In this short note we will re-derive the Gaussian expectation propagation (Gaussian EP) algorithm as presented in Minka (2001) and demonstrate an application of Gaussian EP to approximate multi-dimensional truncated Gaussians. 1 On Gaussian Distributions Here we will summarise some important equalities about the Gaussian density. A Gaussian density in Rn is defined by N (x;μ,6) := (2π)− 2 |6|− ...

This section is devoted to the discussion of two fundamental (partial) differential equations, that arise in the context of Markov diffusion processes. After giving a brief introduction of continuous-time continuous state Markov processes, we introduce the forward and backward equation, and provide a heuristic derivation of these equations for diffusion processes. We also discuss some examples ...

The essentially Σ1 formulae of ΣL are exactly those which are provably equivalent to a disjunction of conjunctions of 2 and Σ1 formulae.

using fixed pointmethods, we investigate approximately higher ternary jordan derivations in banach ternaty algebras via the cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$

We present a direct derivation of the thermodynamic integral equations of the O(3) nonlinear σ-model in two dimensions. January 1992, Phys.Lett.B, in press on leave from Departamento de Fisica, Universidade Federal de S.Carlos, C.P. 676 S.Carlos 13560, Brazil. [email protected] The two-dimensional O(3) nonlinear σ-model is a well known example of an exactly integrable field theory [2, 3] ...

The basic Schema Theorem for genetic algorithms is modiied for a grammatically-based learning system. A context-free grammar is used to deene a language in which each sentence is mapped to a tness value. The derivation trees associated with these sentences are used to deene the structure of schemata. The eeect of crossover and mutation on schemata is described. A schema theorem is developed whi...

porous silicon samples were prepared by electrochemical etching method for different etching times. the structural properties of porous silicon (ps) samples were determined from the atomic force microscopy (afm) measurements. the surface mean root square roughness (σ rms) changes as function of porosity were studied, and the influence of etching time on porosity and roughness was studied too. u...

A signed graph is a graph where the edges are assigned either positive ornegative signs. Net degree of a signed graph is the dierence between the number ofpositive and negative edges incident with a vertex. It is said to be net-regular if all itsvertices have the same net-degree. Laplacian energy of a signed graph is defined asε(L(Σ)) =|γ_1-(2m)/n|+...+|γ_n-(2m)/n| where γ_1,...,γ_n are the ei...