相关论文: Using invariants for phylogenetic tree constructio…
Tree alignment graphs (TAGs) provide an intuitive data structure for storing phylogenetic trees that exhibits the relationships of the individual input trees and can potentially account for nested taxonomic relationships. This paper…
The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov…
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that is…
Phylogenetic trees canonically arise as embeddings of phylogenetic networks. We recently showed that the problem of deciding if two phylogenetic networks embed the same sets of phylogenetic trees is computationally hard, \blue{in…
A simple method of constructing a big stock of algebraic varieties with trivial Makar-Limanov invariant is described, the Derksen invariant of some varieties is computed, the generalizations of the Makar-Limanov and Derksen invariants are…
We construct the non-linear Markov process connected with biological model of bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory.
Null models of binary phylogenetic trees are useful for testing hypotheses on real world phylogenies. In this paper we consider phylogenies as binary trees without edge lengths together with a sampling measure and encode them as algebraic…
Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…
Pedigrees are directed acyclic graphs that represent ancestral relationships between individuals in a population. Based on a schematic recombination process, we describe two simple Markov models for sequences evolving on pedigrees - Model R…
A phylogenetic tree is an important way in Bioinformatics to find the evolutionary relationship among biological species. In this research, a proposed model is described for the estimation of a phylogenetic tree for a given set of data. To…
Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to…
Some integral properties of Jack polynomials, hypergeometric functions and invariant polynomials are studied for real normed division algebras.
The method of flexi-Weighted Least Squares on evolutionary trees uses simple polynomial or exponential functions of the evolutionary distance in place of model-based variances. This has the advantage that unexpected deviations from…
Phylogenetic networks are necessary to represent the tree of life expanded by edges to represent events such as horizontal gene transfers, hybridizations or gene flow. Not all species follow the paradigm of vertical inheritance of their…
Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…
Models of random phylogenetic networks have been used since the inception of the field, but the introduction and rigorous study of mathematically tractable models is a much more recent topic that has gained momentum in the last 5 years.…
We consider novel phylogenetic models with rate matrices that arise via the embedding of a progenitor model on a small number of character states, into a target model on a larger number of character states. Adapting representation-theoretic…
Invariant foliations are complicated random sets useful for describing and understanding the qualitative behaviors of nonlinear dynamical systems. We will consider invariant foliations for stochastic partial differential equation with…
Reconstructing the evolutionary history relating a collection of molecular sequences is the main subject of modern Bayesian phylogenetic inference. However, the commonly used Markov chain Monte Carlo methods can be inefficient due to the…
We show that (as conjectured by Lin and Wang) when a Vassiliev invariant of type $m$ is evaluated on a knot projection having $n$ crossings, the result is bounded by a constant times $n^m$. Thus the well known analogy between Vassiliev…