Abstract: We obtain formulae for the expected number and height distribution of critical points of general smooth isotropic Gaussian random fields parameterized on Euclidean space or spheres of arbitrary dimension. The results hold in general in the sense that there are no restrictions on the covariance function of the field except for smoothness and isotropy. The results are based on a charact...

Multi-class Gaussian Process Classifiers (MGPCs) are often affected by overfitting problems when labeling errors occur far from the decision boundaries. To prevent this, we investigate a robust MGPC (RMGPC) which considers labeling errors independently of their distance to the decision boundaries. Expectation propagation is used for approximate inference. Experiments with several datasets in wh...

We prove a central limit theorem for the nite dimensional marginals of the Gibbs distribution of the macroscopicòverlap'-parameters in the Hoppeld model in the case where the number of random`patterns', M, as a function of the system size N satisses lim N"1 M(N)=N = 0, without any assumptions on the speed of convergence. The covariance matrix of the limiting gaussian distributions is diagonal a...

The solution of the fractional hyperbolic partial differential equation is obtained by means of the variational iteration method. Our numerical results are compared with those obtained by the modified Gauss elimination method. Our results reveal that the technique introduced here is very effective, convenient, and quite accurate to one-dimensional fractional hyperbolic partial differential equa...

This paper focuses on Byzantine attack detection for Gaussian two-way relay network. In this network, two source nodes communicate with each other with the help of an amplify-and-forward relay which may perform Byzantine attacks by forwarding altered symbols to the sources. For simple investigating the detectability of attacks conducted in Gaussian channels, we focus on the MA channel of the ne...

We discuss one known and five new interrelated methods for bounding the hull of the solution set of a system of interval linear equations. Each method involves a polynomial amount of computing; but requires considerably more effort than Gaussian elimination. However, each method can yield sharper results for appropriate problems. For certain problems, our methods can obtain sharp bounds for one...

The first and second order of accuracy stable difference schemes for the numerical solution of the mixed problem for the fractional parabolic equation are presented. Stability and almost coercive stability estimates for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of one-dimension...

In the classical herding literature, agents receive a private signal regarding a binary state of nature, and sequentially choose an action, after observing the actions of their predecessors. When the informativeness of private signals is unbounded, it is known that agents converge to the correct action and correct belief. We study how quickly convergence occurs, and show that it happens more sl...

This paper presents a novel target-driven MLLR adaptation algorithm with multiply layer structure, which is based on the thorough analysis of MLLR using the generation of regression class trees. The new algorithm is constructed on the targetdriven principal. It generates the regression class dynamically, basing on the outcome of the former MLLR transformation. The regression classes is defined ...