منابع مشابه
Transfinite Graphs and Electrical Networks
All prior theories of infinite electrical networks assume that such networks are finitely connected, that is, between any two nodes of the network there is a finite path. This work establishes a theory for transfinite electrical networks wherein some nodes are not connected by finite paths but are connected by transfinite paths. Moreover, the voltages at those nodes may influence each other. Th...
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In Chapter 8 of the book, “Graphs and Networks: Transfinite and Nonstandard,” (published by Birkhauser-Boston in 2004), nonstandard versions of transfinite graphs and of electrical networks having such graphs were defined and examined but only for the first two ranks, 0 and 1, of transfiniteness. In the present work, these results are extended to higher ranks of transfiniteness. Such is done in...
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An ordinal-valued metric, taking its values in the set א1 of all countable ordinals, can be assigned to a metrizable set M of nodes in any transfinite graph. M contains all the nonsingleton nodes, as well as certain singleton nodes. Moreover, this yields a graphical realization of Cantor’s countable ordinals, as well as of the Aristotelian ideas of “potential” and “actual” infinities, the forme...
متن کاملKalman Filtering, Factor Graphs and Electrical Networks
Abstract Factor graphs are graphical models with origins in coding theory. It is well known that Kalman filtering is an instance of the generic sum(mary)-product algorithm on the corresponding factor graph. In this paper, a one-to-one correspondence between such factor graphs and a class of electrical networks is presented. The electrical network “computes” correct Bayesian estimates even for f...
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Factor graphs are graphical models with origins in coding theory. The sum-product and the max-product algorithms, which operate by message passing in a factor graph, subsume a great variety of algorithms in coding, signal processing, and artificial intelligence. In this paper, factor graphs are used to express a one-to-one correspondence (based on results by Dennis) between a class of static el...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1992
ISSN: 0002-9947
DOI: 10.2307/2153970