# Oberseminar Mathematische Modelle

Link and Passcode: https://tum-conf.zoom.us/j/96536097137 Code 101816## WS 2021/22

Vorträge jeweils Mi 13-14 Uhr Datum |
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## SS 2021

Vorträge jeweils Mi 13-14 Uhr Datum |
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21.04.2021 | Michael Ortiz ^{} California Institute of Technology |
Model-Free Data-Driven Science: Cutting Out the Middleman |
We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of approximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within this Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to material data sets that are not graphs. |

28.04.2021 | Aleksei Golubev ^{} Bauman Moscow State Technical University |
Cerebral blood flow regulation using nonlinear control approaches |
We consider the mathematical model of cerebral hemodynamics in the form of two ordinary differential equations suggested by M. Ursino and C.A. Lodi. The control problem in question is to keep the cerebral blood flow treated as the function of arterial-arteriolar blood volume, intracranial pressure and arterial pressure close to some basal value required for tissue metabolism. The rate of change of arterial-arteriolar compliance is taken as the control input. The integrator backstepping approach is used to find tracking control laws. |

05.05.2021 | Felix Dietrich ^{} TUM Wissenschaftliches Rechnen |
Modelling human crowds from first principles and through machine learning methods |
Large human crowds constitute a fascinating research area for mathematical modelling. Even though the individuals forming the crowd are extremely complex, dominant emergent behaviors like density-velocity profiles and lane formation can be captured with relatively simple models. In this talk, we discuss recent "first principle", agent-based approaches, coarser cellular automatons, as well as modelling ideas from fluid dynamics. We also show how machine learning methods can provide a separate path to understanding crowds, with both strengths and shortcomings compared to the traditional approach. |

12.05.2021 | Aurélien Tellier TUM School of Life Sciences Freising |
Using full genome (and epigenome) data to infer past species history and ecological/life-history traits |
The field of evolutionary genetics is profoundly rooted in stochastic mathematical theory and since several years the theory has been extended to model the evolution of full genomes. Indeed, large amount of full genome data are becoming available for human but also non-model organisms. Several methods based on the Sequential Markovian coalescent (SMC) have been developed to use sequence data to uncover population demographic history. While these methods can be applied in principle to all possible species, they have been developed based on the human biological characteristics and have main limitations such as assuming sexual reproduction and no overlap of generations. However, in many plants, invertebrates, fungi and other taxa, these assumptions are often violated due to different ecological and life history traits, such as self-fertilization, long term dormant structures (seed or egg-banking) or large variance in offspring production. I will first describe a novel SMC-based method which we developed to infer 1) the rates of seed/egg-bank and of self-fertilization, and 2) the populations' past demographic history. We also apply our method to Arabidopsis thaliana, Daphnia pulex and to detect seed banking in different populations of the wild tomato species Solanum chilense. Finally, I will show that we can even extend this method to detect and to date the changes of selfing / seed banking in time. I will conclude by discussing more general class of mathematical stochastic models and methods which should be developed for applicability to all species. |

19.05.2021 | Anna Maslovskaya ^{} Amur State University, Mathematics and Computer Science Department Blagoveshchensk, Russia |
Deterministic and fractional approaches for the challenging control and diagnostics problems of bacterial communication |
The deterministic and fractional approaches can be used for in silico research to formalize the bacterial communications in terms of reaction-diffusion mathematical models. The current study continues more in depth the development of reaction-diffusion models of bacterial quorum sensing with a focus on the following directions. The use of external enzymes underlies an alternative way of reducing communication in pathogenic bacteria that may leads to a loss of pathogeneity. We propose an optimal control problem for bacterial quorum sensing degrading under the impact of external enzymes. The problem is to find the minimum of the objective functional that permits one to reduce the signaling molecules and simultaneously to limit the total amount of enzymes. This approach allows the valid strategy of enzyme impact to be specified. The second direction is presented by the time-fractional diffusion-wave modification of the quorum sensing model as a generalization of the classical model in order to analyze different dynamical regimes of the biological system. The study is aimed at developing numerical techniques to solve the time-fractional diffusion-wave problem with application to bacterial communication processes. |

09.06.2021 | Sabrina Neumaier TUM Mathematik |
Introduction of an environmental stress level to model tumor cell growth and survival |
Survival of living cells underlies many influences such as nutrient saturation, oxygen level, drug concentrations or mechanical forces. Data-supported mathematical modeling can be a powerful tool to get a better understanding of cell behavior in different settings. However, under consideration of numerous environmental factors mathematical modeling can get challenging. We present an approach to model the separate influences of each environmental quantity on the cells in a collective manner by introducing the ”environmental stress level”. It is an artificial, immeasurable variable, which quantifies to what extent viable cells would get in a stressed state, if exposed to certain conditions. A high stress level can inhibit cell growth, promote cell death and influence cell movement. As a proof of concept, we compare two systems of ordinary differential equations, which model tumor cell dynamics under various nutrient saturations respectively with and without considering an environmental stress level. Particle-based Bayesian inversion methods are used to calibrate unknown model parameters with time resolved measurements of in vitro populations of liver cancer cells. |

