Related papers: Kunchenko's Polynomials for Template Matching
We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
We present new techniques for reducing a multivariate sparse polynomial to a univariate polynomial. The reduction works similarly to the classical and widely-used Kronecker substitution, except that we choose the degrees randomly based on…
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more…
Let $k$ be a field of characteristic $\neq 2$. We survey a general method of the field intersection problem of generic polynomials via formal Tschirnhausen transformation. We announce some of our recent results of cubic, quartic and quintic…
In this overview paper a direct approach to q-Chebyshev polynomials and their elementary properties is given. Special emphasis is placed on analogies with the classical case. There are also some connections with q-tangent and q-Genocchi…
Kunchenko's method of polynomial maximization provides a semiparametric apparatus for parameter estimation under non-Gaussian errors, but its classical power basis relies on finite higher-order integer moments. This paper introduces the…
We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determine the coefficients of these formulas with the exception of…
Inspired by numerical homotopy methods we propose a combinatorial homotopy algorithm for finding all isolated solutions to a tropical polynomial systems of n tropical polynomials in n variables. In particular, a tropicalisation of the…
We introduce an object that has obvious similarity to the classical one - the algebra of supersymmetric polynomials. Despite the similarity, the known structure theorems on supersymmetric polynomials do not help in the study of the new…
This paper proposes a new paradigm and computational framework for identification of correspondences between sub-structures of distinct composite systems. For this, we define and investigate a variant of traditional data clustering, termed…
The "variance method" has been used to prove many classical inequalities in design theory and coding theory. The purpose of this expository note is to review and present some of these inequalities in a unified setting. I will also discuss…
We give combinatorial formulas for F-polynomials in cluster algebras of classical types in terms of the weighted paths in certain directed graphs. As a consequence we prove the positivity of F-polynomials in cluster algebras of classical…
The foremost aim of this study is to introduce and study several combinatorial properties and highlight specific aspects of a new class of polynomials sequences known as degenerate Krawtchouk Appell polynomials associated with the…
In the paper, we introduce a matrix method to constructively determine spaces of polynomial solutions (in general, multiplied by exponentials) to a system of constant coefficient linear PDE's with polynomial (multiplied by exponentials)…
The classical multidimensional resultant can be defined as the, suitably normalized, generator of a projective elimination ideal in the ring of universal coefficients. This is the approach via the so-called inertia forms or…
We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.