Arkadiusz Majka

I am currently a Ph.D. student at the Interdisciplinary Center for Mathematical and Computational Modeling (ICM) at Warsaw University, Poland, and of the Polish-German Graduate College, operated by ICM and Heidelberg University. I graduated at Physics Department at Warsaw University. My M.Sc. thesis concerned plasma flow in magnetic tubes, embedded in the atmosphere of the Sun. I focused on energy equation and thermodynamic formalism in order to describe flow dynamics and heat exchanges.

However, my interests cover a larger spectrum of sciences, not only physics, and after defending my diploma, I started working at ICM on more interdisciplinary problems. I am interested in applications of physics in social sciences, decision sciences and economics. I am seeking a thermodynamic formalism for economic systems.

My recent research, in collaboration with Prof. Wojciech Wislicki, is related to choice models which are of great importance for many branches of economics, psychology, the behavioral sciences, cognitive science, political science and the social sciences. In discrete choice models, one assumes that there exists the choice set consisting of a countable and finite set of comparable alternatives. These are related to the preferences of each decision maker, what mathematically is described by the so-called utility function. It is itself a random variable for which probability density function has been found. We showed the analogy between the properties of the utility and the total energy functions of finite physical systems, thus enabling applications of thermodynamic formalism to network analysis. We develop equilibrium thermodynamics in the framework of the canonical and the grand canonical ensembles. In addition, we also propose to treat network topology as a random variable and to build up the super canonical statistical ensemble and develop more general models.

I believe that our approach to choice models is useful for other network-related problems. In this sense the International Fellowship Program is a great opportunity for me to learn, to collaborate and to share my experiences with other scientists.

Published Research

Majka, A. and W. Wislicki. "Statistical thermodynamics for choice models on graphs." Condensed Matter Archive 0306717, Los Alamos National Labratory, Los Alamos, NM, 2003 [PDF] 682 KB

Majka, A. and W. Wislicki. "Uniformity of the phase space and fluctuations in thermal equilibrium." Physica A 322 (2003): 313-328 [PDF] 217 KB