Applied Mathematics Days 2023

Our institute organizes the Applied Mathematics Days with the following program.

Date: Dec 6, 2023, 15:00
Location: BME building Q room QAF14


István Scheuring (HUN−REN Centre for Ecological Research): Nonlinear public goods game as a model for bacterial cooperation

The evolutionary origin and stability of cooperation, i.e., a costly act that benefits other cospecific individuals, is one of the most challenging problems in evolutionary biology. There are several possible mechanisms to explain this seemingly counter-intuitive phenomenon, including spatial aggregation of cooperators, punishment of non-cooperators and additional private benefits for cooperators. Bacteria that produce extracellular enzymes or antibiotics as a public good are also cooperators. We study the evolutionary stability of bacterial cooperation, taking into account that the public good is a strongly nonlinear function of the frequency and density of cooperators, but without any assortment giving extra benefits to cooperators. We have shown that, besides the non-cooperative state, the coexistence of cooperators and defectors is another typical evolutionarily stable state of the system in a completely well-mixed population. By studying the density dependence of microbial cooperation, we pointed out that decreasing the density leads to the fixation of cooperators at a certain critical density and to an abrupt transition to the non-cooperative state below another critical density.

Eduardo Altmann (University of Sydney): Can physics help the study of social phenomena? From sociophysics to complex systems and data science

The many successes of Mathematical theories in Physics have long inspired the applications of physics-based methods to the social sciences. In the age of big data, these approaches are increasingly evaluated based on their success in analyzing and describing observations.  In this talk, I will discuss the journey of Physics ideas in the social sciences, focusing on the role played by empirical laws, such as Pareto's law of inequality and Zipf's law of word frequencies. Approaches based on such laws promise not only a quantitative description of the data but also a mechanistic understanding of the underlying generative process, a key advantage over black-box machine-learning techniques. I will argue that the statistical nature of the proposed laws, a facet often overlooked, is essential to evaluate their validity and applicability.