Related papers: Anderson Localization, Non-linearity and Stable Ge…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We consider the Moran model in continuous time with two types, mutation, and selection. We concentrate on the ancestral line and its stationary type distribution. Building on work by Fearnhead (J. Appl. Prob. 39 (2002), 38-54) and Taylor…
Anderson localization is the ubiquitous phenomenon of inhibition of transport of classical and quantum waves in a disordered medium. In dimension one, it is well known that all states are localized, implying that the distribution of an…
For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…
In this study, we construct an evolutionary model of a population of DNA sequences interacting with the surrounding environment on the topological monoid A* of strings on the alphabet A = { a, c, g, t }. A partial differential equation…
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…
We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
Evolution on neutral networks of genotypes has been found in models to concentrate on genotypes with high mutational robustness, to a degree determined by the topology of the network. Here analysis is generalized beyond neutral networks to…
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…
This work is a generic advance in the study of delocalized (ergodic) to localized (non-ergodic) wave propagation phenomena in the presence of disorder. There is an urgent need to better understand the physics of extreme value process in the…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…
Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. We find that off-diagonal one- and two-particle propagators behave as gaussian random variables w.r.t. momentum summations. With this…
In this paper, we inspect well-known population genetics and social dynamics models. In these models, interacting individuals, while participating in a self-organizing process, give rise to the emergence of complex behaviors and patterns.…
The strong Allee effect plays an important role on the evolution of population in ecological systems. One important concept is the Allee threshold that determines the persistence or extinction of the population in a long time. In general, a…
We study the evolution of artificial learning systems by means of selection. Genetic programming is used to generate a sequence of populations of algorithms which can be used by neural networks for supervised learning of a rule that…
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…
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in…
We develop a novel approach to the Anderson localisation problem in a $d$-dimensional disordered sample of dimension $L\times M^{d-1}$. Attaching a perfect lead with the cross-section $M^{d-1}$ to one side of the sample, we derive evolution…