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This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We study a system, called NEL, which is the mixed commutative/non-commutative linear logic BV augmented with linear logic's exponentials. Equivalently, NEL is MELL augmented with the non-commutative self-dual connective seq. In this paper,…
In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between…
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…
This is the first of several monographs to be devoted to the optics of accelerated systems. They are being published for the benefit of those who may wish to have another way of looking at kineoptical problems, and also to demonstrate that…
This paper focuses on defining a measure, appropriate for obtaining optimally sparse solutions to underdetermined systems of linear equations.* The general idea is the extension of metrics in n-dimensional spaces via the Cartesian product…
The problem of separating structured information representing phenomena of differing natures is considered. A structure is assumed to be independent of the others if can be represented in a complementary subspace. When the concomitant…
This paper deals with the approximation of the spectrum of linear and nonautonomous delay differential equations through the reduction of the relevant evolution semigroup from infinite to finite dimension. The focus is placed on classic…
In this paper we give a smooth linearization theorem for nonautonomous differential equations with a nonuniform strong exponential dichotomy. In terms of discretized evolution operator with hyperbolic fixed point 0, we formulate its…
In this article, we discuss some of the recent developments in applying machine learning (ML) techniques to nonlinear dynamical systems. In particular, we demonstrate how to build a suitable ML framework for addressing two specific…
Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious. The leading eigenfunctions of the transition…
Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…
The robustness property of exponential dichotomies refers to the stability of this notion under small linear perturbations. In recent work~\cite{PPX}, the authors have identified a new class of perturbations under which the notion of a…
This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular…
This thesis is divided into three parts. In the first part, we give an introduction to J. Harrison's theory of differential chains. In the second part, we apply these tools to generalize the Cauchy theorems in complex analysis. Instead of…
The purpose of this note is to show how some results from the theory of partial differential equations apply to the study of pseudo-spectra of non-self-adjoint operators, which is a topic of current interest in applied mathematics.
We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…
Traditional methods in educational research often fail to capture the complex and evolving nature of learning processes. This chapter examines the use of complex systems theory in education to address these limitations. The chapter covers…