Related papers: Annihilation and coalescence on binary trees
Viruses constantly undergo mutations with genomic changes. The propagation of variants of viruses is an interesting problem. We perform numerical simulations of the microscopic epidemic model based on network theory for the spread of…
We consider a dynamical process on a graph $G$, in which vertices are infected (randomly) at a rate which depends on the number of their neighbours that are already infected. This model includes bootstrap percolation and first-passage…
We study the problem of identifying the source of a diffusion spreading over a regular tree. When the degree of each node is at least three, we show that it is possible to construct confidence sets for the diffusion source with size…
In this paper we study a nonlinear infection viral propagation model with diffusion, in which, the left boundary is fixed and with homogeneous Dirichlet boundary conditions, while the right boundary is free. We find that the habitat always…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
Inference of species networks from genomic data under the Network Multispecies Coalescent Model is currently severely limited by heavy computational demands. It also remains unclear how complicated networks can be for consistent inference…
The steady state properties of the mean density population of infected cells in a viral spread is simulated by a general forest fire like cellular automaton model with two distinct populations of cells ( permissive and resistant ones) and…
Coalescent models are used to study the transmission dynamics of rapidly evolving pathogens from molecular sequence data obtained from infected individuals. However coalescent parameters, such as effective population size, offer limited…
Null models of binary phylogenetic trees are useful for testing hypotheses on real world phylogenies. In this paper we consider phylogenies as binary trees without edge lengths together with a sampling measure and encode them as algebraic…
Chlamydiae are bacteria with an interesting unusual developmental cycle. A single bacterium in its infectious form (elementary body, EB) enters the host cell, where it converts into its dividing form (reticulate body, RB), and divides by…
An electrical network with the structure of a random tree is considered: starting from a root vertex, in one iteration each leaf (a vertex with zero or one adjacent edges) of the tree is extended by either a single edge with probability $p$…
We study the early stages of viral infection, and the distribution of times to obtain a persistent infection. The virus population proliferates by entering and reproducing inside a target cell until a sufficient number of new virus…
We consider species tree estimation under a standard stochastic model of gene tree evolution that incorporates incomplete lineage sorting (as modeled by a coalescent process) and gene duplication and loss (as modeled by a branching…
We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a…
We present here a new and universal approach for the study of random and/or trees, unifying in one framework many different models, including some novel ones not yet understood in the literature. An and/or tree is a Boolean expression…
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities $\propto 1/(i(m-i))$.…
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent p-coin tosses. Spatial variants of these models are proposed, in which finite…
We investigate extremal statistical properties such as the maximal and the minimal heights of randomly generated binary trees. By analyzing the master evolution equations we show that the cumulative distribution of extremal heights…
Pathogen introduction in plant communities can cause serious impact and biodiversity losses that may take long time to manage and restore. Effective control of epidemic spreading in the wild is a problem of paramount importance, because of…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…