) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Fri, 23. Sep 16, 16:30 |
| "Testing for the maximal rank of the volatility process in noisy diffusion models" | ||
In this talk we present a test for the maximal rank of the volatility process in continuous diffusion models observed with noise. Such models are typically applied in mathematical finance, where latent price processes are corrupted by microstructure noise at ultra high frequencies. Using high frequency observations we construct a test statistic for the maximal rank of the time varying stochastic volatility process. We will show the asymptotic mixed normality of the test statistic and obtain a consistent testing procedure. Finally, we demonstrate some numerical and empirical illustrations. | ||
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| Albert Menkveld (VU. Amsterdam) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Fri, 23. Sep 16, 15:00 |
| "High-Frequency Trading around Large Institutional Orders" | ||
Liquidity suppliers lean against the wind. We analyze whether high-frequency traders (HFTs) lean against large institutional orders that execute through a series of child orders. The alternative is that HFTs go “with the wind” and trade in the same direction. We find that HFTs initially lean against orders but eventually turn around and go with them for long-lasting orders. This pattern explains why institutional trading cost is 46% lower when HFTs lean against the order (by one standard deviation) but 169% higher when they go with it. Further analysis supports recent theory, suggesting HFTs “back-run” on informed orders. | ||
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| Philip Protter (U. Columbia) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Fri, 23. Sep 16, 14:00 |
| "High Frequency Trading and Insider Trading" | ||
The attorney general for New York State, Eric Schneiderman, said at one point that he believed that high frequency trading (in the sense of co-location, that is to say extremely high frequency trading) is used for insider trading. Inspired by his remarks we purport to indicate via a mathematical model how this could come to pass. We use the newly developed theory (by Y. Kchia and this speaker) on the enlargement of filtrations via a stochastic process to show how continual infinitesimal peaks at the order book can beget a type of insider trading, thereby explaining the casual observation of the attorney general. | ||
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| Mathieu Rosenbaum (U. Paris VI) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Fri, 23. Sep 16, 11:30 |
| "How to predict the consequences of a tick value change? Evidence from the Tokyo Stock Exchange pilot program" | ||
The tick value is a crucial component of market design and is often considered the most suitable tool to mitigate the effects of high frequency trading. The goal of this paper is to demonstrate that the approach introduced in Dayri and Rosenbaum (2015) allows for an ex ante assessment of the consequences of a tick value change on the microstructure of an asset. To that purpose, we analyze the pilot program on tick value modifications started in 2014 by the Tokyo Stock Exchange in light of this methodology. We focus on forecasting the future cost of market and limit orders after a tick value change and show that our predictions are very accurate. Furthermore, for each asset involved in the pilot program, we are able to de ne (ex ante) an optimal tick value. This enables us to classify the stocks according to the relevance of their tick value, before and after its modification. This is joint work with Charles-Albert Lehalle and Weibing Huang. | ||
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| Hung Luong (U. Wien) | WPI, OMP 1, Seminar Room 08.135 | Fri, 23. Sep 16, 10:30 |
| "Zakharov-Rubenchik/Benney-Roskes system on the background of a line soliton" | ||
In order to study the transverse (in) stability of a line soliton, we consider the 2-d Zakharov-Rubenchik/Benney-Roskes system with initial data localized by a line soliton. The new terms in perturbed system lead to some diculties, for example, the lack of mass conservation. In this talk, I will present our recent work on this problem. This is a joint work with Norbert Mauser and Jean-Claude Saut. 1 | ||
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| Torben G. Andersen (U. Northwestern) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Fri, 23. Sep 16, 10:00 |
| "Intraday Trading Invariance in Foreign Exchange Futures" | ||
Prior work of Andersen, Bondarenko, Kyle and Obizhaeva (2015) establishes that the intraday trading patterns in the E-mini S&P 500 futures contract are consistent with the following invariance relationship: The return variation per transaction is log-linearly related to trade size, with a slope coefficient of -2. This association applies both across the intraday diurnal pattern and across days in the time series. The factor of proportionality deviates sharply from prior hypotheses relating volatility to transactions count or trading volume. This paper documents that a similar invariance relation holds for foreign exchange futures. However, the log-linear association is not fixed, but shifts over time reflecting an, all else equal, declining trend in the average trade size. The findings are remarkably robust across the full set of currency contracts explored, providing challenges to market microstructure research to rationalize these tight intraday and intertemporal interactions among key market activity variables. Co-authored with Oleg Bondarenko, University of Illinois at Chicago. | ||
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| Felipe Linares (IMPA) | WPI, OMP 1, Seminar Room 08.135 | Fri, 23. Sep 16, 9:30 |
| "On special regularity properties of solutions to the k-generalized Korteweg-de Vries equation" | ||
We will discuss special regularity properties of solutions to the IVP associated to the k-generalized KdV equations. We show that for data u0 2 H3=4+(R) whose restriction belongs to Hk((b;1)) for some k 2 Z+ and b 2 R, the restriction of the corresponding solution u(; t) belongs to Hk(( ;1)) for any 2 R and any t 2 (0; T). Thus, this type of regularity propagates with in nite speed to its left as time evolves. This kind of regularity can be extended to a general class of nonlinear dispersive equations. Recently, we proved that the solution ow of the k-generalized KdV equation does not preserve other kind of regularities exhibited by the initial data u0. | ||
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| Pete Kyle (U. Maryland) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Fri, 23. Sep 16, 9:00 |
| "Dimensional Analysis and Market Microstructure Invariance" | ||
In this talk we focus on the combination of dimensional analysis, leverage neutrality, and a principle of market microstructure invariance to derive scaling laws expressing transaction costs functions, bid-ask spreads, bet sizes, number of bets, and other financial variables in terms of dollar trading volume and volatility. The scaling laws are illustrated using data on bid-ask spreads and number of trades for Russian stocks. These scaling laws provide useful metrics for risk managers and traders; scientific benchmarks for evaluating controversial issues related to high frequency trading, market crashes, and liquidity measurement; and guidelines for designing policies in the aftermath of financial crisis. | ||
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| Jean-Philippe Bouchaud (CFM, Paris) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 22. Sep 16, 18:00 |
| "The square root law of Price Impact and the intrinsic fragility of financial markets" | ||
We will review the accumulating empirical evidence for an approximately square-root impact of a metaorder. Interestingly, this square-root law appears to be universal, i.e. to a large extent ndependent of markets (futures, equities, volatility, Bitcoin), microstructure and epochs (pre and post HFT). This suggests that this law must originate from a simple and robust statistical mechanism. We propose a dynamical theory of the latent market liquidity that predicts that the average supply/demand profile is V shaped and vanishes around the current price, leading to the square-root impact. This result only relies on mild assumptions about the order flow and on diffusive prices. We test our arguments numerically using a minimal model of order flow and provide further theoretical predictions that can be compared to further experimental observations. Our scenario suggests that markets are intrinsically prone to liquidity crises and puts in perspective the recent debate on the role of HFT liquidity. | ||
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| Frank Hatheway (NASDAQ) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 22. Sep 16, 17:00 |
| "We have all become High-Frequency Traders: What are some implications?" | ||
Competitive and regulatory forces in the U.S. have resulted in almost all equity executions being handled using sophisticated electronic trading systems. Empirical evidence from Nasdaq shows that order submission patterns once restricted to proprietary trading firms, the prototypical High Frequency Trader, are now observed in orders originating from almost all types of market participants. One aspect of the widespread automation of trading is that the use of "price taker" algorithms has become increasingly prevalent. The implications for the market where each algorithm's order placement decision is dependent on other algorithms' order placement decisions is not well understood. Some consequences of widespread "price taking" behavior are seen every trading day as well as on occasional events such as the May 6, 2010 and August 24, 2015 market breaks. The public policy discussion around market structure needs a better understanding of how the automated price setting mechanism works under the current structure and would work under future alternative market structure designs. | ||
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| Francois Golse (U.Ecole Polytechnique) | WPI, OMP 1, Seminar Room 08.135 | Thu, 22. Sep 16, 15:30 |
| "The Mean-Field Limit for the Quantum N-Body Problem: Uniform in Convergence Rate" | ||
The Hartree equation can be derived from the N-body Heisenberg equation by the mean-field limit assuming that the particle number N tends to infinity. The first rigorous result in this direction is due to Spohn (1980) (see also [Bardos-Golse-Mauser, Meth. Applic. Anal. 7:275-294, (2000)] for more details), and is based on analyzing the Dyson series representing the solution of the BBGKY hierarchy in the case of bounded interaction potentials.This talk will (1) provide an explicit convergence rate for the Spohn method, and (2) interpolate the resulting convergence rate with the vanishing h bound obtained in [Golse-Mouhot-Paul, Commun. Math. Phys. 343:165-205 (2016)] by a quantum variant of optimal transportation modulo O(h) terms. The final result is a bound for a Monge-Kantorovich-type distance between the Husimi transforms of the Hartree solution and of the first marginal of the N-body Heisenberg solution which is independent of h and vanishes as N tends to infinity. (Work in collaboration with T. Paul and M. Pulvirenti). | ||
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| Terrence Hendershott (UC. Berkeley) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 22. Sep 16, 15:30 |
| "Price Discovery Without Trading: Evidence from Limit Orders" | ||
Adverse selection in financial markets is traditionally measured by the correlation between the direction of market order trading and price movements. We show this relationship has weakened dramatically with limit orders playing a larger role in price discovery and with high-frequency traders’ (HFTs) limit orders playing the largest role. HFTs are responsible for 60–80% of price discovery, primarily through their limit orders. HFTs’ limit orders have 50% larger price impact than non-HFTs’ limit orders, and HFTs submit limit orders 50% more frequently. HFTs react more to activity by non-HFTs than the reverse. HFTs react more to messages both within and across stock exchanges. | ||
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| Mathieu Colin (U. Bordeaux I) | WPI, OMP 1, Seminar Room 08.135 | Thu, 22. Sep 16, 14:30 |
| "Stability properties for a Maxwell-Schrödinger System" | ||
The aim of this talk is to present some qualitative properties of a coupled Maxwell-Schrödinger system. First, I will describe conditions for the existence of minimizers with prescribed charge in terms of a coupling constant e. Secondly, I will study the existence of ground states for the stationary problem, the uniqueness of ground states for small e and finish with the orbital stability for the quadratic nonlinearity. This is a joint work with Tatsuya Watanabe. | ||
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| Thierry Foucault (HEC Paris) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 22. Sep 16, 14:30 |
| "Data Abundance and Asset Price Informativeness" | ||
Investors can acquire either raw or processed information about the payoff of risky assets. Information processing filters out the noise in raw information but it takes time. Hence, investors buying processed information trade with a lag relative to investors buying raw information. As the cost of raw information declines, more investors trade on it, which reduces the value of processed information, unless raw information is very unreliable. Thus, a decline in the cost of raw information can reduce the demand for processed information and, for this reason, the informativeness of asset prices in the long run. | ||
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| Rama Cont (Imperial College London) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 22. Sep 16, 12:00 |
| "Algorithmic trade execution and intraday market Dynamics" | ||
''Optimal execution'' are typically derived assuming an exogenous Price process which is unaffected by the trading behaviour of market participants. On the other hand, in intraday price behavior in electronic markets reveals evidence of the price impact of algorithmic order flow, an extreme example being the 'Flash Crashes' repeatedly observed in such markets. We propose a simple model for analyzing the feedback effects which arise in a market where participants use market signals to minimize the impact of their trade execution. We show that commonly used execution algorithms which aim at reducing market impact of trades can actually lead to unintended synchronization of participants' order flows, increase their market impact and generate large « self-exciting » intraday swings in volume and volatility. We show that such bursts may occur even in absence of large orders, and lead to a systematic underperformance of 'optimal execution' strategies. These results call for a critical assessment of "optimal execution" algorithms and point to a notion of order flow toxicity distinct from information asymmetry or adverse selection. | ||
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| Evelyne Miot (U. Grenoble Alpes) | WPI, OMP 1, Seminar Room 08.135 | Thu, 22. Sep 16, 11:30 |
| "Collision of vortex Filaments" | ||
In this talk we will present some results on the dynamics of vortex filaments according to a model introduced by Klein, Majda and Damodaran, focusing on the issue of collisions. This is a joint work with Valeria Banica and Erwan Faou. | ||
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| Oana Ivanovici (U. Nizza) | WPI, OMP 1, Seminar Room 08.135 | Thu, 22. Sep 16, 10:30 |
| "Dispersion for the wave and the Schrödinger Equations outside strictly convex Domains and counterexamples" | ||
We consider the linear wave equation and the linear Schr dingier equation outside a compact, strictly convex obstacle in R^d with smooth boundary. In dimension d = 3 we show that for both equations, the linear flow satises the (corresponding) dispersive estimates as in R^3. For d>3, if the obstacle is a ball, we show that there exists at least one point (the Poisson spot) where the dispersive estimates fail. This is joint work with Gilles Lebeau. | ||
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| Jonathan Brogaard (U. Washington) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 22. Sep 16, 10:30 |
| "High-Frequency Trading Competition" | ||
Using a firm-identified limit-order book dataset we show that competition among high-frequency trading firms (HFT) influences liquidity. HFT entries increase liquidity. The reverse is true for exits. Market participants’ behavioral changes are consistent with competitive pressure. HFT entries increase total HFT market share and take market share from incumbents. After HFT entry (exit), incumbent HFT spreads tighten (widen). Trading revenue suggests competition reduces HFT firm profitability. Impacts are larger in markets with fewer incumbents. The results show that part of the value of HFT comes from its competitiveness. | ||
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| Thomas Duyckaerts (U. Paris XIII) | WPI, OMP 1, Seminar Room 08.135 | Thu, 22. Sep 16, 9:30 |
| "Dynamics of the energy-critical wave equation" | ||
It is conjectured that bounded solutions of the focusing energy-critical wave equation decouple asymptotically as a sum of a radiation term and a finite number of solitons . In this talk, I will review recent works on the subject, including the proof of a weak form of this conjecture (joint work with Hao Jia, Carlos Kenig and Frank Merle) | ||
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| Andrei Kirilenko (Imperial College London) | SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna | Thu, 22. Sep 16, 9:30 |
| "Latency in Automated Trading Systems" | ||
Time in an automated trading system does not move in a constant deterministic fashion. Instead, it is a random variable drawn from a distribution. This happens because messages enter and exit automated systems though different gateways and then race across a complex infrastructure of parallel cables, safeguards, throttles and routers into and out of the central limit order books. Add to it market fragmentation and you get a pretty complex picture about the effects of latency on price formation. | ||
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| Mauser, Norbert (Inst. CNRS Pauli c/o Fak. Mathematik U. Wien) | OMP 1, Fakultät für Mathematik, 1090 Wien | Wed, 21. Sep 16, 19:00 |
| Austro - Französische Mathematik: ein Diskurs | ||
Warum ist Frankreich das weltweit führende Land in Mathematik ? Warum gibt es in Frankreich eine Sektion 25 und eine Sektion 26 - und in Österreich eine Sektion Forschung und eine Sektion Universitäten ?! Warum gibt es 2 französische Fields-Medaillen zur Boltzmanngleichung ? Warum ist eines der nur 3 europäischen CNRS Institute « extra muros » am WPI in Wien ? Warum kommen viele österreichische Spitzenmathematiker vom Lycée français de Vienne ? Diese und andere interessante Fragen wird uns Herr Prof. Mauser in seinem Vortrag (in deutscher Sprache) beantworten. | ||
| Note: Click here for further information | ||
| Mats Ehrnström (NTNU) | WPI, OMP 1, Seminar Room 08.135 | Wed, 21. Sep 16, 15:30 |
| "Existence of a Highest Wave in a Full-Dispersion Shallow Water Model" | ||
We consider the existence of periodic traveling waves in a bidirectional Whitham equation, combining the full two-way dispersion relation from the incompressible Euler equations with a canonical quadratic shallow water nonlinearity. Of particular interest is the existence of a highest, cusped, traveling wave solution, which we obtain as a limiting case at the end of the main bifurcation branch of $2pi$-periodic traveling wave solutions. Unlike the unidirectional Whitham equation, containing only one branch of the full Euler dispersion relation, where such a highest wave behaves like $|x|^{1/2}$ near its peak, the cusped waves obtained here behave like $|xlog|x||$ at their peak and are smooth away from their highest points. This is joint work with Mathew A. Johnson and Kyle M. Claassen at University of Kansas. | ||
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| Eric Wahlen (NTNU) | WPI, OMP 1, Seminar Room 08.135 | Wed, 21. Sep 16, 14:30 |
| "On the highest wave for Whitham’s wave equation" | ||
In the 1960’s G. B. Whitham suggested a non-local version of the KdV equation as a model for water waves. Unlike the KdV equation it is not integrable, but it has certain other advantages. In particular, it has the same dispersion relation as the full water wave problem and it allows for wave breaking. The equation has a family of periodic, travelling wave solutions for any given wavelength. Whitham conjectured that this family contains a highest wave which has a cusp at the crest. I will outline a proof of this conjecture using global bifurcation theory and precise information about an integral operator which appears in the equation. Joint work with M. Ehrnström. | ||
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| Thomas Alazard (ENS) | WPI, OMP 1, Seminar Room 08.135 | Wed, 21. Sep 16, 11:30 |
| "Control and stabilization of the incompressible Euler equation with free surface" | ||
The incompressible Euler equation with free surface dictates the dynamics of the interface separating the air from a perfect incompressible fluid. This talk is about the controllability and the stabilization of this equation. The goal is to understand the generation and the absorption of water waves in a wave tank. These two problems are studied by two different methods: microlocal analysis for the controllability (this is a joint work with Pietro Baldi and Daniel Han-Kwan), and study of global quantities for the stabilization (multiplier method, Pohozaev identity, hamiltonian formulation, Luke’s variational principle, conservation laws…). | ||
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| Hajer Bahouri (UPEC) | WPI, OMP 1, Seminar Room 08.135 | Wed, 21. Sep 16, 10:30 |
| "Qualitative study of 2D Schrodinger equation with exponential nonlinearity" | ||
In this lecture, we investigate the behavior of the solutions to the nonlinear Schrodinger equation: (1) ( i@tu + u = f(u); ujt=0 = u0 2 H1 rad(R2); where the nonlinearity f : C ! C is de ned by (2) f(u) = p( p 4 juj) u with p > 1 and p(s) = es2 pX1 k=0 s2k k! Recall that the solutions of the Cauchy problem (1)-(2) formally satisfy the conservation laws: (3) M(u; t) = Z R2 ju(t; x)j2dx = M(u0) and (4) H(u; t) = Z R2 jru(t; x)j2 + Fp(u(t; x)) dx = H(u0) ; where Fp(u) = 1 4 p+1 p 4 juj It is known (see [4], [6] and [2]) that global well-posedness for the Cauchy problem (1)-(2) holds in both subcritical and critical regimes in the functional space C(R;H1(R2)) L4(R;W1;4(R2)). Here the notion of criticity is related to the size of the initial Hamiltonian H(u0) with respect to 1. More precisely, the concerned Cauchy problem is said to be subcritical if H(u0) < 1, critical if H(u0) = 1 and supercritical if H(u0) > 1. Structures theorems originates in the elliptic framework in the studies by H. Brezis and J.- M. Coron in [3] and M. Struwe in [8]. The approach that we shall adopt in this article consists in comparing the evolution of oscillations and concentration e ects displayed by sequences of solutions of the nonlinear Schrodinger equation (1)-(2) and solutions of the linear Schrodinger equation associated to the same sequence of Cauchy data. Our source of inspiration here is the pioneering works [1] and [7] whose aims were to describe the structure of bounded sequences of solutions to semilinear defocusing wave and Schrodinger equations, up to small remainder terms in Strichartz norms. The analysis we conducted in this work emphasizes that the nonlinear e ect in this framework only stems from the 1-oscillating component of the sequence of the Cauchy data, using the terminology introduced in [5]. This phenomenon is strikingly di erent from those obtained for critical semi linear dispersive equations, such as for instance in [1, 7] where all the oscillating components induce the same nonlinear e ect, up to a change of scale. To carry out our analysis, we have been led to develop a pro le decomposition of bounded sequences of solutions to the linear Schrodinger equation both in the framework of Strichartz and Orlicz norms. The linear structure theorem we have obtained in this work highlights the distinguished role of the 1-oscillating component of the sequence of the Cauchy data. It turns out that there is a form of orthogonality between the Orlicz and the Strichartz norms for the evolution under the ow of the free Schrodinger equation of the unrelated component to the scale 1 of the Cauchy data (according to the vocabulary of [5]), while this is not the case for the 1-oscillating component. | ||
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| Vincent Duchêne (U. Rennes I) | WPI, OMP 1, Seminar Room 08.135 | Wed, 21. Sep 16, 9:30 |
| "On the well-posedness of the Green-Naghdi System" | ||
The Green-Naghdi system is an asymptotic model for the water-waves system, describing the propagation of surface waves above a layer of ideal, homogeneous, incompressible and irrotational fluid, when the depth of the layer is assumed to be small with respect to wavelength of the flow. It can be seen as a perturbation of the standard quasilinear (dispersionless) Saint-Venant system, with additional nonlinear higher-order terms. Because of the latter, the well-posedness theory concerning the GN system is not satisfactory, in particular outside of the one-dimensional framework. We will discuss novel results, obtained with Samer Israwi, that emphasize the role of the irrotationality assumption. | ||
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| Christian Klein (U.Bourgogne) | WPI, OMP 1, Seminar Room 08.135 | Tue, 20. Sep 16, 15:30 |
| "Numerical study of break-up in Kadomtsev-Petviashvili equations" | ||
The onset of a dispersive shock in solutions to the Kadomtsev-Petviashvili (KP) equations is studied numerically. First we study the shock formation in the dispersionless KP equation by using a map inspired by the characteristic coordinates for the one-dimensional Hopf equation. This allows to numerically identify the shock and to unfold the singularity. A conjecture for the KP solution near this critical point in the small dispersion limit is presented. It is shown that dispersive shocks for KPI solutions can have a second breaking where modulated lump solutions appear. | ||
