Related papers: Matrix representations of multivalued projections …
We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…
This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the…
Equivariance of linear neural network layers is well studied. In this work, we relax the equivariance condition to only be true in a projective sense. We propose a way to construct a projectively equivariant neural network through building…
We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge…
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…
An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are…
Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical…
Based on the property that solving the system of linear matrix equations via the column space and the row space projections boils down to an approximation in the least squares error sense, a formulation for learning the weight matrices of…
Multidimensional systems are becoming increasingly important as they provide a promising tool for estimation, simulation and control, while going beyond the traditional setting of one-dimensional systems. The analysis of multidimensional…
Shape-constrained inference has wide applicability in bioassay, medicine, economics, risk assessment, and many other fields. Although there has been a large amount of work on monotone-constrained univariate curve estimation, multivariate…
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…
The paper studies a general inverse eigenvalue problem which contains as special cases many well studied pole placement and matrix extension problems. It is shown that the studied problem corresponds on the geometric side to a central…
Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor…
We present a generalization of multiview varieties as closures of images obtained by projecting subspaces of a given dimension onto several views, from the photographic and geometric points of view. Motivated by applications in Computer…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.