16.06.2021 | Katharina Kormann ^{} IPP Max-Planck-Institut für Plasmaphysik |
Numerical solution of the Vlasov equation: structure and efficiency |
A kinetic description of a plasma in external and self-consistent fields is given by the Vlasov equation for the particle distribution functions coupled to Maxwell's equation. The model is computational challenging due to its multiscale structure and the its relatively high dimensionality. This talk will give an overview of numerical solution methods and discuss structure-preserving particle methods as well as low-rank tensor discretizations in particular. A framework of structure-preserving particle in cell methods will be presented that allows for a long-time stable solution of the system. On the other hand, low-rank tensor methods are an efficient tool to compress multidimensional functions. We will demonstrate for benchmark problems that the essential features of the solution can be captured with a relatively low-rank. |

23.06.2021 | Sona John TUM Center of Life and Food Sciences Weihenstephan |
Cross-species association statistics to locate genomic regions under coevolution |
Host-parasite coevolution is a well-known example of inter species interaction which has evolutionary consequences in both partners. Detecting the genomic regions under coevolution is of great interest in disease control and drug design. Different genomic regions are expected to contribute differently to the coevolution based on its functionality. Some regions are expected to impact the process substantially, those we call it as the major genes. Regions that have milder effects are called minor genes. Also, some regions that do not influence the coevolution process are called neutral genes. This study aims to develop simple statistical quantities that can measure the level of association between genomic regions and identify major, minor, and neutral genomic regions in host and parasite genome. |

07.07.2021 | Martin Schuster ^{}Oregon State University |
Modeling cooperative behavior in bacteria |
Interactions like communication, cooperation and competition abound in the microbial world. They play an important role in natural ecosystems, infection, and agriculture. This talk focuses on experimental and mathematical approaches to understand two types of interactions in Pseudomonas bacteria: Quorum sensing, a mechanism of cell-cell communication that coordinates other cooperative behaviors, and iron acquisition via diffusible siderophores as both a cooperative and competitive behavior within and between species. |

14.07.2021 | Björn de Rijk ^{} Universität Stuttgart |
Stability of Pattern-Forming Fronts with a Quenching Mechanism |
The onset of pattern formation, where a localized perturbation of a destabilized ground state leads to an invading front leaving periodic patterns in its wake, is well-understood. In spatially homogeneous systems such pattern-forming fronts are unstable as any perturbation ahead of the front grows exponentially in time due to the instability of the ground state. Nevertheless, pattern-forming fronts are observed in various spatially inhomogeneous settings such as light-sensing reaction-diffusion systems, directional solidification of crystals or ion beam milling. In these settings the unstable state is only established in the wake of the heterogeneity after which patterns start to nucleate. Consequently, perturbations cannot grow far ahead of the interface of the pattern-forming front. This begs the question of whether stability can be rigorously established. In this talk, I answer this question affirmative by presenting a stability result for pattern-forming fronts against $L^2$-perturbations in the spatially inhomogeneous complex Ginzburg-Landau equation. A technical challenge is posed by the presence of unstable absolute spectrum which prohibits the use of standard tools such as exponential dichotomies. Instead, we projectivize the linear flow and study the associated matrix Riccati equation on the Grassmannian manifold. Eigenvalues can then be identified as the roots of the meromorphic Riccati-Evans function. This is joint work with Ryan Goh (Boston University). |

## WS 2020/21

Vorträge jeweils Mi 13-14 Uhr Datum |
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25.11.2020 | Eric Sonnendrücker ^{} MPI für Plasmaphysik |
Metriplectic models in plasma physics and structure preserving approximations |
Many problems in plasma physics can be modelled by the addition of an antisymmetric Poisson bracket and a symmetric dissipative bracket. Such models include in a natural way the conservation properties of the system and adhere to the laws of thermodynamics. Accurate long time nonlinear simulations rely on reproducing correctly the energy exchange and dissipation mechanisms of the system. This can be achieved by deriving a discrete approximation that conserves the structure of the continuous model. We shall give a few example of such models commonly used in plasma physics simulations and introduce geometric discretisation methods that enable to conserve at the discrete level the main structure of the continuous model. |

02.12.2020 | Anna Maslovskaya ^{} Amur State University, Mathematics and Computer Science Department Blagoveshchensk, Russia |
Complex dynamics in communication of bacterial populations: Mathematical models and computational techniques |
Bacterial communication is a complex dynamical process, which can be formalized by a deterministic approach and then explored by means of mathematical modeling and computer simulation. To describe bacterial cooperative behavior in the special case of quorum sensing, we propose a series of dynamical mathematical models: the basic nonlinear reaction-diffusion model, the time lagging reaction-diffusion model, the time- and space-fractional reactiondiffusion model. The various model approaches allow us to simulate a different behavior of the biological system. The time lagging model reveals the time-dependent fluctuations of signal substances concentrations observed during bacterial population dynamics. The time-fractional models formalize reaction-diffusion processes in biological systems related to a time memory effect. In addition, the proposed stochastic procedure examines self-similar dynamic processes of bacterial nucleation and growth. |