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| Thomas Kappeler (U. Zürich) | WPI, OMP 1, Seminar Room 08.135 | Tue, 20. Sep 16, 14:30 |
| "Analytic extensions of frequencies of integrable PDEs and applications" | ||
In form of a case study for the mKdV and the KdV2 equation we discuss a novel approach of representing frequencies of integrable PDEs which allows to extend them analytically to spaces of low regularity and to study their asymptotics. Applications include wellposedness results in spaces of low regularity as well as properties of the actions to frequencies map. This is joint work with Jan Molnar. | ||
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| Laurent Thomann (U. Lorraine) | WPI, OMP 1, Seminar Room 08.135 | Tue, 20. Sep 16, 11:30 |
| "Invariant measures for NLS in dimension two" | ||
We consider the defocusing nonlinear Schrödinger equations on a two-dimensional compact Riemannian manifold without boundary or a bounded domain in dimension two. In particular, we discuss the Wick renormalization in terms of the Hermite polynomials and the Laguerre polynomials and construct the Gibbs measures corresponding to the Wick ordered Hamiltonian. Then, we construct global-in-time solutions with initial data distributed according to the Gibbs measure and show that the law of the random solutions, at any time, is again given by the Gibbs measure. | ||
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| Nicola Visciglia (U. Pisa) | WPI, OMP 1, Seminar Room 08.135 | Tue, 20. Sep 16, 10:30 |
| "Existence and Stability of Standing Waves for NLS in a partial confinement" | ||
I will discuss a joint work with Bellazzini, Boussaid, Jeanjean about the existence and orbital stability of standing waves for NLS with a partial confinement in a supercritical regime. The main point is to show the existence of local minimizers of the constraint energy. | ||
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| Philippe Gravejat (U. Cergy-Pontoise) | WPI, OMP 1, Seminar Room 08.135 | Tue, 20. Sep 16, 9:30 |
| "Stability of solitons for the Landau-Lifshitz equation with an easy-plane anisotropy" | ||
We describe recent results concerning the orbital and asymptotic stability of dark solitons and multi- solitons for the Landau-Lifshitz equation with an easy-plane anisotropy. This is joint work with André de Laire (University of Lille Nord de France), and by Yakine Bahri (Nice Sophia Antipolis University). | ||
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| Benavides-Riveros, Carlos (U. Halle-Wittenberg) | WPI, OMP1, Seminar Room 08.135 | Fri, 12. Aug 16, 15:15 |
| “Natural extension of Hartree-Fock through extremal 1-fermion Information” | ||
By employing the simpler structure arising from pinning and quasipinnig a variational optimization method for few fermion ground states is elaborated. We quantitatively confirm its high accuracy for systems whose vector of NON is close to the boundary of the polytope. In particular, we derive an upper bound on the error of the correlation energy given by the ratio of the distance to the boundary of the polytope and the distance of the vector of NON to the Hartree-Fock point. These geometric insights shed some light on the concept of active spaces, correlation energy, frozen electrons and virtual orbitals. | ||
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| Schilling, Christian (U. Oxford) | WPI, OMP1, Seminar Room 08.135 | Fri, 12. Aug 16, 14:00 |
| “Fermionic exchange symmetry: quantifying its influence beyond Pauli's Exclusion Principle" | ||
The Pauli exclusion principle has a strong impact on the properties and the behavior of most fermionic quantum systems. Remarkably, even stronger restrictions on fermionic natural occupation numbers follow from the fermionic exchange symmetry. We develop an operationally meaningful measure which allows one to quantify the potential physical relevance of those generalized Pauli constraints beyond the well-established relevance of Pauli's exclusion principle. It is based on a geometric hierarchy induced by Pauli exclusion principle constraints. The significance of that measure is illustrated for a few-fermion model which also confirms such nontrivial relevance of the generalized Pauli constraints. | ||
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| Brezinova, Iva (TU. Wien) | WPI, OMP1, Seminar Room 08.135 | Fri, 12. Aug 16, 11:00 |
| “Solving time-dependent many-body quantum problems using the two-particle reduced density matrix” | ||
In this talk we will give an overview over our recent progress in solving time-dependent many-body problems using the two-particle reduced density matrix (2RDM) as the fundamental variable. The wavefunction is completely avoided and with this all problems arising from the exponentially increasing complexity with particle number. Key is the reconstruction of the 3RDM which couples to the dynamics of the 2RDM. At this point the approximation to the full solution of the Schrödinger equation enters: while two-particle correlations are fully incorporated, three-particle correlations are only approximated. We will discuss the reconstruction of the 3RDM, how we overcome the N-representability problem, and demonstrate the accuracy of our theory on two-examples: multi-electron atoms in strong fields, and ultra-cold atoms in optical lattices. | ||
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| Gottlieb, Alexander (WPI) | WPI, OMP1, Seminar Room 08.135 | Fri, 12. Aug 16, 10:00 |
| “Quasi-separated electron pairs in small molecules” | ||
Some of the electrons in a molecule are tightly bound to the nuclei. The closely bound "core electrons" can be relatively uncorrelated with the rest of the electrons in the molecule, and may even form what we call a "quasi-separated" pair. [Let F be the electronic wave function of a molecule with N+2 electrons. We say that F features a "quasi-separated pair" if it is approximately equal to the wedge product G ^ H of a geminal G that describes the state of the separated pair and an N-electron wave function H that is strongly orthogonal to G.] We have computational evidence of such quasi-separated electron pairs in the ground states of very small molecules (like LiH or the Be atom) whose correlated electronic structure can be very accurately approximated with full CI calculations. | ||
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| Gottlieb, Alexander (WPI) | WPI, OMP1, Seminar Room 08.135 | Thu, 11. Aug 16, 16:00 |
| “Geometry of the Borland-Dennis setting: the W-type class” | ||
We call the Hilbert space for three fermions in six orbitals the Borland-Dennis setting. It is isomorphic to the alternating tensor product of three copies of the standard 6-dimensional Hilbert space C^6. Slater determinant states in the Borland-Dennis setting correspond to "decomposable" trivectors, i.e., simple wedge products of three vectors from C^6. Generic wave functions in the Borland-Dennis setting can be written as a sum of just two decomposable trivectors. The wave functions that cannot be written as a sum of fewer than three decomposables constitute the "W-type entanglement class." I will discuss the geometry of the W-type class within the ambient Borland-Dennis space. | ||
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| Benavides-Riveros, Carlos (U. Halle-Wittenberg) | WPI, OMP1, Seminar Room 08.135 | Thu, 11. Aug 16, 14:30 |
| “Pinning and quasipinning in quantum chemistry” | ||
It is now known that fermionic natural occupation numbers (NONs) do not only obey Pauli’s exclusion principle but are even stronger restricted by the so-called generalized Pauli constraints (GPC). Whenever given NONs lie on or close to the boundary of the allowed region the corresponding N-fermion quantum state has a significantly simpler structure. We explore this phenomenon in the context of quantum chemistry. | ||
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| Schilling, Christian (U. Oxford) | WPI, OMP1, Seminar Room 08.135 | Thu, 11. Aug 16, 13:30 |
| “Quantum marginal problem and generalized Pauli constraints” | ||
The question whether given reduced density operators (marginals) for subsystems of a multipartite quantum system are compatible to a common total state is called quantum marginal problem (QMP). We present the solution found by A. Klyachko just a few years ago as well as the main steps for its derivation. Applying those concepts to fermionic systems reveals further constraints on fermionic occupation numbers beyond Pauli's famous exclusion principle. We introduce and discuss these so-called generalized Pauli constraints in great detail and comment on their potential physical relevance. | ||
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| Komarov, Sergey (MPA & U. Princeton) | WPI Seminar Room 08.135 | Fri, 5. Aug 16, 10:00 |
| CR Diffusion - "Cosmic ray Diffusion in mirror fluctuations" | ||
TBA | ||
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| Rincon, Francois (U. Toulouse) | WPI Seminar Room 08.135 | Fri, 5. Aug 16, 10:00 |
| Convection - "Turbulent convection theories for the Sun" | ||
TBA | ||
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| Stone, Jim (U. Princeton) | WPI Seminar Room 08.135 | Thu, 4. Aug 16, 17:00 |
| MRI/Turbulence - "Reconnection in shearing box simulations of the MRI" | ||
TBA | ||
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| Schekochikin, Alex (U. Oxford) | WPI Seminar Room 08.135 | Thu, 4. Aug 16, 16:00 |
| Phase Mixing - "Phase-space turbulence in 2, 4 and 5D" | ||
TBA | ||
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| Lesur, Geoffroy (U. Grenbole) | WPI Seminar Room 08.135 | Thu, 4. Aug 16, 10:00 |
| MHD - "Vortex stability in non-ideal MHD" | ||
TBA | ||
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| Loureiro, Nuno (MIT) | WPI Seminar Room 08.135 | Wed, 3. Aug 16, 16:45 |
| "The onset of magnetic reconnection" | ||
TBA | ||
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| Sironi, Lorenzo (U. Harvard & U. Columbia) | WPI Seminar Room 08.135 | Wed, 3. Aug 16, 16:00 |
| Reconnection - "Magnetic reconnection in relativistic astrophysical jets" | ||
TBA | ||
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| Spirkovsky, Anatoly (U. Princeton) | WPI Seminar Room 08.135 | Wed, 3. Aug 16, 10:30 |
| CR Instabilities - "Kinetics of cosmic ray-driven instabilities and winds" | ||
TBA | ||
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| Bethune, William (U. Grenoble) | WPI Seminar Room 08.135 | Wed, 3. Aug 16, 10:00 |
| MRI - "Non-ideal MRI in protoplanetary disks" | ||
TBA | ||
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| Cowley, Steve (UKAEA & U. Oxford) | WPI Seminar Room 08.135 | Tue, 2. Aug 16, 16:30 |
| Transport & Stability - "Stability of the Chapman-Enskog solution in weakly collisional Plasma" | ||
TBA | ||
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| Roberg-Clark, Gareth (U. Maryland) | WPI Seminar Room 08.135 | Tue, 2. Aug 16, 16:00 |
| Transport & Stability - "Suppression of electron thermal conduction in high-beta plasma" | ||
TBA | ||
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| Medvedev, Michael (U. Kansas) | WPI Seminar Room 08.135 | Tue, 2. Aug 16, 11:00 |
| Transport - "Thermal conductivity and effective collisionality of astrophysical plasmas" | ||
TBA | ||
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| Bott, Archie (U. Oxford) | WPI Seminar Room 08.135 | Tue, 2. Aug 16, 10:00 |
| Plasama Dynamo - "Dynamo on Omega laser and kinetic Problems of Proton radiography" | ||
TBA | ||
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| Kunz, Matt (U.Princeton) | WPI Seminar Room 08.135 | Mon, 1. Aug 16, 16:30 |
| MRI/Turbulence - "Kinetic MRI turbulence" & "Kinetic solar-wind turbulence" | ||
TBA | ||
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| St-Onge, Denis (U. Princeton) | WPI Seminar Room 08.135 | Mon, 1. Aug 16, 16:00 |
| Plasma Dynamo - "Hybrid PIC simluations of plasma dynamo" | ||
TBA | ||
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| Strumik, Marek (U. Oxford) | WPI Seminar Room 08.135 | Mon, 1. Aug 16, 11:00 |
| High-Beta - CGL Dynamics and beta Limits on fluctuations in the solar wind" | ||
TBA | ||
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| Squire, Jonathan (Caltech) | WPI Seminar Room 08.135 | Mon, 1. Aug 16, 10:30 |
| High-Beta - "Amplitude limits on alfvenic perturbations in weakly magnetized low-collisionality plasmas" | ||
TBA | ||
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| Ball, Justin (U. Oxford & EPFL) | WPI Seminar Room 08.135 | Fri, 29. Jul 16, 10:00 |
| Up-Down Asymmetry - "Up-down asymmetric tokamaks" | ||
TBA | ||
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| Abel, Ian (U. Princeton & U. Greifswald) | WPI Seminar Room 08.135 | Thu, 28. Jul 16, 16:00 |
| Turbulence & Transport - "Sensitivitiy (to input parameters) calculation in gyrokinetics" | ||
TBA | ||
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| Schekochihin, Alexander (U. Oxford) | WPI Seminar Room 08.135 | Thu, 28. Jul 16, 10:00 |
| Turbulence & Transport - "Some updates on ion- and electron-scale turbulence in MAST" | ||
TBA | ||
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| St. Onge, Denis (U. Princeton) | WPI Seminar Room 08.135 | Wed, 27. Jul 16, 16:00 |
| Turbulence & Transport - "Dimits shift in one- and two-field models" | ||
TBA | ||
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| Citrin, Jonathan (CEA) | WPI Seminar Room 08.135 | Wed, 27. Jul 16, 11:00 |
| Turbulence & Transport - "Comparision between measured and predicted turbulence frequency spectra in ITG and TEM regimes" | ||
TBA | ||
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| Calvo, Ivan (CIEMAT) | WPI Seminar Room 08.135 | Wed, 27. Jul 16, 10:00 |
| Stellarators - "The effect of tangential drifts on neoclassical Transport in stellarator close to omnigeneity" | ||
TBA | ||
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| Hammett, Greg (U. Princeton) | WPI Seminar Room 08.135 | Tue, 26. Jul 16, 16:30 |
| SOL - "5D turbulence simluations with Gkeyll, in the presence of open field lines and sheath boundary conditions, in a torpex/helimak helical model of a SOL" | ||
TBA | ||
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| Geraldini, Alessandro (U. Oxford) | WPI Seminar Room 08.135 | Tue, 26. Jul 16, 16:00 |
| SOL - "Kinetic theory of Ions in the magnetic presheath" | ||
TBA | ||
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| Ricci, Paolo (EPFL) | WPI Seminar Room 08.135 | Tue, 26. Jul 16, 10:00 |
| SOL - "Physics at EPFL" | ||
TBA | ||
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| Pusztai, Istvan (U. Chalmers) | WPI Seminar Room 08.135 | Mon, 25. Jul 16, 16:00 |
| EDGE - "Momentum Transport due to neutrals in the edge" & "Neoclassical Transport in the pedestal in the presence of non-trace impurities" | ||
TBA | ||
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| Citrin, Jonathan (CEA) | WPI Seminar Room 08.135 | Mon, 25. Jul 16, 11:00 |
| Transport Optimisation - "Multichannel fluxdriven quasilinear turbulent transport prediciton over many confinement times" | ||
TBA | ||
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| Highcock, Edmund (U. Oxford & U. Chalmers) | WPI Seminar Room 08.135 | Mon, 25. Jul 16, 10:30 |
| Transport Optimisation - "Optimistically optimising optimisation: the Story so far... (and results!)" | ||
TBA | ||
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| Shatah, Jalal (Courant Inst. NY) | WPI, Seminar Room 08.135 | Tue, 12. Jul 16, 11:00 |
| Large Box Limit of Nonlinear Schrödinger equations | ||
The long time dynamics of the nonlinear Schrödinger equation, on a bounded domain, is very rich. Even for small amplitude initial data there can be quasi-periodic solutions, or solutions whose energy cascades between characteristically different length scales. Our aim in this talk is to explain how the long-time dynamics of the equation begin{equation*} left{ begin{array}{l} - i partial_t u + frac{1}{2pi} Delta u = epsilon^{2p} |u|^{2p} u qquad mbox{set on $(t,x) in mathbb{R} times mathbb{T}^n_L$} u(t=0) =epsilon u_0 end{array} right. end{equation*} can be described when $epsilon$ is small and $L$ is large. We will show how to derive an equation that describe the dynamics beyond the nonlinear time scale which is of order $mathcal{O}(frac1{epsilon^2})$. | ||
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| Wunderlich, Ralf (TU Brandenburg) | Lecture Room 13 | Thu, 7. Jul 16, 12:30 |
| "Partially Observable Stochastic Optimal Control Problems for an Energy Storage" | ||
We address the valuation of an energy storage facility in the presence of stochastic energy prices as it arises in the case of a hydro-electric pump station. The valuation problem is related to the problem of determining the optimal charging/discharging strategy that maximizes the expected value of the resulting discounted cash ows over the life- time of the storage. We use a regime switching model for the energy price which allows for a changing economic Environment described by a non-observable Markov chain. The valuation problem is formulated as a stochastic control problem under partial information in continuous time. Applying ltering theory we and an alternative state process containing the lter of the Markov chain, which is adapted to the observable ltration. For this alternative control problem we derive the associated Hamilton- Jacobi-Bellman (HJB) equation which is not strictly elliptic. Therefore we study the HJB equation using regularization arguments. We use numerical methods for computing approximations of the value function and the optimal strategy. Finally, we present some numerical results. Joint work with Anton Shardin. | ||
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| Gonzalez, Jhonny (U. Manchester) | Lecture Room 13 | Thu, 7. Jul 16, 12:00 |
| "Bayesian Calibration and Number of Jump Components in Electricity Spot Price Models" | ||
The price spikes observed in electricity spot markets may be understood to arise from fundamental drivers on both the supply and demand sides. Each driver can potentially create spikes with di erent frequencies, height distributions and rates of decay. This behaviour can be accounted for in models with multiple superposed components, however their calibration is challenging. Given a price history we apply a Markov Chain Monte Carlo (MCMC) based procedure to generate posterior samples from an augmented state space comprising parameters and multiple driving jump processes. This also enables posterior predictive checking to assess model adequacy. The procedure is used to determine the number of signed jump components required in two di erent markets, in time periods both before and after the recent global financial crises. Joint work with John Moriarty and Jan Palczewski. | ||
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| Pflug, Georg (U. Wien) | Lecture Room 13 | Thu, 7. Jul 16, 11:00 |
| "Pricing of Electricity Contracts" | ||
It is typical for electricity contracts, that the time of concluding the contract and the time of delivery are quite different. For this reason, these contracts are subject to risk and risk premia are and must be part of the pricing rules. In the rst part of the talk, we investigate electricity futures to nd out pricing rules, which the market is applying, such as the distortion priciple, the certainty equivalence priciple or the ambiguity priciple. We then investigate a no-arbitrage principle in the presence of capacity contraints on production and storage. We review then the idea of acceptance pricing and indi erence pricing using a concrete model. Finally we present a bilevel problem, where the pricing decision depends on the behavioral pattern of the counterparty. Some algorithmic aspects will be discussed as well. Joint work with Raimund Kovacevic | ||
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| Lange, Nina (U. Sussex) | Lecture Room 13 | Thu, 7. Jul 16, 10:30 |
| "Presence of Joint Factors in Term Structure Modelling of Oil Prices and Exchange Rates" | ||
The paper studies the time-varying correlation between oil prices and exchange rates and their volatilities. Generally, when the value of the dollar weakens against other major currencies, the prices of commodities tend move higher. The signi cance of this relationship has increased since 2000 with indications of structural breaks around the beginning of the so-called nancialization of commodity markets-regime and again around the beginning of the nancial crisis. Also the correlation between the volatility of oil prices and the volatility of exchange rates seems to experience the same behaviour as the returns correlation. This paper introduces and estimates a term structure model for futures contracts and option contracts on WTI crude oil and EURUSD. The model is tted a panel data of futures prices covering 2000-2013. The model allows for stochastic volatility and correlation and identi es how the number of joint factors increases over time. | ||
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| Davison, Matt (U. Western Canada) | Lecture Room 13 | Thu, 7. Jul 16, 9:00 |
| "A Real Options Analysis of the Relation between Ethanol Producers and Corn and Ethanol Markets" | ||
In recent years, for a variety of reasons, it has become popular in North American to produce Ethanol (for blending with gasoline) from Corn. The resulting industrial process can be modelled as an option on the "crush spread" between Ethanol and Corn. Under a price - taker assumption, real options models of ethanol production can be made incorporating random corn and ethanol prices. In the rst part of my talk I will report work done in my group, together with Natasha Burke and Christian Maxwell, on creating and solving real options models of the corn-ethanol industry. These models provide interesting insights about the relationship between corn prices, ethanol prices, and their correlation with valuations and operational decisions. Using a jump process, we are also able to incorporate the impact of random changes in government subsidies on the valuation and operation of ethanol facilities. However, while in the relatively fragmented US corn ethanol market it might be (just) reasonable to model any given ethanol producer as a price taker, all producers taken together do have market impact. In the second part of my talk I report work, joint with Nicolas Merener (Universidad Torcuata di Tella, Buenos Aires) on creating tractable models for this price impact. I will also sketch our progress toward solving the models and confronting them with data. | ||
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| Lässig, Yves (U. Freiburg) | Lecture Room 13 | Wed, 6. Jul 16, 17:00 |
| "Control of an Energy Storage under Stochastic Consumption" | ||
We consider a typical optimal control problem from the viewpoint of an energy utility company. The company faces a varying energy demand of its associated consumers, modelled by a stochastic process. Demands can be satis ed by either buying energy at an exchange or the utilisation of an energy storage system. Furthermore the company is able to buy energy on a larger scale - than needed to satisfy demands - and enlarge the storage level or respectively sell energy from the storage directly to the market. In contrast to previous lit- erature the storing facility therefore serves as a hedge against market price and demand volume risks and is not considered isolated from other market activities of the operator. Therefor the value function - which can be interpreted as a real option value of the storage - di ers from classical optimal storage control prob- lems and delivers a better quanti cation of the storage value for a speci c user. We formulate a stochastic control problem including these features and pay par- ticular attention to the operational constraints of the storage. Furthermore we will introduce methods to model the energy spot price and the consumption rate stochastically. Subsequently we will derive a candidate for the optimal policy, verify its optimality and solve the arising Hamilton-Jacobi-Bellman equation for the value function numerically using a novel nite elements discretization. | ||
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| Mora, Andres (U. de los Andes) | Lecture Room 13 | Wed, 6. Jul 16, 16:30 |
| "Risk Quanti cation for Commodity ETFs: Backtesting Value-at-Risk and Expected Shortfall" | ||
This paper studies the risk assessment of alternative methods for a wide variety of Commodity ETFs. We implement well-known as well as and recently proposed backtesting techniques for both value-at-risk (VaR) and ex- pected shortfall (ES) under extreme value theory (EVT), parametric, and semi- nonparametric techniques. The application of the latter to ES was introduced in this paper and for this purpose we derive a straightforward closed form of ES. We show that, for the con dence levels recommended by Basel Accords, EVT and Gram-Charlier expansions have the best coverage and skewed-t and Gram-Charlier the best relative performance. Hence, we recommend the ap- plication of the above mentioned distributions to mitigate regulation concerns about global nancial stability and commodities risk assessment. Joint work with Esther Del Brio and Javier Perote. | ||
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| Deschatre, Thomas (EDF) | Lecture Room 13 | Wed, 6. Jul 16, 16:30 |
| "On the Control of the Di erence between two Brownian Motions: A Dynamic Copula Approach" | ||
We propose new copulae to model the dependence between two Brow- nian motions and to control the distribution of their di erence. Our approach is based on the copula between the Brownian motion and its re ection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copu- lae. These copulae allow for the survival function of the di erence between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. We derive two models based on the structure of the Re ection Brownian Copula which present two states of correlation ; one is directly based on the re ection of the Brownian motion and the other is a local correlation model. These models can be used for risk management and option pricing in commodity energy markets. | ||
