Related papers: Stabilization Time for a Type of Evolution on Bina…

We study the stabilization time of two common types of influence propagation. In majority processes, nodes in a graph want to switch to the most frequent state in their neighborhood, while in minority processes, nodes want to switch to the…

We study the stabilization time of a wide class of processes on graphs, in which each node can only switch its state if it is motivated to do so by at least a $\frac{1+\lambda}{2}$ fraction of its neighbors, for some $0 < \lambda < 1$. Two…

We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…

We consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to $N$. The behaviour of the automaton is mainly determined by the support of the random variable that selects one…

Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring…

We consider permutations of $\{1,...,n\}$ obtained by $\lfloor\sqrt{n}t\rfloor$ independent applications of random stirring. In each step the same marked stirring element is transposed with probability $1/n$ with any one of the $n$…

In this paper, we propose a new numerical strategy for the stabilization of evolution systems. The method is based on the methodology given by Ammari, Nicaise andPignotti in ''Stabilization by switching time-delay, Asymptot. Anal., 83…

The most common representation in evolutionary computation are bit strings. This is ideal to model binary decision variables, but less useful for variables taking more values. With very little theoretical work existing on how to use…

For a random variable $N = 0, 1, 2, \ldots$ we study the following question: When does the sum of $N$ many independent and identically distributed copies of a random variable $X$ have the same law a a nontrivial rescaling of $X$? We show…

We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…

We consider N strings connected to one another and forming a particular network which is a chain of strings. We study a stabilization problem and precisley we prove that the energy of the solutions of the dissipative system decay…

A minority process in a weighted graph is a dynamically changing coloring. Each node repeatedly changes its color in order to minimize the sum of weighted conflicts with its neighbors. We study the number of steps until such a process…

We extend and develop our previous work on the evolution of a network of cosmic strings. The new treatment is based on an analysis of the probability distribution of the end-to-end distance of a randomly chosen segment of left-moving string…

In string bit models, the superstring emerges as a very long chain of "bits", in which s fermionic degrees of freedom contribute positively to the ground state energy in a way to exactly cancel the destabilizing negative contributions of…

We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that…

This paper analyses a $(1,\lambda)$-Evolution Strategy, a randomised comparison-based adaptive search algorithm, on a simple constraint optimisation problem. The algorithm uses resampling to handle the constraint and optimizes a linear…

We consider the dynamical evolution of a Brownian particle undergoing stochastic resetting, meaning that after random periods of time it is forced to return to the starting position. The intervals after which the random motion is stopped…

The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…

Consider a one-dimensional stepping stone model with colonies of size $M$ and per-generation migration probability $\nu$, or a voter model on $\mathbb{Z}$ in which interactions occur over a distance of order $K$. Sample one individual at…

Let $N_n=\{1,2,...,n\}$. Elements are drawn from the set $N_n$ with replacement, assuming that each element has probability $1/n$ of being drawn. We determine the limiting distributions for the waiting time until the given portion of pairs…