相关论文: Strong Bounds for Evolution in Undirected Graphs
We consider the so called Moran process with frequency dependent fitness given by a certain pay-off matrix. For finite populations, we show that the final state must be homogeneous, and show how to compute the fixation probabilities. Next,…
Based on a combination of insights afforded by Rainer Picard and Serge Nicaise, we extend a set of abstract piezo-electromagnetic impedance boundary conditions. We achieve this by accommodating for the influence of heat with the inclusion…
We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…
Evolutionary graph theory models the effects of natural selection and random drift on structured populations of competing mutant and non-mutant individuals. Recent studies have found that fixation times in such systems often have…
In this paper, we consider the multiplier spectrum of periodic points, which is a natural morphism defined on the moduli space of rational maps on the projective line. A celebrated theorem of McMullen asserts that aside from the…
We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur…
We study probabilities of various rare events for the limiting point process that appears at the random matrix hard edge. We also show a transition from hard edge to bulk behavior. Asymptotic events studied include a central limit theorem…
We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
Benjamini and Schramm introduced the notion of distributional limit of a sequence of graphs with uniformly bounded valence and studied such limits in the case that the involved graphs are planar. We investigate distributional limits of…
We introduce a new framework for the analysis of the dynamics of networks, based on randomly reinforced urn (RRU) processes, in which the weight of the edges is determined by a reinforcement mechanism. We rigorously explain the empirical…
Yin, Rinaldo, and Fadnavis classified the extremal behavior of the edge-triangle exponential random graph model by first taking the network size to infinity, then the parameters diverging to infinity along straight lines. Lubetzky and Zhao…
We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…
We give lower and upper bounds for the separation profile (introduced by Benjamini, Schramm & Tim\'ar) for various graphs using the isoperimetric profile, growth and Hilbertian compression. For graphs which have polynomial isoperimetry and…
The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of…
Leveraging algorithmic stability to derive sharp generalization bounds is a classic and powerful approach in learning theory. Since Vapnik and Chervonenkis [1974] first formalized the idea for analyzing SVMs, it has been utilized to study…
An evolving Riemannian manifold $(M,g_t)_{t\in I}$ consists of a smooth $d$-dimensional manifold $M$, equipped with a geometric flow $g_t$ of complete Riemannian metrics, parametrized by $I=(-\infty,T)$. Given an additional $C^{1,1}$ family…
Biological networks often encapsulate promotion/inhibition as signed edge-weights of a graph. Nodes may correspond to genes assigned expression levels (mass) of respective proteins. The promotion/inhibition nature of co-expression between…
We study a population model of fixed size undergoing strong selection where individuals accumulate beneficial mutations, namely the Moran model with selection. In a specific setting with strong selection, Schweinsberg showed that the…
The unpredictability of chaotic nonlinear dynamics leads naturally to statistical descriptions, including probabilistic limit laws such as the central limit theorem and large deviation principle. A key tool in the Nagaev-Guivarc'h spectral…