We provide a general framework for computing upper bounds on mixing times of finite Markov chains when its minimal ideal is left zero. Our analysis based combining results by Brown and Diaconis with our previous work stationary distributions chains. Stationary can be computed from the Karnofsky--Rhodes McCammond expansion right Cayley graph semigroup underlying chain. Using loop graphs, which a...

In this thesis we compare several combinatorial models for the Moduli space of open-closed cobordisms and their compactifications. More precisely, we study Godin’s category of admissible fat graphs, Costello’s chain complex of black and white graphs, and Bödigheimer’s space of radial slit configurations. We use Hatcher’s proof of the contractibility of the arc complex to give a new proof of a r...

The problem of efficiently sampling from a set of (undirected, or directed) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The switch chain is known to be rapidly mixing for regular degree sequences, both in the undirected and directed setting. We prove that the switch c...

‎‎let r be a non-commutative ring with unity‎. ‎the commuting graph‎ ‎of $r$ denoted by $gamma(r)$‎, ‎is a graph with a vertex set‎ ‎$rsetminus z(r)$ and two vertices $a$ and $b$ are adjacent if and only if‎ ‎$ab=ba$‎. ‎in this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. it is shown that‎, ‎$gamma(r)$ is the disjoint ...

Abstract: This paper proposes a novel representation of decomposable graphs based on semi-latent tree-dependent bipartite graphs. The novel representation has two main benefits. First, it enables a form of subclustering within maximal cliques of the graph, adding informational richness to the general use of decomposable graphs that could be harnessed in applications with behavioural type of dat...

Bayesian networks (BNs) are useful for coding conditional independence statements between a given set of measurement variables. On the other hand, event trees (ETs) are convenient for representing asymmetric structure and how situations unfold. In this paper we report the development of a new graphical framework for discrete probability models called the Chain Event Graph (CEG). The class of CE...

Graphical Markov models use graphs, either undirected, directed, or mixed, to represent possible dependences among statistical variables. Applications of undirected graphs (UGs) include models for spatial dependence and image analysis, while acyclic directed graphs (ADGs), which are especially convenient for statistical analysis, arise in such fields as genetics and psychometrics and as models ...