MODUS Seminar Program

Weekly talks in the MODUS Seminar in the summer semester 2024:
Wednesday, 12:15-13:45, Room S102, FAN-B
Individual talks may be held via zoom or at different times, see the information, below.
The list of talks is still incomplete and further talks will be added.

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24.04.2024, 12:15h
Julia Slipantschuk
Dynamical Systems and Data, Universität Bayreuth
Transfer operators and applications

Abstract: A fruitful approach for providing effective statistical descriptions of chaotic dynamical systems is to lift the dynamics to linear evolution operators on infinite dimensional Banach spaces. Spectral data of these operators, known as Koopman or transfer operators, yield insight into the long-term behaviour of the underlying system. In this talk I will give a short introduction into the spectral theory of transfer operators associated to (mostly) low-dimensional discrete chaotic dynamical systems, and present a complete description of eigenvalues of these operators for a certain special class of non-linear maps. In general, such explicit descriptions of eigendata are rarely available, and in various applications algorithms or numerical schemes to approximate these are required. I will present strong spectral convergence and consistency results for a popular numerical approximation scheme -- extended dynamic mode decomposition (EDMD) -- applied to examples of chaotic systems given by one-dimensional expanding maps.

Monday, 6.05.2024, 10:30h, S102
Talk in the lecture series Scientific Computing, Coffee and Tea at 10:00h
Luca Bonaventura
Dipartimento di Matematica, Politecnico di Milano, Italy
A deeper look at shallow water models

Abstract: The derivation of the classical hydrostatic, vertically averaged shallow water equations will be presented and revisited to highlight typical conceptual errors. The choice of time scales determined implicitly by the identification of standard flow regimes will be discussed. Examples of non-hydrostatic shallow water models will be presented and the prospects for their rigorous derivation will be discussed.

8.05.2024, 12:15h
Jirka Vomlel
Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic   and   Faculty of Arts, Charles University, Prague
Uncovering Relationships: Using Bayesian Networks to Analyze Open-Minded Thinking and Conspiracy Beliefs in Czech University Candidates

Abstract: I will begin with a brief introduction to one of the glass-box models of artificial intelligence called Bayesian Networks (BNs), a model named after the English statistician Rev. Thomas Bayes. BNs represent a probabilistic model that can help visualize relationships between variables. I will illustrate the use of Bayesian networks on data from a Czech university entrance exam. This data included a test of open-minded thinking designed by Jonathan Baron and also examined students' attitudes towards various conspiracies. Using BNs, we can identify conspiracy clusters and their relationships with open-minded thinking.

15.05.2024, 12:15h
April Herwig
AG Numerik komplexer Systeme, TU München
An introduction to pseudospectra and application to validated computational dynamics

5.06.2024, 12:05h, Kolloquium zur Masterarbeit
Florian Streifinger
Modellierung, Analyse und Simulation von Krankheiten

5.06.2024, 13:00h, Kolloquium zur Masterarbeit
Kilian Bernreuther
Analyse, Simulation und Optimale Steuerung eines Krankheitsmodells

12.06.2024, 12:15h
Lisa Jagau
Lehrstuhl Scientific Computing, Universität Bayreuth
Hydrodynamische Modellierung von Mikroplastik-Transport und Sedimentierung in Seen

Abstract: Mikroplastikpartikel (MP) sind für Organismen in der Hydrosphäre potenziell schädlich. Um die Exposition und das damit verbundene Risiko besser einschätzen zu können, muss das Transport- und Sedimentierungsverhalten von MP in aquatischen Systemen quantifiziert werden. Wir erstellen ein dreidimensionales hydrodynamisches Modell und validieren dieses anhand gemessener Daten für den Großen Brombachsee. Anschließend nutzen wir das Modell, um MP-Transport und Sedimentierung zu modellieren.
Unser Schwerpunkt ist die Modellierung von Polymeren mit unterschiedlichen Dichten und Partikelgrößen, um Muster der Partikelverweilzeit und Sedimentierung zu identifizieren. Die Verteilung von MP im Rechengebiet wird sowohl von der Partikeldichte als auch von der Partikelgröße stark beeinflusst. Kleinere, leichtere Partikel verteilen sich über die gesamte horizontale Ausdehnung des Sees und Partikel mit höherer Dichte oder größerem Durchmesser setzen sich in einem begrenzten Bereich um den Einströmungsort ab, was auf eine höhere Absetzgeschwindigkeit hindeutet.

19.06.2024, 12:15h
Ronan Richter
Lehrstuhl Wirtschaftsmathematik, Universität Bayreuth
Towards Analyzing small DNNs by Robust Adversarial Examples created with MILPs

Abstract: As DNN-based systems are gaining increasing popularity and governments begin to regulate AI systems, there is a growing demand for methods to analyze the trustworthiness of a DNN and the limits of its application. One classical method of showing weaknesses of DNNs are Adversarial Examples. These are slightly modified versions of input data, that lead a DNN into wrong classifications. As Fischetti and Jo (2018) have shown, Adversarial Examples can systematically be generated by ILPs, leading to Adversarial Examples, that are provably optimal in respect to a given criterion, e.g. the distance to some given input data. Thus, these methods may be used to analysis the vulnerability of a DNN. However, the structure of these examples highly depends on the parameters of the network, which are often unknown to an attacker. For a broader view, a lager class of DNNs should be considered. Thus, a mixed-integer programming model for generating Adversarial Examples, that are robust with respect to small changes in the weights and biases of a DNN will be given. For relaxations of the model, we will illustrate the impact of robustification on Adversarial Examples. Especially, we present experimental results on the influence of training data on the distance of Adversarial Examples and on the transferability of our examples.