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| Erwan, Pierre (EDF) | Lecture Room 13 | Wed, 6. Jul 16, 15:30 |
| "Numerical Approximation of a Cash-Constrained Firm Value with In- vestment Opportunities" | ||
We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equa- tion. Moreover, we give regularity properties of the value function as well as a description of the shape of the control regions. Based on these theoretical results, a numerical deter- ministic approximation of the related HJB variational inequality is provided. We nally show that this numerical approximation converges to the value function. This allows us to describe the investment and dividend optimal policies. Joint work with Stephane Villeneuve and Xavier Warin. | ||
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| Sgarra, Carlo (U. Politecnico di Milano) | Lecture Room 13 | Wed, 6. Jul 16, 14:00 |
| "A Branching Process Approach to Power Markets" | ||
Energy markets, and in particular, electricity markets, exhibit very peculiar features. The historical series of both futures and spot prices include seasonality, mean reversion, spikes and small uctuations. Very often a stochastic volatility dynamics is postulated in order to explain their high degree of variability. Moreover, as it also appears in other kind of markets, they exhibit also the USV (Unspanned Stochastic Volatility) phaenomenon [7]. After the pioneering paper by Schwartz, where an Ornstein-Uhlenbeck dy- namics is assumed to describe the spot price behavior, several different approaches have been investigated in order to describe the price evolution. A comprehensive presentation of the literature until 2008 is o ered in the book by F.E. Benth, J. Saltyte-Benth and S. Koekebakker [4]. High frequency trading, on the other hand, introduced some new features in com- modity prices dynamics: in the paper by V. Filimonov, D. Bicchetti, N. Maystre and D. Sornette [5] evidence is shown of endogeneity and structural regime shift, and in order to quantify this level the branching ratio is adopted as a measure of this endoge- nous impact and a Hawkes processes dynamics is assumed as a reasonable modelling framework taking into account the self- exciting properties [1]. The purpose of the present paper is to propose a new modeling framework including all the above mentioned features, still keeping a high level of tractability. The model considered allows to obtain the most common derivatives prices in closed or semi-closed form. Here with semi-closed we mean that the Laplace transform of the derivative price admits an explicit expression. The models we are going to introduce can describe the prices dynamics in two di erent forms, that can be proved to be equivalent: the rst is a representation based on random elds, the second is based on Continuous Branching Processes with Immigration (CBI in the following). The idea of adopting a random felds framework for power prices description is not new: O.E. Barndor -Nielsen, F.E. Benth and A. Veraart introduced the Ambit Fields to this end, showing how this approach can provide a very exible and still tractable setting for derivatives pricing [2], [3]. A model based on CBI has been proposed recently by Y. Jiao, C. Ma and S. Scotti in view of short interest rate modelling, and in that paper it was shown that, with a suitable choice of the Levy process driving the CBI dynamics, the model can o er a signi cant extension of the poular CIR model [6]. We shall propose two di erent types of dynamics for the prices evolution. The rst class will be named the Arithmetic models class, and the second will be named the Geometric model class; in adopting the present terminology we are following the classi cation proposed in [4]. We shall compare the Advantages and the limitations implied by each model class and we shall investigate the risk premium behavior for each of the classes considered. The paper will be organized as follows: in the rst Section we introduce the stochastic processes we are going to consider, while in the second Section we discuss how these pro- cesses can be successfully applied to power markets description. In the third Section we derive some closed formulas for Futures and Option prices when the underlying dynamics is assumed to be given by the model introduced. In the fourth Section we shall investigate the risk premium term structure for the models under consideration. In the fth Section, we provide some suggestions about estimation and/or calibration methods for the same model. We complete our presentation with a statistical analysis on the two cases and some numerical illustrations of the results obtained. In the final section we provide some concluding remarks and discuss futures extensions of the present work. Joint work with Ying Jiao, Chunhua Ma and Simone Scotti. References: [1] Bacry, E., Mastromatteo, J., Muzy, J.-F. Hawkes Processes in Finance, PREPRINT(2015). [2] Barndor -Nielsen, O.E., Benth, F.E., Veraart, A. Modelling energy spot prices by volatil- ity modulated Levy driven Volterra processes, Bernoulli, 19, 803-845 (2013). [3] Barndor -Nielsen, O.E., Benth, F.E., Veraart, A. Modelling Electricity Futures by Am- bit Fields, Advances in Applied Probability, 46 (3), 719-745 (2014). [4] Benth, F.E., Saltyte-Benth J., Koekebakker S. Stochastic Modelling of Elec- tricity and Related Markets , World Scienti c, Singapore (2008). [5] Filimonov, V., Bicchetti, D., Maystre, N., Sornette, D. Quanti cation of the High Level of Endogeneity and Structural Regime Shifts in Commodity Markets, PREPRINT (2015). [6] Jiao, Y., Ma, C., Scotti, S. Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling, PREPRINT (2016). [7] Schwarz, A.B., Trolle, E.S. Unspanned Stochastic Volatility and the Pricing of Com- modity Derivatives, PREPRINT (2014). | ||
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| Ronn, Ehud (U. Texas) | Lecture Room 13 | Wed, 6. Jul 16, 11:00 |
| "Risk and Expected Return in the Oil-Futures Market" | ||
This paper considers two elements of the oil-futures markets: Ex- pected return and risk. 3 With respect to expected return, the paper presents a parsimonious and theoretically-sound basis for extracting forward-looking measures of equity and commodity betas, and the risk-premium on crude-oil futures contracts. De ning forward-looking betas as perturbations of historical estimates, we use the mar- ket prices of equity, index and commodity options under a single-factor market model to estimate the appropriate forward-looking perturbation to apply to the historical beta. This permits us to compute forward-looking term structures of equity and commodity betas. In the commodity arena, we use both one- and two-factor models to obtain estimates of a forward-looking measure of the correlation between crude-oil and the S&P 500. Combining these with forward- looking (i.e., implied) volatilities on commodities and stock-market indices, we utilize these forward-looking betas and correlations to provide an ex-ante esti- mate of the expected future crude-oil spot price through the use of an equity ex-ante risk premium and the conditional CAPM. With respect to risk, we use the market prices for crude-oil futures options and the prices of their underlying futures contracts to calibrate the volatility skew using the Merton (1976) jump-di usion option-pricing model. We demon- strate the jump-di usion parameters bear a close relationship to concurrent eco- nomic, nancial and geopolitical events. This produces an informationally-rich structure covering the time period of the turbulent post-2007 time period. | ||
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| Krühner, Paul (TU Wien) | Lecture Room 13 | Wed, 6. Jul 16, 10:30 |
| "Representation of In nite Dimensional Forward Price Models in Commodity Markets" | ||
The Heath Jarrow Morton (HJM) approach treats the family of futures - written on a commodity as primary assets and models them directly. This approach has been used for the modelling of future prices in various markets by several authors and it has found its use by practitioners. We derive several representations of possible future dynamics and implications on futures and the spot from an in nite dimensional point of view. To be more speci cally, let us denote the spot price by St and the future prices by ft(x) := E(St+xjFt); x; t 0. Due to the well-known Heath Jarrow Morton Musiela drift condition the dy- namics of ft cannot be speci ed arbitrarily under the pricing measure. We model it by dft = @xftdt + tdLt in a suitable function space where L is some Levy process. Then we derive a series representation for the futures in terms of the spot price process and Ornstein-Uhlenbeck type processes, we represent the spot as a Levy-semistationary process and nd formulae for the correlation between the spot and futures. | ||
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| Kholodnyi, Valerie (Verbund) | Lecture Room 13 | Wed, 6. Jul 16, 9:00 |
| "Extracting Forward-Looking Marked-Implied Risk-Neutral Probabilities for the Intraday Power Spots in the Unified Framework of the Non-Markovian Approach" | ||
Bene ts of a uni ed modeling framework The non-Markovian approach as a uni ed framework for the consistent modeling of power spots, forwards and swaps Extracting forward-looking market-implied risk-neutral probabilities for the intraday hourly and intra-hourly power spots from a single or multiple market forward curves Taking into account: { daily, weekly, annual and meta-annual cyclical patterns, { linear and nonlinear trends, { upwards and downwards spikes, { positive and negative prices Interpolating and extrapolating power market forward curves: { intra-hourly, hourly, daily, weekly and monthly power forward curves, { extending power market forward curves beyond their liquidity hori- zons Modeling the German Intraday Cap Week Futures as an hourly strip of Asian call options on forwards on the intraday hourly power spots | ||
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| Palczewski, Jan (U. Leeds) | Lecture Room 13 | Tue, 5. Jul 16, 17:00 |
| "Energy Imbalance Market Call Options and the Valuation of Storage" | ||
In this paper we assess the real option value of operating reserve pro- vided by an electricity storage unit. The contractual arrangement is a series of American call options in an energy imbalance market (EIM), physically covered and delivered by the store. The EIM price is a general regular one-dimensional Diffusion. Necessary and sucient conditions are provided for a unique optimal strategy and value. We provide a straightforward procedure for numerical solution and several examples. Joint work with John Moriarty. | ||
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| Gruet, Pierre (EDF) | Lecture Room 13 | Tue, 5. Jul 16, 16:30 |
| "Ecient Estimation in a Two-Factor Model from Historical Data: Application to Electricity Prices" | ||
We aim at modeling the prices of forward contracts on electricity, by adopting a stochastic model with two Brownian motions as stochastic factors to describe their evolution over time. In contrast to the model of (Kiesel et al., 2009), the diffusion coecients are stochastic processes; the one of the rst factor is left totally unspecified, and the other one is the product of an unspecified process and of an exponential function of time to the maturity of the forward contract, which allows to account for some short-term e ect in the increase of volatility. We will consider that price processes following this model are observed simultaneously, at n observation times, over a given time interval [0; T]. The time step T=n between two observation times is small with respect to T, in the asymptotics n ! 1. We estimate some parameter of the exponential factor in volatility, with the usual rate, and we explain how it can be estimated eciently in the Cramr-Rao sense. We are also able to estimate the trajectories of the two unspeci ed volatility processes, using nonparametric methods, with the standard rate of convergence. Numerical tests are performed on simulated data and on real prices data, so that we may see how appropriate our two-factor model is when applied to those data. Joint work with Olivier Feron (EDF, France) and Marc Hoffmann (Universite Paris-Dauphine). | ||
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| Kostrzewski, Maciej (U. Krakau) | Lecture Room 13 | Tue, 5. Jul 16, 16:00 |
| "Bayesian Analysis of Electricity Spot Price under SVLEJX Model" | ||
In the study, the Bayesian stochastic volatility model with normal errors, a leverage effect, a jump component and exogenous variables (SVLEJX) is proposed. This Bayesian framework, founded upon the idea of latent variables is computationally facilitated with Markov Chain Monte Carlo methods. In this paper, the Gibbs sampler is employed. The SVLEJX structure is applied to model electricity spot price. The results of Bayesian estimation, jump detection and forecasting are presented and discussed. The series of waiting times between two consecutive jumps is also of interest in the paper. Periods of no jumps alternating with the ones of frequent jumps could be indicative of existence of the jump clustering phenomenon. The impact of exogenous variables on electricity spot price dynamic is explored. Moreover, the leverage e ect and the stochastic volatility clustering are tested. | ||
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| Ziel, Florian (Europa-Universitat Viadrina) | Lecture Room 13 | Tue, 5. Jul 16, 15:30 |
| "Electricity Price Forecasting using Sale and Purchase Curves: The X- Model" | ||
Our paper aims to model and forecast the electricity price in a completely new and promising style. Instead of directly modeling the electricity price as it is usually done in time series or data mining approaches, we model and utilize its true source: the sale and purchase curves of the electricity exchange. We will refer to this new model as X-Model, as almost every deregulated electricity price is simply the result of the intersection of the electricity supply and demand curve at a certain auction. Therefore we show an approach to deal with a tremendous amount of auction data, using a subtle data processing technique as well as dimension reduction and lasso based estimation methods. We incorporate not only several known features, such as seasonal behavior or the impact of other processes like renewable energy, but also completely new elaborated stylized facts of the bidding structure. Our model is able to capture the non-linear behavior of the electricity price, which is especially useful for predicting huge price spikes. Using simulation methods we show how to 11 derive prediction intervals. We describe and show the proposed methods for the dayahead EPEX spot price of Germany and Austria. Joint work with Rick Steinert. | ||
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| Veraart, Almut (Imperial College) | Lecture Room 13 | Tue, 5. Jul 16, 14:00 |
| "Ambit stochastics in Energy Markets" | ||
This talk gives an introduction to the area of ambit stochastics with a particular focus on applications in energy markets. In particular, we will describe models for energy spot and forward prices based on so-called ambit felds. These models are very flexible and at the same time highly analytically tractable making them interesting from a mathematical perspective, but also very useful for applications. | ||
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| Callegaro, Giorgia (U. Padova) | Lecture Room 13 | Tue, 5. Jul 16, 11:00 |
| "Utility Indifference Pricing and Hedging for Structured Contracts in Energy Markets" | ||
In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indi erence pricing approach in a general incomplete multivariate market model driven by nitely many stochastic factors. The buyer of such contracts is allowed to trade in the forward market in order to hedge the risk of his position. We fully characterize the buyers utility indi erence price of a given product in terms of continuous viscosity solutions of suitable nonlinear PDEs. This gives a way to identify reasonable candidates for the optimal exercise strategy for the structured product as well as for the corresponding hedging strategy. Moreover, in a model with two correlated assets, one traded and one nontraded, we obtain a representation of the price as the value function of an auxiliary simpler optimization problem under a risk neutral probability, that can be viewed as a perturbation of the minimal entropy martingale measure. Finally, numerical results are provided. | ||
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| Vargiolu, Tiziano (U. Padova) | Lecture Room 13 | Tue, 5. Jul 16, 10:30 |
| "Additive Models for Forward Curves in Multicommodity Energy Markets" | ||
In contrast to geometric models, additive models in energy markets, in particular in markets where forward contracts are delivered during a period like electricity and natural gas, allows easily the computation of forward prices in closed form. Moreover they naturally allow the presence of negative prices, which start to appear more and more frequently in electric markets. In this paper we present an additive multicommodity model which allows for mean-reverting dynamics consistent with no-arbitrage, based on the observed prices of forward contracts based on the mean on a period, which are the most liquid instruments in natural gas and electricity markets. This allows to compute the price of more complex derivatives and of risk measures of portfolios in a way which is consistent with market data. Joint work with Luca Latini. | ||
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| Gulisashvili, Archil (U. Ohio) | Lecture Room 13 | Tue, 5. Jul 16, 9:00 |
| "Peter Laurence as friend and collaborator" | ||
My talk is dedicated to the memory of Peter Laurence, whose untimely death has left a void in many peoples hearts. Peter was a truly great mathematician and a wonderful person. In the first part of the talk, Peter's scientific biography will be presented. I will also share personal recollections of my meetings with Peter face-to-face and in the skype world. The second part of the talk will be more mathematical. I will speak about my joint work with Peter on Riemannian geometry of the Heston model, which is one of the classical stock price models with stochastic volatility. My collaboration with Peter resulted in the paper "The Heston Riemannian distance function", which was published in 2014 by "Journal de Mathematiques Pures et Appliquees". In the paper, we found two explicit formulas for the Riemannian Heston distance, using geometrical and analytical methods. Geometrical approach is based on the study of the Heston geodesics, while the analytical approach exploits the links between the Heston distance function and a similar distance function in the Grushin plane. We also proved a partial large deviation principle for the Heston and the Grushin models. After completing our work on the paper, we started discussing future projects, but fate interfered. I will finish the talk by briefly presenting my recent results on the distance to the line in the Heston plane, and how such results can be used in nancial mathematics. Peter's scientific in fluence continues after his untimely departure from this world. | ||
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| Lorz, Alexander (U. Paris VI & KAUST) | Lecture Room 11 | Sat, 2. Jul 16, 15:20 |
| "Population dynamics and therapeutic resistance: mathematical models" | ||
We are interested in the Darwinian evolution of a population structured by a phenotypic trait. In the model, the trait can change by mutations and individuals compete for a common resource e.g. food. Mathematically, this can be described by non-local Lotka-Volterra equations. They have the property that solutions concentrate as Dirac masses in the limit of small diffusion. We review results on long-term behaviour and small mutation limits. A promising application of these models is that they can help to quantitatively understand how resistances against treatment develop. In this case, the population of cells is structured by how resistant they are to a therapy. We describe the model, give first results and discuss optimal control problems arising in this context. | ||
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| Botesteanu, Dana-Adriana (U. Maryland) | Lecture Room 11 | Sat, 2. Jul 16, 14:30 |
| "Modeling the Dynamics of High-grade Serous Ovarian Cancer Progression for Transvaginal Ultrasound-Based Screening and Early Detection" | ||
High-grade serous ovarian cancer (HGSOC) represents the majority of ovarian cancers and disease recurrence is common, and leads to incurable disease. Emerging insights into disease progression suggest that timely detection of low volume HGSOC, not necessarily also early stage, should be the goal of any screening study. However, numerous transvaginal ultrasound (TVU) detection-based studies aimed at detecting low-volume ovarian cancer have not yielded reduced mortality rates and thus invalidate TVU as an effective HGSOC monitoring strategy in improving overall survival. Our mathematical modeling approach proposes a quantitative explanation behind the reported failure of TVU to improve HGSOC low-volume detectability and overall survival rates. We develop a novel in silico mathematical assessment of the efficacy of a unimodal TVU monitoring regimen as a strategy aimed at detecting low-volume HGSOC in cancer-positive cases, defined as cases for which the inception of the first malignant cell has already occurred. Focusing on a malignancy poorly studied in the mathematical oncology community, our model recapitulates the dynamic, temporal evolution of HGSOC progression, and is characterized by several infrequent, rate-limiting events. Our results suggest that multiple frequency TVU monitoring across various detection sensitivities does not significantly improve detection accuracy of HGSOC in an in silico cancer-positive population. This is a joint work with Doron Levy (University of Maryland, College Park) and Jung-Min Lee (Women’s Malignancies Branch, National Cancer Institute) | ||
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| Eder, Thomas (Ludwig Boltzmann Institute) | Lecture Room 11 | Sat, 2. Jul 16, 14:00 |
| "The Normalization Visualization Tool or how to choose an adequate normalization strategy for RNA-Seq experiments" | ||
Differential gene expression analysis between healthy and cancer samples is a common task. In order to identify differentially expressed genes, it is crucial to normalize the raw count data of RNA-Seq experiments. There are multiple normalization methods available but all of them are based on certain assumptions. These may or may not be suitable for the type of data they are applied on and especially if an experiment compares gene expression levels of healthy vs. rapidly growing tumor cells, the assumptions of non-differentially expressed genes or equal amounts of mRNA might not apply. Researchers therefore need to select an adequate normalization strategy for each RNA-Seq experiment. This selection includes exploration of different normalization methods as well as their comparison. We developed the NVT package, which provides a fast and simple way to analyze and evaluate multiple normalization methods via visualization and representation of correlation values, based on a user-defined set of uniformly expressed genes. | ||
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| Hanson, Shalla (U. Duke) | Lecture Room 11 | Sat, 2. Jul 16, 13:30 |
| "Toxicity Management in CAR T cell therapy for B-ALL: Mathematical modelling as a new avenue for improvement" | ||
Advances in genetic engineering have made it possible to reprogram individual immune cells to express receptors that recognise markers on tumour cell surfaces. The process of re-engineering T cell lymphocytes to express Chimeric Antigen Receptors(CARs), and then re-infusing the CAR-modified T cells into patients to treat various cancers is referred to as CAR T cell therapy. This therapy is being explored in clinical trials - most prominently for B Cell Acute Lymphoblastic Leukaemia (B-ALL), a common B cell malignancy, for which CAR T cell therapy has led to remission in up to 90% of patients. Despite this extraordinary response rate, however, potentially fatal inflammatory side effects occur in up to 10% of patients who have positive responses. Further, approximately 50% of patients who initially respond to the therapy eventually relapse. Significant improvement is thus necessary before the therapy can be made widely available for use in the clinic. To inform future development, we develop a mathematical model to analyze the interaction dynamics between CAR T cells, inflammatory toxicity, and individual patients' tumour burdens in silico. This talk outlines an underlying system of coupled ordinary differential equations, designed based on well-known immunological principles and widely accepted views on the mechanism of toxicity development in CAR T cell therapy for B-ALL, to form novel hypotheses on key factors in toxicity development, and reports in silico outcomes in relationship to standard and recently conjectured predictors of toxicity in a heterogeneous, randomly generated patient population. Our initial results and analyses are consistent with and connect immunological mechanisms to the clinically observed, counterintuitive hypothesis that initial tumour burden is a stronger predictor of toxicity than is the dose of CAR T cells administered to patients. We outline how the mechanism of action in CAR T cell therapy can give rise to such non-standard trends in toxicity development, and demonstrate the utility of mathematical modelling in understanding the relationship between predictors of toxicity, mechanism of action, and patient outcomes. | ||
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| Stiehl, Thomas (U. Heidelberg) | Lecture Room 11 | Sat, 2. Jul 16, 11:10 |
| "Heterogeneity in acute leukemias and its clinical relevance – Insights from mathematical modeling" | ||
