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Game dynamics theory, as a field of science, the consistency of theory and experiment is essential. In the past 10 years, important progress has been made in the merging of the theory and experiment in this field, in which dynamics cycle is…
Mathematical aspects of the theory of interfaces in statistical mechanics are discussed.
Within the continuous endeavour of improving the efficiency and resilience of air transport, the trend of using concepts and metrics from statistical physics has recently gained momentum. This scientific discipline, which integrates…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
By drawing a parallel between metadynamics and self interacting models for polymers, we study the longtime convergence of the original metadynamics algorithm in the adiabatic setting, namely when the dynamics along the collective variables…
We consider a system of $N$ individuals consisting of $S$ species that interact pairwise: $x_m+x_\ell \rightarrow 2x_m\,\,$ with arbitrary probabilities $p_m^\ell $. With no spatial structure, the master equation yields a simple set of rate…
This paper investigates applicability of thermodynamic concepts and principles to competitive systems. We show that Tsallis entropies are suitable for characterisation of systems with transitive competition when mutations deviate from Gibbs…
In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible…
This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living,…
Because the decathlon tests many facets of athleticism, including sprinting, throwing, jumping, and endurance, many consider it to be the ultimate test of athletic ability. On this view, estimating the maximal decathlon score and…
We study the reaction-diffusion system, its stationary solutions, the behavior of the system near them and discuss similarities and differences for different boundary conditions.
The equilibrium behavior of binary mixtures can be understood through the competition of energy scales, which classifies their corresponding phase diagrams into distinct topological regimes (Types I-IV). However, in many soft-matter…
We consider the motion of a finite though large number of particles in the whole space R n. Particles move freely until they experience pairwise collisions. We use our recent theory of divergence-controlled positive symmetric tensors in…
The paper studies the convergence properties of (continuous) best-response dynamics from game theory. Despite their fundamental role in game theory, best-response dynamics are poorly understood in many games of interest due to the…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
We introduce a general contagion-like model for competing opinions that includes dynamic resistance to alternative opinions. We show that this model can describe candidate vote distributions, spatial vote correlations, and a slow approach…
We study dynamic multi-battle contests and examine how the contest structure shapes dynamic incentives and determines the extent of rent dissipation. A discouragement effect often arises -- such as in tug-of-war and best-of-$K$ contests --…
The goal of this work is to study an infectious disease spreading in a medium size population occupying a confined environment. For this purpose, we consider a kinetic theory approach to model crowd dynamics in bounded domains and couple it…