Related papers: Compound matrices in systems and control theory
We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
When inclusions in a composite are separated by a very small gap, high contrast between the inclusion and matrix properties can induce strong amplification of the underlying field inside the narrow region. Quantifying this field…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
Attention mechanisms are developing into a viable alternative to convolutional layers as elementary building block of NNs. Their main advantage is that they are not restricted to capture local dependencies in the input, but can draw…
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…
We consider the basic features of complex dynamical and control systems. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of…
Several matrix variate hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted hypergeometric type distributions with matrix arguments are then…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
Matrix models have wide applications in nuclear theory, condensed matter theory and quantum field theory. I discuss supersymmetric extensions of matrix models and their applications to branched polymers, the meander problem, and…
We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…
In this note, we offer a palatable introduction to the field of arithmetic dynamics. That is, we study the patterns that arise when iterating a polynomial map. This note is accessible to those who have taken an introductory proof based…
We explain connections among several, a priori unrelated, areas of mathematics: combinatorics, algebraic statistics, topology and enumerative algebraic geometry. Our focus is on discrete invariants, strongly related to the theory of…
Why is it that after so many years matrices continue to play such an important roll in Physics and mathematics? Is there a geometric way of looking at matrices, and linear transformations in general, that lies at the roots of their success?…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
We prove new quantitative bounds on the additive structure of sets obeying an $L^3$ 'control' assumption, which arises naturally in several questions within additive combinatorics. This has a number of applications - in particular we…
Recent years have witnessed a wave of research activities in systems science toward the study of population systems. The driving force behind this shift was geared by numerous emerging and ever-changing technologies in life and physical…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…
A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems,…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…