Keywords: Systems with time delays Distributed delay Exponential stability Perturbations a b s t r a c t We consider preservation of exponential stability for a system of linear equations with a distributed delay under the addition of new terms and a delay perturbation. As particular cases, the system includes models with concentrated delays and systems of integrodifferential equations. Our met...

Weighted labelled transition systems are LTSs whose transitions are given weights drawn from a commutative monoid, subsuming a wide range of systems with quantitative aspects. In this paper we extend this theory towards other behavioural equivalences, by considering semirings of weights. Taking advantage of this extra structure, we consider a general notion of weak weighted bisimulation, which ...

Integral equation techniques are often used to extract models of integrated circuit structures. This extraction involves solving a dense system of linear equations, and using direct solution methods is prohibitive for large problems. In this paper, we present IES (pronounced \ice cube"), a fast Integral Equation Solver for three-dimensional problems with arbitrary kernels. Extraction methods ba...

One of the oldest problems in algebra is the solution of a system of linear equations over certain domains. The Gaussian elimination algorithm provides an effective solution over fields. The Smith normal form algorithm yields a method over the integers. Here we consider another variation of this theme. Let A be a finite (additive) abelian group, let αi,j ∈ End(A) for 1 ≤ i ≤ n and 1 ≤ j ≤ m and...

By further generalizing the concept of Hermitian (or normal) and skew-Hermitian splitting for a non-Hermitian and positive-definite matrix, we introduce a new splitting, called positive-definite and skew-Hermitian (PS) splitting, and then establish a class of positivedefinite and skew-Hermitian splitting (PSS) methods similar to the Hermitian (or normal) and skew-Hermitian splitting (HSS or NSS...

In our recent work [30, 33] we considered solving under-determined systems of linear equations with sparse solutions. In a large dimensional and statistical context we proved results related to performance of a polynomial l1-optimization technique when used for solving such systems. As one of the tools we used a probabilistic result of Gordon [18]. In this paper we revisit this classic result i...

This project has aimed to develop predictive, analytical tools to help determine the ability of marine mammal populations to respond to behavioral disturbances. These tools are to be generic and applicable in a wide range of conditions, including scenarios where data might be limited. Building on recent advances in in the field of behavioral ecology, we have focussed on defining the state resil...

We discuss one known and five new interrelated methods for bounding the hull of the solution set of a system of interval linear equations. Each method involves a polynomial amount of computing; but requires considerably more effort than Gaussian elimination. However, each method can yield sharper results for appropriate problems. For certain problems, our methods can obtain sharp bounds for one...

The subject of the paper are scalar delay-differential equations with large delay. Firstly, we describe the asymptotic properties of the spectrum of linear equations. Using these properties, we classify possible types of destabilization of steady states. In the limit of large delay, this classification is similar to the one for parabolic partial differential equations. We present a derivation a...