arXiv subjects

Christopher McClain

Publications and source records attributed to Christopher McClain.

2 recordsLinked to original sources

arXiv2024

Maximum likelihood degree of the $β$-stochastic blockmodel

Log-linear exponential random graph models are a specific class of statistical network models that have a log-linear representation. This class includes many stochastic blockmodel variants. In this paper, we focus on $β$-stochastic blockmodels, which combine the $β$-model with a stochastic blockmodel. Here, using recent results by Almendra-Hernández, De Loera, and Petrović, which describe a Markov basis for $β$-stochastic block model, we give a closed form formula for the maximum likelihood degree of a $β$-stochastic blockmodel. The maximum likelihood degree is the number of complex solutions to the likelihood equations. In the case of the $β$-stochastic blockmodel, the maximum likelihood degree factors into a product of Eulerian numbers.

math.ST↗

arXiv2014

Bounding the Porous Exponential Domination Number of Apollonian Networks

Given a graph G with vertex set V, a subset S of V is a dominating set if every vertex in V is either in S or adjacent to some vertex in S. The size of a smallest dominating set is called the domination number of G. We study a variant of domination called porous exponential domination in which each vertex v of V is assigned a weight by each vertex s of S that decreases exponentially as the distance between v and s increases. S is a porous exponential dominating set for G if all vertices in S distribute to vertices in G a total weight of at least 1. The porous exponential domination number of G is the size of a smallest porous exponential dominating set. In this paper we compute bounds for the porous exponential domination number of special graphs known as Apollonian networks.

math.CO↗