Acute leukemias are cancerous diseases of the blood forming (hematopoietic) system. A hallmark of acute leukemias is heterogeneity of their clinical course. Similar as the hematopoietic system, leukemias originate from a small population of leukemic stem cells that resist treatment and trigger relapse. Recent gene sequencing studies demonstrate that the leukemic cell mass is composed of multiple clones the contribution of which changes over time. We propose compartmental models of hierarchical cell populations to study interaction of leukemic and healthy cells. The models are given as nonlinear ordinary differential equations. They include different feedback mechanisms that mediate competition and selection of the leukemic clones and the decline of healthy cells. Examples for considered mechanism are hormonal (cytokine) feedback loops, competition within the stem cell niche and overcrowding of the bone marrow space. A combination of computer simulations and patient data analysis is applied to provide insights in the following questions: (1) Which mechanisms allow leukemic cells to out-compete their benign counterparts? (2) How do properties of leukemic clones in terms of self-renewal and proliferation change during the course of the disease? What is the impact of treatment on clonal properties? (3) How do leukemic stem cell parameters affect the clinical course and patient prognosis? (4) What is the impact of leukemic cell properties on the number of leukemic clones and their genetic interdependence? (5) How does responsiveness of leukemic cells to signals of healthy hematopoiesis influence treatment response? Do inter-individual differences in signal sensitivity of leukemic cells matter? The talk is based on joint works with Anna Marciniak-Czochra (Institute of Applied Mathematics, Heidelberg University), Anthony D. Ho, Natalia Baran and Christoph Lutz (Heidelberg University Hospital). | ||
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| Almeida, Luis (U. UPMC Paris) | Lecture Room 11 | Sat, 2. Jul 16, 10:30 |
| "Mathematical models for epithelial tissue integrity restoration" | ||
We will present work on the mechanisms used for establishing or restoring epithelial integrity which are motivated by experimental work on development and wound healing in Zebrafish and drosophila and on gap closure in monolayers of MDCK cells or keratinocytes. These works concern mathematical modeling of the dynamics of epithelial tissues pulled by lamellipodal crawling or the contraction of actomyosin cables at the gap boundary. We are particularly interested in the influence of the wound/gap geometry and of the adhesion to the substrate on the closure mechanism. | ||
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| Xu, Zhou (U. UPMC Paris VI) | Lecture Room 11 | Sat, 2. Jul 16, 9:30 |
| "Telomere length dynamics and senescence heterogeneity: when size matters" | ||
Failure to maintain telomeres leads to their progressive erosion at each cell division. This process is heterogeneous but eventually triggers replicative senescence, a pathway shown to protect from unlimited cell proliferation, characteristic of cancer cells. However, the mechanisms underlying its variability and its dynamics are not characterized. Here, we used a microfluidics-based live-cell imaging assay to investigate replicative senescence in individual Saccharomyces cerevisiae cell lineages. We show that most lineages experience an abrupt and irreversible transition from a replicative to an arrested state, contrasting with the common idea of a progressive transition. Interestingly, senescent lineages displayed an important heterogeneity in their timing to enter senescence despite starting from the same initial telomeres. To understand this, we built several mathematical models, successively adding layers of molecular details. We find that, in a stochastic model where the first telomere reaching a critical short length triggers senescence, the variance of the initial telomere distribution mostly accounts for senescence heterogeneity. Unexpectedly, the residual heterogeneity is structurally built in the asymmetrical telomere replication mechanism. We then theoretically studied different senescence regimes, depending on the initial telomere variance, and provided analytical solutions to derive senescence onset from telomere length. Furthermore, the microfluidics approach also revealed another class of lineages that undergo frequent reversible cell-cycle arrests. Cells with this phenotype persist only at low frequency in bulk cultures but could initiate both genomic instability and post-senescence survival through adaptation mechanisms. These data suggest that another source of heterogeneity of senescence onset consists of stochastic telomere damages that may be the basis of cancer emergence. | ||
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| Lorenzi, Tommaso (U. St. Andrews) | Lecture Room 11 | Fri, 1. Jul 16, 16:00 |
| " Observing the dynamics of cancer cell populations through the mathematical lens of structured equations " | ||
A growing body of evidence supports the idea that solid tumours are complex ecosystems populated by heterogeneous cells, whose dynamics can be described in terms of evolutionary and ecological principles. In this light, it has become increasingly recognised that models that are akin to those arising from mathematical ecology can complement experimental cancer research by capturing the crucial assumptions that underlie given hypotheses, and by offering an alternative means of understanding experimental results that are currently available. This talk deals with partial differential equations modelling the dynamics of structured cancer cell populations. Analyses and numerical simulations of these equations help to uncover fresh insights into the critical mechanisms underpinning tumour progression and the emergence of resistance to anti-cancer therapies. | ||
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| Berger, Walter (MedUni Wien) & Mohr, Thomas (MedUni Wien) | Lecture Room 11 | Fri, 1. Jul 16, 15:20 |
| "Modeling factors contributing to glioblastoma aggressiveness" | ||
Glioblastoma represents the most frequent and aggressive primary brain tumor. Despite intense research and availability of extended in silico data, the mean patient survival after diagnosis is only around 15 months. Classical alkylating chemotherapy with concomitant radiation is still the standard therapeutic approach. This demonstrates that the revolution of modern precision medicine based on “big data” strategies has not resulted in approved therapeutic options and patient prognosis in this deadly disease so far. This implies that simple big data collection with bioinformatic evaluation might not be sufficient to translate into clinical benefit and close cooperations between systems biology and whet lab research is essential. Accordingly, we focus in our research cooperation on a multi-strategy approach focusing on a tight integration of 1) large-scale biobanking of viable malignant cells and cancer stem cells, 2) wet-lab cell and molecular biology and xenograft experiments; 3) extended omics analysis and 4) advanced computational biology methods. Regarding molecular factor driving tumor aggressiveness, data on a recently discovered non-coding mutation in the promoter of the telomerase reverse transcriptase (TERT) gene in human glioblastoma will be elucidated. Additionally, using publicly available gene expression profiles of glioblastoma patients we tried to bridge the existing gap of understanding the association of individual genes/mutations to complex physiological processes by the systematic investigation of the observed relationship between gene products and clinical traits. A weighted gene co-expression network approach (WGCNA) has been proposed to reconstruct gene co-expression networks in terms of large-scale gene expression profiles and as well as for the distinction genes potentially driving key cellular signaling pathways based on the centrality – lethality theorem. The WGCNA approach provides a functional interpretation in Systems Biology and leads to new insights into cancer pathophysiology. Here, we applied a systematic framework for constructing gene co-expression networks (modules) and pin-pointing key genes that may drive tumorigenesis and progression in different subclasses of GBM. Microarray data were downloaded from The Cancer Genome Atlas, corrected for batch effects using ComBat and normalized using rma and quantil normalization. Outliers were excluded using co-expression network parameters and co-expression network similarity. The resulting dataset was stratified according to the classification of Verhaak et al. and subjected to comparative Weighted Gene Co-expression analysis. The resulting modules were tested for module preservation across GBM subtypes using the connectivity and density measures. Modules of interest (both preserved and differentially interconnected) were analyzed for biological function using Term Enrichment Analysis methods and correlated to clinical traits (e.g. survival) to identify potential key driving co-expression networks. The lead modules will be then subject to cell biological and in vivo evaluation in glioblastoma models. In summary this multidisciplinary approach offers novel insights into glioblastoma aggressiveness and might uncover novel therapeutic targets. | ||
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| Pouchol, Camille (INRIA) | Lecture Room 11 | Fri, 1. Jul 16, 14:25 |
| "Optimal control of combined chemotherapies in phenotype-structured cancer cell populations evolving towards drug resistance" | ||
We investigate optimal therapeutical strategies combining cytotoxic and cytostatic drugs for the treatment of a solid tumour. The difficulty comes from the usual pitfalls of such treatments: emergence of drug-resistance and toxicity to healthy cells. We consider an integro-differential model for which the structuring variable is a continuous phenotype. Such models come from theoretical ecology and have been developed to understand how selection occurs in a given population of individuals. Two populations of healthy and cancer cells, both structured by a phenotype representing resistance to the drugs, are thus considered. The optimal control problem consists of minimising the number of cancer cells after some fixed time T. We first analyse the effect of constant doses on the long-time asymptotics through a Lyapunov functional. The optimal control problem is solved numerically, and for large T, we also theoretically determine the optimal strategy in a restricted class of controls. | ||
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| Vallette, Francois (U. Nantes) | Lecture Room 11 | Fri, 1. Jul 16, 13:45 |
| "Biological analysis of the drug resistance acquisition in a glioma cell line" | ||
Cancer evolution, including resistance to treatments, can be explained by classical evolutionary principles. This contention implies that cancer cells may be confronted to several “bottlenecks” or “evolutionary traps” during the natural course or adaptation to this “new environment”. It has been shown that despite an important heterogeneity at the start, cancer cells may rely, at some stage, on few survival mechanisms or on restricted populations that exhibit cancer stem cells / de-differentiation features. We used two cell lines (U251 and U87 both derived from human glioma) treated with the most clinical relevant chemotherapy (Temozolomide, TMZ) in vitro for few days and analyzed their relative sensitivity to several drugs interfering with epigenetics. Deep sequencing of control and TMZ treated U251 cell lines allowed us to identify new genes implicated in their survival that are transiently overexpressed shortly after TMZ addition. Using single cell analysis by microfluidic Fluidigm technologies (combined C1 single cell analysis plus Biomark HD system), we have studied the expression of these genes plus some implicated in cell death program and survival mechanisms) in isolated cells (>60) from control and cells treated with TMZ. Analysis of the expression of these genes reveals that the level of genomic heterogeneity appeared to be reduced in treated cells at early stages. These preliminary results, coupled to phenotypic analyses on cell death and proliferation rates, suggest that the cell lines can undergo a first rapid selection process that reduces their heterogeneity (and proliferation capacity) but improve their resistance capacity through limited survival pathways. | ||
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| Ciccolini, Joseph (U. Aix Marseille) | Lecture Room 11 | Fri, 1. Jul 16, 11:30 |
| "Not enough money on this earth: will pharmacometrics save oncology ?" | ||
Oncology has benefited from major ground-breaking innovations over the last 15-years. Beyond standard chemotherapy, targeted therapies, antio-angiogenics and now immune check-point inhibitors have all fueled high expectancies in terms of increased response rate and extended survival in patients. Of note, despite huge resources engaged now to better understand tumor biology and to identify relevant genetic and/or molecular biomarkers for choosing the best drugs, increase in survival has been mostly achieved in an incremental fashion so far, with the notable exception of CML and more recently of melanoma. The ever-increasing number of druggable targets, along with the rise of new concepts such as cancer immunology, has contributed to a considerable complexification of the decision-making at bedside. Indeed, it is widely acknowledged now that combination therapy is the future of cancer treatment. As such, defining the optimal association between cytotoxics, radiotherapy, anti-angiogenic drugs, targeted therapies and now immunotherapy is a major issue that remains to be addressed. Optimal solution will not be reached anymore by standard trial-and-error empirical practice, owing to the near-infinite number of possible combinations to be tested now that would require unsustainable efforts in terms of clinical development by pharmaceutical companies. In this respect, pharmacometrics (i.e., mathematical PK/PD models) could help to identify, using in silico simulations, a reduced number of working hypothesis to be tested in priority as part of clinical trials. Reviewing recent literature in the field and giving some examples in experimental and clinical oncology with chemotherapy, anti-angiogenics and immunotherapy, we will discuss how pharmacometrics could indeed help to optimize anticancer treatments. The paradigm shift from empirical to more rationale practice is probably the next challenge in oncology. | ||
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| Obenauf, Anna (U. Wien) | Lecture Room 11 | Fri, 1. Jul 16, 10:50 |
| "Unintended consequences of targeted cancer therapy: Therapy induced tumor secretomes fuel drug resistance and tumor Progression" | ||
The identification of molecular drivers in cancer has paved the way for targeted therapy. However, incomplete responses and relapse on therapy remain the biggest problem for improving patient survival. Evidence suggests that a tumor consists of a majority of cells that are sensitive to targeted therapy while few cells that are intrinsically resistant or poised to quickly adapt to drug treatment already pre-exist within this heterogeneous tumor population. Although a multitude of resistance mechanisms have been described, it was largely unknown how resistant cells behave in a heterogeneous tumor during treatment and whether a regressing tumor microenvironment could influence disease relapse. We found that targeted therapy with BRAF, ALK, or EGFR kinase inhibitors induces a complex network of secreted signals in drug-stressed melanoma and lung adenocarcinoma cells. This therapy-induced secretome (TIS) stimulates the outgrowth, dissemination, and metastasis of drug-resistant cancer cell clones in the heterogenous tumors and supports the survival of drug-sensitive cancer cells, contributing to incomplete tumour regression. The vemurafenib reactive secretome in melanoma is driven by down-regulation of the transcription factor FRA1. In situ transcriptome analysis of drug-resistant melanoma cells responding to the regressing tumour microenvironment revealed hyperactivation of multiple signalling pathways, most prominently the AKT pathway. Dual inhibition of RAF and PI3K/AKT/mTOR pathways blunted the outgrowth of the drug-resistant cell population in BRAF mutant melanoma tumours, suggesting this combination therapy as a strategy against tumour relapse. Thus, therapeutic inhibition of oncogenic drivers induces vast secretome changes in drug-sensitive cancer cells, paradoxically establishing a tumour microenvironment that supports the expansion of drug-resistant clones, but is susceptible to combination therapy. | ||
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| Clairambault, Jean (INRIA) | Lecture Room 11 | Fri, 1. Jul 16, 9:50 |
| "Heterogeneity and drug resistance in cancer cell populations: an evolutionary point of view with possible therapeutic consequences" | ||
I will present an evolutionary viewpoint on cancer, seen as the 2 time scales of (large-time) evolution in the genomes and of (short-time) evolution in the epigenetic landscape of a constituted genome. These views, based on pioneering works by Lineweaver, Davies and Vincent (cancer as anatomically localised backward evolution in multicellular organisms, aka atavistic theory of cancer) and by Sui Huang and collaborators (revisited Waddington epigenetic landscape), respectively, may serve as guidelines to propose a global conception of cancer as a disease that impinges on all multicellular organisms, and they may lead to innovating therapeutic strategies. Drug-induced drug resistance, the medical question we are tackling from a theoretical point of view, may be due to biological mechanisms of different natures, mere local regulation, epigenetic modifications (reversible, nevertheless heritable) or genetic mutations (irreversible), according to the extent to which the genome of the cells in the population is affected. In this respect, the modelling framework of adaptive dynamics presented here is more likely to correspond biologically to epigenetic modifications than to mutations, although eventual induction of emergent resistant cell clones due to mutations under drug pressure is not to be completely excluded. From the biologist's point of view, we study phenotypically heterogeneous, but genetically homogeneous, cancer cell populations under stress by drugs. The built-in targets for theoretical therapeutic control present in the phenotype-structured PDE models we advocate are not supposed to represent well-defined molecular effects of the drugs in use, but rather functional effects, i.e., related to cell death (cytotoxic drugs), or to proliferation in the sense of slowing down the cell division cycle without killing cells (cytostatic drugs). We propose that cell life-threatening drugs (cytotoxics) induce by far more resistance in the highly plastic cancer cell populations than drugs that only limit their growth (cytostatics), and that a rational combination of the two classes of drugs may be optimised to propose innovating therapeutic control strategies to avoid the emergence of drug resistance in tumours. | ||
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| Kalinin, Alexander (U. Mannheim) | WPI, Seminar Room 08.135 | Wed, 6. Apr 16, 16:30 |
| “Mild and Viscosity Solutions of Parabolic Path-Dependent Partial Differential Equations” | ||
In this talk, we consider a class of parabolic semilinear path-dependent PDEs that can be associated with a class of stochastic integral equations, which may depend on the entire sample paths of a time-inhomogeneous diffusion process. For instance, such integral equations can determine the log-Laplace functionals of historical superprocesses. By exploiting this relationship, we show uniqueness, existence and non-extendibility of mild solutions, and verify that every mild solution turns out to be a viscosity solution of the path-dependent PDE in question. | ||
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| Cosso, Andrea (Université Paris 7) | WPI, Seminar Room 08.135 | Wed, 6. Apr 16, 15:00 |
| “Functional versus Banach space stochastic calculus, and strong-viscosity solutions to path-dependent PDEs” | ||
In the first part of the talk we revisit the basic theory of functional Ito calculus, using the regularization approach. This allows us to explore its relations with the corresponding Banach space stochastic calculus. In the second part of the talk, we introduce a viscosity type solution for path-depenendent partial differential equations, called strong-viscosity solution, with the peculiarity that it is a purely analytic object. We discuss its properties and we present an existence and uniqueness result for strong-viscosity solutions to semilinear parabolic path-dependent partial differential equations. | ||
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| Cont, Rama (Imperial College London) | WPI, Seminar Room 08.135 | Wed, 6. Apr 16, 14:00 |
| “Kolmogorov without Markov: path-dependent Kolmogorov equations” | ||
Path-dependent Kolmogorov equations are a class of infinite dimensional partial differential equations on the space of cadlag functions which extend Kolmogorov's backward equation to path-dependent functionals of stochastic processes. Solutions of such equations are non-anticipative functionals which extend the notion of harmonic function to a non-Markovian, path-dependent setting. We discuss existence, uniqueness and properties of weak and strong solutions of path-dependent Kolmogorov equations using the Functional Ito calculus. Time permitting, some applications to mathematical finance and non-Markovian stochastic control will be discussed. | ||
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| Davis, Mark (Imperial College, London) | WPI, Seminar Room 08.135 | Wed, 6. Apr 16, 11:30 |
| “Infinite-dimensional linear programming and robust hedging of contingent claims” | ||
We consider a market including a traded asset whose forward price St is unambiguously defined and on which put options are traded with maturity/strike pairs {(Tj,Kji), i = 1, . . . , ij, j = 1, . . . , n}. The prices of these options, and the underlying asset price, are known at the current time t = 0, and are assumed to satisfy the Davis-Hobson (2007) conditions for consistency with an arbitrage-free model. Given a path-dependent contingent claim with exercise value ö(ST1, . . . , STn) we look for the cheapest semi-static superhedging portfolio, consisting of static positions in the traded options together with dynamic trading in the underlying where rebalancing takes place only at the option exercise times Tj. This problem is naturally formulated as an infinite-dimensional linear program (LP) and (under stated conditions) we can apply interior point conditions to show that there is no duality gap, the dual problem being maximization of expectation over martingale measures. One advantage of this approach is that computations can be done by finite-dimensional LP algorithms, following a 2-stage discretization process where we firstly restrict the dynamic trading integrands to finite linear combinations of basis functions, and then discretize the state space; we present some examples. Finally, we comment on possible extensions of these results to models with transaction costs. This is joint work with Sergey Badikov and Antoine Jacquier. | ||
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| Acciaio, Beatrice (London School of Economics) | WPI, Seminar Room 08.135 | Wed, 6. Apr 16, 10:30 |
| “Model-independent pricing with additional information” | ||
We consider a continuous-time financial market that consists of securities available for dynamic trading, and securities only available for static trading. We work in a robust framework and discuss two different ways of including additional information. In the first case, the informed agent's information flow is modeled by a filtration which is finer that the one of the uninformed agent. This clearly leads to a richer family of trading strategies, and to a smaller set of pricing measures. In the second case, we assume that the additional information consists in being able to exclude some evolution of the asset price process. In particular, super-replication of a contingent claim is required only along paths falling in the smaller set of admissible paths, and the pricing measures to be considered are only those supported on this set. The talk is based on joint works with Martin Larsson, Alex Cox and Martin Huesmann. | ||
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| Obloj, Jan (U. Oxford) | WPI, Seminar Room 08.135 | Wed, 6. Apr 16, 9:00 |
| “Robust pricing-hedging duality with path constraints and applications to information quantification” | ||
We consider robust (pathwise) approach to pricing and hedging. Motivated by the notion of prediction set in Mykland (2003), we include in our setup modelling beliefs by allowing to specify a set of paths to be considered, e.g. super-replication of a contingent claim is required only for paths falling in the given set. The framework interpolates between model--independent and model--specific settings. We establish a general pricing--hedging duality. The setup is parsimonious and includes the case of no traded options as well as the so-called martingale optimal transport duality of Dolinsky and Soner (2013) which we extend to multiple dimensions and multiple maturities. In presence of non-trivial beliefs, the equality is obtained between limiting values of perturbed problems indicating that the duality holds only if the market is stable under small perturbations of the inputs. Our framework allows to quantify the impact of making assumptions or gaining information. We focus in particular on the latter and study if the pricing-hedging duality is preserved under additional information. Joint work with Zhaoxu Hou and Anna Aksamit. | ||
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| Nutz, Marcel (Columbia University) | WPI, Seminar Room 08.135 | Tue, 5. Apr 16, 17:00 |
| “Martingale Optimal Transport and Beyond” | ||