09.12.2020 | Christian Mendl TUM Informatik |
Nonlinear fluctuating hydrodynamics for anharmonic particle chains on mesoscopic scales |
The statistical physics description of classical particle chains on mesoscopic scales has surprising connections to a nonlinear extension of fluctuating hydrodynamics elevated to a stochastic PDE, which is then identified as the famous Kardar-Parisi-Zhang (KPZ) equation. Specifically, the framework starts from a microscopic (Fermi-Pasta-Ulam type) model of interacting particles in one dimension, and then uses the microscopic conservation laws to arrive at a stochastic description on a mesoscopic scale. Intuitively, one assumes that local regions of the system are close to thermal equilibrium. The stochastic description predicts dynamical correlation functions in the long-time limit, which are of large interest since they determine (heat) transport properties, for example. We find good agreement between the prediction and microscopic molecular dynamics simulations. Furthermore, the framework reveals how the Tracy-Widom distribution emerges from the microscopic dynamics with carefully prepared domain-wall initial conditions. Finally, the hydrodynamic description has recently been generalized to integrable models with an "infinite" number of conservation laws; we will present recent work on the Toda lattice as representative instance. |

16.12.2020 | Michael Kurschilgen TUM Wirtschaftswissenschaften |
Communication is more than information sharing: The role of status-relevant knowledge |
In cheap talk games where senders’ accuracy of information depend on their background knowledge, a sender with image concerns may want to signal that she is knowledgeable despite having material incentives to lie. These image benefits may, in turn, depend on the type of knowledge and its perceived social status. Theoretically, we show that when some senders care sufficiently about their image, there is both a non-informative babbling equilibrium, and a separating equilibrium, in which the average sender’s message is informative and receivers always follow. In a laboratory experiment, we vary the social status of knowledge (1) by providing senders with multiple-choice questions on either(a) broadsheet topics (general knowledge) or (b) tabloid topics, and (2) by systematically modifying the degree of difficulty. We find truth-telling rates to be significantly higher when senders can signal high-status knowledge. |

EIN GESUNDES NEUES JAHR ! |
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13.01.2021 | Renée Lampe Klinikum rechts der Isar Varvara Turova TUM Mathematik Irina Sidorenko TUM Mathematik |
Mathematical modeling for the prevention of neonatal cerebral hemorrhage |
Intracerebral hemorrhage is the major complication in the development of premature infants. The early childhood cerebral hemorrhage can lead to the clinical picture of cerebral palsy characterized by disorders of motor development and posture as well as other partial performance disorders such as deficits in speech, perception, learning disabilities and epilepsy. Cerebral hemorrhage is often triggered by fluctuations of cerebral blood flow (CBF). Therefore, regular monitoring of CBF is an important task in medical care of preterm infants. Although several measuring techniques have been developed during last years, they are still not the part of the clinical routine. We present a mathematical model for the calculation of CBF. The model takes into account peculiarities of the immature cerebral circulation, such as presence of a specific area in the developing brain with a highly fragile blood vessel network, called germinal matrix, and an impaired ability of the cerebral blood vessels to vary their diameter in response to fluctuations of main medical parameters. Furthermore, finite element analysis of critical stresses, exerted on vessels’ walls, will be presented based on calculated CBF. Additionally, machine learning models for identifying of preterm infants at risk of cerebral hemorrhage and a viability theory based approach to control impaired cerebral autoregulation will be outlined. |

20.01.2021 | Phaedon-Stelios Koutsourelakis TUM Maschinenwesen |
Physics-aware, data-driven discovery of slow and stable coarse-grained dynamics in the Small Data regime |
Despite recent successes from applications of machine learning tools in the field of computational physics, critical challenges persist in problems involving Small Data and multiscale systems. Given high-dimensional time-series’ data from a multiscale dynamical system, we present a probabilistic framework that learns an interpretable, lower-dimensional, coarse-grained model whose long-term stability is guaranteed. We include a layer of physically motivated latent variables and enable the incorporation of known physical constraints. Such domain knowledge can be extremely useful when training in the Small Data regime and for out-of-sample predictions. In contrast to existing schemes, the proposed model does not require the a priori definition of projection operators and, being fully probabilistic, is capable of capturing the predictive uncertainty due to the information loss resulting from model compression. We illustrate its performance in high-dimensional particle systems and demonstrate its efficacy and accuracy by generating extrapolative, long-term predictions with quantified uncertainty. |

27.01.2021 | Interner Termin | ||

03.02.2021 | Martin Brokate TUM Mathematik |
A variational inequality for the derivative of the scalar play operator |
We show that the directional derivative of the scalar play operator is the unique solution of a certain variational inequality. Due to the nature of the discontinuities involved, the variational inequality has an integral form based on the Kurzweil-Stieltjes integral. |

10.02.2021 | Interner Termin |