相关论文: A geometrical setting for the classification of mu…

Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in…

Transport phenomena in parallel coupled scatterers are studied by transfer matrix formulism. We derive a simple recurrence relation for transfer matrix of one-dimensional two-terminal systems consisting of $N$ arbitrary scattering unit…

We report an advanced formulation of the Fourier modal method developed for two-dimensionally periodic multilayered structures containing materials with non-zero macroscopic magneto-electric coefficients (also known as coefficients of…

We define compactifications of vector spaces which are functorial with respect to certain linear maps. These "many-body" compactifications are manifolds with corners, and the linear maps lift to b-maps in the sense of Melrose. We derive a…

Interpretability has become an important issue in the machine learning field, along with the success of layered neural networks in various practical tasks. Since a trained layered neural network consists of a complex nonlinear relationship…

We consider rank-one non-symmetric tensor estimation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat it completely in a simpler fashion than previous proofs using…

The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…

We consider the problem of learning low-dimensional representations for large-scale Markov chains. We formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, called the…

Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this…

We introduce and study matrix transfers to achieve elementary models for bivariant $K$-theory. They share lots of common properties with Voevodsky's framed correspondences and lead to symmetric matrix motives of algebraic varieties…

We construct linear operators factorizing the three bases of symmetric polynomials: monomial symmetric functions m(x), elementary symmetric polynomials E(x), and Schur functions s(x), into products of univariate polynomials.

In polarization optics, an important role play Mueller matrices -- real four-dimensional matrices which describe the effect of action of optical elements on the polarization state of the light, described by 4-dimensional Stokes vectors. An…

Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…

Clustering on the data with multiple aspects, such as multi-view or multi-type relational data, has become popular in recent years due to their wide applicability. The approach using manifold learning with the Non-negative Matrix…

The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…

A three-tiered specification approach is developed to formally specify collections of collaborating objects, say micro-architectures. (i) The structural properties to be maintained in the collaboration are specified in the lowest tier. (ii)…

Let $R=K[x_{1},x_{2},\cdots, x_{m}]$ and $S=$ $K[y_{1},y_{2},\cdots, y_{m}]$ where $K$ is a field. %commutative ring with unity. In this paper, we propose a method showing how to obtain $3$-matrix factors for a given polynomial using either…

The Clustered Factor (CF) model induces a block structure on the correlation matrix and is commonly used to parameterize correlation matrices. Our results reveal that the CF model imposes superfluous restrictions on the correlation matrix.…

Transport properties of magnetic multilayers in current perpendicular to the plane of the layers geometry are defined by diffusive scattering in the bulk of the layers, and diffusive and ballistic scattering across the interfaces. Due to…

Interferences in multi-path systems for single and multiple particles are theoretically analyzed. A holistic method is presented, which allows to construct the unitary transition matrix describing interferometers for any port number d and…