We study the Monge-Kantorovich transport between two probability measures, where the transport plans are subject to a probabilistic constraint. For instance, in the martingale optimal transport problem, the transports are laws of martingales. Interesting new couplings emerge as optimizers in such problems. Constrained transport arises in the context of robust hedging in mathematical finance via linear programming duality. We formulate a complete duality theory for general performance functions, including the existence of optimal hedges. This duality leads to an analytic monotonicity principle which describes the geometry of optimal transports. Joint work with Mathias Beiglböck, Florian Stebegg and Nizar Touzi. | ||
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| Badikov, Sergey (Imperial College, London) | WPI, Seminar Room 08.135 | Tue, 5. Apr 16, 16:00 |
| “No-arbitrage bounds for the forward smile given marginal” | ||
We explore the robust replication of forward-start straddles given quoted (Call and Put options) market data. One approach to this problem classically follows semi-infinite linear programming arguments, and we propose a discretisation scheme to reduce its dimensionality and hence its complexity. Alternatively, one can consider the dual problem, consisting in finding optimal martingale measures under which the upper and the lower bounds are attained. Semi-analytical solutions to this dual problem were proposed by Hobson and Klimmek (2013) and by Hobson and Neuberger (2008). We recast this dual approach as a finite dimensional linear programme, and reconcile numerically, in the Black-Scholes and in the Heston model, the two approaches. | ||
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| Siorpaes, Pietro (U. Oxford) | WPI, Seminar Room 08.135 | Tue, 5. Apr 16, 14:30 |
| “Pathwise local time and robust pricing of realized variance” | ||
Davis, Obloj and Raval (2013) developed a theory of robust pricing and hedging of weighted variance swaps given market prices of co-maturing put options. They make use of Föllmer’s quadratic variation for continuous paths, and of an analogous notion of local time. Here we develop a theory of pathwise local time, defined as a limit of suitable discrete quantities along a general sequence of partitions of the time interval. We provide equivalent conditions for the existence of pathwise local time. Our approach agrees with the usual (stochastic) local times for a.e. path of a continuous semimartingale. We establish pathwise versions of the Itô-Tanaka, change of variables and change of time formulae. Finally, we study in detail how the limiting objects, the quadratic variation and the local time, depend on the choice of partitions. In particular, we show that an arbitrary given non-decreasing process can be achieved a.s. by the pathwise quadratic variation of a standard Brownian motion for a suitable sequence of (random) partitions; however, such degenerate behavior is excluded when the partitions are constructed from stopping times. | ||
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| Blacque-Florentin, Pierre (Imperial College, London) | WPI, Seminar Room 08.135 | Tue, 5. Apr 16, 11:30 |
| “Functional calculus and martingale representation formula for integer-valued random measures” | ||
We develop a pathwise calculus for functionals of integer-valued measures. We show that smooth functionals in the sense of this pathwise calculus are dense in the space of square-integrable (compensated) integrals with respect to a large class of integer-valued random measures. Using these results, we extend the framework of Functional Itô Calculus to functionals of integer-valued random measures. We construct a 'stochastic derivative' operator with respect to such integer-valued random measures and obtain an explicit martingale representation formula for square-integrable martingales with respect to the filtration generated by such integer-valued random measures. Our results hold beyond the class of Poisson random measures and allow for random and time-dependent compensators. This is joint work with R. Cont. | ||
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| Lu, Yi (Université Pierre & Marie Curie, Paris VI) | WPI, Seminar Room 08.135 | Tue, 5. Apr 16, 10:30 |
| “Weak derivatives of non-anticipative functionals” | ||
In his seminal paper "Calcul d'Ito sans probabilités", Hans Föllmer proposed a non-probabilistic version of the Itô formula, which was recently generalized by Rama Cont and David-Antoine Fournié in a functional framework. Using the notion of pathwise quadratic variation, we derive first a pathwise isometry formula for functionals of a given path. This formula allows to generalize the notion of vertical derivatives and allows to define a weak version of vertical derivatives for functionals which are not necessarily smooth in the classical sense. The whole approach involves only pathwise arguments and does not rely on any probability notions. Nevertheless, we show that when applying to a stochastic process, this notion of weak derivatives coincides with the weak derivatives proposed by Cont and Fournié in a probabilistic framework. | ||
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| Ananova, Anna (Imperial College, London) | WPI, Seminar Room 08.135 | Tue, 5. Apr 16, 9:00 |
| “Pathwise integration with respect to paths of finite quadratic variation.” | ||
We study a notion of pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums, as defined by Follmer (1979) and extended by Cont & Fournie (2010). We prove a pathwise isometry property for this integral, analogous to the well-known Ito isometry for stochastic integrals. This property is then used to represent the integral as a continuous map on an appropriately defined vector space of integrands. Finally, we obtain a pathwise 'signal plus noise' decomposition, which is the pathwise analog of the semimartingale decomposition, for a large class of irregular paths obtained through functional transformations of a reference path with non-vanishing quadratic variation. The relation with controlled rough paths is discussed. | ||
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| Beiglböck, Mathias (TU Wien) | WPI, Seminar Room 08.135 | Mon, 4. Apr 16, 16:30 |
| “Pathwise super-replication via Vovk's outer measure” | ||
Since Hobson's seminal paper the connection between model-independent pricing and the skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing-hedging duality for financial derivatives which are susceptible to the Skorokhod approach. Using Vovk's approach to mathematical finance we derive a model-independent super-replication theorem in continuous time, given information on finitely many marginals. Our result covers a broad range of exotic derivatives, including lookback options, discretely monitored Asian options, and options on realized variance. | ||
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| Prömel, David (Humboldt-Universität zu Berlin) | WPI, Seminar Room 08.135 | Mon, 4. Apr 16, 15:00 |
| “Pathwise Tanaka formula and local times for typical price paths” | ||
We present a pathwise Tanaka formula for absolutely continuous functions with weak derivative of finite q-variation provided the local time is of finite p-variation with 1/p + 1/q >1. To justify the assumption on the local time, we follow Vovk's hedging based approach to model free financial mathematics. We prove that it is possible to make an arbitrarily large profit by investing in those one-dimensional paths which do not possess local times fulfilling the aforementioned assumptions. This talk is based on a joint work with Nicolas Perkowski. | ||
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| Perkowski, Nicolas (Humboldt-Universität zu Berlin) | WPI, Seminar Room 08.135 | Mon, 4. Apr 16, 14:00 |
| "Stochastic integration and game-theoretic martingales" | ||
Vovk recently introduced a pathwise approach to continuous time mathematical finance which does not require any measure-theoretic foundation and allows us to describe properties of “typical price paths” or “game-theoretic martingales" by only relying on superhedging arguments. I will show how to construct a model free Itô integral in this setting. We will also see that every typical price paths a rough path in the sense of Lyons. Based on joint work with David Prömel. | ||
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| Vovk, Vladimir (Royal Holloway, London) | Skylounge (12th floor) | Mon, 4. Apr 16, 11:30 |
| “Financial applications of game-theoretic supermartingales” | ||
This talk will introduce a class of game-theoretic supermartingales, whose main advantage over their measure-theoretic counterparts is that they do not presuppose a given probability measure; instead, they can be used to define an outer measure motivated by economic considerations combined only with topological (but not statistical) assumptions. Under the continuity assumption, it is possible to show that a typical continuous price path "looks like Brownian motion" with a possibly deformed time axis. A weaker assumption of boundedness of jumps still implies the almost sure existence of pathwise stochastic integrals of functions with finite p-variation for some p with respect to cadlag price paths with bounded jumps. | ||
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| Teichmann, Josef (ETH Zürich) | Skylounge (12th floor) | Mon, 4. Apr 16, 10:00 |
| “Rough term structures” | ||
In the realm of Martin Hairer's regularity structures we aim to introduce topologies on spaces of modelled distributions, which enable on the one hand reconstruction and which allow on the other hand a rich class of modelled distribution valued semi-martingales. This is done to have tools from regularity structures and semi-martingale theory at hand. Examples from the theory of term structures in mathematical Finance are shown. Joint work with David Prömel, ETH Zürich. | ||
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| Pansu, Pierre (U. Paris) | WPI, Seminar Room 08.135 | Wed, 24. Feb 16, 12:00 |
| "The quasisymmetric Hölder equivalence Problem" | ||
What is the optimal pinching of curvature on spaces quasiisometric to complex hyperbolic spaces ? This leads to the following problem: what is the best Hölder continuity exponent for a homeomorphism of Euclidean space to a metric space quasisymmetric to the Heisenberg group, when the inverse map is assumed to be Lipschitz ? We give a partial result on this question. | ||
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| Swiatoslaw, Gal (U. Wroclaw) | OMP 1, Seminar Room 08.135 | Wed, 24. Feb 16, 10:30 |
| "Uniform simplicity of groups of dynimical origin" | ||
A group is called $N$]uniformly simple if for every nontrivial conjugacy class $C$, $(C^\pm)^{\leq N}$ covers the whole group. Every uniformly simple group is simple. It is known that many group with geometric or dynamical origin are simple. In the talk we prove that, in fact, many of them are uniformly simple. The result are due to the speaker, Kuba Gis] matullin, and Nir Lazarovich. | ||
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| Ghosh, Sourav (U. Heidelberg) | WPI, Seminar Room 08.135 | Wed, 24. Feb 16, 9:15 |
| "Moduli space of Margulis Spacetimes" | ||
In this talk I will describe the stable and unstable leaves for the geodesic flow on the space of non-wandering space like geodesics of a Margulis Spacetime. I will also describe how monodromy of Margulis Spacetimes are “Anosov representations in non semi-simple Lie groups”. Finally using the Anosov property I will define the Pressure metric on the Moduli Space of Margulis Spacetimes and discuss some of its properties. | ||
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| Guichard, Olivier (U. Strasbourg) | WPI, Seminar Room 08.135 | Tue, 23. Feb 16, 16:00 |
| "Symplectic Maximal Representations" | ||
Jointly with Anna Wienhard, we obtain a better understanding of the compact $\mathbf{R}\mathbb{P}^{2n-1}$-manifolds coming from maximal representations into the symplectic group $\mathrm{Sp}(2n, \mathbf{R}$, and in particular of their topology. This is based on the special properties of the boundary map into the Lagrangian variety. | ||
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| Kassel, Fanny (U. Lille) | WPI, Seminar Room 08.135 | Tue, 23. Feb 16, 14:30 |
| "Proper affine actions for right-angled Coxeter Groups" | ||
We prove that any right-angled Coxeter group on k generators admits a proper affine action on R^{k(k-1)/2}. This yields proper affine actions for many other groups, including all Coxeter groups. Joint work with J. Danciger and F. Guéritaud. | ||
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| Caprace, Pierre-Emmanuel (U. Louvain) | WPI, Seminar Room 08.135 | Tue, 23. Feb 16, 9:15 |
| "Linear representations of lattices in Euclidean buildings" | ||
When is a lattice in a Euclidean building linear? We will explain that answers to that question can be obtained by combining tools of various origins: ergodic theory, structure theory of disconnected locally compact groups, and classical theory of projective planes. Based on joint work with Uri Bader and Jean Lécureux. | ||
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| Leeb, Bernhard (U. München) | WPI, Seminar Room 08.135 | Mon, 22. Feb 16, 15:45 |
| "Geometry and dynamics of Anosov representations II" | ||
We give a geometric interpretation of the maximal Satake compactification of symmetric spaces X=G/K of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable G-invariant "polyhedral" Finsler metric on X. We then discuss the topological dynamics of discrete subgroups Gamma"<"G on this compactification. We show that there exist natural domains of proper discontinuity for Gamma extending X, and that the Gamma-action on these domains is cocompact if Gamma is an Anosov subgroup. This leads to natural bordifications resp compactifications of the locally symmetric spaces X/Gamma as orbifolds with corners by attaching quotients of domains of discontinuity at infinity. This is joint work with Misha Kapovich. | ||
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| Porti, Joan (U. Barcelone) | WPI, Seminar Room 08.135 | Mon, 22. Feb 16, 14:15 |
| "Geometry and dynamics of Anosov representations I" | ||
In this talk I give a definition of Anosov representation that does not use geodesic flow. Then I give a characterization in terms of coarse geometry of the orbit map in the symmetric space. This leads to the notion of Morse subgroups and to a Morse lemma for higher rank symmetric spaces. This is joint work with B. Leeb and M. Kapovich. | ||
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| Lee, Gye-Seon (U. Heidelberg) | WPI, Seminar Room 08.135 | Mon, 22. Feb 16, 13:00 |
| "Collar lemma for Hitchin representations" | ||
There is a classical result first due to Keen known as the collar lemma for hyperbolic surfaces. A consequence of the collar lemma is that if two closed curves A and B on a closed orientable hyperbolizable surface have non-zero geometric intersection number, then there is an explicit lower bound for the length of A in terms of the length of B, which holds for any hyperbolic structure on the surface. By slightly weakening this lower bound, we generalize this statement to hold for all Hitchin representations. Joint work with Tengren Zhang. | ||
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| Marquis, Ludovic (U. Rennes) | WPI, Seminar Room 08.135 | Mon, 22. Feb 16, 10:30 |
| "Projectivization of some Dehn-filling on hyperbolic 4-orbifold" | ||
A theorem of Thurston says that if M is a finite volume non-compact hyperbolic manifold of dimension 3 (say with one cusp to simplify) then the manifold of dimension 3 obtained by filling (Dehn filling) the cusp is hyperbolic except in a finite number of cases. The hyperbolization of finite volume non-compact orbifold is possible only in dimension 2 or 3. We will exhibit examples of hyperbolic polytopes of dimension 4 which admit a projectivization of their Dehn filling. During this talk, "projectivize" will mean realise as the quotient of a properly convex open set of the real projective space by a discrete subgroup of projective transformation (preserving the convex). This is a joint work with Suhyoung Choi (KAIST) and Gye-Seon Lee (Heidelberg). | ||
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| Osajda, Damian (U. Wroclaw) | WPI, Seminar Room 08.135 | Mon, 22. Feb 16, 10:30 |
| "Gromov boundaries with the combinatorial Loewner property." | ||
This is joint work with Antoine Clais (Technion). The combinatorial Loewner property (CLP) is a property of metric spaces invariant under quasi-Moebius homeomorphisms. It has been introduced by M. Bonk and B. Kleiner as a combinatorial counterpart of the classical Loewner property. Conjecturally, Gromov group boundaries satisfying the CLP are quasi-Moebius homeomorphic to Loewner spaces. For Loewner boundaries various quasi-conformal analysis techniques have been developed in order to achieve rigidity results. Not many group boundaries with the CLP are known. We present new classes of Gromov boundaries, in dimensions greater than one, satisfying the CLP. The underlying groups are hyperbolic right-angled Coxeter groups and lattices in associated buildings. | ||
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| Lubotzky, Alexander (U. Jerusalem) | WPI, Seminar Room 08.135 | Mon, 22. Feb 16, 9:15 |
| "Arithmetic quotients of the mapping class group" | ||
Let M=M(g) be the mapping class group of a surface of genus g > 1 (resp. M=Aut(F_g) the automorphism group of the Free group on g generators ). As it is well known, M is mapped onto the symplectic group Sp(2g,Z) (resp. the general linear group GL(g,Z) ). We will show that this is only a first case in a series: in fact, for every pair (S,r) when S is a finite group with less than g generators and r is a Q-irreducible representation of S, we associate an arithmetic group which is then shown to be a virtual quotient of M. The case when S is the trivial group gives the above Sp(2g,Z) ( resp. GL(g,Z) ) but many new quotients are obtained. For example it is used to show that M(2) (resp. Aut(F_3) ) is virtually mapped onto a non-abelian free group. Another application is an answer to a question of Kowalski: generic elements in the Torelli groups are hyperbolic and fully irreducible. Joint work with Fritz Gruenwald, Michael Larsen and Justin Malestein . | ||
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| Constantin, Peter (U. Princeton) | WPI Seminar Room 08.135 | Fri, 18. Dec 15, 11:00 |
| "Nonlocal equations in bounded Domains" | ||
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| Hittmeir, Sabine (U. Vienna) | WPI Seminar Room 08.135 | Fri, 18. Dec 15, 10:00 |
| "Multiscale asymptotics and analysis for atmospheric flow models with moisture" | ||
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| Li, Jinkai (U. Weizmann) | WPI Seminar Room 08.135 | Thu, 17. Dec 15, 15:30 |
| "Recent advances on the primitive equations of oceanic and atmospheric dynamics" | ||
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| Mucha, Piotr (U. Warsaw) | WPI Seminar Room 08.135 | Thu, 17. Dec 15, 14:30 |
| "Slightly compressible Navier-Stokes system connection to incompressible flows" | ||
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| Szekelyhidi, Laszlo (U. Leipzig) | WPI Seminar Room 08.135 | Thu, 17. Dec 15, 11:00 |
| "Hölder continuous weak solutions of the Euler equations" | ||
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| Boldrighini, Carlo (U. Rome) | WPI Seminar Room 08.135 | Thu, 17. Dec 15, 10:00 |
| "Li-Sinai solutions of the 3-d Navier-Stokes equations and related real solutions: theory and computer simulations" | ||
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| Brenier, Yann (Ecole Polytechnique & CNRS) | WPI Seminar Room 08.135 | Wed, 16. Dec 15, 15:30 |
| "Rearrangement methods in convective and compressible fluid motions" | ||
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| Kukavica, Igor (U. Southern California) | WPI Seminar Room 08.135 | Wed, 16. Dec 15, 14:30 |
| "Analyticity results for the incompressible Euler equations " | ||
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| Besse, Nicolas (Obs. Nice & UCA) | WPI Seminar Room 08.135 | Wed, 16. Dec 15, 11:00 |
| "Time-analyticity of Lagrangian incompressible Euler flow in a bounded Domain" | ||
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| Frisch, Uriel (Obs. Nice & CNRS) | WPI Seminar Room 08.135 | Wed, 16. Dec 15, 10:00 |
| "The Cauchy-Lagrangian method for numerical analysis of Euler Flow" | ||
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| Nguyen, Toan (U. Penn State) | WPI Seminar Room 08.135 | Tue, 15. Dec 15, 15:30 |
| "The stability of boundary layers: an overview" | ||
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| Mazzucato, Anna (U. Penn State) | WPI Seminar Room 08.135 | Tue, 15. Dec 15, 14:30 |
| "The vanishing viscosity limit in the presence of a porous medium" | ||
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| Dalibard, Anne-Laure (U. Paris 6) | WPI Seminar Room 08.135 | Tue, 15. Dec 15, 11:00 |
| "Separation for the stationary Prandle equation" | ||
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| Vicol, Vlad (U. Princeton) | WPI Seminar Room 08.135 | Tue, 15. Dec 15, 10:00 |
| "Remarks on the vanishing viscosity problem with Dirichlet boundary conditions" | ||
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| Wiedemann, Emil (U. Bonn) | WPI Seminar Room 08.135 | Mon, 14. Dec 15, 16:30 |
| "The issue of weak-strong uniqueness in contrast to non-uniqueness for 'wild' solutions" | ||
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| Dong, Li (U. British Colombia) | WPI Seminar Room 08.135 | Mon, 14. Dec 15, 15:45 |
| "Ill posedness of the Euler Equation in Cm and related issues" | ||
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| Gibbon, John (Imperial College London) | WPI Seminar Room 08.135 | Mon, 14. Dec 15, 15:00 |
| “Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations” | ||
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| WPI Seminar Room 08.135 | Mon, 14. Dec 15, 14:20 | |
| Opening of Workshop and self presentation of participants | ||
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| Ning, Jiang (U. Wuhan) | WPI Seminar Room 08.135 | Fri, 11. Dec 15, 14:30 |
| "Boundary layers and the fluid limits of the Boltzmann equation" | ||
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| Golse, Francois (Ecole Polytechnique) | WPI Seminar Room 08.135 | Fri, 11. Dec 15, 11:30 |
| "From N-body Schrödinger to Vlasov" | ||
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| Jabin, Pierre-Emmanuel (U. Maryland) | WPI Seminar Room 08.135 | Fri, 11. Dec 15, 10:00 |
| "Mean field limits for bounded force kernels" | ||
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| Brenier, Yann (Ecole Polytechnique & CNRS) | WPI Seminar Room 08.135 | Thu, 10. Dec 15, 14:30 |
| "A double large deviation principle for the gravitational Vlasov-Poisson system via Monge-Ampere approximation" | ||
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| Han-Kwan, Daniel (Ecole Polytechnique & CNRS) | WPI Seminar Room 08.135 | Thu, 10. Dec 15, 11:00 |
| "Quasineutral limit for Vlasov-Poisson: a review" | ||
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| Nguyen, Toan (U. Penn State) | WPI Seminar Room 08.135 | Thu, 10. Dec 15, 9:30 |
| "Ill-posedness of the hydrostatic Euler and singular Vlasov equations" | ||
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| Diamond, Patrick (UCSD) | WPI Seminar Room 08.135 | Wed, 9. Dec 15, 14:30 |
| "The quasilinear theory for the Vlasov plasma dynamics: content, success, failures" | ||
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| Hauray, Maxime (U. AMU) | WPI Seminar Room 08.135 | Wed, 9. Dec 15, 12:00 |
| "Weak-strong stability and mean-field limit for Vlasov equations" | ||
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| Bardos, Claude (WPI & ICP c/o Paris 6 & 7) | WPI Seminar Room 08.135 | Wed, 9. Dec 15, 11:00 |
| "About the Maxwell Boltzmann equation" | ||
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| Gerard-Varet, David (U. Paris 7) | WPI Seminar Room 08.135 | Wed, 9. Dec 15, 9:30 |
| "Trend to equilibrium in the Kuramoto model" | ||
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| Hahn, Oliver (Obs. Nice & UNS) | WPI Seminar Room 08.135 | Tue, 8. Dec 15, 14:40 |
| "Cosmic structure formation in the continuum limit" | ||
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| Sobolevski, Andrei + Frisch, Uriel (Obs. Nice & CNRS) + Besse, Nicolas (Obs. Nice & UCA) | WPI Seminar Room 08.135 | Tue, 8. Dec 15, 12:00 |
| "Work in Progress on Lagrangian time-analyticity of the Vlasov-Poisson flow" | ||
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| Sousbie, Thierry (IAP & CNRS) | WPI Seminar Room 08.135 | Tue, 8. Dec 15, 11:00 |
| "ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation" | ||
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| Colombi, Stephane (IAP & CNRS) | WPI Seminar Room 08.135 | Tue, 8. Dec 15, 9:30 |
| "Evolution of collisionless, initially cold, self-gravitating Systems in one dimension" | ||
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| Besse, Nicolas (Obs. Nice & UCA) | WPI Seminar Room 08.135 | Mon, 7. Dec 15, 15:30 |
| "On the eigenvalue problem for the gyrokinetic equations" | ||
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| WPI Seminar Room 08.135 | Mon, 7. Dec 15, 14:30 | |
| Presentation of participants | ||
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| WPI Seminar Room 08.135 | Mon, 7. Dec 15, 14:20 | |
| Opening of Workshop and self presentation of participants (5 min each) | ||
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| Peter Weibel | Künstlerhaus Vienna | Mon, 12. Oct 15, 18:00 |
| "Gotthard Günther and the Digital Revolution" | ||
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| Gerhard Widmer | Künstlerhaus Vienna | Mon, 12. Oct 15, 17:00 |
| "Con Espressione! Towards a New Level of Music Understanding in Computers" | ||
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| Kurt Hofstetter | Künstlerhaus Vienna | Mon, 12. Oct 15, 16:00 |
| "On the Event Horizon of Order" | ||
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| Dirk Frettlöh | Künstlerhaus Vienna | Mon, 12. Oct 15, 15:00 |
| "Mathematical Quasicrystals And Inductive Rotation Tilings" | ||
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| Texier, Benjamin (Univ. de Paris VII) | WPI, Seminar Room 08.135 | Fri, 2. Oct 15, 10:30 |
