Related papers: Anderson Localization, Non-linearity and Stable Ge…
This study is concerned with destruction of Anderson localization by a nonlinearity of the power-law type. We suggest using a nonlinear Schr\"odinger model with random potential on a lattice that quadratic nonlinearity plays a dynamically…
Speciation is of fundamental importance to understanding the huge diversity of life on Earth. In contrast to current phenomenological models, we develop a biophysically motivated approach to study speciation involving the co-evolution of…
Biological evolution can be conceptualized as a search process in the space of gene sequences guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each genotype. Here we discuss probabilistic models of…
We study the spreading of initially localized states in a nonlinear disordered lattice described by the nonlinear Schr\"odinger equation with random on-site potentials - a nonlinear generalization of the Anderson model of localization. We…
It is well known that in Anderson localized systems, starting from a random product state the entanglement entropy remains bounded at all times. However, we show that adding a single boundary term to an Anderson localized Hamiltonian leads…
We consider a class of continuous-time stochastic growth models on $d$-dimensional lattice with non-negative real numbers as possible values per site. The class contains examples such as binary contact path process and potlatch process. We…
The quasispecies model of biological evolution for asexual organisms such as bacteria and viruses has attracted considerable attention of biological physicists. Many variants of the model have been proposed and subsequently solved using the…
An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
We analyze the geometry of the species- and genotype-size distribution in evolving and adapting populations of single-stranded self-replicating genomes: here programs in the Avida world. We find that a scale-free distribution (power law)…
In an isolated single-particle quantum system a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that dissipation can drive…
Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial…
Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that…
Genetic Programming yields interpretable programs, but small syntactic mutations can induce large, unpredictable behavioral shifts, degrading locality and sample efficiency. We frame this as an operator-design problem: learn a continuous…
We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schr\"odinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization…
The exploration of vast genotype spaces poses fundamental challenges for evolving populations. As the number of genotypes encoding viable phenotypes grows exponentially with genome length, populations can only explore a tiny fraction of…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of…
The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional…
The deterministic selection-recombination equation describes the evolution of the genetic type composition of a population under selection and recombination in a law of large numbers regime. So far, an explicit solution has seemed out of…