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Many Physics Education Researchers have discussed the positive correlation between students' incoming mathematics skills and performance in their physics classes. Thus, in order to strengthen their performance gains in their physics…
Transmission line theory enables the bottom up study of networks based on wireline infrastructures. This technique is here applied to a simulator that brings together powerline communication networks with small radio cells ones in a hybrid…
This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated boundary conditions in this formalism. In…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
The ever-changing telecommunication industry is in severe need of a highly-skilled workforce to shape and deploy future generation communication systems. This article presents an innovative telecommunication training that is designed to…
The paper investigates random fields in the ball. It studies three types of such fields: restrictions of scalar random fields in the ball to the sphere, spin, and vector random fields. The review of the existing results and new spectral…
Next generation mobile networks will rely ever more heavily on resource sharing. In this article we study the sharing of radio access network and spectrum among mobile operators. We assess the impact of sharing these two types of resources…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
What is the probability that a random triangle is acute? We explore this old question from a modern viewpoint, taking into account linear algebra, shape theory, numerical analysis, random matrix theory, the Hopf fibration, and much much…
The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with…
The recent progresses in Machine Learning opened the door to actual applications of learning algorithms but also to new research directions both in the field of Machine Learning directly and, at the edges with other disciplines. The case…
Networks and network computations have become a primary mathematical tool for analyzing the structure of many kinds of complex systems, ranging from the Internet and transportation networks to biochemical interactions and social networks. A…
We study a new class of matrix models, formulated on a lattice. On each site are $N$ states with random energies governed by a Gaussian random matrix Hamiltonian. The states on different sites are coupled randomly. We calculate the density…
In this paper, we first introduce the new class of vertically-recurrent matrices, using a generalization of "the Hockey stick and Puck theorem" in Pascal's triangle. Then, we give an interesting formula for the lower triangular…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
We report on the development of students' ideas of probability and probability density in a University of Maine laboratory-based general education physics course called Intuitive Quantum Physics. Students in the course are generally math…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular…
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…
We briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative…