Related papers: On discriminants of polylinear forms

We give a new complexity bound for calculating the complex dimension of an algebraic set. Our algorithm is completely deterministic and approaches the best recent randomized complexity bounds. We also present some new, significantly sharper…

It is a well established fact, that any projective algebraic variety is a moduli space of representations over some finite dimensional algebra. This algebra can be chosen in several ways. The counterpart in algebraic geometry is…

Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of…

Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation…

We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…

A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…

By using the Poisson formula for resultants and the variants of chip-firing game on graphs, we provide a combinatorial method for computing a class of of resultants, i.e. the characteristic polynomials of the adjacency tensors of starlike…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

In this paper, we tackle the parametric complete multiplicity problem for a univariate polynomial. Our approach to the parametric complete multiplicity problem has a significant difference from the classical method, which relies on repeated…

The generators of the algebra $gl_{n+1}$ in a form of differential operators of the first order acting on ${\bf R}^n$ with matrix coefficients are explicitly written. The algebraic Hamiltonians for a matrix generalization of $3-$body…

Some sharp inequalities of Gruss type for sequences of vectors in real or complex normed linear spaces are obtained. Applications for the discrete Fourier and Mellin transform are given. Estimates for polynomials with coefficients in normed…

A family of nonlinear partial differential equations of divergence form is considered. Each one is the Euler-Lagrange equation of a natural Riemaniann variational problem of geometric interest. New uniqueness results for the entire…

What polynomial in the coefficients of a system of algebraic equations should be called its discriminant? We prove a package of facts that provide a possible answer. Let us call a system typical, if the homeomorphic type of its set of…

In this paper, we improve Generative Adversarial Networks by incorporating a manifold learning step into the discriminator. We consider locality-constrained linear and subspace-based manifolds, and locality-constrained non-linear manifolds.…

We study realizations of polynomial deformations of the sl(2,R)- Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear,…

We provide simple criteria and algorithms for expressing homogeneous polynomials as sums of powers of independent linear forms, or equivalently, for decomposing symmetric tensors into sums of rank-1 symmetric tensors of linearly independent…

We extend Gegenbauer Polynomials technique to evaluate a class of complicated Feynman diagrams. New results in the form of $_3F_2$-hypergeometrical series of unit argument, are presented. As a by-product, we present a new transformation…

An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…

We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…

We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the…