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Concepts—An Object-Oriented Software Package for Partial Differential Equations

Philipp Frauenfelder, Christian Lage (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Object oriented design has proven itself as a powerful tool in the field of scientific computing. Several software packages, libraries and toolkits exist, in particular in the FEM arena that follow this design methodology providing extensible, reusable, and flexible software while staying competitive to traditionally designed point tools in terms of efficiency. However, the common approach to identify classes is to turn data structures and algorithms of traditional implementations into ...

Conceptual base of feature selection consulting system

Pavel Pudil, Jana Novovičová, Petr Somol, Radek Vrňata (1998)

Kybernetika

The paper briefly reviews recent advances in the methodology of feature selection (FS) and the conceptual base of a consulting system for solving FS problems. The reasons for designing a kind of expert or consulting system which would guide a less experienced user are outlined. The paper also attempts to provide a guideline which approach to choose with respect to the extent of a priori knowledge of the problem. The methods discussed here form the core of the software package being developed for...

Conceptual Information Compression and Efficient Pattern Search

Angelova, Galia, Mihov, Stoyan (2008)

Serdica Journal of Computing

This paper introduces an encoding of knowledge representation statements as regular languages and proposes a two-phase approach to processing of explicitly declared conceptual information. The idea is presented for the simple conceptual graphs where conceptual pattern search is implemented by the so called projection operation. Projection calculations are organised into off-line preprocessing and run-time computations. This enables fast run-time treatment of NP-complete problems, given that the intermediate...

Concurrently controlled grammars

Gairatzhan Mavlankulov, Mohamed Othman, Sherzod Turaev, Mohd Hasan Selamat, Laula Zhumabayeva, Tamara Zhukabayeva (2018)

Kybernetika

This paper introduces a new variant of Petri net controlled grammars, namely a concurrently controlled grammar, where the control over the application of the productions of a grammar is realized by a Petri net with different parallel firing strategies. The generative capacity of these grammars is investigated with respect to transition labeling strategies, definitions of final marking sets and parallel transition firing modes. It is shown that the labeling strategies do not effect the computational...

Conditional Lindenmayer systems with subregular conditions: The non-extended case

Jürgen Dassow, Stefan Rudolf (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider conditional tabled Lindenmayer sytems without interaction, where each table is associated with a regular set and a table can only be applied to a sentential form which is contained in its associated regular set. We study the effect to the generative power, if we use instead of arbitrary regular languages only finite, nilpotent, monoidal, combinational, definite, ordered, union-free, star-free, strictly locally testable, commutative regular, circular regular, and suffix-closed regular...

Conditional problem for objective probability

Otakar Kříž (1998)

Kybernetika

Marginal problem (see [Kel]) consists in finding a joint distribution whose marginals are equal to the given less-dimensional distributions. Let’s generalize the problem so that there are given not only less-dimensional distributions but also conditional probabilities. It is necessary to distinguish between objective (Kolmogorov) probability and subjective (de Finetti) approach ([Col,Sco]). In the latter, the coherence problem incorporates both probabilities and conditional probabilities in a unified...

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...

Connectedness of fractals associated with Arnoux–Rauzy substitutions

Valérie Berthé, Timo Jolivet, Anne Siegel (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limit of a sequence of compact sets, where each set is a renormalized projection of a finite union of faces of unit cubes. We exploit this combinatorial definition to prove the connectedness of the Rauzy fractal associated with any finite product of three-letter Arnoux–Rauzy substitutions.

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