In multiple regression problems when covariates can be naturally grouped, it is important to carry out feature selection at the group and within-group individual variable levels simultaneously. The existing methods, including the lasso and group lasso, are designed for either variable selection or group selection, but not for both. We propose a group bridge approach that is capable of simultane...

the aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. the state and co-state are approximated by the lowest order raviart-thomas mixed finite element spaces and the control is not discreted. optimal error estimates in l2 are established for the state...

Through changing the equivalence relation in the incomplete information system, a new variable precision rough set model and an approach for knowledge reduction are proposed. To overcome no monotonic property of the lower approximation, a cumulative variable precision rough set model is explored, and the basic properties of cumulative lower and upper approximation operators are investigated. Th...

Common metrics of correlation are based on the degree to which the value of one random variable can be used to predict the value of another random variable. However, there are forms of correlation that do not lead to a high ability to predict actual values. We identify such a correlation, and suggest it can be measured by a certain monotonicity property among distributions of the dependent vari...

The paper studies the consequences of the Null Player Out (NPO) property for single-valued solutions on the class of cooperative games in characteristic function form. We allow for variable player populations (supports or carriers). A solution satisses the NPO property, if elimination of a null player does not aaect the payoos of the other players. Our main emphasis lies on individual values. F...

This work presents thermoplastic analysis of FG rotating diskswith variable thickness and constant angular velocity. The solutions are obtained by variable material property (VMP) theory. In this theory, the domain is divided into some finite sub-domains in the radial direction, in which the properties are assumed to be constant and the form of the elastic response is used to solve elastic-plas...

The paper studies the consequences of the Null Player Out NPO property for single valued solutions on the class of cooperative games in characteristic function form We allow for variable player popula tions supports or carriers A solution satis es the NPO property if elimination of a null player does not a ect the payo s of the other players Our main emphasis lies on individual values For linea...

In this paper we prove a unique continuation property for vector valued functions of one variable satisfying certain differential inequality.

Elsewhere, I have promoted the notion of (univariate continuous) “transformation of scale” (ToS) distributions which have densities of the form 2g(W(x)) where g is a symmetric distribution and W is a transformation function with a special property. Here, I develop particular bivariate (readily multivariate) ToS distributions. Univariate ToS distributions have a transformation of random variable...

In this correspondence, construction of balanced Boolean functions with maximum possible algebraic (annihilator) immunity (AI) is studied with an additional property which is necessary to resist fast algebraic attack. The additional property considered here is, given an n-variable (n even) balanced function f with maximum possible AI n 2 , and given two n-variable Boolean functions g, h such th...