We examine the relationship between the Cooper-Herskovitz score of a Bayesian network and the conditional entropies of the nodes of the networks conditioned on the probability distributions of their parents. We show that minimizing the conditional entropy of each node of the BNS conditioned on its set of parents amounts to maximization of the CH score. The main result is a lower bound on the si...

In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: frightarrow ucdot fcirc varphi$ on $L^2(Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(Sigma_B)$ where $Bin Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form...

Traditional multivariate statistical methods, which are often used to monitor stationary processes, not applicable nonstationary processes. Cointegration analysis (CA) is considered an effective method deal with variables. If there a cointegration relationship among the series in system, it indicates that stable long-term dynamic equilibrium exists these However, due complexity of modern indust...

A Correction to this paper has been published: 10.1007/s12220-020-00602-z