Related papers: Compound matrices in systems and control theory: a…
The concept of the "modulus" in the CAD system drawings is characterized, being a base of developing of the problem-oriented extensions. The modulus consists of visible geometric elements of the drawing and invisible parametric…
We study the problem of determining a matrix whose $k$th multiplicative compound is a prescribed matrix~$M$. The cardinality of the set of matrices whose $k$th multiplicative compound equals~$M$ is characterized in terms of $\rank(M)$. On…
This article serves as an introduction to the study of networks of social systems. First, we introduce the reader to key mathematical tools to study social networks, including mathematical representations of networks and essential…
This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings,…
Connection matrices are one of the central tools in Conley's approach to the study of dynamical systems, as they provide information on the existence of connecting orbits in Morse decompositions. They may be considered a generalisation of…
This is an overview of recent developments regarding the complexity of matrix multiplication, with an emphasis on the uses of algebraic geometry and representation theory in complexity theory.
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
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…
We develop a new framework for the study of complex continuous time dynamical systems based on viewing them as collections of interacting control modules. This framework is inspired by and builds upon the groupoid formalism of Golubitsky,…
The study of Complex Systems is considered by many to be a new scientific field, and is distinguished by being a discipline that has applications within many separate areas of scientific study. The study of Neural Networks, Traffic…
Modular forms appear in many facets of mathematics, and have played important roles in geometry, mathematical physics, number theory, representation theory, topology, and other areas. Around 1994, motivated by technical issues in homotopy…
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…
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…
A matroid is a combinatorial structure that captures and generalizes the algebraic concept of linear independence under a broader and more abstract framework. Matroids are closely related with many other topics in discrete mathematics, such…
In this series of three articles, we give an exposition of various results and open problems in three areas of algebraic and geometric combinatorics: totally non-negative matrices, representations of the symmetric group, and hyperplane…
Copositive and completely positive matrices play an increasingly important role in Applied Mathematics, namely as a key concept for approximating NP-hard optimization problems. The cone of copositive matrices of a given order and the cone…
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…
Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structures are presented. These include techniques for designing non-separable multidimensional paraunitary matrices. Properties of the…
The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…