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Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

Clément Mouhot, Lorenzo Pareschi, Thomas Rey (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically O(N2d + 1) where d is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, C. R. Acad. Sci. Paris Sér. I Math. 339 (2004) 71–76, C. Mouhot and L. Pareschi, Math. Comput. 75 (2006) 1833–1852], we derive fast summation techniques for the evaluation of...

Conway's Games and Some of their Basic Properties

Robin Nittka (2011)

Formalized Mathematics

We formulate a few basic concepts of J. H. Conway's theory of games based on his book [6]. This is a first step towards formalizing Conway's theory of numbers into Mizar, which is an approach to proving the existence of a FIELD (i.e., a proper class that satisfies the axioms of a real-closed field) that includes the reals and ordinals, thus providing a uniform, independent and simple approach to these two constructions that does not go via the rational numbers and hence does for example not need...

Coproducts of ideal monads

Neil Ghani, Tarmo Uustalu (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly [Bull. Austral. Math. Soc. 22 (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell. 2309 (2002) 18–32],...

Coproducts of Ideal Monads

Neil Ghani, Tarmo Uustalu (2010)

RAIRO - Theoretical Informatics and Applications

The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly  [Bull.  Austral. Math. Soc.22 (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell.2309 (2002)...

Correctness of horizontal and vertical composition for implementation concepts based on constructors and abstractors.

Hartmut Ehrig, Hans-Jörg Kreowski, Fernando Orejas (1997)

Revista Matemática de la Universidad Complutense de Madrid

A new implementation concept for parameterized specifications based on constructors and abstractors was recently introduced by Orejas, Navarro and Sánchez which includes most of the implementation concepts in the literature for initial as well as loose semantics. In this paper we redefine vertical and different kinds of horizontal compositions using the new concept of semi-pushout defined for a mixture of signature and specification morphisms. The main results concerning correctness of horizontal...

Correlation-based feature selection strategy in classification problems

Krzysztof Michalak, Halina Kwaśnicka (2006)

International Journal of Applied Mathematics and Computer Science

In classification problems, the issue of high dimensionality, of data is often considered important. To lower data dimensionality, feature selection methods are often employed. To select a set of features that will span a representation space that is as good as possible for the classification task, one must take into consideration possible interdependencies between the features. As a trade-off between the complexity of the selection process and the quality of the selected feature set, a pairwise...

Corrigendum

Joffroy Beauquier (1979)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Corrigendum : “Complexity of infinite words associated with beta-expansions”

Christiane Frougny, Zuzana Masáková, Edita Pelantová (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We add a sufficient condition for validity of Propo- sition 4.10 in the paper Frougny et al. (2004). This condition is not a necessary one, it is nevertheless convenient, since anyway most of the statements in the paper Frougny et al. (2004) use it.

Corrigendum: Complexity of infinite words associated with beta-expansions

Christiane Frougny, Zuzana Masáková, Edita Pelantová (2010)

RAIRO - Theoretical Informatics and Applications

We add a sufficient condition for validity of Propo- sition 4.10 in the paper Frougny et al. (2004). This condition is not a necessary one, it is nevertheless convenient, since anyway most of the statements in the paper Frougny et al. (2004) use it.


Corrigendum: On multiperiodic words

Štěpán Holub (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

An algorithm is corrected here that was presented as Theorem 2 in [Š. Holub, RAIRO-Theor. Inf. Appl. 40 (2006) 583–591]. It is designed to calculate the maximum length of a nontrivial word with a given set of periods.

Corrigendum: On multiperiodic words

Štěpán Holub (2012)

RAIRO - Theoretical Informatics and Applications

An algorithm is corrected here that was presented as Theorem 2 in [Š. Holub, RAIRO-Theor. Inf. Appl. 40 (2006) 583–591]. It is designed to calculate the maximum length of a nontrivial word with a given set of periods.

Corrigendum to our paper: How Expressions Can Code for Automata

Sylvain Lombardy, Jacques Sakarovitch (2010)

RAIRO - Theoretical Informatics and Applications

In a previous paper, we have described the construction of an automaton from a rational expression which has the property that the automaton built from an expression which is itself computed from a co-deterministic automaton by the state elimination method is co-deterministic. It turned out that the definition on which the construction is based was inappropriate, and thus the proof of the property was flawed. We give here the correct definition of the broken derived terms of an...

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