‎Some functional inequalities‎ ‎in variable exponent Lebesgue spaces are presented‎. ‎The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non‎- ‎increasing function which is‎‎$$‎‎int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq‎‎Cint_0^infty f(x)^{p(x)}u(x)dx‎,‎$$‎ ‎is studied‎. ‎We show that the exponent $p(.)$ for which these modular ine...

Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with functional data. In this context, variable selection techniques are especially attractive because they reduce the dimensionality, facilitate the interpretati...

By JIAN HUANG Departments of Statistics & Actuarial Science and Biostatistics, University of Iowa, 221 Schaeffer Hall, Iowa City, Iowa 52242, U.S.A. [email protected] PATRICK BREHENY Departments of Statistics and Biostatistics, University of Kentucky, 817 Patterson Office Tower, Lexington, KY 40506, U.S.A. [email protected] SHUANGGE MA School of Public Health, Yale University, New Have...

Table 1 provides the average computational time (in minutes) for the eight methods under the simulation settings. SIS clearly requires the least computational effort, whereas RLASSO as well as Scout require much longer computational time. But all methods except RLASSO(CLIME) can be computed under a reasonable amount of time for p = 5000 and n = 100. RLASSO(CLIME) takes much longer because of in...

This work proposes an “ad hoc” new method for variable selection in classification, specifically in Discriminant Analysis. This new method is based on the metaheuristic strategy Tabu Search. From a computational point of view variable selection is a NP-Hard problem and therefore there is no guarantee of finding the optimum solution (NP = Nondeterministic Polynomial Time). This means that when t...

Compositional proof systems for shared variable concurrent programs can be devised by including the interference information in the speciica-tions. The formalism falls into a category called rely{guarantee (or assumption{ commitment), in which a speciication is explicitly (syntactically) split into two corresponding parts. This paper summarises existing work on the rely-guarantee method and giv...

This thesis addresses dimensionality reduction problems in classification for both high-dimensional multivariate and functional data. High-dimensional data refers to data with a large number of variables, often larger than the number of observations. High-dimensional data are encountered in a wide range of areas such as engineering, biometrics, psychometrics, and neuroimaging. Classifying these...

There are practical situations in which the quality of a process or product can be better characterized by a functional relationship between a response variable and one or more explanatory variables, which is called profile. Such profiles frequently can be represented adequately using linear or nonlinear models. While there are several studies in monitoring profiles, there are few studies to ev...

The Finite Formulation is an alternative to the widely used Finite Elements or Edge Elements methods and adopts the global variables as a starting point. The Finite Formulation allows one to straightforwardly deduce the set of algebraic equations. This method has been applied to the solution of plane electrostatic problems on the basis of two different topologies of the primal mesh elements: tr...