Abstract – Bachelorarbeit

Helene Feilitzsch – „Representation of Agent-based Models by Markov Chains on the Example of Schelling’s Segregation Model“

Vorgestellt zur ersten Orientierung für Erstsemester – ein Beispiel für eine Bachelorarbeit am FB Mathematik und Informatik.

Agent-based models (ABMs), such as T. Schelling’s Segregation Model (SSM), are widely used in simulating how micro-level interactions generate unintended macro-level phenomena. Despite their utility, ABMs frequently lack a rigorous formal mathematical framework. This thesis addresses this gap by evaluating the formalisation of ABMs as Markov chains, specifically representing the SSM as a discrete-time, homogeneous Markov chain. By identifying the configuration space of the model with the state space of a Markov chain, a formalisation to bridge the gap between micro-level agent interactions and macro-level system behaviour can be found.

Abstract – Dissertation

Margarita Kostré – „Particle-Based Simulation and Optimization“

Particle-based models are widely used to describe stochastic dynamics in areas such as biochemistry, social dynamics, and optimization, but they become challenging when multiple scales are involved.

In this talk, we address how particle-based simulations can be consistently linked to macroscopic PDE descriptions, and how particle-based optimization methods can balance exploration and exploitation in complex landscapes.

We illustrate these ideas with examples from multiscale modeling in biochemistry to particle swarm optimization, including applications to SIR-type models and to inference in historical spreading processes.