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Directive words of episturmian words : equivalences and normalization

Amy Glen, Florence Levé, Gwénaël Richomme (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing the same episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words. As a consequence...

Directive words of episturmian words: equivalences and normalization

Amy Glen, Florence Levé, Gwénaël Richomme (2008)

RAIRO - Theoretical Informatics and Applications

Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing the same episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words. As a consequence...

Discrete approximation of the Mumford-Shah functional in dimension two

Antonin Chambolle, Gianni Dal Maso (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of vergence by a sequence of integral functionals defined on piecewise affine functions.

Discrete planes, ℤ 2 -actions, Jacobi-Perron algorithm and substitutions

Pierre Arnoux, Valérie Berthé, Shunji Ito (2002)

Annales de l’institut Fourier

We introduce two-dimensional substitutions generating two-dimensional sequences related to discrete approximations of irrational planes. These two-dimensional substitutions are produced by the classical Jacobi-Perron continued fraction algorithm, by the way of induction of a ℤ 2 -action by rotations on the circle. This gives a new geometric interpretation of the Jacobi-Perron algorithm, as a map operating on the parameter space of ℤ 2 -actions by rotations.

Discrete-time symmetric polynomial equations with complex coefficients

Didier Henrion, Jan Ježek, Michael Šebek (2002)

Kybernetika

Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial Toolbox for Matlab.

Discriminating between causal structures in Bayesian Networks given partial observations

Philipp Moritz, Jörg Reichardt, Nihat Ay (2014)

Kybernetika

Given a fixed dependency graph G that describes a Bayesian network of binary variables X 1 , ⋯ , X n , our main result is a tight bound on the mutual information I c ( Y 1 , ⋯ , Y k ) = ∑ j = 1 k H ( Y j ) / c - H ( Y 1 , ⋯ , Y k ) of an observed subset Y 1 , ⋯ , Y k of the variables X 1 , ⋯ , X n . Our bound depends on certain quantities that can be computed from the connective structure of the nodes in G . Thus it allows to discriminate between different dependency graphs for a probability distribution, as we show from numerical experiments.

Dislocation dynamics - analytical description of the interaction force between dipolar loops

Vojtěch Minárik, Jan Kratochvíl (2007)

Kybernetika

The interaction between dislocation dipolar loops plays an important role in the computation of the dislocation dynamics. The analytical form of the interaction force between two loops derived in the present paper from Kroupa’s formula of the stress field generated by a single dipolar loop allows for faster computation.

Distance desert automata and the star height problem

Daniel Kirsten (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We introduce the notion of nested distance desert automata as a joint generalization of distance automata and desert automata. We show that limitedness of nested distance desert automata is PSPACE-complete. As an application, we show that it is decidable in 2 2 𝒪 ( n ) space whether the language accepted by an n -state non-deterministic automaton is of a star height less than a given integer h (concerning rational expressions with union, concatenation and iteration), which is the first ever complexity bound...

Distance desert automata and the star height problem

Daniel Kirsten (2010)

RAIRO - Theoretical Informatics and Applications

We introduce the notion of nested distance desert automata as a joint generalization of distance automata and desert automata. We show that limitedness of nested distance desert automata is PSPACE-complete. As an application, we show that it is decidable in 22O(n) space whether the language accepted by an n-state non-deterministic automaton is of a star height less than a given integer h (concerning rational expressions with union, concatenation and iteration), which is the first ever complexity...

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