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We generalize the evolution model introduced by Guiol, Machado and Schinazi (2010). In our model at odd times a random number X of species is created. Each species is endowed with a random fitness with arbitrary distribution on $[0, 1]$. At even times a random number Y of species is removed, killing the species with lower fitness. We show that there is a critical fitness $f_c$ below which the number of species hits zero i.o. and above of which this number goes to infinity. We prove uniform convergence for the distribution of surviving species and describe the phenomena which could not be observed in previous works with uniformly distributed fitness.
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 individuals fitness by $s_N$. Each individual dies at rate one, and w
Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis. Other mutat
Deficiency zero is an important network structure and has been the focus of many celebrated results within reaction network theory. In our previous paper textit{Prevalence of deficiency zero reaction networks in an ErdH os-Renyi framework}, we provid
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal is to estab
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal is to estab