Related papers: Random Artin groups
In this thesis, which is supervised by Dr. David Penman, we examine random interval graphs. Recall that such a graph is defined by letting $X_{1},\ldots X_{n},Y_{1},\ldots Y_{n}$ be $2n$ independent random variables, with uniform…
If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability…
We consider the outer automorphism group Out(A_Gamma) of the right-angled Artin group A_Gamma of a random graph Gamma on n vertices in the Erdos--Renyi model. We show that the functions (log(n)+log(log(n)))/n and 1-(log(n)+log(log(n)))/n…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
Impartial selection has recently received much attention within the multi-agent systems community. The task is, given a directed graph representing nominations to the members of a community by other members, to select the member with the…
A model of $s$ interacting species is considered with two types of dynamical variables. The fast variables are the populations of the species and slow variables the links of a directed graph that defines the catalytic interactions among…
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…
Evolutionary graph theory studies the evolutionary dynamics in a population structure given as a connected graph. Each node of the graph represents an individual of the population, and edges determine how offspring are placed. We consider…
Social networks have become an inseparable part of human life and processing them in an efficient manner is a top priority in the study of networks. These networks are highly dynamic and they are growing incessantly. Inspired by the concept…
In this paper, we focus on exploiting the group structure for large-dimensional factor models, which captures the homogeneous effects of common factors on individuals within the same group. In view of the fact that datasets in…
We consider $\Sigma$-invariants of Artin groups that satisfy the $K(\pi,1)$-conjecture. These invariants determine the cohomological finiteness conditions of subgroups that contain the derived subgroup. We extend a known result for even…
By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables,…
Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications.…
Much is known about random right-angled Coxeter groups (i.e., right-angled Coxeter groups whose defining graphs are random graphs under the Erd\"os-R\'enyi model). In this paper, we extend this model to study random general Coxeter groups…
In this paper, we focus on statistical region-based active contour models where image features (e.g. intensity) are random variables whose distribution belongs to some parametric family (e.g. exponential) rather than confining ourselves to…
We establish the central limit theorem for the number of groups at the equilibrium of a coagulation-fragmentation process given by a parameter function with polynomial rate of growth. The result obtained is compared with the one for random…
Probabilistic generative models of graphs are important tools that enable representation and sampling. Many recent works have created probabilistic models of graphs that are capable of representing not only entity interactions but also…
We show that for a large class of Artin groups with Dynkin diagrams being a tree, the $K(\pi,1)$-conjecture holds. We also establish the $K(\pi,1)$-conjecture for another class of Artin groups whose Dynkin diagrams contain a cycle, which…
According to the Tits conjecture proved by Crisp and Paris, [CP], the subgroups of the braid group generated by proper powers of the Artin elements are presented by the commutators of generators which are powers of commuting elements. Hence…
In this note, we study the notion of random Dehn function and compute an asymptotic upper bound for finitely presented acylindrically hyperbolic groups whose Dehn function is at most polynomial. By showing that in these cases, if the group…