Algebraic model counting

Weighted model counting (WMC) is a well-known inference task on knowledge bases, and the basis for some of the most efficient techniques for probabilistic inference in graphical models. We introduce algebraic model counting (AMC), a generalization of WMC to a semiring structure that provides a unified view on a range of tasks and existing results. We show that AMC generalizes many well-known tasks in a variety of domains such as probabilistic inference, soft constraints and network and database analysis. Furthermore, we investigate AMC from a knowledge compilation perspective and show that all AMC tasks can be evaluated using sd-DNNF circuits, which are strictly more succinct, and thus more efficient to evaluate, than direct representations of sets of models. We identify further characteristics of AMC instances that allow for evaluation on even more succinct circuits

Topological expansion of mixed correlations in the hermitian 2 Matrix Model and x-y symmetry of the F_g invariants

We compute expectation values of mixed traces containing both matrices in a two matrix model, i.e. generating function for counting bicolored discrete surfaces with non uniform boundary conditions. As an application, we prove the $x-y$ symmetry of the algebraic curve invariants introduced in math-ph/0702045.Comment: 37 pages, late

Semi-Markov Graph Dynamics

In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs.Comment: 25 pages, 4 figures, submitted to PLoS-ON

Quark liberation and coalescence at CERN SPS

The mischievous linear coalescence approach to hadronization of quark matter is shown to violate strangeness conservation in strong interactions. The simplest correct quark counting is shown to coincide with the non-linear algebraic coalescence rehadronization model, ALCOR. The non-linearity of the ALCOR model is shown to cancel from its simple predictions for the relative yields of (multi-)strange baryons. We prove, model independently, that quark degrees of freedom are liberated before hadron formation in 158 AGeV central Pb + Pb collisions at CERN SPS.Comment: Latex file, 6 pages, improved text and conclusio

New steps in walks with small steps in the quarter plane

In this article we obtain new expressions for the generating functions counting (non-singular) walks with small steps in the quarter plane. Those are given in terms of infinite series, while in the literature, the standard expressions use solutions to boundary value problems. We illustrate our results with three examples (an algebraic case, a transcendental D-finite case, and an infinite group model).Comment: 47 pages, 8 figures, to appear in Annals of Combinatoric