相关论文: Brownian motion tree models are toric

Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability…

In this article we apply results of \cite{W} on the twisted Mellin transform to problems in toric geometry. In particular we use these results to describe the asymptotics of probability densities associated with the monomial eigenstates,…

We investigate Gauss maps of (not necessarily normal) projective toric varieties over an algebraically closed field of arbitrary characteristic. The main results are as follows: (1) The structure of the Gauss map of a toric variety is…

We present an alternative method for calculating likelihoods in molecular phylogenetics. Our method is based on partial likelihood tensors, which are generalizations of partial likelihood vectors, as used in Felsenstein's approach.…

We find presentations for subalgebras of invariants of the coordinate algebras of binary symmetric models of phylogenetic trees studied by Buczynska and Wisniewski in \cite{BW}. These algebras arise as toric degenerations of rings of global…

In this paper, we address the problem of sampling-based motion planning under motion and measurement uncertainty with probabilistic guarantees. We generalize traditional sampling-based tree-based motion planning algorithms for deterministic…

Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…

Phylogenetic trees describe the relationships between species in the evolutionary process, and provide information about the rates of diversification. To understand the mechanisms behind macroevolution, we consider a class of multitype…

In this paper, we present a flexible and probabilistic framework for tracking topological features in time-varying scalar fields using merge trees and partial optimal transport. Merge trees are topological descriptors that record the…

The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…

We study the problem of determining the distribution of vertices of a particular given type in the set of all Feynman tree graphs in quantum field theories. We show that in almost all cases a Gaussian distribution arises asymptotically, and…

Phylogenetic comparative methods correct for shared evolutionary history among a set of non-independent organisms by modeling sample traits as arising from a diffusion process along on the branches of a possibly unknown history. To…

Motivated by [G. Cannizzaro, M. Hairer, Comm. Pure Applied Math., '22], we provide a construction of the Brownian Web (see [T\'oth B., Werner W., Probab. Theory Related Fields, '98] and [L. R. G. Fontes, M. Isopi, C. M. Newman, and K.…

Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. They are also objects of interest in pure mathematics, such as algebraic geometry and combinatorics, due to their discrete geometry.…

Classification of gene trees is an important task both in the analysis of multi-locus phylogenetic data, and assessment of the convergence of Markov Chain Monte Carlo (MCMC) analyses used in Bayesian phylogenetic tree reconstruction. The…

This chapter shows how toroidal diffusions are convenient methodological tools for modelling protein evolution in a probabilistic framework. The chapter addresses the construction of ergodic diffusions with stationary distributions equal to…

Phylogenetic trees are widely used to understand the evolutionary history of organisms. Tree shapes provide information about macroevolutionary processes. However, macroevolutionary models are unreliable for inferring the true processes…

Phylogenetic trees provide a fundamental representation of evolutionary relationships, yet the combinatorial explosion of possible tree topologies renders inference computationally challenging. Classical approaches to characterizing tree…

Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…

Bayesian inference is now a leading technique for reconstructing phylogenetic trees from aligned sequence data. In this short note, we formally show that the maximum posterior tree topology provides a statistically consistent estimate of a…