Related papers: On a population model with memory
We consider the evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size, which implies that each mutation generates a new fitness value drawn from a probability…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
In varying environments it is beneficial for organisms to utilize available cues to infer the conditions they may encounter and express potentially favorable traits. However, external cues can be unreliable or too costly to use. We consider…
Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank…
If the dynamics of an open quantum systems is non-Markovian, its {asymptotic} state strongly depends on the initial conditions, even if the dynamics possesses an {invariant} state. This is the very essence of memory effects. In particular,…
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…
In continual learning, a system learns from non-stationary data streams or batches without catastrophic forgetting. While this problem has been heavily studied in supervised image classification and reinforcement learning, continual…
Test-time scaling has emerged as a promising direction for enhancing the reasoning capabilities of Large Language Models in last few years. In this work, we propose Population-Evolve, a training-free method inspired by Genetic Algorithms to…
We present two adaptive schemes for dynamically choosing the number of parallel instances in parallel evolutionary algorithms. This includes the choice of the offspring population size in a (1+$\lambda$) EA as a special case. Our schemes…
We present an individual based model of evolutionary ecology. The reproduction rate of individuals characterized by their genome depends on the composition of the population in genotype space. Ecological features such as the taxonomy and…
We consider a model of stationary population with random size given by a continuous state branching process with immigration with a quadratic branching mechanism. We give an exact elementary simulation procedure of the genealogical tree of…
We study the problem of learning associative memory -- a system which is able to retrieve a remembered pattern based on its distorted or incomplete version. Attractor networks provide a sound model of associative memory: patterns are stored…
There are two contrasting explanations of sleep: as a proximate, essential physiological function or as an adaptive state of inactivity and these hypotheses remain widely debated. To investigate the adaptive significance of sleep, we…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
In unicellular organisms such as bacteria and in most viruses, mutations mainly occur during reproduction. Thus, genotypes with a high birth rate should have a higher mutation rate. However, standard models of asexual adaptation such as the…
Despite increasing data from population-wide sequencing studies, the risk for recessive disorders in consanguineous partnerships is still heavily debated. An important aspect that has not sufficiently been investigated theoretically, is the…
We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk.…
Short-term memory in the brain cannot in general be explained the way long-term memory can -- as a gradual modification of synaptic weights -- since it takes place too quickly. Theories based on some form of cellular bistability, however,…
Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of…
In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…