| Space-time resonances and high-frequency instabilities in two-fluid Euler-Maxwell systems | ||
We show that space-time resonances induce high-frequency instabilities in the two-fluid Euler-Maxwell system. This implies in particular that the Zakharov approximation to Euler-Maxwell is stable if and only if the group velocity vanishes. The instability proof relies on a short-time representation formula for the flows of pseudo-differential operators of order zero. This is joint work with Eric Dumas (Grenoble) and Lu Yong (Prague). | ||
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| Watanabe, Tatsuya (Kyoto Sangyo University) | WPI, Seminar Room 08.135 | Fri, 2. Oct 15, 9:15 |
| Uniqueness and asymptotic behavior of ground states for quasilinear Schrodinger equations arising in plasma physics | ||
In this talk, we consider a quasiinear Schrodinger equation which appears in the study of plasma physics. We are interested in the uniqueness of ground states without assuming any restriction on a physical parameter. We also study asymptotic behavior of ground states as the parameter goes to zero. | ||
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| Stimming, Hans-Peter (Univ. Wien) | WPI, Seminar Room 08.135 | Thu, 1. Oct 15, 11:15 |
| Non-local NLS of derivative type for modeling highly nonlocal optical nonlinearities | ||
A new NLS type equation is employed for modeling long-range interactions in nonlinear optics, in a collaboration with experimental physicists. It is of quasilinear type and models fluctuations around a 'continuous-wave polariton' which are chosen according to Bogoliubov theory. We present a numerical discretization method and simulation results. Mathematical theory for this equation is work in progress. | ||
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| Pomponio, Alessio (Politecnico di Bari) | WPI, Seminar Room 08.135 | Thu, 1. Oct 15, 10:30 |
| Born-Infeld equations in the electrostatic case | ||
The equation in (BI) appears for instance in the Born-Infeld nonlinear electromagnetic theory: in the electrostatic case it corresponds to the Gauss law in the classical Maxwell theory and so is the electric potential and is an assigned extended charge density. We discuss existence, uniqueness and regularity of the solution of (BI). The results have been obtained in a joint work with Denis Bonheure and Pietro d’Avenia. | ||
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| Ohta, Masahito (Science University of Tokyo) | WPI, Seminar Room 08.135 | Thu, 1. Oct 15, 9:15 |
| Stability of standing waves for a system of nonlinear Schrodinger equations with cubic nonlinearity | ||
We consider a system of nonlinear Schrodinger equations with cubic nonlinearity, called a coherently coupled NLS system (CCNLS) in nonlinear optics, in one space dimension. We study orbital stability and instability of standing wave solutions of (CCNLS), and prove similar results to Colin and Ohta (2012) which studies a system of NLS equations with quadratic nonlinearity. This is a joint work with Shotaro Kawahara (Tokyo University of Science). | ||
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| Melinand, Benjamin (Univ. de Bordeaux) | WPI, Seminar Room 08.135 | Wed, 30. Sep 15, 11:15 |
| The Proudman resonance | ||
In this talk, I will explain the Proudman resonance. It is a resonant respond in shallow waters of a water body on a traveling atmospheric disturbance when the speed of the disturbance is close to the typical water wave velocity. In order to explain this phenomenon, I will prove a local well-posedness of the water waves equations with a non constant pressure at the surface, taking into account the dependence of small physical parameters. Then, I will justify mathematically the historical work of Proudman. Finally, I will study the linear water waves equations and I will give dispersion estimates in order to extend The Proudman resonance to deeper waters. To complete these asymptotic models, I will show some numerical simulations. | ||
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| Le Coz, Stefan (Univ. De Toulouse) | WPI, Seminar Room 08.135 | Wed, 30. Sep 15, 10:30 |
| On a singularly perturbed Gross-Pitaevskii equation | ||
We consider the 1D Gross-Pitaevskii equation perturbed by a Dirac potential. Using a fine analysis of the properties of the linear propagator, we study the well-posedness of the Cauchy Problem in the energy space of functions with modulus 1 at infinity. Then we study existence and stability of the black solitons with a combination of variational and perturbation arguments. This is a joint work with Isabella Ianni and Julien Royer. | ||
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| Klein, Christian (Univ. de Bourgogne) | WPI, Seminar Room 08.135 | Wed, 30. Sep 15, 9:15 |
| Numerical study of fractional nonlinear Schrödinger equations | ||
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation. | ||
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| Hirayama; Hiroyuki (Nagoya Univ.) | WPI, Seminar Room 08.135 | Tue, 29. Sep 15, 14:15 |
| Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with periodic initial data. | ||
We consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin as a model of laser-plasma interaction. In this talk, we prove the well-posedness of this system for the periodic initial data. In particular, if the coefficients of Laplacian satisfy some conditions, then the well-posedness is proved at the scaling critical regularity by using U^2 and V^2 spaces. | ||
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| Hayashi, Nakao (Osaka Univ.) | WPI, Seminar Room 08.135 | Tue, 29. Sep 15, 11:15 |
| Asymptotics of solutions to fourth-order nonlinear Schrödinger equations | ||
We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation with a critical nonlinearity and prove the asymptotic stability of solutions in the neighborhood of the self similar solutions under the non zero mass condition and the smallness on the data. | ||
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| González de Alaiza Martínez, Pedro (CEA) | WPI, Seminar Room 08.135 | Tue, 29. Sep 15, 10:30 |
| Mathematical models for terahertz emissions by laser-gas interaction | ||
Terahertz (THz) emissions have nowadays important applications such as security screening and imaging. Laser-gas interaction reveals itself to be a promising technique to generate broadband and intense THz sources suitable for these applications. In this talk, I will explain recent mathematical models and their underlying physics explaining the THz radiation generated when ultrafast laser pulses ionize a gas at high intensities. Solutions to the model equations will be compared with direct numerical simulations. | ||
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| Dumas, Eric (Univ. de Grenoble) | WPI, Seminar Room 08.135 | Tue, 29. Sep 15, 9:15 |
| Some variants of the focusing NLS equations Derivation, justification and open problems | ||
The usual model of nonlinear optics given by the cubic NLS equation is too crude to describe large intensity phenomenas such as filamentation, which modifies the focusing of laser beams. I shall explain how to derive some more appropriate variants of the NLS model from Maxwell's equations, using improved approximations of the original dispersion relation or taking ionization effects into account. I shall provide rigorous error estimates for the models considered, and also discuss some open problems related to these modified NLS equations. This is joint work with David Lannes and Jeremie Szeftel. | ||
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| Saut, Jean-Claude (Univ. Paris d'Orsay) | WPI, Seminar Room 08.135 | Mon, 28. Sep 15, 15:30 |
| Full dispersion water waves models | ||
We will survey recent results and open problems on various nonlocal "full dispersion" models of surface water waves. | ||
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| Colin, Mathieu (Univ. de Bordeaux) | WPI, Seminar Room 08.135 | Mon, 28. Sep 15, 14:30 |
| Solitons in quadratic media | ||
In this talk, we investigate the properties of solitonic structures arising in quadratic media. More precisely, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or nonelliptic systems and we address the problem of orbital stability. Finally, we present some numerical experiments in order to compute localized states for several regimes. | ||
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| Esther Daus (TU Wien) | WPI, Seminar Room 08.135 | Wed, 16. Sep 15, 10:45 |
| Cross-diffusion systems: "Population dynamics model (Joint work with A. Jüngel), Diffusion through obstacles (Joint work with M. Bruna, A. Jüngel)" | ||
In this talk we will discuss two different cross-diffusion models. The first model is used in population dynamics in biology and can be derived from a lattice in the case when we are not taking into account any volume-filling effects. We will present recent results concerning the existence of global weak solutions under the assumption that the system possesses a formal gradient-flow structure using ideas of [A. Jüngel: Boundedness-by-entropy method. Nonlinearity 28 (2015)]. The second model describes diffusion through obstacles. The underlying cross-diffusion system can be derived from a two species mixture of Brownian hard spheres. We will discuss open questions concerning this model. | ||
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| Ulisse Stefanelli (Univ. Wien) | WPI, Seminar Room 08.135 | Wed, 16. Sep 15, 10:00 |
| "The WED principle in metric spaces" | ||
I will present the WED variational approach to gradient-flow evolution in metric spaces. A reference application is to densities and empirical measures. In the linear-space case, the WED strategy entails in an elliptic-in-time regularization of the problem. The picture in the metric case is confined to the variational level and the discussion relies on a Pontyagin-type principle. This is joint work with Riccarda Rossi (Brescia), Giuseppe Savar' (Pavia), and Antonio Segatti (Pavia). | ||
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| Ruediger Müller (Univ. WIAS) | WPI, Seminar Room 08.135 | Tue, 15. Sep 15, 14:45 |
| "Modeling of Ion Transport in Nanopores" | ||
Until recently, the (Poisson-)Nernst-Planck equations have been the standard model for the description of ion transport in diluted electrolyte solutions, although it was known that they fail to reasonably limit the ion concentration in diffuse double layers. This weakness can be remedied by a thermodynamic consistent coupling to the momentum balance and introducing an appropriate elastic law, rather than by a mere modification of the entropy of mixing. In many electrochemical applications, the Debye length --that controls the width of the diffuse layers-- is typically very small compared to the macroscopic dimensions of the system. In these situations a spacial resolution of the layers is often not necessary. By the method of formal asymptotic analysis we derive a reduced model that is locally electric neutral and does not resolve the layers but incorporates all relevant features of the layers into a new set of interface equations. Nanopores typically have a strongly anisotropic geometry where the diameter is close to the Debye length but the length in axial direction is larger by at least one order of magnitude. We discuss the scaling to dimensionless quantities and present a reduced 1d-model for arbitrary geometries with rotational symmetry. Multi-dimensional solutions that resolve boundary layers can be recovered from the lower-dimensional solution. | ||
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| Ulrich Dobramysl (Univ. Oxford) | WPI, Seminar Room 08.135 | Tue, 15. Sep 15, 14:00 |
| "Exploring unknown environments - from robot experiments to numerical modelling" | ||
I will present examples of modelling collective movement via robot experiments. In the first part I will focus on an investigation on how two communicating individuals can most efficiently navigate a corridor without external sensory input. The second part of my talk will be about robot swarms and their strategies for target finding in an unknown environment. These studies where performed via a combination of robot experiments and numerical simulations. | ||
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| Hartmut Loewen (Univ. Düsseldorf) | WPI, Seminar Room 08.135 | Tue, 15. Sep 15, 11:15 |
| "Phase separation and turbulence in active Systems" | ||
Ordinary materials are "passive" in the sense that their constituents are typically made by inert particles which are subjected to thermal fluctuations, internal interactions and external fields but do not move on their own. Living systems, like schools of fish, swarms of birds, pedestrians and swimming microbes are called "active matter" since they are composed of self-propelled constituents. Active matter is intrinsically in nonequilibrium and exhibits a plethora of novel phenomena as revealed by a recent combined effort of statistical theory, hydrodynamics and real-space experiments. The talk provides an introduction into the modelling of active matter focussing on biological and artificial microswimmers as key examples of active systems. A number of single-particle and collective phenomena in active matter will be addressed ranging from the most disordered state of matter (turbulence) to the purely kinetic phase separation in active systems. | ||
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| Jay Newby (Univ. MBI Ohio) | WPI, Seminar Room 08.135 | Tue, 15. Sep 15, 10:00 |
| Metastable dynamics in gene circuits driven by intrinsic noise | ||
Metastable transitions are rare events, such as bistable switching, that occur under weak noise conditions, causing dramatic shifts in the expression of a gene. Within a gene circuit, one or more genes randomly switch between regulatory states, each having a different mRNA transcription rate. The circuit is self regulating when the proteins it produces affect the rate of switching between gene regulatory states. Under weak noise conditions, the deterministic forces are much stronger than fluctuations from gene switching and protein synthesis. A general tool used to describe metastability is the quasi stationary analysis (QSA). A large deviation principle is der ived so that the QSA can explicitly account for random gene switching without using an adiabatic limit or diffusion approximation, which are unreliable and inaccurate for metastable events.This allows the existing asymptotic and numerical methods that have been developed for continuous Markov processes to be used to analyze the full model. | ||
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| Jon Chapman (Univ. Oxford) | WPI, Seminar Room 08.135 | Mon, 14. Sep 15, 16:15 |
| "Excluded volume effects in drift Diffusion" | ||
When diffusing agents interact with each other their motions are correlated, and the configuration space is of very high dimension. Often an equation for the marginal distribution function of one particle (the “concentration”) is sought by “integrating out” the positions of all the others. This leads to the classic problem of closure, since the equation for the concentration so derived depends on the two-point correlation function. A common closure is to assume independence at this stage, leading to some form of nonlinear (drift) diffusion equation. Such an approach works well for long range interactions (such as electric fields), but fails for short range interactions (such as steric effects). Here we consider an alternative approach using matched asymptotic expansions, in which the approximation is entirely systematic. We show how information about correlations can be recovered from the concentration. Finally we consider some of the difficulties when both long and short range forces are present. | ||
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| Ansgar Juengel (TU Wien) | WPI, Seminar Room 08.135 | Mon, 14. Sep 15, 15:30 |
| "Modeling and analysis of multi-species systems in biology" | ||
The nature is dominated by systems composed of many individuals with a collective behavior. Examples include wildlife populations, biological cell dynamics, and tumor growth. There is a fast growing interest in multispecies systems both in theoretical biology and applied mathematics, but because of their enormous complexity, the scientific understanding is still very poor. Instead of calculating the trajectories of all individuals, it is computationally much simpler to describe the dynamics of the individuals on a macroscopic level by averaged quantities such as population densities. This leads to systems of highly nonlinear partial differential equations with cross diffusion, which may reveal surprising effects such as uphill diffusion and diffusioninduced instabilities, seemingly contradicting our intuition on diffusion. Major difficulties of the mathematical analysis of the crossdiffusion equations are their highly nonlinear structure and the lack of positive definiteness of the diffusion matrix. In this talk, a method inspired from nonequilibrium thermodynamics is proposed, which allows for a mathematical theory of some classes of such systems. It is based on a transformation of entropy variables which make the diffusion matrix positive definite. This property is a purely algebraic condition and may be shown by computer algebra systems. We explain the technique for systems modeling populations and transport through ion channels. | ||
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| Marie-Therese Wolfram (Univ. Wien) | WPI, Seminar Room 08.135 | Mon, 14. Sep 15, 14:30 |
| "Interaction with fluids" | ||
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| Jan-Frederick Pietschmann (Univ. Münster) | WPI, Seminar Room 08.135 | Mon, 14. Sep 15, 14:00 |
| "Cross-Diffusion from on-lattice and inverse problems" | ||
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| Maria Bruna (Univ. Oxford) | WPI, Seminar Room 08.135 | Mon, 14. Sep 15, 13:30 |
| "Cross-diffusion models for offlattice and gradient flow" | ||
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| Stimming, Hans-Peter (WPI c/o U. Wien) | WPI Seminar Room 08.135 | Thu, 6. Aug 15, 14:30 |
| “Absorbing Boundary Conditions for Schrodinger and Wave equations: PML vs ECS” | ||
The perfectly matched layers (PML) and exterior complex scaling (ECS) methods for absorbing boundary conditions are analyzed using spectral decomposition. Both methods are derived as analytical continuations of unitary to contractive transformations. We find that the methods are mathematically and numerically distinct: ECS is complex stretching that rotates the operator's spectrum into the complex plane, whereas PML is a complex gauge transform which shifts the spectrum. Consequently, the schemes differ in their time-stability. Numerical examples are given. | ||
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| Zhang, Yong (WPI c/o U. Wien) | WPI Seminar Room 08.135 | Thu, 6. Aug 15, 13:30 |
| “Efficient evaluation of nonlocal potentials: NUFFT and Gaussian Sum Approximations” | ||
We introduce accurate and efficient methods for nonlocal potentials evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipole-dipole potentials. Both methods rely on the same assumption: the density is smooth and fast decaying. The first method,proposed by Jiang, Greengard and Bao, evaluates the potential in spherical/polar coordinates using NonUniform FFT algorithm, where the singularity of the Fourier representation disappears automatically, while the second one is based on a Gaussian-sum approximation of the singular convolution kernel and Taylor expansion of the density. Both methods are accelerated by fast Fourier transforms (FFT). They are accurate (14-16 digits), efficient ($O(Nlog N)$ complexity), low in storage, easily adaptable to other different kernels, applicable for anisotropic densities and highly parallelizable. | ||
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| Descombes, Stephane (U. Nice) | WPI Seminar Room 08.135 | Thu, 6. Aug 15, 11:00 |
| “Exponential operator splitting methods for evolutionary problems and applications to nonlinear Schrödinger equations in the semi-classical regime“ | ||
In this talk, I investigate the error behaviour of exponential operator splitting methods for nonlinear evolutionary problems. In particular, I will present an exact local error representation that is suitable in the presence of critical parameters. Essential tools in the theoretical analysis including time-dependent nonlinear Schrödinger equations in the semi-classical regime as well as parabolic initial-boundary value problems with high spatial gradients are an abstract formulation of differential equations on function spaces and the formal calculus of Lie-derivatives. | ||
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| Besse, Christophe (U. Toulouse) | WPI Seminar Room 08.135 | Thu, 6. Aug 15, 10:00 |
| “Exponential integrators for NLS equations with application to rotating BECs“ | ||
In this talk, I will present various time integrators for NLS equations when the potentials are time dependent. In this case, the usual time splitting schemes fail. I will introduce exponential Runge-Kutta scheme and Lawson scheme and present some of their properties. | ||
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| Luong, Hung (U. Wien) | WPI Seminar Room 08.135 | Wed, 5. Aug 15, 12:00 |
| “On the Cauchy problem of some 2-d models on the background of 1-d soliton solution of the cubic nonlinear Schrödinger equation" | ||
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| Bardos, Claude (WPI & ICP c/o Paris) | WPI Seminar Room 08.135 | Wed, 5. Aug 15, 11:00 |
| “Formal derivation of the Vlasov Boltzmann relation” | ||
I report on current work with Toan Nguyen and Francois Golse. | ||
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| Gottlieb, Alex (WPI) | WPI Seminar Room 08.135 | Wed, 5. Aug 15, 10:00 |
| “Entropy measures for quantum correlation” | ||
We use quantum Rényi divergences to define "correlation" functionals of many-fermion states (density operators on a Fock space). The "reference" state for the relative entropy functional is the unique gauge-invariant quasi-free (g.i.q.f.) state with the same 1-RDM as the state of interest. That is, the "correlation" of the state of interest is its Rényi divergence from the uniquely associated g.i.q.f. state. Correlation functionals defined in this way enjoy the following properties: (a) they take only non-negative values, possibly infinity; (b) they assign the value 0 to all Slater determinant states; (c) they are monotone with respect to restriction of states; (d) they are additive over independent subsystems; and (e) they are invariant under changes of the 1-particle basis (Bogoliubov transformations). The quantum relative entropy or quantum Kullback-Leibler divergence is a special and distinguished member of any family of quantum Rényi divergences (of which there are at least two). The associated correlation functional, defined using quantum Kullback-Leibler divergence, we call "nonfreeness." Nonfreeness enjoys further appealing properties not shared by related correlation functionals: (f) the nonfreeness of a state X is the minimum possible value for the entropy of X relative to any g.i.q.f. reference state; (g) there is a simple formula for a pure state's nonfreeness in terms of it's natural occupation numbers; and (h) within the convex set of n-fermion states with given 1-RDM, the nonfreeness minimizer equals the entropy maximizer, which is the Gibbs canonical (n-particle) state. | ||
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| Nguyen, Toan (Penn State) | WPI Seminar Room 08.135 | Tue, 4. Aug 15, 14:00 |
| "Grenier's iterative scheme for instability and some new applications" | ||
"The talk is planned to revisit Grenier's scheme for instability of Euler and Prandtl, introduced in his CPAM-2000 paper, and to present some new applications in the instability of generic boundary layers and instability of Vlasov-Maxwell in the classical limit". | ||
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| Pawilowski, Boris (U. Wien & U. Rennes) | WPI Seminar Room 08.135 | Tue, 4. Aug 15, 12:00 |
| “Mean field limits for discrete NLS: analysis and numerics” | ||
In my thesis, jointly supervised by N.J. Mauser and F. Nier, we deal with approximations of the time-dependent linear many body Schrödinger equation with a two particles interaction potential, by introducing a discrete version of the equation and mean field limits. We consider the bosonic Fock space in a finite dimensional setting. Mathematical tools include the reduced density matrices and Wigner measure techniques exploiting the formal analogy to semi-classical limits. | ||
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| Nier, Francis (U. Paris 13) | WPI Seminar Room 08.135 | Tue, 4. Aug 15, 11:00 |
| “Phase-space approach to the bosonic mean field dynamics : a review” | ||
After recalling old or more recent point of views on bosonic quantum field theory and mean field problems, the series of works in collaboration with Z. Ammari will be summarized. This phase-space presentation implements the old dream of an infinite dimensional microlocal analysis. In particular the mean field dynamics is nothing but a propagation of singularity result in the semiclassical regime. This talk will put the stress on the key issues related with the infinite dimensional setting and on the new results for the mean field problem provided by this approach. | ||
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| Golse Francois (X) | WPI Seminar Room 08.135 | Tue, 4. Aug 15, 10:00 |
| “On the mean-field and classical limits for the N-body Schrödinger equation” | ||
This talk proposes a quantitative convergence estimate for the mean-field limit of the N-body Schrödinger equation that is uniform in the classical limit. It is based on a new variant of the Dobrushin approach for the mean field limit in classical mechanics, which avoids the use of particle trajectories and empirical measures, and has a very natural quantum analogue. (Work in collaboration with C. Mouhot and T. Paul). | ||
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| Germain, Pierre (Courant) | WPI Seminar Room 08.135 | Mon, 3. Aug 15, 15:15 |
