Related papers: Strong Amplifiers of Natural Selection: Proofs
Let M be a compact manifold of dimension at least 2, Diff^r(M) be the space of C^r diffeomorphisms of M. Define for any diffeomorphism f in Diff^r(M) number of isolated periodic points of period n by P_n(f)=# {isolated x in M: f^n(x)=x}.…
We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of $N \geq 2$ populations, specified by unknown distributions. Over some time horizon, at each time $n = 1, 2, \ldots$, the…
In recent work on equiangular lines, Jiang, Tidor, Yuan, Zhang, and Zhao showed that a connected bounded degree graph has sublinear second eigenvalue multiplicity. More generally they show that there cannot be too many eigenvalues near the…
We define the incentive process, a natural generalization of the Moran process incorporating evolutionary updating mechanisms corresponding to well-known evolutionary dynamics, such as the logit, projection, and best-reply dynamics.…
Impartial selection has recently received much attention within the multi-agent systems community. The task is, given a directed graph representing nominations to the members of a community by other members, to select the member with the…
This paper provides time-dependent expressions for the expected degree distribution of a given network that is subject to growth, as a function of time. We consider both uniform attachment, where incoming nodes form links to existing nodes…
In this short article we propose a full large $N$ asymptotic expansion of the probability that the $m^{\text{th}}$ power of a random unitary matrix of size $N$ has all its eigenvalues in a given arc-interval centered in $1$ when $N$ is…
The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to…
We prove that for the Activated Random Walks model on transitive unimodular graphs, if there is fixation, then every particle eventually fixates, almost surely. We deduce that the critical density is at most 1. Our methods apply for much…
We consider a Moran model with two allelic types, mutation and selection. In this work, we study the behaviour of the proportion of fit individuals when the size of the population tends to infinity, without any rescaling of parameters or…
Let $\Gamma_{g}$ be the fundamental group of a closed connected orientable surface of genus $g\geq2$. We develop a new method for integrating over the representation space $\mathbb{X}_{g,n}=\mathrm{Hom}(\Gamma_{g},S_{n})$ where $S_{n}$ is…
An important part of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov Random Field. The belief propagation algorithm, which is an exact procedure to compute…
The probability that an advantageous mutant rises to fixation in a viral quasispecies is investigated in the framework of multi-type branching processes. Whether fixation is possible depends on the overall growth rate of the quasispecies…
Random planar graphs have been the subject of much recent work. Many basic properties of the standard uniform random planar graph P_{n}, by which we mean a graph chosen uniformly at random from the set of all planar graphs with vertex set…
We study the influence of complex graphs on the metastability and fixation properties of a set of evolutionary processes. In the framework of evolutionary game theory, where the fitness and selection are frequency-dependent and vary with…
Optical communication systems are always evolving to support the need for ever-increasing transmission rates. This demand is supported by the growth in complexity of communication systems which are moving towards ultra-wideband transmission…
We investigate two classes of inflationary models, which lead to a stiff period after inflation that boosts the signal of primordial gravitational waves (GWs). In both families of models studied, we consider an oscillating scalar…
We study the evolution of majority dynamics on Erd\H{o}s-R\'enyi $G(n,p)$ random graphs. In this process, each vertex of a graph is assigned one of two initial states. Subsequently, on every day, each vertex simultaneously updates its state…
We study the relation between the growth rate of a graph property and the entropy of the graph limits that arise from graphs with that property. In particular, for hereditary classes we obtain a new description of the colouring number,…
We consider the task of compression of information when the source of the information and the destination do not agree on the prior, i.e., the distribution from which the information is being generated. This setting was considered…