We propose a separating-hyperplane algorithm for finding a nearest pair of points in two polytopes, where each polytope is expressed as the convex hull of given points in a Euclidian space. The proposed algorithm is an extension of the authors dual algorithm for finding t.he minimum-norm point in a polytope.

If X"0, Xx_ is an arbitrarily-dependent sequence of random variables taking values in [0,1] and if V( X0,X¡,... ) is the supremum, over stop rules /, of EX,, then the set of ordered pairs {(.*, v): x V(X0, Xx,.. .,Xn) and y £(maxyS„X¡) for some X0,..., Xn] is precisely the set C„= {(x,y):x<y<x(\ + n(\ *'/")); 0 « x « l}; and the set of ordered pairs {(x, y): x V(X0, X,,...) and y £(sup„ X„) for...

Abstract. Previously, self-dual codes have been constructed from weighing matrices, and in particular from conference matrices (skew and symmetric). In this paper, codes constructed from matrices of skew symmetric type whose determinants reach the EhlichWojtas’ bound are presented. A necessary and sufficient condition for these codes to be self-dual is given, and examples are provided for lengt...

This paper addresses the DATA-DIFF problem: given a dataset and a subsequent version of the dataset, find the shortest sequence of operations that transforms the dataset to the subsequent version, under a restricted family of operations. We consider operations similar to SQL UPDATE, each with a condition (WHERE) that matches a subset of tuples and a modifier (SET) that makes changes to those ma...

In this work we consider a stabilized Lagrange multiplier method in order to approximate the Coulomb frictional contact model in linear elastostatics. The particularity of the method is that no discrete inf-sup condition is needed. We study the existence and the uniqueness of solution of the discrete problem.

Let k be an algebraically closed field of positive characteristic, G a reductive group over k, and V a finite dimensional G-module. Let P be a parabolic subgroup of G, and UP its unipotent radical. We prove that if S = SymV has a good filtration, then SUP is strongly F -regular.

We present a fast algorithm for multiple kernel learning (MKL). Our matrix multiplicative weight update (MWUMKL) algorithm is based on a well-known QCQP formulation [5]. In addition, we propose a novel fast matrix exponentiation routine for QCQPs which might be of independent interest. Our method avoids the use of commercial nonlinear solvers and scales efficiently to large data sets. 1

Overweight and obesity affects more than 66% of the adult population and is associated with a variety of chronic diseases. Weight reduction reduces health risks associated with chronic diseases and is therefore encouraged by major health agencies. Guidelines of the National Heart, Lung, and Blood Institute (NHLBI) encourage a 10% reduction in weight, although considerable literature indicates r...

While injecting weight noise during training has been proposed for more than a decade to improve the convergence, generalization and fault tolerance of a neural network, not much theoretical work has been done to its convergence proof and the objective function that it is minimizing. By applying the Gladyshev Theorem, it is shown that the convergence of injecting weight noise during training an...

Computerized framework development is alternate to the Manual Method (MM) of cervical cancer analysis since MM suffers from the human errors, bulk quantities of Pap smear images, work loading and time complexities. Also, severity level prediction via counting of nucleus leads to incorrect prediction under geometric-based feature extraction. The cell-based segmentation evolved in research studie...