Related papers: Hadamard Product Decomposition and Mutually Exclus…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
We give a complete structural characterisation of the map the positive branch of a one-way pattern implements. We start with the representation of the positive branch in terms of the phase map decomposition, which is then further analysed…
In this work we use matrix models to study the problem of strength distributions. This is motivated by noticing near exponential fall offs of strengths in calculated magnetic dipole excitations. We emphasize that the quality of the…
We review matrix methods as applied to tracer transport. Because tracer transport is linear, matrix methods are an ideal fit for the problem. A gridded, Eulerian tracer simulation can be approximated as a system of linear ordinary…
We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
In this paper, we extend the uniqueness theorem for meromorphic mappings to the case where the family of hyperplanes depends on the meromorphic mapping and where the meromorphic mappings may be degenerate.
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…
In this review, we discuss the impact of interfaces and heterojuctions on the electronic and thermoelectric transport properties of materials. We review recent progress in understanding electronic transport in two-dimensional (2D) materials…
We study some spectral properties of a matrix that is constructed as a combination of a Laplacian and an adjacency matrix of simple graphs. The matrix considered depends on a positive parameter, as such we consider the implications in…
Attribute reduction is a basic issue in knowledge representation and data mining. Rough sets provide a theoretical foundation for the issue. Matroids generalized from matrices have been widely used in many fields, particularly greedy…
The semi-tensor product (STP) of matrices is extended to the STP of hypermatrices. Some basic properties of the STP of matrices are extended to the STP of hypermatrices. The hyperdeterminant of hypersquares is introduced. Some algebraic and…
We consider Gallai's graph Modular Decomposition theory for network analytics. On the one hand, by arguing that this is a choice tool for understanding structural and functional similarities among nodes in a network. On the other, by…
Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
In a Systems Engineering setting, various models are produced using a variety of methods and tools. Focusing on a type of models -- called descriptive models -- which we shall describe, we argue that, while the clarity and precision of…
Within the scattering matrix approach to electronic transport, the scattering and transport properties of tight-binding random graphs are analyzed. In particular, we compute the scattering matrix elements, the transmission, the…
We study examples of fourth-order Picard-Fuchs operators that are Hadamard products of two second-order Picard-Fuchs operators. Each second-order Picard-Fuchs operator is associated with a family of elliptic curves, and the Hadamard product…
This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.