| “On the derivation of the kinetic wave equation” | ||
The kinetic wave equation is of central importance in the theory of weak turbulence, but no rigorous derivation of it is known. I will show how it can be derived from NLS on the torus with random forcing, in the small nonlinearity / big box limit. This is joint work with Isabelle Gallagher and Zaher Hani. | ||
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| Brenier, Yann (CNRS X) | WPI Seminar Room 08.135 | Mon, 3. Aug 15, 14:15 |
| "When Madelung comes up...." | ||
After recalling the remarkable formulation made in 1926 by Erwin Madelung of the Schrödinger equation in terms of fluid mechanics, I will introduce a rational scheme, based on the least action principle and some non-linear rescaling of the time variable, starting from Euler's equations of isothermal compressible fluids (1755), followed by Fourier's heat conduction equation (1807), leading to Schrödinger's equation of quantum mechanics (1925). Finally, I will suggest the application of this scheme to Magneto-hydrodynamics. Madelung, E. (1926). "Eine anschauliche Deutung der Gleichung von Schrödinger". Naturwissenschaften 14 (45): 1004–1004. | ||
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| Mauser, Norbert J (WPI & ICP c/o U. Wien) | WPI Seminar Room 08.135 | Mon, 3. Aug 15, 14:00 |
| “Welcome to Vienna, birthplace of Boltzmann, Schrödinger and Pauli” | ||
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| Dorland, Bill (Maryland) | WPI Seminar Room 08.135 | Fri, 31. Jul 15, 10:00 |
| Turbulent dissipation challenge: what ought to be done | ||
Many naturally occurring and man-made plasmas are collisionless and turbulent. It is not yet well understood how the energy in fields and fluid motions is transferred into the thermal degrees of freedom of constituent particles in such systems. The debate at present primarily concerns proton heating. Multiple possible heating mechanisms have been proposed over the past few decades, including cyclotron damping, Landau damping, heating at intermittent structures and stochastic heating. Recently, a community-driven effort was proposed (Parashar & Salem, 2013, arXiv:1303.0204) to bring the community together and understand the relative contributions of these processes under given conditions. In this paper, we propose the first step of this challenge: a set of problems and diagnostics for benchmarking and comparing different types of 2.5D simulations. These comparisons will provide insights into the strengths and limitations of different types of numerical simulations and will help guide subsequent stages of the challenge. | ||
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| Kunz, Matt (Princeton) | WPI Seminar Room 08.135 | Thu, 30. Jul 15, 16:15 |
| Firehose and mirror: old and new results | ||
Hybrid-kinetic numerical simulations of firehose and mirror instabilities in a collisionless plasma are performed in which pressure anisotropy is driven as the magnetic field is changed by a persistent linear shear S . For a decreasing field, it is found that mostly oblique firehose fluctuations grow at ion Larmor scales and saturate with energies ∝S 1/2 ; the pressure anisotropy is pinned at the stability threshold by particle scattering off microscale fluctuations. In contrast, nonlinear mirror fluctuations are large compared to the ion Larmor scale and grow secularly in time; marginality is maintained by an increasing population of resonant particles trapped in magnetic mirrors. After one shear time, saturated order-unity magnetic mirrors are formed and particles scatter off their sharp edges. Both instabilities drive sub-ion-Larmor–scale fluctuations, which appear to be kinetic-Alfvén-wave turbulence. Our results impact theories of momentum and heat transport in astrophysical and space plasmas, in which the stretching of a magnetic field by shear is a generic process. | ||
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| Schekochihin, Alex (Oxford) | WPI Seminar Room 08.135 | Thu, 30. Jul 15, 10:00 |
| Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence | ||
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| Komarov, Sergey (MPA Garching) | WPI Seminar Room 08.135 | Wed, 29. Jul 15, 10:00 |
| Suppression of thermal conductivity by mirror fields | ||
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| Spitovsky, Anatoly (Princeton) | WPI Seminar Room 08.135 | Tue, 28. Jul 15, 16:15 |
| Magnetogenesis in collisionless shear flows | ||
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| Quataert, Eliot (Berkeley) | WPI Seminar Room 08.135 | Tue, 28. Jul 15, 10:00 |
| Sheared electron kinetics: whistler and mirror instabilities | ||
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| Catto, Peter (MIT) | WPI Seminar Room 08.135 | Mon, 27. Jul 15, 16:15 |
| Three dimensional magnetized and rotating hot plasma equilibria in a gravitational field | ||
A rotating and magnetized three-dimensional axisymmetric equilibrium for hot plasma confined by a gravitational field is found. The plasma density and current can exhibit strong equatorial plane localization, resulting in disk equilibria with open magnetic field lines. The associated equatorial plane pinching results in magnetic field flaring, implying a strong gravitational squeezing of the plasma carrying ambient magnetic field lines toward the gravitational source. At high plasma pressure, the magnetic field becomes strongly radial outside the disk. The model predicts the rotation frequency bound, the condition for a plasma disk, and the requirement for strong magnetic field flaring. | ||
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| Roberg-Clark, Gareth (Maryland) | WPI Seminar Room 08.135 | Mon, 27. Jul 15, 10:00 |
| Heat-flux driven instabilities in high-beta plasmas and their relevance for AGN feedback in galaxy clusters | ||
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| Wilkie, Georg (Maryland) | WPI Seminar Room 08.135 | Fri, 24. Jul 15, 10:00 |
| Coupled radius-energy transport of alpha particles in GK turbulence | ||
To rigorously model fast ions in fusion plasmas, a non-Maxwellian equilibrium distribution must be used. In this work, the response of high-energy alpha particles to electrostatic turbulence has been analyzed for several different tokamak parameters. Our results are consistent with known scalings and experimental evidence that alpha particles are generally well confined: on the order of several seconds. It is also confirmed that the effect of alphas on the turbulence is negligible at realistically low concentrations, consistent with linear theory. It is demonstrated that the usual practice of using a high-temperature Maxwellian, while previously shown to give an adequate order-of-magnitude estimate of the diffusion coefficient, gives incorrect estimates for the radial alpha particle flux, and a method of correcting it in general is provided. Furthermore, we see that the timescales associated with collisions and transport compete at moderate energies, calling into question the assumption that alpha particles remain confined to a flux surface that is used in the derivation of the slowing-down distribution. | ||
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| Hammett, Greg (Princeton PPL) | WPI Seminar Room 08.135 | Thu, 23. Jul 15, 16:15 |
| Lithium vapour boxes | ||
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| Citrin, Jonathan (CEA/DIFFER) | WPI Seminar Room 08.135 | Thu, 23. Jul 15, 10:00 |
| Overview and open questions on electromagnetic effects on tokamak transport | ||
The impact of electromagnetic stabilization and flow shear stabilization on ITG turbulence is investigated. Analysis of a low-β JET L-mode discharge illustrates the relation between ITG stabilization and proximity to the electromagnetic instability threshold. This threshold is reduced by suprathermal pressure gradients, highlighting the effectiveness of fast ions in ITG stabilization. Extensive linear and nonlinear gyrokinetic simulations are then carried out for the high-β JET hybrid discharge 75225, at two separate locations at inner and outer radii. It is found that at the inner radius, nonlinear electromagnetic stabilization is dominant and is critical for achieving simulated heat fluxes in agreement with the experiment. The enhancement of this effect by suprathermal pressure also remains significant. It is also found that flow shear stabilization is not effective at the inner radii. However, at outer radii the situation is reversed. Electromagnetic stabilization is negligible while the flow shear stabilization is significant. These results constitute the high-β generalization of comparable observations found at low-β at JET. This is encouraging for the extrapolation of electromagnetic ITG stabilization to future devices. An estimation of the impact of this effect on the ITER hybrid scenario leads to a 20% fusion power improvement. | ||
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| Waelbroek, Francois (IFS, UT Austin) | WPI Seminar Room 08.135 | Wed, 22. Jul 15, 10:00 |
| Magnetic islands and Hamiltonian gyrofluid models | ||
A Lie- Poisson bracket is presented for a four-field gyrofluid model with compressible ions and magnetic field curvature, thereby showing the model to be Hamiltonian. In particular, we find that in addition to commonly adopted magnetic curvature terms present in the continuity equations, analogous terms must be retained also in the momentum equations, in order to have a Lie-Poisson structure. The corresponding Casimir invariants are presented, and shown to be associated to four Lagrangian invariants, that get advected by appropriate ''velocity'' fields during the dynamics. This differs from a cold ion limit, in which the Lie-Poisson bracket transforms into the sum of direct and semidirect products, leading to only three Lagrangian invariants. | ||
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| Citrin, Jonathan (CEA/DIFFER) | WPI Seminar Room 08.135 | Tue, 21. Jul 15, 16:15 |
| New approach for realtime capable and first-principle based transport modelling | ||
A real-time capable core turbulence tokamak transport model is developed. This model is constructed from the regularized nonlinear regression of quasilinear gyrokinetic transport code output. The regression is performed with a multilayer perceptron neural network. The transport code input for the neural network training set consists of five dimensions, and is limited to adiabatic electrons. The neural network model successfully reproduces transport fluxes predicted by the original quasilinear model, while gaining five orders of magnitude in computation time. The model is implemented in a real-time capable tokamak simulator, and simulates a 300s ITER discharge in 10s. This proof-of-principle for regression based transport models anticipates a significant widening of input space dimensionality and physics realism for future training sets. This aims to provide unprecedented computational speed coupled with first-principle based physics for real-time control and integrated modelling applications. | ||
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| Mandell, Noah (Princeton) | WPI Seminar Room 08.135 | Tue, 21. Jul 15, 10:00 |
| New gyrofluid closures, hybrid gyrofluid simulations with gyrokinetic zonal flows, Trinity/GryfX coupling, etc. | ||
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| Hammett, Greg (Princeton PPL) | WPI Seminar Room 08.135 | Mon, 20. Jul 15, 16:15 |
| Progress towards continuum gyrokinetic simulations of the edge region | ||
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| Abel, Ian (Princeton) | WPI Seminar Room 08.135 | Mon, 20. Jul 15, 10:00 |
| Multiscale kinetic edge models | ||
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| Czirok, Andras (University of Kansas) | Lecture room HS 13, 2nd floor | Fri, 3. Jul 15, 15:30 |
| Contribution of cell contractility to mesothelioma nodule formation | ||
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| Szakacs, Gergely (Medical University Vienna) | Lecture room HS 13, 2nd floor | Fri, 3. Jul 15, 14:20 |
| Modeling in vitro selection of drug resistant cancer cells using a cellular automaton model | ||
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| Menche, Jörg (CEU Budapest) | Lecture room HS 13, 2nd floor | Fri, 3. Jul 15, 13:30 |
| Human diseases in the interactome | ||
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| Berger, Walter (Medical University Vienna) | Lecture room HS 13, 2nd floor | Fri, 3. Jul 15, 11:00 |
| Activity of defense: modeling the anticancer drug response | ||
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| Perthame, Benoit (University of Paris 6) | Lecture room HS 13, 2nd floor | Fri, 3. Jul 15, 10:10 |
| The derivation of free-‐ boundary (incompressible) models for tumor growth and the Hele-‐ Shaw asymptotic | ||
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| Marciniak-‐Czochra, Anna (University of Heidelberg) | Lecture room HS 13, 2nd floor | Fri, 3. Jul 15, 9:00 |
| Mathematical models of clonal selection and therapy resistance in acute leukemias | ||
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| Gerner, Christopher (Institute for Analytical Chemistry, Univ. Wien) | Lecture room HS 13, 2nd floor | Thu, 2. Jul 15, 16:20 |
| Investigation of anticancer drug effects via proteome and metabolome profiling: do we really understand what these drugs are doing? | ||
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| Levy, Doron (University of Maryland) | Lecture room HS 13, 2nd floor | Thu, 2. Jul 15, 15:30 |
| Modeling the immune response to chronic myeloid leukemia | ||
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| Sykacek, Peter (Department of Biotechnology, BOKU, Vienna) | Lecture room HS 13, 2nd floor | Thu, 2. Jul 15, 14:20 |
| Probabilistic models in translational cancer research: converting low level leads to comprehensible predictions | ||
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| Clairambault, Jean (INRIA, Rocquencourt) | Lecture room HS 13, 2nd floor | Thu, 2. Jul 15, 13:30 |
| Drug resistance in cancer: biology, medicine, and modeling | ||
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| Saut, Olivier (CNRS, INRIA, Bordeaux) | Lecture room HS 13, 2nd floor | Thu, 2. Jul 15, 11:00 |
| Data assimilation in tumor growth modeling: towards patient calibrated models using imaging devices | ||
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| Grebien, Florian (Boltzmann Institute for Cancer Research, Vienna) | Lecture room HS 13, 2nd floor | Thu, 2. Jul 15, 10:10 |
| Functional studies of leukemia oncoproteins using integrated approaches | ||
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| Anderson, Alexander (Moffitt Cancer Center) | Lecture room HS 13, 2nd floor | Thu, 2. Jul 15, 9:00 |
| An integrated approach to understanding tumor-‐ stromal interactions in cancer progression and treatment | ||
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| QingLin Tang (University of Singapore) | WPI, OMP 1, Seminar Room 08.135 | Thu, 25. Jun 15, 10:00 |
| Computing ground states of spin 2 Bose-Einstein condensates by the normalized gradient flow | ||
In this talk, an efficient and accurate numerical method will be proposed to compute the ground state of spin-2 Bose-Einstein condensates (BECs) by using the normalized gradient flow (NGF) or imaginary time method (ITM). The key idea is twofold. One is to find the five projection or normalization conditions that are used in the projection step of NGF/ITM, while the other one is to find a good initial data for the NGF/ITM. Based on the relations between chemical potentials and the two physical constrains given by the conservation of the totlal mass and magnetization, these five projection or normalization conditions can be completely and uniquely determined in the context of the the discrete scheme of the NGF discretized by back-Euler finite difference (BEFD) method, which allows one to successfully extend the most powerful and popular NGF/ITM to compute the ground state of spin-2 BECs. Additionally, the structures and properties of the ground states in a uniform system are analysed so as to construct efficient initial data for NGF/ITM. Extensive numerical results on ground states of spin-2 BECs with ferromagnetic/nematic/cyclic interaction and harmonic/optical lattice potential in one/two dimensions are reported to show the efficiency of our method and to demonstrate some interesting physical phenomena. | ||
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| Suciu, Dan (University of Washington) | Zemanek seminar room; TU Wien | Sat, 6. Jun 15, 11:35 |
| Query Compilation: the View from the Database Side | ||
We study knowledge compilation for Boolean formulas that are given as groundings of First Order formulas. This problem is motivated by probabilistic databases, where each record in the database is an independent probabilistic event, and the query is given by a SQL expression or, equivalently, a First Order formula. The query’s probability can be computed in linear time in the size of the compilation representation, hence the interest in studying the size of such a representation. We consider the “data complexity” setting, where the query is fixed, and the input to the problem consists only of the database instance. We consider several compilation targets, of increasing expressive power: OBDDs, FBDDs, and decision-DNNFs (a subclass of d-DNNFs). For the case of OBDDs we establish a dichotomy theorem for queries in restricted languages FO(\exists, \wedge, \vee) and FO(\forall, \wedge, \vee): for each such query the OBDD is either linear in the size of the database, or grows exponentially, and the complexity can be determined through a simple analysis of the query expression. For the other targets we describe a class of queries for which (a) the decision-DNNF is exponentially large in the size of the database, and (b) the probability of the query can be computed in polynomial time in the size of the database. This suggests that the compilation target decision-DNNF is too weak to capture all tractable cases of probabilistic inference. Our lower bound for decision-DNNF’s relies on a translation into FBDD’s, which is of independent interest. Joint work with Paul Beame, Abhay Jha, Jerry Li, and Sudeepa Roy. | ||
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| Olteanu, Dan (University of Oxford) | Zemanek seminar room; TU Wien | Sat, 6. Jun 15, 10:05 |
| Factorized Databases. | ||
will overview recent work on compilation of join queries (First Order formulas with conjunction and existential quantification) into lossless factorized representations. The primary motivation for this compilation is to avoid redundancy in the representation of results (satisfying assignments) of queries in relational databases. The relationship between a relation encoded as a set of tuples and an equivalent factorized representation is on a par with the relationship between propositional formulas in disjunctive normal form and their equivalent nested formulas obtained by algebraic factorization. For any fixed join query, we give asymptotically tight bounds on the size of their factorized results by exploiting the structure of the query, and we quantify the size gap between factorized and standard relational representation of query results. Factorized databases allow for constant-delay enumeration of represented tuples and provide efficient support for subsequent queries and analytics, such as linear regression. Joint work with Jakub Zavodny. | ||
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| Kratsch, Stefan (Universität Bonn) | Zemanek seminar room; TU Wien | Sat, 6. Jun 15, 9:15 |
| Kernelization: Efficient Preprocessing for NP-hard Problems | ||
Efficient preprocessing is a widely applied opening move when faced with a combinatorially hard problem. The framework of parameterized complexity and its notion of kernelization offer a rigorous approach to understanding the capabilities of efficient preprocessing. In particular, it is possible to prove both upper and lower bounds on the output sizes that be achieved by polynomial-time algorithms. Crucially, using the perspective of parameterized complexity, these bounds are given in relation to problem-specific parameters, whereas unless P = NP there can be no efficient algorithm that shrinks every instance of an NP-hard problem. The talk will give an introduction to kernelization and cover several different problems like \textsc{Point Line Cover}, \textsc{$d$-Hitting Set}, and \textsc{Planar Steiner Tree}. We will discuss some recent examples of kernelizations that may be of particular interest to this meeting. Finally, we will briefly address the basic intuition behind lower bounds for kernelization. | ||
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| Bova, Simone (TU Wien) | Zemanek seminar room; TU Wien | Fri, 5. Jun 15, 14:20 |
| A Strongly Exponential Separation of DNNFs from CNFs | ||
Decomposable Negation Normal Forms (DNNFs) are Boolean circuits in negation normal form where the subcircuits leading into each AND gate are defined on disjoint sets of variables. We prove a strongly exponential lower bound on the size of DNNFs for a class of CNF formulas built from expander graphs. As a corollary, we obtain a strongly exponential separation between DNNFs and CNF formulas in prime implicates form. This settles an open problem in the area of knowledge compilation (Darwiche and Marquis, 2002). This is joint work with Florent Capelli (Universite Paris Diderot), Stefan Mengel (Ecole Polytechnique), and Friedrich Slivovsky (Technische Universitat Wien). | ||
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| Razgon, Igor (Birkbeck University of London) | Zemanek seminar room; TU Wien | Fri, 5. Jun 15, 13:30 |
| On the relationship between Non-deterministic read-once branching programs and DNNFs | ||
This talk consists of two parts. In the first part I will present a result published in (Razgon,IPEC2014) stating that for each $k$ there is an infinite class of monotone 2-CNFs of primal graph treewidth at most $k$ for which the equivalent Non-Deterministic Read-Once Branching programs (NROBPs) require space $\Omega(n^{k/c})$ for some constant $c$. Then I will show that, essentially, replacing $k$ with $\log n$ we obtain a class of monotone 2-CNFs with pseudopolynomial space complexity of the equivalent NROBPs. Using a well known result of Darwiche about space fixed parameter tractability of DNNFs for CNFs of bounded primal graph treewidth, it is easy to show that the space complexity of DNNFs on this class of CNFs is polynomial. Thus we obtain a pseudopolynomial separation between NROBPs and DNNFs. In the second part of the talk I will show that the above separation is essentially tight. In particular I will present a transformation of a DNNF of size $m$ with $n$ variables into an equivalent NROBP of size $O(m^{\log n+2})$. It follows for this transformation that an exponential lower bound (on the space complexity of) NROBP for any class of functions implies an exponential lower bound for DNNFs for this class of functions. Since NROBPs are much better studied than DNNFs from the lower bounds perspective with many exponential lower bounds known, I believe this result is a significant progress in our understanding of the complexity of DNNFs. The proposed transformation is an adaptation of the approach for transformation of a decision DNNF into an FBDD presented in (Beame et al, UAI2013). | ||
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| Kullmann, Oliver (Swansea University) | Zemanek seminar room; TU Wien | Fri, 5. Jun 15, 11:40 |
| A measured approach towards “good representations” | ||
I want to give an overview on the usage of “hardness measures” in the theory of representations of boolean functions via CNF’s. A special focus will be on separation of classes (given by the levels of the hardness measures), showing that increasing various hardness measures enables much shorter representations.The measures we consider are closely related to SAT solving, that is, making the implicit knowledge explicit happens with SAT solvers in mind. This makes for good connections to proof complexity, but now in a stronger setting — satisfiable clause-sets are the target, and we wish to represent the underlying boolean function as good as possible. “As good as possible” means that the hidden(!) unsatisfiable subinstances are as easy as possible. Since we are aiming at making the life easier for SAT solvers, the concrete nature of the hardness measures becomes of importance, different from general Knowledge Compilation, where one uses whatever polynomial time offers. | ||
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| Cepek, Ondrej (Karlsuniversität Prag) | Zemanek seminar room; TU Wien | Fri, 5. Jun 15, 11:15 |
| Complexity aspects of CNF to CNF compilation | ||
Knowledge compilation usually deals with transforming some input representation of a given knowledge to some other type of representation on the output. In this talk we will concentrate on compilation where both input and output representation are of the same type, namely in the CNF format. In this case the purpose of the compilation process is to add clauses to the input CNF in order to improve its inference properties. We will look at this process in more detail and study its complexity. | ||
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| Simon, Laurent (IASI, Université de Orsay Paris 11) | Zemanek seminar room; TU Wien | Fri, 5. Jun 15, 10:20 |
| SAT and Knowledge Compilation: a Just-in-Time Approach | ||
Knowledge Compilation (KC) principles rely on an off-line phase to rewrite the Knowledge base in an appropriate form, ready to be efficiently queried. In our talk, we propose an alternative approach, built on top of an efficient SAT solver. The recent progresses in the practical solving of SAT problems allows us to directly use them to answer the set of classical queries used in most KC works. We show that this very simple approach gives very good practical results. In addition, the learning mechanism is fully exploited from queries to queries, allowing to amortize previous calls by speeding up the process of new queries. | ||
