Related papers: Exactly solvable models through the generalized em…
We discuss a nonlinear model for the relaxation by energy redistribution within an isolated, closed system composed of non-interacting identical particles with energy levels e_i with i=1,2,...,N. The time-dependent occupation probabilities…
The master equations describing processes of biological evolution in the framework of the random neighbor Bak-Sneppen model are studied. For the eqosystem of $N$ species they are solved exactly and asymptotical behavior of this solution for…
Effective interactions can be obtained from a renormalization group analysis in two complementary ways. One can either explicitly integrate out higher energy modes or impose given conditions at low energies for a cut-off theory. While the…
The process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent, covering more than one lattice site. We expand the well studied Totally Asymmetric Exclusion…
First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit (but still…
Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population…
We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The…
By using a time-dependent operator converting a distribution function (statistical operator) of a total system under consideration into the relevant form, new exact nonlinear generalized master equations (GMEs) are derived. The…
We derive a new exact evolution equation for the scale dependence of an effective action. The corresponding equation for the effective potential permits a useful truncation. This allows one to deal with the infrared problems of theories…
Evolutionary game theory combines game theory and dynamical systems and is customarily adopted to describe evolutionary dynamics in multi-agent systems. In particular, it has been proven to be a successful tool to describe multi-agent…
Co-evolution is a powerful problem-solving approach. However, fitness evaluation in co-evolutionary algorithms can be computationally expensive, as the quality of an individual in one population is defined by its interactions with many (or…
We consider linear systems of equations and inequalities with coefficients varying inside given intervals. We define their solutions (so called AE solutions) and solvability (so called AE solvability) by using forall-exists quantification…
A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The…
We introduce the multispecies totally asymmetric simple exclusion process (mTASEP) with long-range swap, a new interacting particle system combining the backward-push rule with the forward-jump rule. Although governed by local dynamics, the…
Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression…
A general framework of evolutionary dynamics under heterogeneous populations is presented. The framework allows continuously many types of heterogeneous agents, heterogeneity both in payoff functions and in revision protocols and the entire…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
We consider the question of global existence of smooth solutions to a multi-species aggregation-diffusion equation for a class of singular interaction kernels. We establish a smallness condition on the initial data which yields global…
We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site $i=1,...,N$ is occupied by a particle of type $\a=A,B,C,$ with the average density of each particle species…
We consider a 1D lattice gas model in which the atoms interact via an infinite number of cluster interactions within contiguous atomic chains plus the next nearest neighbor pairwise interaction. All interactions are of arbitrary strength.…