This paper presents a variational Bayes (VB) method for normalized Gaussian network, which is a mixture model of local experts. Based on the Bayesian framework, we introduce a meta-learning mechanism to optimize the prior distribution and the model structure. In order to search for the optimal model structure efficiently, we also develop a hierarchical model selection method. The performance of...

This article deals with the specification of a locally flexible and theory-consistent system of mixed demand functions, a framework that allows for a rich set of possibilities about what is assumed as exogenous in a demand model. A coherent mixed demand system is derived by using the restricted expenditure function typically studied in the related area of rationed demands. The method is impleme...

called maximum shear modulus, Gmax. It can be determined by in-situ methods from the measurements of the shear wave velocity, Vs, by means of crosshole, down-hole, up-hole, or surface wave testing. The relationship between maximum shear modulus and shear wave velocity is rigorous: 2 max s G V    where ρ is soil density. This parameter can be also obtained in laboratory by resonant column or ...

Using a multicanonical Metropolis algorithm we have performed Monte Carlo simulations of the 3D 3-state Potts model on L lattices with L = 20, 30, 40, 50. Covering a range of inverse temperatures from βmin = 0 to βmax = 0.33 we calculated the infinite volume limit of the entropy density s(β) with its normalization obtained from s(0) = ln 3. At the transition temperature the entropy and energy e...

‎Let $G$ be a graph without an isolated vertex‎, ‎the normalized Laplacian matrix $tilde{mathcal{L}}(G)$‎ ‎is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$‎, where ‎$mathcal{D}$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎G‎$‎‎. ‎The eigenvalues of‎ $tilde{mathcal{L}}(G)$ are ‎called as ‎the ‎normalized Laplacian eigenva...