Several important pattern recognition applications are based on feature extraction and vector clustering. Directional patterns may be represented by rotation-variant directional vectors, formed from M features uniformly extracted in M directions. It is often required that pattern recognition algorithms are invariant under pattern rotation or, equivalently, invariant under circular shifts of suc...

Nonnegative Matrix Factorization (NMF) is an efficient tool for clustering and supervised classification of various objects, including text document, musical recordings, gene expressions, and images. In this paper, we are concerned with supervised classification of texture patterns. NMF is used for creating localized nonnegative feature vectors and low-dimensional nonnegative encoding vectors f...

We present the method of group foliation for constructing non-invariant solutions of partial differential equations on an important example of the Boyer-Finley equation from the theory of gravitational instantons. We show that the commutativity constraint for a pair of invariant differential operators leads to a set of non-invariant solutions of this equation. In the second part of the paper we...

A‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. For this reason, many researchers have used various numerical methods to solve fuzzy linear systems. In this paper, we define the concepts of midpoint a...

In this paper, we present an efficient multi-scale similarity matching method for shape-based image indexing and retrieval. This method is affine-invariant and stable against noise and shape deformations. Shapes which have undergone mirror reflection can also be retrieved in a unified manner. In this approach, similarity matching is cast as correspondence matching of two shapes which is then so...

Here, we will consider one approach for extending the ideas underlying the least-squares algorithm we discussed in class to non-tall matrices. Let A ∈ Rn×d matrix, where both n and d are large, and where rank(A) = k exactly, and let B ∈ Rn×t. Consider the problem minX∈Rn×t‖AX −B‖, where ‖ · ‖ is a unitarily-invariant matrix norm. The solution to this problem is Xopt = AB, and here we consider a...

We address problems of the general form: given a J-dimensional binary (0-or 1-valued) vector a, a system of E of linear equations which a satisfies and a domain 3 C ~J which contains a, when is a the unique solution of E in 2,? More generally, we aim at finding conditions for the invariance of a particular position j, 1 <~j<<,J (meaning that bj = ag, for all solutions b of E in 3). We investiga...

In this paper, we are going to estimate the domain of attraction of tumor-free equilibrium points in a perturbed cancer tumor model describing the tumor-immune system competition dynamics. The proposed method is based on an optimization problem solution for a chosen Lyapunov function that can be casted in terms of Linear Matrix Inequalities constraint and Taylor expansion of nonlinear terms. We...

The interaction of Magnesium hydrate at the phosphate oxygen atom of the pyrimidine nucleotides (CMP,UMP,dTMP) were studied at the Hartree-Fock level Theory. We used LANL2DZ basis set for Mg and 6-31g* basis set for atoms.The basis set superposition error (BSSE) begins to converge for used Method/basis set. The gauge-invariant atomic orbital (GIAO) method and the continuous-set-of-gauge-transfo...

in this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist.