相关论文: A consistency lemma in statistical phylogenetics

We apply symbolic method to deduce functional equation which generating function of counting sequence of dependency trees must satisfy. Then we use Lagrange inversion theorem to obtain concrete expression of the counting sequence. We apply…

We investigate how the pattern of contacts between species in mutualistic ecosystems is affected by the phylogenetic proximity between the species of each guild. We develop a dynamical model geared to establish the role of such proximity in…

A consensus tree is a phylogenetic tree that captures the similarity between a set of conflicting phylogenetic trees. The problem of computing a consensus tree is a major step in phylogenetic tree reconstruction. It also finds applications…

We consider the genealogy tree for a critical branching process conditioned on non-extinction. We enumerate vertices in each generation of the tree so that for each two generations one can define a monotone map describing the…

It has been claimed in Aldous, Miermont and Pitman [PTRF, 2004] that all L\'evy trees are mixings of inhomogeneous continuum random trees. We give a rigorous proof of this claim in the case of a stable branching mechanism, relying on a new…

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted…

Phylogenetics is now fundamental in life sciences, providing insights into the earliest branches of life and the origins and spread of epidemics. However, finding suitable phylogenies from the vast space of possible trees remains…

Comparative analyses of phylogenetic trees typically require identical taxon sets, however, in practice, trees often include distinct but overlapping taxa. Pruning non-shared leaves discards phylogenetic signal, whereas tree completion can…

Textual analysis of typical microbial genomes reveals that they have the statistical characteristics of a DNA sequence of a much shorter length. This peculiar property supports an evolutionary model in which a genome evolves by random…

In this note we record a comparison theorem on the B-model variation of semi-infinite Hodge structures. This result is considered a folklore theorem by experts in the field. We only take this opportunity to write it down. Our motivation is…

Inequality in human success may emerge through endogenous success-breeds-success dynamics but may also originate in pre-existing differences in talent. It is widely recognized that the skew in static frequency distributions of success…

For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population…

To determine whether a number is congruent or not is an old and difficult topic and progress is slow. The paper presents a new theorem when a prime number is a congruent number or not. The proof is not necessarily any simpler or shorter…

A very simple but useful almost sure convergence theorem of probability is given.

Phylogenetic trees and networks are leaf-labelled graphs that are used to describe evolutionary histories of species. The Tree Containment problem asks whether a given phylogenetic tree is embedded in a given phylogenetic network. Given a…

The present contribution investigates multivariate bootstrap procedures for general stabilizing statistics, with specific application to topological data analysis. Existing limit theorems for topological statistics prove difficult to use in…

Decision trees and logistic regression are one of the most popular and well-known machine learning algorithms, frequently used to solve a variety of real-world problems. Stability of learning algorithms is a powerful tool to analyze their…

A source sequence is to be guessed with some fidelity based on a rate-limited description of an observed sequence with which it is correlated. The trade-off between the description rate and the exponential growth rate of the least power…

A fundamental problem in the study of phylogenetic networks is to determine whether or not a given phylogenetic network contains a given phylogenetic tree. We develop a quadratic-time algorithm for this problem for binary nearly-stable…