62,586 research outputs found
BURNING NUMBER OF GRAPH PRODUCTS
International audienceGraph burning is a deterministic discrete time graph process that can be interpreted as a model for the spread of influence in social networks. The burning number of a graph is the minimum number of steps in a graph burning process for that graph. In this paper, we consider the burning number of graph products. We find some general bounds on the burning number of the Cartesian product and the strong product of graphs. In particular, we determine the asymptotic value of the burning number of hypercube graphs and we present a conjecture for its exact value. We also find the asymptotic value of the burning number of the strong grids, and using that we obtain a lower bound on the burning number of the strong product of graphs in terms of their diameters. Finally, we consider the burning number of the lexicographic product of graphs and we find a characterization for that
Reasoning about Independence in Probabilistic Models of Relational Data
We extend the theory of d-separation to cases in which data instances are not
independent and identically distributed. We show that applying the rules of
d-separation directly to the structure of probabilistic models of relational
data inaccurately infers conditional independence. We introduce relational
d-separation, a theory for deriving conditional independence facts from
relational models. We provide a new representation, the abstract ground graph,
that enables a sound, complete, and computationally efficient method for
answering d-separation queries about relational models, and we present
empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related
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Studying Self-Organized Criticality with Exactly Solved Models
This is a somewhat expanded version of the notes of a series of lectures
given at Lausanne and Stellenbosch in 1998-99. They are intended to provide a
pedagogical introduction to the abelian sandpile model of self-organized
criticality, and its related models : the q=0 state Potts model, Takayasu
aggregation model, the voter model, spanning trees, Eulerian walkers model etc.
It provides an overview of the known results, and explains the equivalence of
these models. Some open questions are discussed in the concluding section.Comment: Latex with epsf, 47 pages, 14 figure
Method and device for determining heats of combustion of gaseous hydrocarbons
A method and device is provided for a quick, accurate and on-line determination of heats of combustion of gaseous hydrocarbons. First, the amount of oxygen in the carrier air stream is sensed by an oxygen sensing system. Second, three individual volumetric flow rates of oxygen, carrier stream air, and hydrocrabon test gas are introduced into a burner. The hydrocarbon test gas is fed into the burner at a volumetric flow rate, n, measured by a flowmeter. Third, the amount of oxygen in the resulting combustion products is sensed by an oxygen sensing system. Fourth, the volumetric flow rate of oxygen is adjusted until the amount of oxygen in the combustion product equals the amount of oxygen previously sensed in the carrier air stream. This equalizing volumetric flow rate is m and is measured by a flowmeter. The heat of combustion of the hydrocrabon test gas is then determined from the ratio m/n
Multipoint correlators in the Abelian sandpile model
We revisit the calculation of height correlations in the two-dimensional
Abelian sandpile model by taking advantage of a technique developed recently by
Kenyon and Wilson. The formalism requires to equip the usual graph Laplacian,
ubiquitous in the context of cycle-rooted spanning forests, with a complex
connection. In the case at hand, the connection is constant and localized along
a semi-infinite defect line (zipper). In the appropriate limit of a trivial
connection, it allows one to count spanning forests whose components contain
prescribed sites, which are of direct relevance for height correlations in the
sandpile model. Using this technique, we first rederive known 1- and 2-site
lattice correlators on the plane and upper half-plane, more efficiently than
what has been done so far. We also compute explicitly the (new) next-to-leading
order in the distances ( for 1-site on the upper half-plane,
for 2-site on the plane). We extend these results by computing new correlators
involving one arbitrary height and a few heights 1 on the plane and upper
half-plane, for the open and closed boundary conditions. We examine our lattice
results from the conformal point of view, and confirm the full consistency with
the specific features currently conjectured to be present in the associated
logarithmic conformal field theory.Comment: 60 pages, 21 figures. v2: reformulation of the grove theorem, minor
correction
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