Related papers: Gorenstein property for phylogenetic trivalent tre…
We study spanning trees on Sierpinski graphs (i.e., finite approximations to the Sierpinski gasket) that are chosen uniformly at random. We construct a joint probability space for uniform spanning trees on every finite Sierpinski graph and…
Let $F$ be a finite field with the characteristic $p > 2$ and let $G$ be the unitary Grassmann algebra generated by an infinite dimensional vector space $V$ over $F$. In this paper, we determine a basis for $\mathbb{Z}_{2}$-graded…
We study phylogenetic complexity of finite abelian groups - an invariant introduced by Sturmfels and Sullivant. The invariant is hard to compute - so far it was only known for $Z_2$, in which case it equals $2$. We prove that phylogenetic…
Trees corresponding to $\Lambda$- and $\Xi$-$n$-coalescents can be both quite similar and fundamentally different compared to bifurcating tree models based on Kingman's $n$-coalescent. This has consequences for inference of a well-fitting…
For any integer $n\ge 0$ and any ring $R$, \ $(\mathcal {PGF}_n, \ \mathcal P_n^\perp \cap \mathcal {PGF}^{\perp})$ proves to be a complete hereditary cotorsion pair in $R$-Mod, where $\mathcal {PGF}$ is the class of PGF modules, introduced…
We present the notion of Gorenstein categories relative to G-admissible triples. This is a relativization of the concept of Gorenstein category (an abelian category with enough projective and injective objects, in which the suprema of the…
We compute, with Symplectic Field Theory techniques, the Gromov-Witten theory of the complex projective line with orbifold points. A natural subclass of these orbifolds, the ones with polynomial quantum cohomology, gives rise to a family of…
We provide an explicit characterization of the covariant isotropy group of any Grothendieck topos, i.e. the group of (extended) inner automorphisms of any sheaf over a small site. As a consequence, we obtain an explicit characterization of…
Phylogenetic species trees typically represent the speciation history as a bifurcating tree. Speciation events that simultaneously create more than two descendants, thereby creating polytomies in the phylogeny, are possible. Moreover, the…
This paper aims to investigate the self-similarity property in finitely-generated torsion-free nilpotent groups. We establish connections between geometric equivalence and self-similarity in these groups. Moreover, we show that any…
The multispecies coalescent process models the genealogical relationships of genes sampled from several species, enabling useful predictions about phenomena such as the discordance between the gene tree and the species phylogeny due to…
In mathematical phylogenetics, evolutionary relationships are often represented by trees and networks. The latter are typically used whenever the relationships cannot be adequately described by a tree, which happens when so-called…
On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…
For a given length and a given degree and an arbitrary partition of the positive integers, there always is a cell containing a polynomial progression of that length and that degree; moreover, the coefficients of the generating polynomial…
Given a connected 2-complex X with fundamental group G, we show how pi_3(X) may be computed as a module over Z[G]. Further we show that if X is a finite connected 2-complex with G (the fundamental group) finite of odd order, then the stable…
Consider a population that is expanding in two-dimensional space. Suppose we collect data from a sample of individuals taken at random either from the entire population, or from near the outer boundary of the population. A quantity of…
We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at…
A grove is a spanning forest of a planar graph in which every component tree contains at least one of a special subset of vertices on the outer face called nodes. For the natural probability measure on groves, we compute various connection…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
Let $K= \mathbb{Q}(\sqrt{d})$ be a real quadratic field with $d$ having three distinct prime factors. We show that the $2$-class group of each layer in the $\mathbb{Z}_2$-extension of $K$ is $\mathbb{Z}/2\mathbb{Z}$ under certain elementary…