Related papers: Non-Archimedean Replicator Dynamics and Eigen's Pa…
Theories in which gravity is weaker on cosmological scales have been proposed to explain the observed acceleration of the universe. The nonlinear regime in such theories is not well studied, though it is likely that observational tests of…
We consider the dynamics of $N$ interacting bosons initially exhibiting Bose-Einstein condensation. Due to an external trapping potential, the bosons are strongly confined in two spatial directions, with the transverse extension of the trap…
In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a…
The macroscopic curvature of double helical DNA induced by regularly repeated adenine tracts is well-known but still puzzling. Its physical origin remains controversial even though it is perhaps the best-documented sequence modulation of…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
We consider an infinitely-many neutral allelic model of population genetics where all alleles are divided into a finite number of classes, and each class is characterized by its own mutation rate. For this model the allelic composition of a…
In this article we study a \emph{non-directed} polymer model in dimension $d\ge 2$: we consider a simple symmetric random walk on $\mathbb{Z}^d$ which interacts with a random environment, represented by i.i.d. random variables…
We present a model for semiflexible polymers in Hamiltonian formulation which interpolates between a Rouse chain and worm-like chain. Both models are realized as limits for the parameters. The model parameters can also be chosen to match…
In this paper, we discuss the fitness landscape evolution of permanent replicator systems using a hypothesis that the specific time of evolutionary adaptation of the system parameters is much slower than the time of internal evolutionary…
The anomalous dynamical evolution and the crossing of nonadiabatic energy levels are investigated for exactly solvable time-dependent quantum systems through a reverse-engineering scheme. By exploiting a typical driven model, we elucidate…
We study populations of agents evolving in fitness landscapes constructed according to the rules of a modified NK model with a tunable amount of neutral paths. In the `punctuated equilibrium' regime evolutionary events are identified as…
Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these topologies is the emergence of a power law. Power law behavior with different scaling factors can also be…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
This theory seeks to define species and to explore evolutionary forces and genetic elements in speciation and species maintenance. The theory explains how speciation and species maintenance are caused by natural selection acting on…
By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables,…
We examine a model of biological evolution of Eigen's quasispecies in a holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). So, the evolution dynamics is determined by…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a 3-type…
We propose a re-formulation of the Einstein evolution equations that cleanly separates the conformal degrees of freedom and the non-conformal degrees of freedom with the latter satisfying a first order strongly hyperbolic system. The…
A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct…