Related papers: Adaptive walks and extreme value theory
Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between population genetics and evolutionary optimization and formulate a…
This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
We study the evolution of asexual microorganisms with small mutation rate in fluctuating environments, and develop techniques that allow us to expand the formal solution of the evolution equations to first order in the mutation rate. Our…
In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonous…
We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability $r$, and with…
The career of an employee can be described (under certain circumstances) by a random walk, where the states of the random walk are determined by the level and position of an employee. At each decision moment the state of the employee is…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
We propose a minimal model to simulate long waiting times followed by evolutionary bursts on rugged landscapes. It combines point and inversions-like mutations as sources of genetic variation. The inversions are intended to simulate one of…
Background: Recent experimental and theoretical studies have shown that small asexual populations evolving on complex fitness landscapes may achieve a higher fitness than large ones due to the increased heterogeneity of adaptive…
Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of…
We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in the case where the random walk terminates at some boundary. We recently found…
We study a discrete-time stochastic process that can also be interpreted as a model for a viral evolution. A distinguishing feature of our process is power-law tails due to dynamics that resembles preferential attachment models. In the…
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…
A theoretical and experimental analysis is made of the effects of self-adaptation in a simple evolving system. Specifically, we consider the effects of coding the mutation and crossover probabilities of a genetic algorithm evolving in…
We re-examine the evolutionary dynamics of RNA secondary structures under directional selection towards an optimum RNA structure. We find that the punctuated equilibria lead to a very slow approach to the optimum, following on average an…
We study the evolution of mutation rates for an asexual population living on a static fitness landscape, consisting of multiple peaks forming an evolutionary staircase. The optimal mutation rate is found by maximizing the diffusion towards…
We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at…
We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A {\bf 293},…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…