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Inverse problems of symbolic dynamics

Alexei Ya. Belov, Grigorii V. Kondakov, Ivan V. Mitrofanov (2011)

Banach Center Publications

This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by a substitutional system, and dynamical properties are considered...

Inversion of square matrices in processors with limited calculation abillities

Krzysztof Janiszowski (2003)

International Journal of Applied Mathematics and Computer Science

An iterative inversion algorithm for a class of square matrices is derived and tested. The inverted matrix can be defined over both real and complex fields. This algorithm is based only on the operations of addition and multiplication. The numerics of the algorithm can cope with a short number representation and therefore can be very useful in the case of processors with limited possibilities, like different neuro-computers and accelerator cards. The quality of inversion can be traced and tested....

Is GPU the future of Scientific Computing ?

Georges-Henri Cottet, Jean-Matthieu Etancelin, Franck Perignon, Christophe Picard, Florian De Vuyst, Christophe Labourdette (2013)

Annales mathématiques Blaise Pascal

These past few years, new types of computational architectures based on graphics processors have emerged. These technologies provide important computational resources at low cost and low energy consumption. Lots of developments have been done around GPU and many tools and libraries are now available to implement efficiently softwares on those architectures.This article contains the two contributions of the mini-symposium about GPU organized by Loïc Gouarin (Laboratoire de Mathématiques d’Orsay),...

Isomorphisms of Direct Products of Cyclic Groups of Prime Power Order

Hiroshi Yamazaki, Hiroyuki Okazaki, Kazuhisa Nakasho, Yasunari Shidama (2013)

Formalized Mathematics

In this paper we formalized some theorems concerning the cyclic groups of prime power order. We formalize that every commutative cyclic group of prime power order is isomorphic to a direct product of family of cyclic groups [1], [18].

Isomorphisms of Direct Products of Finite Commutative Groups

Hiroyuki Okazaki, Hiroshi Yamazaki, Yasunari Shidama (2013)

Formalized Mathematics

We have been working on the formalization of groups. In [1], we encoded some theorems concerning the product of cyclic groups. In this article, we present the generalized formalization of [1]. First, we show that every finite commutative group which order is composite number is isomorphic to a direct product of finite commutative groups which orders are relatively prime. Next, we describe finite direct products of finite commutative groups

Isomorphisms of Direct Products of Finite Cyclic Groups

Kenichi Arai, Hiroyuki Okazaki, Yasunari Shidama (2012)

Formalized Mathematics

In this article, we formalize that every finite cyclic group is isomorphic to a direct product of finite cyclic groups which orders are relative prime. This theorem is closely related to the Chinese Remainder theorem ([18]) and is a useful lemma to prove the basis theorem for finite abelian groups and the fundamental theorem of finite abelian groups. Moreover, we formalize some facts about the product of a finite sequence of abelian groups.

Iteration of rational transductions

Alain Terlutte, David Simplot (2010)

RAIRO - Theoretical Informatics and Applications

The purpose of this paper is to show connections between iterated length-preserving rational transductions and linear space computations. Hence, we study the smallest family of transductions containing length-preserving rational transductions and closed under union, composition and iteration. We give several characterizations of this class using restricted classes of length-preserving rational transductions, by showing the connections with "context-sensitive transductions" and transductions associated...

Iterative feature selection in least square regression estimation

Pierre Alquier (2008)

Annales de l'I.H.P. Probabilités et statistiques

This paper presents a new algorithm to perform regression estimation, in both the inductive and transductive setting. The estimator is defined as a linear combination of functions in a given dictionary. Coefficients of the combinations are computed sequentially using projection on some simple sets. These sets are defined as confidence regions provided by a deviation (PAC) inequality on an estimator in one-dimensional models. We prove that every projection the algorithm actually improves the performance...

Iterative Learning Control - monotonicity and optimization

David H. Owens, Steve Daley (2008)

International Journal of Applied Mathematics and Computer Science

The area if Iterative Learning Control (ILC) has great potential for applications to systems with a naturally repetitive action where the transfer of data from repetition (trial or iteration) can lead to substantial improvements in tracking performance. There are several serious issues arising from the "2D" structure of ILC and a number of new problems requiring new ways of thinking and design. This paper introduces some of these issues from the point of view of the research group at Sheffield University...

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