Nobuaki Obata (2011)
Colloquium Mathematicae
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We show positivity of the Q-matrix of four kinds of graph products: direct product (Cartesian product), star product, comb product, and free product. During the discussion we give an alternative simple proof of the Markov product theorem on positive definite kernels.
Giacomo Aletti, Ely Merzbach (2006)
Journal of the European Mathematical Society
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Given a strongly stationary Markov chain (discrete or continuous) and a finite set of stopping rules, we show a noncombinatorial method to compute the law of stopping. Several examples are presented. The problem of embedding a graph into a larger but minimal graph under some constraints is studied. Given a connected graph, we show a noncombinatorial manner to compute the law of a first given path among a set of stopping paths.We prove the existence of a minimal Markov chain without oversized...
Paolo Boldi, Violetta Lonati, Massimo Santini, Sebastiano Vigna (2006)
RAIRO - Theoretical Informatics and Applications
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PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and , a particular kind of Markov chains that include the PageRank one as a special case. This fact provides constraints on the values that PageRank...
R. Vasuki, A. Nagarajan (2012)
Kragujevac Journal of Mathematics
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Jaroslav Markl (1993)
Acta Mathematica et Informatica Universitatis Ostraviensis
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Leroux, Philippe (2005)
International Journal of Mathematics and Mathematical Sciences
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Milan Studený, Alberto Roverato, Šárka Štěpánová (2009)
Kybernetika
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In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of feasible merging components, which is related to classic LWF (Lauritzen, Wermuth and Frydenberg) Markov equivalence of chain graphs. These results are used to get a graphical characterisation of factorisation equivalence of classic chain graphs. As another example...
Filip Guldan (1980)
Aplikace matematiky
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This paper presents the solution of a basic problem defined by J. Černý which solves a concrete everyday problem in railway and road transport (the problem of optimization of time-tables by some criteria).