The fixation probability of a mutant in the evolutionary dynamics of Moran process is calculated by the Monte-Carlo method on a few families of clique-based graphs. It is shown that the complete suppression of fixation can be realized with the generalized clique-wheel graph in the limit of small wheel-clique ratio and infinite size. The family of clique-star is an amplifier, and clique-arms gra...

We study the local majority protocol on simple graphs of a given degree sequence, for a certain class of degree sequences. We show that for almost all such graphs, subject to a sufficiently large bias, within time A logd logd n the local majority protocol achieves consensus on the initial global majority with probability 1− n−Ω((logn)ε), where ε > 0 is a constant. A is bounded by a universal co...

A main question in graphical models and causal inference is whether, given a probability distribution P (which is usually an underlying distribution of data), there is a graph (or graphs) to which P is faithful. The main goal of this paper is to provide a theoretical answer to this problem. We work with general independence models, which contain probabilistic independence models as a special ca...

OFFICE HOURS: 1-2 MWF. TEXT: None. I will try to point out the sections of some relevant books, which will address the corresponding material we cover. Some of these books are listed below in bibliography. PREREQUISITE: Math 310 (first course in Linear Algebra), and Stat 401 (Introduction to Probability) or equivalent courses. Basic knowledge of graphs is welcome, (some parts of MCS 261), but n...

We generalize an equation introduced by Benamou and Brenier in [BB00] and characterizing Wasserstein Wp-geodesics for p > 1, from the continuous setting of probability distributions on a Riemannian manifold to the discrete setting of probability distributions on a general graph. Given an initial and a final distributions (f0(x))x∈G, (f1(x))x∈G, we prove the existence of a curve (ft(x))t∈[0,1],x...

We consider the following activation process in undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least r active neighbors. A contagious set is a set whose activation results with the entire graph being active. Given a graph G, let m(G, r) be the minimal size of a contagious set. We study this process on the binomia...

a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

We study a problem on percolation on product graphs G×K2. Here G is any finite graph and K2 consists of two vertices {0, 1} connected by an edge. In edge percolation every edge in G × K2 is present with probability p. In [3] Olle Häggström stated a conjecture (which he claimed to be folklore) that for all G and p the probability that (u, 0) is in the same component as (v, 0) is greater than the...

Tabling in logic programming has been used to eliminate redundant computation and also to stop infinite loop. In this paper we investigate another possibility of tabling, i.e. to compute an infinite sum of probabilities for probabilistic logic programs. Using PRISM, a logic-based probabilistic modeling language with a tabling mechanism, we generalize prefix probability computation for probabili...