相关论文: Domination Between Trees and Application to an Exp…

The mutational heterogeneity of tumours can be described with a tree representing the evolutionary history of the tumour. With noisy sequencing data there may be uncertainty in the inferred tree structure, while we may also wish to study…

We consider a probability distribution on the set of Boolean functions in n variables which is induced by random Boolean expressions. Such an expression is a random rooted plane tree where the internal vertices are labelled with connectives…

Decision trees built with data remain in widespread use for nonparametric prediction. Predicting probability distributions is preferred over point predictions when uncertainty plays a prominent role in analysis and decision-making. We study…

We consider excursions for a class of stochastic processes describing a population of discrete individuals experiencing density-limited growth, such that the population has a finite carrying capacity and behaves qualitatively like the…

We consider two varieties of labeled rooted trees, and the probability that a vertex chosen from all vertices of all trees of a given size uniformly at random has a given rank. We prove that this probability converges to a limit as the tree…

This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…

We consider systems of interacting diffusions with local population regulation. Our main result shows that the total mass process of such a system is bounded above by the total mass process of a tree of excursions with appropriate drift and…

An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…

We study contextual stochastic optimization problems, where we leverage rich auxiliary observations (e.g., product characteristics) to improve decision making with uncertain variables (e.g., demand). We show how to train forest decision…

Given a graph G=(V, E), a vertex is said to ve-dominate an edge if it is either incident with the edge or adjacent to one of its endpoints. A set of vertices is a ve-dominating set if it ve-dominates every edge of the graph. We introduce…

In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be…

Tree-size distribution is one of the most investigated subjects in plant population biology. The forestry literature reports that tree-size distribution trajectories vary across different stands and/or species, while the metabolic scaling…

There are two types of particles interacting on a homogeneous tree of degree d + 1. The particles of the first type colonize the empty space with exponential rate 1, but cannot take over the vertices that are occupied by the second type.…

We propose the conjecture that every tree with order $n$ at least $2$ and total domination number $\gamma_t$ has at most $\left(\frac{n-\frac{\gamma_t}{2}}{\frac{\gamma_t}{2}}\right)^{\frac{\gamma_t}{2}}$ minimum total dominating sets. As a…

We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…

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…

A polynomial is said to be unimodal if its coefficients are non-decreasing and then non-increasing. The domination polynomial of a graph $G$ is the generating function of the number of dominating sets of each cardinality in $G$. In…

Finite-size fluctuations arising in the dynamics of competing populations may have dramatic influence on their fate. As an example, in this article, we investigate a model of three species which dominate each other in a cyclic manner.…

A set $S$ of vertices in a graph $G$ is a paired dominating set if every vertex of $G$ is adjacent to a vertex in $S$ and the subgraph induced by $S$ contains a perfect matching (not necessarily as an induced subgraph). The paired…

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…