相关论文: Matrix methods for arithmetic functions
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…
In this short note we collect together known results on the use of Random Matrix Theory in lattice statistical mechanics. The purpose here is two fold. Firstly the RMT analysis provides an intrinsic characterization of integrability, and…
We present our public-domain software for the following tasks in sparse (or toric) elimination theory, given a well-constrained polynomial system. First, C code for computing the mixed volume of the system. Second, Maple code for defining…
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…
We show how to construct highly symmetric algorithms for matrix multiplication. In particular, we consider algorithms which decompose the matrix multiplication tensor into a sum of rank-1 tensors, where the decomposition itself consists of…
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…
We define tensors, corresponding to cubic polynomials, which have the same exponent $\omega$ as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor $sM_n$ defined on an $n\times n$ matrix…
A new method of algebraic nature is proposed for the study of the asymptotic properties of special polynomials. The technique we foresee is based on the use of umbral operators, allowing a unified treatment of a large body of polynomial…
Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A…
Matrix Factorization (MF) has found numerous applications in Machine Learning and Data Mining, including collaborative filtering recommendation systems, dimensionality reduction, data visualization, and community detection. Motivated by the…
An operatorial method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various type. This technique provide a very flexible and powerful tool yielding new results…
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.
We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in…
Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
We consider certain examples of applications of the general methods, based on geometry and integrability of matrix models, described in hep-th/0601212. In particular, the nonlinear differential equations, satisfied by quasiclassical…
We discuss how methods developed in the context of perturbation theory can be applied to the computation of lattice correlation functions, in particular in the non perturbative regime. The techniques we consider are integration-by-parts…
In this paper, we give one possible definition for functions of several variables applied to endomorphisms of finite dimensional C-vector spaces. This definition is consistent with the usual notion of a function of a square matrix. Some…
In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.