Related papers: Majority dynamics on finite trees
Generating function equation has been derived for the probability distribution of the number of nodes with $k \ge 0$ outgoing lines in randomly evolving special trees. The stochastic properties of end-nodes (k=0) have been analyzed, and it…
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statistically translation-invariant. We show that, for small…
In this work, it is pointed out that in the mean-field version of majority-rule opinion dynamics, the dependence of the consensus time on the population size exhibits two regimes. This is determined by the size distribution of the groups…
We consider infinite harmonic chain with completely deterministic dynamics. Initial data are assumed absolutely bounded. Nevertheless maximum of the variables can grow infinitely in time. We give conditions for this phenomenon. It coincides…
We develop the complex-analytic viewpoint on the tree convolutions studied by the second author and Weihua Liu in "An operad of non-commutative independences defined by trees" (Dissertationes Mathematicae, 2020, doi:10.4064/dm797-6-2020),…
A fundamental problem in the fields of population genetics, evolution, and community ecology, is the fate of a single mutant, or invader, introduced in a finite population of wild types. For a fixed-size community of $N$ individuals, with…
In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain. Using a recent approach based on finite-time stabilization, we show that the system is…
We investigate the finite-time stabilization of a tree-shaped network of strings. Transparent boundary conditions are applied at all the external nodes. At any internal node, in addition to the usual continuity conditions, a modified…
We introduce a 2-state opinion dynamics model where agents evolve by majority rule. In each update, a group of agents is specified whose members then all adopt the local majority state. In the mean-field limit, where a group consists of…
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
In this paper we study the stability problem of a tree of elastic strings with local Kelvin-Voigt damping on some of the edges. Under the compatibility condition of displacement and strain and continuity condition of damping coefficients at…
We study stochastic evolutionary game dynamics in a population of finite size. Individuals in the population are divided into two dynamically evolving groups. The structure of the population is formally described by a Wright-Fisher type…
Consider the stochastic PDE, $\partial_tu = \partial^2_x u + \sigma(u) \dot{W}$ on $\mathbb{R}_+\times\mathbb{R}$, subject to $u(0)\equiv1$, where $\dot{W}$ denotes space-time white noise on $\mathbb{R}_+\times\mathbb{R}$ and…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
We study computational questions related with the stability of discrete-time linear switching systems with switching sequences constrained by an automaton. We first present a decidable sufficient condition for their boundedness when the…
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic…
A stabilization theorem for processes of opinion dynamics is presented. The theorem is applicable to a wide class of models of continuous opinion dynamics based on averaging (like the models of Hegselmann-Krause and Weisbuch-Deffuant). The…
A general class of mass transport models with Q species of conserved mass is considered. The models are defined on a lattice with parallel discrete time update rules. For one-dimensional, totally asymmetric dynamics we derive necessary and…
We consider two-dimensional dependent dynamical site percolation where sites perform majority dynamics. We introduce the critical percolation function at time t as the infimum density with which one needs to begin in order to obtain an…
One of the ways to characterize a probability distribution is to show that it is moment-determinate, uniquely determined by knowing all its moments. The uniqueness, in the absolutely continuous case, depends entirely on the behaviour of the…