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Computing guided modes for an unbounded stratified medium in integrated optics

Fabrice Mahé (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem...

Computing with words and life data

Przemysław Grzegorzewski, Olgierd Hryniewicz (2002)

International Journal of Applied Mathematics and Computer Science

The problem of statistical inference on the mean lifetime in the presence of vague data is considered. Situations with fuzzy lifetimes and an imprecise number of failures are discussed.

Configuration spaces and limits of voronoi diagrams

Roderik Lindenbergh, Wilberd van der Kallen, Dirk Siersma (2003)

Banach Center Publications

The Voronoi diagram of n distinct generating points divides the plane into cells, each of which consists of points most close to one particular generator. After introducing 'limit Voronoi diagrams' by analyzing diagrams of moving and coinciding points, we define compactifications of the configuration space of n distinct, labeled points. On elements of these compactifications we define Voronoi diagrams.

Connected components of sets of finite perimeter and applications to image processing

Luigi Ambrosio, Vicent Caselles, Simon Masnou, Jean-Michel Morel (2001)

Journal of the European Mathematical Society

This paper contains a systematic analysis of a natural measure theoretic notion of connectedness for sets of finite perimeter in ℝ N , introduced by H. Federer in the more general framework of the theory of currents. We provide a new and simpler proof of the existence and uniqueness of the decomposition into the so-called M -connected components. Moreover, we study carefully the structure of the essential boundary of these components and give in particular a reconstruction formula of a set of finite...

Connections between object classification criteria using an ultrasonic bi-sonar system

Bogdan Kreczmer (2016)

International Journal of Applied Mathematics and Computer Science

The paper presents connections between the criteria which make three types of objects possible to be recognized, namely, edges, planes and corners. These criteria can be applied while a binaural sonar system is used. It is shown that the criteria are specific forms of a general equation. The form of the equation depends on a single coefficient. In the paper, the meaning of this coefficient is discussed. The constructions of the arrangement of objects are presented and are bound with values of the...

Cross-task code reuse in genetic programming applied to visual learning

Wojciech Jaśkowski, Krzysztof Krawiec, Bartosz Wieloch (2014)

International Journal of Applied Mathematics and Computer Science

We propose a method that enables effective code reuse between evolutionary runs that solve a set of related visual learning tasks. We start with introducing a visual learning approach that uses genetic programming individuals to recognize objects. The process of recognition is generative, i.e., requires the learner to restore the shape of the processed object. This method is extended with a code reuse mechanism by introducing a crossbreeding operator that allows importing the genetic material from...

Cubical approximation and computation of homology

William Kalies, Konstantin Mischaikow, Greg Watson (1999)

Banach Center Publications

The purpose of this article is to introduce a method for computing the homology groups of cellular complexes composed of cubes. We will pay attention to issues of storage and efficiency in performing computations on large complexes which will be required in applications to the computation of the Conley index. The algorithm used in the homology computations is based on a local reduction procedure, and we give a subquadratic estimate of its computational complexity. This estimate is rigorous in two...

Currently displaying 21 – 40 of 44