Let (X , d,m) be a metric measure space with a local regular Dirichlet form. We establish necessary and sufficient conditions for upper heat kernel bounds with subdiffusive space-time exponent to hold. This characterization is stable under rough isometries, that is it is preserved under bounded perturbations of the Dirichlet form. Further, we give a criterion for stochastic completeness in term...

Mathematical programming applications often require an objective function to be approximated by one of simpler form so that an available computational approach can be used. An a priori bound is derived on the amount of error (suitably defined) which such an approximation can induce. This leads to a natural criterion for selecting the "best" approximation from any given class. We show that this ...

We consider model selection based on information criteria for classi cation. In classi cation, a class y is guessed from an attribute x based on the true conditional probability P (yjx), where x 2 X, y 2 Y , and X and Y are in nite and nite sets. In model selection, given examples, we select the model that minimizes an information criterion. The information criteria we address in this paper are...

A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from uniform limit theorems for rescaled and reparametrized criterion functions. The new method can handle cases where the standard approach does not yield the compl...

Based on the problem of detecting the number of signals, this paper provides a systematic empirical investigation on model selection performances of several classical criteria and recently developed methods (including Akaike’s information criterion (AIC), Schwarz’s Bayesian information criterion, Bozdogan’s consistent AIC, Hannan-Quinn information criterion, Minka’s (MK) principal component ana...

monitoring of road traffic noise is becoming an important issue in modern cities due to the spreading of noise pollution and the extension of monitored areas. thus, the stratified spatial sampling is frequently applied to reduce the costs and provide adequate accuracy in order to obtain reliable noise maps. the definition of the strata in the sampling may refer to the legislative classification...

In this paper, we find an explicit combinatorial criterion for the existence of a nonzero GLn−1(K)-high weight vector of weight (λ1, . . ., λi−1, λi−d, λi+1, . . . , λn−1), where d < char(K) and K is an algebraically closed filed, in the irreducible rational GLn(K)-module Ln(λ1, . . ., λn) with highest weight (λ1, . . . , λn). For this purpose, new modular lowering operators are introduced.