Related papers: Difference Sets with Few Character Values

The classical decision problem, as it is understood today, is the quest for a delineation between the decidable and the undecidable parts of first-order logic based on elegant syntactic criteria. In this paper, we treat the concept of…

This study presents a divide-and-conquer (DC) approach based on feature space decomposition for classification. When large-scale datasets are present, typical approaches usually employed truncated kernel methods on the feature space or DC…

Many properties of groups can be defined by the existence of a particular normal series. The classic examples being solvability, supersolvability and nilpotence. Among the nilpotent groups are the so-called nested GVZ-groups --- groups…

Geometrically characterized (GC) sets were introduced by Chung-Yao in their work on polynomial interpolation in R^d. Conjectures on the structure of GC sets have been proposed by Gasca-Maeztu for the planar case, and in higher dimension by…

Let $p$ be a prime. For $p=2$, the fields of values of the complex irreducible characters of finite groups whose degrees are not divisible by $p$ have been classified; for odd primes $p$, a conjectural classification has been proposed. In…

In real world everything is an object which represents particular classes. Every object can be fully described by its attributes. Any real world dataset contains large number of attributes and objects. Classifiers give poor performance when…

This paper considers a problem that relates to the theories of covering arrays, permutation patterns, Vapnik-Chervonenkis (VC) classes, and probability thresholds. Specifically, we want to find the number of subsets of [n]:={1,2,....,n} we…

We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…

We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules over a topological ring K. This calculus…

Let $G$ be a finite group. In order to determine the smallest cardinality $d(G)$ of a generating set of $G$ and a generating set with this cardinality, one should repeat many times the test whether a subset of $G$ of small cardinality…

The additive closedness in the subset of an additive group is termed as r-value. The nature of closedness in different subsets of fixed size is observed as a spectrum of r-values. We enumerate r-values of subsets in finite fields of…

We construct a set $M_d$ whose points parametrize families of Meixner polynomials in $d$ variables. There is a natural bispectral involution $b$ on $M_d$ which corresponds to a symmetry between the variables and the degree indices of the…

In this paper we study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over R are separable by a polynomial. For that we isolate a dense subfamily of Spaces of Orderings, named Geometric, which…

We consider the problem of minimizing the size of a family of sets G such that every subset of 1,...,n can be written as a disjoint union of at most k members of G, where k and n are given numbers. This problem originates in a real-world…

Feature selection is one of the most prominent learning tasks, especially in high-dimensional datasets in which the goal is to understand the mechanisms that underly the learning dataset. However most of them typically deliver just a flat…

We present a variety of new results on finite sets A of integers for which the sumset A+A is larger than the difference set A-A, so-called MSTD (more sums than differences) sets. First we show that there is, up to affine transformation, a…

This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no…

We study the problem of building models that disentangle independent factors of variation. Such models could be used to encode features that can efficiently be used for classification and to transfer attributes between different images in…

Set classification problems arise when classification tasks are based on sets of observations as opposed to individual observations. In set classification, a classification rule is trained with $N$ sets of observations, where each set is…

We present a case study investigating feature descriptors in the context of the analysis of chemical multivariate ensemble data. The data of each ensemble member consists of three parts: the design parameters for each ensemble member, field…