Related papers: Complete intersection for equivariant models
The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we…
Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
A complete intersection $f_1=\cdots=f_k=0$ is sch\"on, if $f_1=\cdots=f_j=0$ defines a sch\"on subvariety of an algebraic torus for every $j\leqslant k$. This class includes nondegenerate complete intersections, critical loci of their…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies…
Motivated by phylogenetics, our aim is to obtain a system of equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based…
Many of the stochastic models used in inference of phylogenetic trees from biological sequence data have polynomial parameterization maps. The image of such a map --- the collection of joint distributions for a model --- forms the model…
We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…
Phylogenetic methods typically rely on an appropriate model of how data evolved in order to infer an accurate phylogenetic tree. For molecular data, standard statistical methods have provided an effective strategy for extracting…
We continue the study of engineered complete intersections (ECI) -- an umbrella generality for a number of important objects in combinatoiral and applied algebraic geometry (such as nondegenerate toric complete intersections, critical loci…
We study the relationship between two notions of pattern avoidance for involutions in the symmetric group and their restriction to fixed-point-free involutions. The first is classical, while the second appears in the geometry of certain…
For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set theoretic…
Evolution is a process that is influenced by various environmental factors, e.g. the interactions between different species, genes, and biogeographical properties. Hence, it is interesting to study the combined evolutionary history of…
For zero-dimensional complete intersections with homogeneous ideal generators of equal degrees over an algebraically closed field of characteristic zero, we give a combinatorial proof of the smoothness of the corresponding catalecticant…
The tangential ramification locus $B_{X/Y}^t\subset B_{X/Y}$ is the subset of points in the ramification locus where the sheaf of relative vector fields $T_{X/Y}$ fails to be locally free. It was conjectured by Zariski and Lipman that if…
We study the problem of unlikely intersections for automorphisms of Markov surfaces of positive entropy. We show for certain parameters that two automorphisms with positive entropy share a Zariski dense set of periodic points if and only if…
We apply the theory of markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies. We consider the Cavender-Farris-Neyman model of evolution on trees, where all the inner…
Efforts to reconstruct phylogenetic trees and understand evolutionary processes depend fundamentally on stochastic models of speciation and mutation. The simplest continuous-time model for speciation in phylogenetic trees is the Yule…
A simple way to model phenotypic evolution is to assume that after splitting, the trait values of the sister species diverge as independent Brownian motions. Relying only on a prior distribution for the underlying species tree (conditioned…
We suggest a natural approach that leads to a modification of classical quasispecies models and incorporates the possibility of population extinction in addition to growth. The resulting modified models are called open. Their essential…