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| Marques-Silva, Joao (IST/INESC-ID, Portugal and University College Dublin) | Zemanek seminar room; TU Wien | Fri, 5. Jun 15, 9:30 |
| Prime Compilation of Non-Clausal Formulae | ||
Formula compilation by generation of prime implicates or implicants finds a wide range of applications in AI. Recent work on formula compilation by prime implicate/implicant generation often assumes a Conjunctive/Disjunctive Normal Form (CNF/DNF) representation. However, in many settings propositional formulae are naturally expressed in non-clausal form. Despite a large body of work on compilation of non-clausal formulae, in practice existing approaches can only be applied to fairly small formulae, containing at most a few hundred variables. This paper describes two novel approaches for the compilation of non-clausal formulae either with prime implicants or implicates, that is based on propositional Satisfiability (SAT) solving. These novel algorithms also find application when computing all prime implicates of a CNF formula. The proposed approach is shown to allow the compilation of non-clausal formulae of size significantly larger than existing approaches. | ||
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| Darwiche, Adnan (University of California) | Zemanek seminar room; TU Wien | Thu, 4. Jun 15, 16:50 |
| Beyond NP: Keeping up with solvers that reach beyond NP! | ||
We will discuss in this presentation a new community website, BeyondNP.org, which is planned to launch later this summer. Beyond NP aims to disseminate and promote research on solvers that reach beyond NP, including model counters, knowledge compilers, QBF solvers and function-problem solvers (e.g. MaxSAT, MUS and MCS). Beyond NP will serve as a news and information aggregator for such solvers, including a catalog of open-source solvers, repositories of corresponding benchmarks, and news on related academic activities. The presentation aims to raise awareness about this initiative, to discuss its underlying vision and objectives, and to seek input and participation from the broader community. | ||
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| Niveau, Alexandre (Université de Caen–Basse-Normandie) | Zemanek seminar room; TU Wien | Thu, 4. Jun 15, 16:25 |
| Towards a knowledge compilation map for heterogeneous representation languages | ||
The knowledge compilation map introduced by Darwiche and Marquis takes advantage of a number of concepts (mainly queries, transformations, expressiveness, and succinctness) to compare the relative adequacy of representation languages to some AI problems. However, the framework is limited to the comparison of languages that are interpreted in a homogeneous way (formulas are interpreted as Boolean functions). This prevents one from comparing, on a formal basis, languages that are close in essence, such as OBDD, MDD, and ADD.To fill the gap, we present a generalized framework into which comparing formally heterogeneous representation languages becomes feasible. In particular, we explain how the key notions of queries and transformations, expressiveness, and succinctness can be lifted to the generalized setting. The talk is based on the IJCAI’13 paper by Fargier, Marquis, and Niveau. | ||
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| Fargier, Hélène (IRIT-CNRS, Université Paul Sabatier) | Zemanek seminar room; TU Wien | Thu, 4. Jun 15, 15:35 |
| A KC Map of Valued Decision Diagrams – application to product configuration | ||
Valued decision diagrams (VDDs) are data structures that represent functions mapping variable-value assignments to non-negative real numbers. Existing languages in VDD family, including ADD, AADD , and those of the SLDD family, seem to be valuable target languages for compiling utility functions, probability distributions and, in the domain of application we are interested in, cost functions over a catalog of configurable products.This talks first presents a compilation map of such structures and shows that many tasks that are hard on valued CSPs are actually tractable on VDDs. Indeed, languages from the VDD family (especially, ADD, SLDD, AADD) benefit from polynomial-time algorithms for some tasks of interest (e.g., the optimization one) for which no polynomial-time algorithm exists when the input is the VCSP considered at start.However, the efficiency of these algorithms is directly related to the size of the compiled formulae. The target languages and the heuristics under consideration have been tested on two families of benchmarks, additive VCSPs representing car configuration problems with cost functions and multiplicative VCSPs representing Bayesian nets. It turns out that even if the AADD language is strictly more succinct (from the theoretical side) than SLDD$_{+}$ (resp. SLDD$_{\times}$), the language SLDD$_{+}$ (resp. SLDD$_{\times}$) proves to be good enough in practice when purely additive (resp. purely multiplicative) problems are to be compiled. This talk is based on a joint work with Pierre Marquis, Alexandre Niveau and Nicolas Schmidt, partially supported by the project BR4CP ANR-11-BS02-008 of the French National Agency for Research: Hélène Fargier, Pierre Marquis, Nicolas Schmidt: Semiring Labelled Decision Diagrams, Revisited: Canonicity and Spatial Efficiency Issues. IJCAI 2013. Hélène Fargier, Pierre Marquis, Alexandre Niveau, Nicolas Schmidt: A Knowledge Compilation Map for Ordered Real-Valued Decision Diagrams. AAAI 2014. | ||
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| Slivovsky, Friedrich (TU Wien) | Zemanek seminar room; TU Wien | Thu, 4. Jun 15, 14:40 |
| On Compiling CNFs into Structured Deterministic DNNFs | ||
We show that the traces of recently introduced dynamic programming algorithms for #SAT can be used to construct structured deterministic DNNF (decomposable negation normal form) representations of propositional formulas in CNF (conjunctive normal form). This allows us prove new upper bounds on the complexity of compiling CNF formulas into structured deterministic DNNFs in terms of parameters such as the treewidth and the clique-width of the incidence graph. Joint work with Simone Bova, Florent Capelli, and Stefan Mengel. | ||
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| Oztok, Umut (University of California LA) | Zemanek seminar room; TU Wien | Thu, 4. Jun 15, 14:15 |
| Exhaustive DPLL for Model Counting and Knowledge Compilation. | ||
DPLL-based methods have played a crucial role in the success of modern SAT solvers, and it is also known that running DPLL-based methods to exhaustion can yield model counters and knowledge compilers. However, a clear semantics of exhaustive DPLL and a corresponding proof of correctness have been lacking, especially in the presence of techniques such as clause learning and component caching. This seems to have hindered progress on model counting and knowledge compilation, leading to a limited number of corresponding systems, compared to the variety of DPLL-based SAT solvers. In this talk, we will present an exhaustive DPLL algorithm with a formal semantics and a corresponding proof of correctness, showing how it can be used for both model counting and knowledge compilation. The presented algorithm is based on a formal framework that abstracts primitives used in SAT solvers in a manner that makes them suitable for use in an exhaustive setting. We will also introduce an upcoming open-source package that implements this framework, which aims to provide the community with a new basis for furthering the development of model counters and knowledge compilers based on exhaustive DPLL. Joint work with Adnan Darwiche. | ||
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| de Haan, Ronald (TU Wien) | Zemanek seminar room; TU Wien | Thu, 4. Jun 15, 13:50 |
| Parameterized Compilability | ||
In the framework of Knowledge Compilation (KC), knowledge bases are preprocessed (or compiled) once in order to decrease the computational efforts needed for performing queries on the knowledge base. However, in many cases such compilations lead to a exponential blow-up in the size of the knowledge base. Such an incompilability result occurs for example in the case of clause entailment (CE), where the knowledge base is a propositional formula, and the queries consist of deciding whether a given clause is entailed by the formula. With the aim of relativizing such negative results, following work by Chen (IJCAI 2005), we extend the framework of KC with concepts from parameterized complexity where structure in the input is captured by a problem parameter. In the resulting framework, we focus on fpt-size compilations whose size is polynomial in the input size, but can depend exponentially (or worse) in the problem parameter. We argue that this approach combines the power of KC and parameterized complexity. Concretely, for the problem of CE, we identify several parameters that allow the problem to be compiled in fpt-size. In addition, we provide evidence that for several other parameters, such compilations are not possible. Joint work with: Simone Bova, Neha Lodha and Stefan Szeider. | ||
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| Chen, Hubie (Universidad del País Vasco and Ikerbasque) | Zemanek seminar room; TU Wien | Thu, 4. Jun 15, 13:00 |
| Parameter Compilation | ||
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is relatively expensive. In this talk, we introduce a complexity-theoretic framework for classifying problems according to their compilability, which includes complexity classes and a notion of reduction.The basic object in our framework is that of a parameterized problem, which here is a language along with a parameterization—a map which provides, for each instance, a so-called parameter on which compilation may be performed. Our framework is positioned within the paradigm of parameterized complexity, and our notions are relatable to established concepts in the theory of parameterized complexity. Indeed, we view our framework as playing a unifying role, integrating together parameterized complexity and compilability theory. Prior to presenting the framework, we will provide some motivation by discussing our work on model checking existential positive queries (see http://arxiv.org/abs/1206.3902). The talk will be mainly based on the article available at http://arxiv.org/abs/1503.00260 | ||
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| Korice, Frédéric (CRIL-CNRS, Université d’Artois) | Zemanek seminar room; TU Wien | Thu, 4. Jun 15, 11:10 |
| Affine Decision Tree | ||
Decision trees have received a great deal of interest in various areas of computer science. In this talk, we examine a family of tree-like languages which include decision trees as a special case. Notably, we investigate the class of “affine” decision trees (ADT), for which decision nodes are labeled by affine (xor) clauses, and its extension (EADT) to decomposable and-nodes. The key interest of this family is that (possibly conditioned) model counting can be solved in polynomial-time, by exploiting Gauss elimination. After presenting a knowledge compilation map for this family, we describe a top-down compiler “cnf2eadt”, together with comparative experimental results on various benchmarks for #SAT problems. We conclude by mentioning two current research perspectives: probabilistic inference with weighted EADTs, and structure learning of maximum likelihood EADTs. | ||
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| Darwiche, Adnan (University of California Los Angeles, USA) | Zemanek seminar room; Vienna University of Technology | Thu, 4. Jun 15, 10:20 |
| Knowledge Compilation and Machine Learning: A New Frontier. | ||
Knowledge compilation has seen much progress in the last decade, especially as work in this area has been normalized into a systematic study of tractable languages, their relative succinctness, and their efficient support for various queries. What has been particularly exciting is the impact that knowledge compilation has had on several areas, such as probabilistic reasoning and probabilistic databases. In this talk, I will discuss a new area, machine learning, which is bound to be significantly impacted by knowledge compilation. In particular, I will discuss recent work in which knowledge compilation has been used to learn probabilistic models under massive logical constraints, and over combinatorial objects, such as rankings and game traces. I will further identify and discuss three specific roles for knowledge compilation in machine learning, which arise in defining (a) more structured probability spaces, (b) more expressive queries, and (c) new types of datasets that significantly generalize the standard datasets used in the machine learning literature. Joint work with Arthur Choi and Guy Van den Broeck. | ||
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| Darwiche, Adnan (University of California) | Zemanek seminar room; TU Wien | Thu, 4. Jun 15, 10:20 |
| Knowledge Compilation and Machine Learning: A New Frontier | ||
Knowledge compilation has seen much progress in the last decade, especially as work in this area has been normalized into a systematic study of tractable languages, their relative succinctness, and their efficient support for various queries. What has been particularly exciting is the impact that knowledge compilation has had on several areas, such as probabilistic reasoning and probabilistic databases. In this talk, I will discuss a new area, machine learning, which is bound to be significantly impacted by knowledge compilation. In particular, I will discuss recent work in which knowledge compilation has been used to learn probabilistic models under massive logical constraints, and over combinatorial objects, such as rankings and game traces. I will further identify and discuss three specific roles for knowledge compilation in machine learning, which arise in defining (a) more structured probability spaces, (b) more expressive queries, and (c) new types of datasets that significantly generalize the standard datasets used in the machine learning literature. Joint work with Arthur Choi and Guy Van den Broeck. | ||
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| Wolfram , Marie-Therese (RICAM Linz) | WPI Seminar room 8.135 OMP1 | Wed, 20. May 15, 13:30 |
| "Mean-field transportation models in the life and social sciences" | ||
| Levina, Galina; Russian Academy of Sciences, Moscow | WPI Seminar Room 08.135 | Wed, 6. May 15, 15:00 |
| Role of helical turbulence in the dynamics of tropical cyclones | ||
Tropical cyclones in the Earth’s atmosphere are amongst the most dangerous and mighty weather events. Despite considerable efforts of modern science their genesis remains one the most intricate enigmas of meteorology as well as no a clear consensus of opinion has yet emerged concerning physical mechanisms contributing to it. In this contribution, a role of helical turbulence in the genesis and further evolution of tropical cyclones (TCs) is discussed. Our first finding of non-zero helicity in a real natural system [1], namely, the tropical atmosphere of the Earth during TC formation gave us an impetus to try and further characterize the large-scale vortex instability. In works [2-6], we proposed a helical scenario of TC formation based on the fundamental ideas on self-organization in turbulence. Building on the known cases of large-scale alpha-like instabilities – the alpha-effect in magnetohydrodynamics (Steenbeck et al., 1966), hydrodynamic alpha-effect (Moiseev et al., 1983), and anisotropic kinetic alpha (AKA)-effect (Frisch et al., 1987) – we are developing an interpretation for TC formation as a threshold extreme event in the helical atmospheric turbulence of a vorticity-rich environment of a pre-depression cyclonic recirculation zone in the tropical atmosphere. To trace and analyze processes of self-organization in the tropical atmosphere, spanning convective clouds with horizontal dimensions of 1-5 km to mesoscale vortices of hundreds of kilometers, we use data of near cloud-resolving numerical simulations [7]. Helicity is the scalar product of velocity and vorticity vectors. It characterizes the degree of linkage of vortex lines and is also a measure of departure from the mirror symmetry of turbulence [8]. In a case of TC formation, we define the helicity of the associated flow by the corresponding integral [8] being over all space of mesoscale vortex core, approximately 300x300x20 km in horizontal and vertical directions, respectively. Our research approach developed and applied in [2-6] allows diagnosis of WHEN a nascent large vortex becomes energy self-sustaining. For purposes of quantitative diagnosis of TC genesis we analyze the evolution of structure and energetics of the forming vortex. It has been found that the onset of large-scale vortex instability requires a special topology of the vortex velocity field – the newly forming mesoscale vortex becomes energy-self-sustaining when a helical structure of the system-scale circulation organizes and interacts with the moisture rich boundary layer. Such helical mesoscale organization is only possible due to the linkage of TC-scale tangential and transverse circulation which is realized through rotating convective structures of cloud scales, which were first found in [9] and dubbed ‘vortical hot towers’ (VHTs). Thus, we use a pseudoscalar – helicity of the velocity field (helicity density, integral helicity as well as its horizontal and vertical contributions) to quantitatively analyze the topology, and the integral kinetic energy of tangential and transverse circulation to diagnose the onset of large-scale vortex instability. The moment in time when the mutual intensification of both circulations starts can be considered as a beginning of tropical cyclogenesis. The chosen quantitative criterion has a clear physical motivation. This criterion contributes to the development of a universally accepted definition of tropical cyclogenesis, which does not currently exist. The presented contribution suggests the usefulness of combining the fundamental ideas on self-organization in turbulence and the most advanced modern tools of numerical analysis of atmospheric processes. As a practical perspective, we consider applications of our approach to analyze data of real observations and field experiments in order to implement the diagnosis and forecasting of TC genesis by means of operational weather models. | ||
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| Jimenez, Javier; Universidad Politécnica de Madrid | WPI Seminar Room 08.135 | Wed, 6. May 15, 14:15 |
| The temporal evolution of inertial eddies in wall-bounded turbulence | ||
The flux of any conserved quantity with a nontrivial spectrum can be considered as representing a turbulent cascade, since it has to ‘traverse’ the different scales before the quantity is dissipated. Note that such fluxes are the natural objects in which to study the transfer, since, for example, production or dissipation tend to represent only one of the end-points. Well-known examples are the energy cascade in two- or three-dimensional turbulence, whose flux is = -ijSij, or the enstrophy cascade in two-dimensional flows. Less attention has been paid in the cascade literature to the transfer of momentum in shear flows, although the corresponding flux, the tangential Reynolds stress = - | ||
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| Biferale, Luca; University of Rome | WPI Seminar Room 08.135 | Wed, 6. May 15, 11:00 |
| Turbulence on a fractal Fourier set | ||
The dynamical effects of mode reduction in Fourier space for three dimensional turbulent flows is studied. We focus on fully resolved numerical simulations of Navier-Stokes equations with Fourier modes constrained to live on a fractal set of dimension D [1]. The robustness of the forward energy cascade and vortex stretching mechanisms is tested at changing D, from the standard, fully resolved field, corresponding to fractal dimension D=3, to a strongly decimated field where only up to a 3% of the Fourier modes interact, at D=2.5. The direct energy cascade persist, but deviations from the Kolmogorov scaling are observed in the kinetic energy spectra. A model in terms of a correction with a linear dependency on the codimension of the fractal set explains the results. At small scales, the intermittent behavior due to the vorticity production is strongly modified by the fractal decimation, leading to an almost Gaussian statistics already at D=2.98. These effects are connected to a genuine modification in the triad-to-triad nonlinear energy transfer mechanism as proven by the fact that when the fractal mode-reduction is applied a posteriori to configurations obtained from fully resolved Navier-Stokes equations the reduction in the fluctuations is much smaller. | ||
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| Bodenschatz, Eberhard; Max Planck Institute Göttingen | WPI Seminar Room 08.135 | Wed, 6. May 15, 10:00 |
| Irreversibility equals small-scale generation in 3D turbulent flows | ||
In three-dimensional turbulent flows energy is supplied at large scales and cascades down to the smallest scales where viscosity dominates. The generation of small scales from larger ones results in a flux of energy through scales and implies the irreversibility fundamental to the dynamics of turbulent flows. As we have shown recently, this irreversibility manifests itself by an asymmetry of the probability distribution of the instantaneous power p ≡ u·a of the forces acting on fluid elements, where u and a are the fluid velocity and acceleration, respectively. In particular, the third moment of p was found to be negative. Establishing a physical connection between the negative third moment of p and the energy flux or small-scale generation is the main result of this work. With analytical calculations and support from numerical simulation of fully developed turbulence we connect the asymmetry in the power distribution, i.e., the negativity of ⟨p3⟩, directly to the generation of small scales, or more precisely, to the amplification (stretching) of vorticity in turbulent flows. This work is joined with: Alain Pumir (Ecole Normale Superieure de Lyon), Haitao Xu (Max Planck Institute for Dynamics and Self-Organization), Rainer Grauer (Ruhr University Bochum) | ||
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| Peinke, Joachim; Universität Oldenburg | WPI Seminar Room 08.135 | Tue, 5. May 15, 16:00 |
| Extreme events as a multi-point feature - Entropy production as a criterion for cascade process | ||
Examples of extreme events will be presented. In particular we discuss the impact of wind gusts an wind energy, the appearance of rough waves and extreme stock market uctuations. The aim of this presentation is to show evidence that there is a class of systems characterized by building up extreme events which are due to hierarchical cascade processes. For the case of turbulence we show that the turbulent cascade process satisfy a generalized 2nd law of thermodynamics for non-equilibrium conditions, namely the integral uctuation theorem. The nding of Markow properties of velocity increments statistics conditioned on di erent scales opened up the possibility to describe the cascade process by stochastic equations, like Fokker-Planck or the Kolmogorov equations. In this framework it is even possible to get access to the general n-point statistics of [1]. The stochastic cascade process is evolving in an instationary way with the scale. Thus the statistics, expressed by probability density functions of velocity increments, are changing with the scale too, which is the central feature of intermittency and producing extreme events. The common multifractal cascade models for turbulence will be expressed in terms of such instationary cascade processes. Using concepts of non-equilibrium thermodynamics an integral uctuation theorem for the entropy production associated with the stochastic evolution of velocity increments along the cascade has been proposed [4], which demonstrates that the instationarity of the process appears to be crucial for the correct modeling of the intermittency found in turbulent ows. The integral uctuation theorem allows to rule out which cascades. Here we show how this concept of the integral uctuation theorem can be used as a test of the validity of multifractal models for turbulence and to validate di erent features of the cascade, like for example scaling behavior, or log normal statistics. Finally we show how based on the stochastic description of the cascade a model for synthetic data can be set up. We show that the extreme events can be modeled correctly, thus give evidence that for these systems extreme events are multi-point quantities, which is equivalent to the saying the the extreme events are caused by cascade process. | ||
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| Grauer, Rainer; Ruhr-Universität Bochum | WPI Seminar Room 08.135 | Tue, 5. May 15, 15:00 |
| Turbulence and Instantons | ||
It is evident that coherent nearly singular structures play a dominant role in understanding the anomalous scaling behavior in turbulent systems. We ask the question, which role these singular structures play in turbulence statistics. More than 15 years ago, for certain turbulent systems the door for attacking this issue was opened by getting access to the probability density function to rare and strong fluctuations by the instanton approach. We address the question whether one can identify instantons in direct numerical simulations of the stochastically driven Burgers equation. For this purpose, we first solve the instanton equations using the Chernykh‐Stepanov method [2001]. These results are then compared to direct numerical simulations by introducing a filtering technique to extract prescribed rare events from massive data sets of realizations. In addition, we solve the issue why earlier simulations by Gotoh [1999] were in disagreement with the asymptotic prediction of the instanton method and demonstrate that this approach is capable to describe the probability distribution of velocity differences for various Reynolds numbers. Finally, we will present and discuss first results on the instanton solution for vorticity in 3D Navier‐Stokes turbulence. | ||
| Note: Click here for the presentation | ||
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