Related papers: Domination Between Trees and Application to an Exp…
Fricke, Hedetniemi, Hedetniemi, and Hutson asked whether every tree with domination number $\gamma$ has at most $2^\gamma$ minimum dominating sets. Bien gave a counterexample, which allows to construct forests with domination number…
We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected…
This work considers a number of optimization problems and reductive relations between them. The two main problems we are interested in are the \emph{Optimal Decision Tree} and \emph{Set Cover}. We study these two fundamental tasks under…
In this paper, we establish a sufficient condition to compare linear combinations of independent and identically distributed (iid) infinite-mean random variables under usual stochastic order. We introduce a new class of distributions that…
A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…
The dynamics of infectious diseases spread is crucial in determining their risk and offering ways to contain them. We study sequential vaccination of individuals in networks. In the original (deterministic) version of the Firefighter…
We investigate properties of node centrality in random growing tree models. We focus on a measure of centrality that computes the maximum subtree size of the tree rooted at each node, with the most central node being the tree centroid. For…
We analyse the friendship paradox on finite and infinite trees. In particular, we monitor the vertices for which the friendship-bias is positive, neutral and negative, respectively. For an arbitrary finite tree, we show that the number of…
Dynamic mean field theory is applied to the problem of forest fires. The starting point is the Monte Carlo simulation in a lattice of million cells. The statistics of the clusters is obtained by means of the Hoshen--Kopelman algorithm. We…
The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence…
We consider stochastic processes indexed by the vertices of an infinite binary tree having a simple recursive structure. The value at any vertex is some fixed function of the values at the two daughter vertices together with some…
We demonstrate a method for proving precise concentration inequalities in uniformly random trees on $n$ vertices, where $n\geq1$ is a fixed positive integer. The method uses a bijection between mappings…
Imagine being able to ask questions to a black box model such as "Which adversarial examples exist?", "Does a specific attribute have a disproportionate effect on the model's prediction?" or "What kind of predictions could possibly be made…
A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
Consider a weighted branching process generated by a point process on $[0,1]$, whose atoms sum up to one. Then the weights of all individuals in any given generation sum up to one, as well. We define a nested occupancy scheme in random…
We study a competitive stochastic growth model called chase-escape in which red particles spread to adjacent uncolored sites and blue only to adjacent red sites. Red particles are killed when blue occupies the same site. If blue has rate-1…
Place one active particle at the root of a graph and a Poisson-distributed number of dormant particles at the other vertices. Active particles perform simple random walk. Once the number of visits to a site reaches a random threshold, any…
In a deterministic or random tree, a notion of ancestral diversity can be defined as follows. Sample independently $n$ groups of $k$ leaves and count the number $N_n(k)$ of distinct most recent common ancestors of each of the groups. As $n$…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…