Related papers: Core-EP Decomposition and its Applications

The present work is dedicated to searching parameters, alternative to entropy, applicable for description of highly organized systems. The general concept has been offered, in which the system complexity and order are functions of the order…

We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…

In this paper, we show that if we decompose a polygon into two smaller polygons, then by comparing the number of extremal vertices in the original polygon versus the sum of the two smaller polygons, we can gain at most two globally extremal…

The weak-map order on the matroid base polytopes is the partial order defined by inclusion. Lucas proved that the base polytope of no binary matroid includes the base polytope of a connected matroid. A matroid base polytope is said to be…

We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the…

We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained…

Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density…

We propose a data-driven approach for intrinsic image decomposition, which is the process of inferring the confounding factors of reflectance and shading in an image. We pose this as a two-stage learning problem. First, we train a model to…

The $k$-core of a graph is defined as the maximal subgraph in which every vertex is connected to at least $k$ other vertices within that subgraph. In this work we introduce a distance-based generalization of the notion of $k$-core, which we…

We give a necessary and sufficient condition for extremality of a supermodular function based on its min-representation by means of (vertices of) the corresponding core polytope. The condition leads to solving a certain simple linear…

In this paper we give convex-ear decompositions for the order complexes of several classes of posets, namely supersolvable lattices with non-zero Mobius functions and rank-selected subposets of such lattices, rank-selected geometric…

Tensor decomposition on big data has attracted significant attention recently. Among the most popular methods is a class of algorithms that leverages compression in order to reduce the size of the tensor and potentially parallelize…

A linear polarization field on the sphere can be uniquely decomposed into an E-mode and a B-mode component. These two components are analytically defined in terms of spin-2 spherical harmonics. Maps that contain filtered modes on a partial…

Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…

We investigate the structure of the Tukey types of ultrafilters on countable sets partially ordered by reverse inclusion. A canonization of cofinal maps from a p-point into another ultrafilter is obtained. This is used in particular to…

In this paper, we investigate *-DMP elements in $*$-semigroups and $*$-rings. The notion of *-DMP element was introduced by Patr\'{i}cio in 2004. An element $a$ is *-DMP if there exists a positive integer $m$ such that $a^{m}$ is EP. We…

This paper introduces AL$\ell_0$CORE, a new form of probabilistic non-negative tensor decomposition. AL$\ell_0$CORE is a Tucker decomposition where the number of non-zero elements (i.e., the $\ell_0$-norm) of the core tensor is constrained…

The expression for polarized electric dipole moment of well-deformed reflection asymmetric nuclei is obtained in the framework of liquid-drop model in the case of geometrically similar proton and neutron surfaces. The expression for…

We study a correspondence between numerical sets and integer partitions that leads to a bijection between simultaneous core partitions and the integer points of a certain polytope. We use this correspondence to prove combinatorial results…

Medical images can be decomposed into normal and abnormal features, which is considered as the compositionality. Based on this idea, we propose an encoder-decoder network to decompose a medical image into two discrete latent codes: a normal…