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

We develop a transfer matrix formalism for four-flux radiative transfer models, which is ideally suited for studying transport through multiple scattering layers. The model, derived for spherical particles within the diffusion…

Factor models are widely used across diverse areas of application for purposes that include dimensionality reduction, covariance estimation, and feature engineering. Traditional factor models can be seen as an instance of linear embedding…

Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…

Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…

In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to…

Matrix factorizations of a hypersurface yield a description of the asymptotic structure of minimal free resolutions over the hypersurface. We introduce a new concept of matrix factorizations for complete intersections that allows us to…

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…

Multilayer networks provide a powerful framework for modeling complex systems that capture different types of interactions between the same set of entities across multiple layers. Core-periphery detection involves partitioning the nodes of…

Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex m x n matrices. The theory of operator spaces provides a set up which describes 4 norm optimal factorizations of Grothendieck's sort.…

Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…

Many selection problems are multilayered: agents first decide whether to participate and then sort among ordered or unordered categories. This paper shows that the sorting layer changes the geometry of identification. Unlike binary…

Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…

We present a simple proof of the factorization of (complex) symmetric matrices into a product of a square matrix and its transpose, and discuss its application in establishing a uniqueness property of certain antilinear operators.

Accurate and fast modeling of electric fields in layered structures have a great scientific and practical value. Prevalent method for that is transfer-matrix method. However, transfer matrix method is limited to infinite plane wave…

We provide a detailed discussion on the electromagnetic modeling and classification of polarization converting bianisotropic metasurfaces. To do so, we first present a general approach to compute the scattering response of such…

Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…

Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats the fundamentals of the multivector differential…

We analyze single and multilayered metamaterials by modeling each layer as a metasurface with effective surface electric and magnetic susceptibility derived through a thin film approximation. Employing a transfer matrix method, these…

Theory of matrix factorizations is useful to study hypersurfaces in commutative algebra. To study noncommutative hypersurfaces, which are important objects of study in noncommutative algebraic geometry, we introduce a notion of…

Geometric representations provide a principled framework for structuring the description of latent constructs and clarifying sources of uncertainty in their dimensional characterisation. We introduce a novel geometric representation of…