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تسجيل مستخدم جديدA Spatial Mutation Model with Increasing Mutation Rates
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We consider a spatial model of cancer in which cells are points on the $d$-dimensional torus $mathcal{T}=[0,L]^d$, and each cell with $k-1$ mutations acquires a $k$th mutation at rate $mu_k$. We will assume that the mutation rates $mu_k$ are increasing, and we find the asymptotic waiting time for the first cell to acquire $k$ mutations as the torus volume tends to infinity. This paper generalizes results on waiting for $kgeq 3$ mutations by Foo, Leder, and Schweinsberg, who considered the case in which all of the mutation rates $mu_k$ were the same. In addition, we find the limiting distribution of the spatial distances between mutations for certain values of the mutation rates.
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Motivated by models of cancer formation in which cells need to acquire $k$ mutations to become cancerous, we consider a spatial population model in which the population is represented by the $d$-dimensional torus of side length $L$. Initially, no sit
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