MODUS Seminar Program

Weekly talks in the MODUS Seminar in the winter semester 2024/2025:
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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Winter Semester 2024/2025

27.11.2024, 12:15h, also via zoom
Aditi Jain
Applied Mathematics, University of Bayreuth
Investigation of Complex Intracellular Dynamics through the lens of Cooperative Dynamical Systems

Abstract: Movement is an important part of life. For example, in a central and fundamental process known as gene expression, there is a movement of biological particles called RNA polymerases on the DNA strand to produce messenger RNA (mRNA). Understanding these complex transport phenomena has been a significant area of research in mathematics, biology, and physics. Over the years, the Ribosome Flow Model (RFM), obtained via a mean-field approximation of a stochastic model called the Totally Asymmetric Simple Exclusion Process (TASEP), has provided a rigorous mathematical framework for the analysis. It is a deterministic, continuous-time model for analyzing the flow of interacting particles, and its dynamics are described by ordinary differential equations (ODEs). The results of the RFM analysis can be used to model and engineer gene expression. In this talk, I rely on the framework of RFM to model and analyze the dynamical flow of particles along an ordered chain of sites encapsulating various biologically observed features. The presentation will focus on formulating a system of non-linear ordinary differential equations, where the densities of each site on a lattice serve as the state variables and understand their asymptotic behavior. Exploring cooperative irreducible systems of ODEs with a first integral exhibiting positive gradient, results are leveraged on the global phase portrait of such systems in the proposed models. These frameworks yield deeper insights into how parameters influence system dynamics, enhancing our comprehension of the underlying processes.

04.12.2024, 12:15h
Christoph Helbig
Ecological Resource Technology, University of Bayreuth
Modelling, Simulating, and Evaluating Global Material Cycles with Methods of Industrial Ecology

Abstract: The increasing demand for resources and the associated environmental impacts of extraction, processing, and consumption pose significant sustainability challenges from greenhouse gas emissions to land and water use. To address these challenges, it is essential to understand and manage global material cycles effectively. This presentation will introduce quantitative approaches to modelling, simulating, and evaluating global material cycles using industrial ecology methods. Combining material flow analysis, life cycle assessment, and raw material criticality assessment allows us to understand the complex interactions between human activities, natural systems, and material flows. The presentation will draw on my research experience in developing and applying innovative methods for studying mining, production, recycling, and dissipation of metal and mineral resources. The work is rooted in industrial ecology, which views human activities as part of the natural environment and seeks to optimise material and energy flows to minimise environmental impacts. Using case studies and examples, I will demonstrate how our Ecological Resource Technology group at the University of Bayreuth applies these methods to evaluate the sustainability of global material cycles, specifically focusing on strategically relevant technologies in energy, mobility, and electronics. The presentation will highlight the benefits of our approaches, such as their ability to provide a comprehensive understanding of material cycles, and their limitations, such as the complexity of data collection and analysis, and discuss future research directions for improving the understanding and management of global material cycles.

11.12.2024, 12:15h
Carsten Hartmann
Fachgebiet Stochastik und ihre Anwendungen, BTU Cottbus-Senftenberg
Duality of estimation and control, with application to the simulation of rare events

Abstract: A computational problem in statistics concerns the reduction of the variance of an estimator of some quantity of interest. A typical example is rare event simulation, for which the standard deviation of most Monte Carlo estimators can be orders of magnitude larger than the quantity of interest. In this talk, I will explain how the development of variance reduction algorithms for rare events can benefit from exploiting variational principles from statistical mechanics in combination with techniques from stochastic optimal control. A particular focus will be on stochastic differential equations and rare events that involve unbounded random stopping times, which pose a particular challenge because the computational complexity of the rare event simulation also depends on average simulation time per sample that is not controlled by the variance. I will present recent results that reveal an unexpected connection between different rare event simulation algorithms and discuss further applications of statistical mechanics principles in computational stochastics.

08.01.2025, 12:15h
Dominik Kamp
Wirtschaftsmathematik, University of Bayreuth
A Delta-Debugger for Mixed-Integer Programming Solvers

Abstract: Recent performance improvements of mixed-integer programming (MILP) solvers went along with a significantly increased complexity of their source codes. This poses challenges in investigating solver behavior, especially if something goes wrong due to implementation errors (aka bugs). In this talk, an open-source delta-debugger for MILP solvers is presented. Delta-debugging is a general trial-and-error approach to isolate the cause of a software failure by simplifying the input data for an implemented algorithm. In practice, applying this tool within the development of the open-source MILP solver SCIP contributed to an increase of approximately 71 % more bugfixes than in the year before. As highlighted in case studies, instances which trigger bugs in reasonable time could usually be reduced to a few variables and constraints in less than an hour. The resulting input instance then makes it significantly easier to discover the root cause of the solver behavior of interest. This way, even performance analysis could already benefit of this automized approach to generate simple performance-adversarial examples.

22.01.2025, 12:15h
Philipp Braun
School of Engineering, Australian National University Canberra
Orchestrating control laws for reach-and-avoid problems: Lyapunov based approaches

Abstract: Control design for robotic systems guaranteeing safety and convergence properties in cluttered environments is intrinsically challenging due to their potentially conflicting objectives. While several research streams tackle the problem from different angles, a general solution for nonlinear dynamical systems is still out of reach. In this presentation we discuss difficulties, solution concepts and tools in controllers designs for reach-and-avoid problems (i.e., simultaneous target set stabilization and obstacle avoidance). While various approaches exist, we focus on the presentation of related Lyapunov methods.

29.01.2025, 12:15h
Michael Baumann
Applied Mathematics, University of Bayreuth
On fair outcomes and how to detect them - Rabin'93 revisited

Abstract: Rabin fairness was published in 1993. We explain the concept, discuss questions, and clarify some notable points. Further, we show whether and how fairness equilibria can be calculated via Python/SymPy.

05.02.2025, 12:15h
Ronan Richter
Wirtschaftsmathematik, University of Bayreuth
Methods and measurements for robust adversarial examples

Abstract: After demonstrating their capabilities in everyday tasks, this machine learning models will get increasingly prevalent in critical applications as well. However, their vulnerability to adversarial examples is one of the longest known traits, that raises concerns about their reliability. Building on a previous talk in this seminar, this talk will focus on the creation and analysis of robust adversarial examples for deep neural networks. These kinds of adversarial examples are of particular interest, since they may abstract away from one specific AI model towards a more general class of DNNs. Thus, robust adversarial examples can give insights to the broader limitations of AI approaches and thus help assess the trustworthiness of AI systems. Particularly, in this talk, various methods, from literature and newly designed ones, for generating these adversarial examples will be presented. In this context, we also see, how several notions of adversarial examples exist in different context. Furthermore, will discuss measurements for the robustness of an adversarial example and evaluate the various methods on small examples based on these measurements.