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This paper concerns the geometric treatment of graphical models using Bayes linear methods. We introduce Bayes linear separation as a second order generalised conditional independence relation, and Bayes linear graphical models are constructed using this property. A system of interpretive and diagnostic shadings are given, which summarise the analysis over… (More)

- Michael Goldstein, Wilhelm Schlag
- 2005

The purpose of this article is to review some of the recent work on the operator (Hxψ)n = −ψn−1 − ψn+1 + λV (T n x)ψn (0.1) on 2 (Z), where T : X → X is an ergodic transformation on (X, ν) and V is a real-valued function. λ is a real parameter called coupling constant. Typically, X = T d = (R/Z) d with Lebesgue measure, and V will be a trigonometric… (More)

This research assumes that a problem-solving method has an applicabdtty condmon which specifies the properties of "good" problem-dependent parameters for the method Such a condition Is used as the basis of a computer program that mechamcally generates good parameters for the method to use in solving the problem Such problem-dependent parameters for a method… (More)

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