Related papers: Sufficient condition for root reconstruction by pa…
We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event…
We examine a mathematical question concerning the reconstruction accuracy of the Fitch algorithm for reconstructing the ancestral sequence of the most recent common ancestor given a phylogenetic tree and sequence data for all taxa under…
Phylogenetic networks are often constructed by merging multiple conflicting phylogenetic signals into a directed acyclic graph. It is interesting to explore whether a network constructed in this way induces biologically-relevant…
We consider the decentralized binary hypothesis testing problem on trees of bounded degree and increasing depth. For a regular tree of depth t and branching factor k>=2, we assume that the leaves have access to independent and identically…
We analyze the complexity of learning directed acyclic graphical models from observational data in general settings without specific distributional assumptions. Our approach is information-theoretic and uses a local Markov boundary search…
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen at random with probability proportional to its weight. In the case where the total…
The standard models of sequence evolution on a tree determine probabilities for every character or site pattern. A flattening is an arrangement of these probabilities into a matrix, with rows corresponding to all possible site patterns for…
Binary trait data record the presence or absence of distinguishing traits in individuals. We treat the problem of estimating ancestral trees with time depth from binary trait data. Simple analysis of such data is problematic. Each homology…
We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other…
Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given `far away' observations. Several theoretical results (and simple algorithms) are available when…
The maximum parsimony phylogenetic tree reconstruction problem is NP-hard, presenting a computational bottleneck for classical computing and motivating the exploration of emerging paradigms like quantum computing. To this end, we design…
Distance-based approaches in phylogenetics such as Neighbor-Joining are a fast and popular approach for building trees. These methods take pairs of sequences from them construct a value that, in expectation, is additive under a stochastic…
We study the growth of a time-ordered rooted tree by probabilistic attachment of new vertices to leaves. We construct a likelihood function of the leaves based on the connectivity of the tree. We take such connectivity to be induced by the…
Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…
In the spirit of Duqesne and Winkel (2007) and Berestycki et al. (2011) we show that supercritical continuous-state branching process with a general branching mechanism and general immigration mechanism is equal in law to a continuous-time…
To the known fact that Parsimony method sometimes fails on the problem of inferring species trees from gene trees, here we proved that no mater of what topology the true 9-taxon and greater species tree is the only thing one needs to break…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
The constant rate birth--death process is a popular null model for speciation and extinction. If one removes extinct and non-sampled lineages, this process induces `reconstructed trees' which describe the relationship between extant…
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…
The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…