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Graph Models (graph + models)
Selected AbstractsGraph models applied to specification, simulation, allocation, and scheduling of real-time computer vision applicationsINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 5 2000F. Torres This paper describes how graph models are applied to specification, simulation, allocation, and scheduling of real-time computer vision applications. Furthermore, we present a new environment that allows the user to specify a Computer Vision program using graphic schemes and evaluates allocation and scheduling methods for the schemes. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 11, 287,291, 2000 [source] Chain graph models and their causal interpretations,JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2002Steffen L. Lauritzen Chain graphs are a natural generalization of directed acyclic graphs and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are many simple and apparently plausible, but ultimately fallacious, interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to flawed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated from the equilibrium distributions of dynamic models with feed-back. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for directed acyclic graphs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feed-back in econometrics. [source] Asymptotic equivalence and contiguity of some random graphsRANDOM STRUCTURES AND ALGORITHMS, Issue 1 2010Svante Janson Abstract We show that asymptotic equivalence, in a strong form, holds between two random graph models with slightly differing edge probabilities under substantially weaker conditions than what might naively be expected. One application is a simple proof of a recent result by van den Esker, van der Hofstad, and Hooghiemstra on the equivalence between graph distances for some random graph models. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010 [source] The phase transition in inhomogeneous random graphsRANDOM STRUCTURES AND ALGORITHMS, Issue 1 2007Béla Bollobás Abstract The "classical" random graph models, in particular G(n,p), are "homogeneous," in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in the real world do not have this property, having, for example, power-law degree distributions. Thus there has been a lot of recent interest in defining and studying "inhomogeneous" random graph models. One of the most studied properties of these new models is their "robustness", or, equivalently, the "phase transition" as an edge density parameter is varied. For G(n,p), p = c/n, the phase transition at c = 1 has been a central topic in the study of random graphs for well over 40 years. Many of the new inhomogeneous models are rather complicated; although there are exceptions, in most cases precise questions such as determining exactly the critical point of the phase transition are approachable only when there is independence between the edges. Fortunately, some models studied have this property already, and others can be approximated by models with independence. Here we introduce a very general model of an inhomogeneous random graph with (conditional) independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p = c/n scaling for G(n,p) used to study the phase transition; also, it seems to be a property of many large real-world graphs. Our model includes as special cases many models previously studied. We show that, under one very weak assumption (that the expected number of edges is "what it should be"), many properties of the model can be determined, in particular the critical point of the phase transition, and the size of the giant component above the transition. We do this by relating our random graphs to branching processes, which are much easier to analyze. We also consider other properties of the model, showing, for example, that when there is a giant component, it is "stable": for a typical random graph, no matter how we add or delete o(n) edges, the size of the giant component does not change by more than o(n). © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 31, 3,122, 2007 [source] | ||||||||||