26.06.2024, 12:15h
Bismark Singh
Operational Research Group, University of Southampton, UK
Balancing accessibility and fairness: Optimally closing recycling centers

Abstract: Typically, within facility location problems, fairness is defined in terms of accessibility of users. However, for facilities perceived as undesirable by communities hosting them - such as recycling centers - fairness between the usage of facilities becomes especially important. We develop a series of optimization models for the allocation of populations of users to such recycling centers such that access for users is balanced with a fair utilization of facilities. The optimality conditions of the underlying nonconvex quadratic models state the precise balance between accessibility and fairness. We define new classes of fairness and a metric to quantify the extent to which fairness is achieved in both optimal and suboptimal allocations.
Within the state of Bavaria in Germany, such centers have closed in the last few decades. Using mobility survey data we show how selective closures of these centers can still lead to high levels of recycling access. Our analysis ensures that even when 20% of facilities are closed smartly, the median travel distance by residents to their assigned recycling center increases by only 450 m. Additionally, we find Bavaria suffers from disparity in recycling patterns in rural and urban regions, both in terms of motivation to recycle and the locations of the facilities. We promote a policy that favors retention of recycling centers in rural regions by reserving 75% of open facilities to be in rural areas, while selectively closing facilities in urban regions, to remove these regional differences.
This work is based on two recently published articles in the INFORMS Journal on Computing and Networks.

3.07.2024, 12:15h
Alfred Wassermann
Lehrstuhl Mathematik und ihre Didaktik, Universität Bayreuth
Solve Ax=b with 0/1 variables

Abstract: Finding 0/1 solutions for a system of linear equations Ax=b, where A is an integer matrix and b is an integer vector, is a well-known NP-complete problem with many applications, e.g. in combinatorics, coding theory, and cryptography. In fact, it is one version of integer linear programming. There are many practical algorithms available to solve this problem, for example, integer linear programming solvers like CPLEX and Gurobi, backtracking algorithms like "dancing links", or SAT solvers.
In this talk, the author's software "solvediophant" is presented as an alternative to solve such kinds of problems.
For instances where the vector b consists of large integers, it seems to be faster than other approaches. Moreover, in contrast to other backtracking approaches, the matrix A might also have integer entries of mixed signs. So far, many new combinatorial objects and new record-breaking error-correcting codes have been constructed with "solvediophant".
The algorithm is based on lattice basis reduction together with an exhaustive enumeration of points in a high dimensional lattice. Additionally, solvediophant can be used with a non-standard backtracking approach called "least discrepancy search" which seems to be especially well suited for reduced lattice bases.
solvediophant solves instances up to 1500 variables and can be used not only for 0/1 variables but also for integer variables in a finite interval.

Monday, 8.07.2024, 12:15h, H33 (Inf)
Talk in the lecture series of the CRC 1357 Microplastics
Gholamreza Shiravani
Niedersächsischer Landesbetrieb für Wasserwirtschaft, Küsten- und Naturschutz
3D-Modeling of microplastic transport in tidal rivers by including the bio-geological effects

Abstract: Microplastic-transport mechanisms are using a developed 3D-numerical model for a tidal river from microplastic-sources (point form and diffusive sources) to accepting seas presented. The role of the bio-geological parameters on the fate of microplastics and their corresponding parametrization are explained. Moreover, the model capabilities and uncertainties are through the application of the model for microplastics-transport in the Weser estuary discussed. Finally, the model performance is through the comparison of the model results with microplastic-measurements for the Weser river evaluated. (Participation via zoom possible, see the announcement on the CRC Microplastic seminar site.)

17.07.2024, 12:15h
Ronny Bergmann
Department of Mathematical Sciences, NTNU Trondheim, Norway
The Riemannian Difference of Convex Algorithm in Manopt.jl

Abstract: In many applications nonlinear data is measured, for example when considering unit vectors, rotations, or (bases of) subspaces of a vector space. Modelling this on a Riemannian manifold allows to both reduce the dimension of the data stored as well as focusing on geometric properties of the measurement space compared to constraining a total space the data is represented in. In optimisation this yields unconstrained optimization algorithms, where we have to take the geometry of the optimization domain into consideration. In this talk we consider the task of minimizing the difference of two convex functions defined on a manifold and present the Difference of Convex Algorithm. To make algorithms in general more accessible, we then present the two Julia packages Manifolds.jl and Manopt.jl, that allow to define and use Riemannian manifolds and optimization algorithms employing numerical differential geometry, respectively.