Related papers: Breadth first search coding of multitype forests w…
We present here the notion of breadth-first signature and its relationship with numeration system theory. It is the serialisation into an infinite word of an ordered infinite tree of finite degree. We study which class of languages…
We define a multi-type coalescent point process of a general branching process with finitely many types. This multi-type coalescent fully describes the genealogy of the (quasi-stationary) standing population, providing types along ancestral…
We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…
We present a new branch-and-bound type search method for mixed integer linear optimization problems based on the concept of offshoots (introduced in this paper). While similar to a classic branch-and-bound method, it allows for changing the…
A number of methods have been developed to infer differential rates of species diversification through time and among clades using time-calibrated phylogenetic trees. However, we lack a general framework that can delineate and quantify…
The Maximum Agreement Forest problem has been extensively studied in phylogenetics. Most previous work is on two binary phylogenetic trees. In this paper, we study a generalized version of the problem: the Maximum Agreement Forest problem…
The main goal of this paper is to provide an algorithm for the random sampling of Butcher trees and the probabilistic numerical solution of ordinary differential equations (ODEs). This approach complements and simplifies a recent approach…
Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation of continuous-state branching processes. We provide a…
Consider a search from the root of an ordered tree with $n$ edges to some target node at a fixed distance $\ell$ from that root. We compare the average time complexity of the breadth-first search (BFS) and depth-first search (DFS)…
We introduce a model for the evolution of species triggered by generation of novel features and exhaustive combination with other available traits. Under the assumption that innovations are rare, we obtain a bursty branching process of…
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…
We revisit the discrete additive and multiplicative coalescents, starting with $n$ particles with unit mass. These cases are known to be related to some "combinatorial coalescent processes": a time reversal of a fragmentation of Cayley…
We consider the reconstruction of a phylogeny from multiple genes under the multispecies coalescent. We establish a connection with the sparse signal detection problem, where one seeks to distinguish between a distribution and a mixture of…
We study a set of linear transformations on the Fourier series representation of a sequence that can be used as the basis for similarity queries on time-series data. We show that our set of transformations is rich enough to formulate…
A zero-one sequence describes a path through a rooted directed binary tree $T$; it also encodes a real number in $[0,1]$. We regard the level of the external node of $T$ along the path as a function on the unit interval, the silhouette of…
The reconstruction of a species phylogeny from genomic data faces two significant hurdles: 1) the trees describing the evolution of each individual gene--i.e., the gene trees--may differ from the species phylogeny and 2) the molecular…
Large spatial datasets often represent a number of spatial point processes generated by distinct entities or classes of events. When crossed with covariates, such as discrete time buckets, this can quickly result in a data set with millions…
We consider a general class of branching processes in discrete time, where particles have types belonging to a Polish space and reproduce independently according to their type. If the process is critical and the mean distribution of types…
We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, for checking node fathoming,…
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…