다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

This collaborative volume presents recent trends arising from the fruitful interaction between the themes of combinatorics on words, automata and formal language theory, and number theory. Presenting several important tools and concepts, the authors also reveal some of the exciting and important relationships that exist between these different fields. Topics include numeration systems, word complexity function, morphic words, Rauzy tilings and substitutive dynamical systems, Bratelli diagrams, frequencies and ergodicity, Diophantine approximation and transcendence, asymptotic properties of digital functions, decidability issues for D0L systems, matrix products and joint spectral radius. Topics are presented in a way that links them to the three main themes, but also extends them to dynamical systems and ergodic theory, fractals, tilings and spectral properties of matrices. Graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, fractals, tilings and stringology will find much of interest in this book.

/pdf/combinatorics-automata-and-number-theory-54vcmxgyks.pdf

Combinatorics, Automata and Number Theory

During the last decade the Subspace Theorem found several quite unexpected applications, mainly in the Diophantine Analysis and in the Transcendence Theory. Among the great variety of spectacular results, I have chosen several which are technically simpler and which allow one to appreciate how miraculously does the Subspace Theorem emerge in numerous situations, implying beautiful solutions to difficult problems hardly anybody hoped to solve so easily. The three main topics discussed in this article are: the work of Adamczewski and Bugeaud on complexity of algebraic numbers; the work of Corvaja and Zannier on Diophantine equations with power sums; the work of Corvaja and Zannier on integral points on curves and surfaces, and the subsequent development due to Levin and Autissier. In particular, we give a complete proof of the beautiful theorem of Levin and Autissier: an affine surface with 4 (or more) properly intersecting ample divisors at infinity cannot have a Zariski dense set of integral points.

The Many Faces of the Subspace Theorem (after Adamczewski, Bugeaud, Corvaja, Zannier...)

https://hal.archives-ouvertes.fr/hal-00403684/document

Ce travail presente des contributions theoriques et pratiques a la theorie des codages symboliques de systemes dynamiques. Les applications concernent differents champs mathematiques et la modelisation en biologie moleculaire. Le but est d'illustrer comment des methodes de discretisation de systemes dynamiques et une approche algorithmique permettent d'exploiter au mieux les connaissances disponibles sur le systeme, meme partielles. Un premier objectif est d'exhiber des informations au sujet d'une dynamique que l'on connait explicitement et les traduire en proprietes concretes. Un deuxieme objectif est de produire de la connaissance sur une dynamique ou un modele lorsqu'on ne le connait pas explicitement.Dans ce document, ces deux questions sont abordees sur deux grandes classes de systemes dynamiques. Les premiers systemes consideres sont des automorphismes et des translations sur un tore. Inspires par les cas unidimensionnels (beta-numeration, etude des suites sturmiennes), la question principale qui se pose est de trouver un domaine fondamental pour le tore dans lequel les trajectoires de la dynamique consideree se codent par des systemes symboliques simples. Dans le cas ou l'automorphisme du tore considere admet une unique direction dilatante (le cas Pisot), un bon candidat pour ces partitions est donne par un domaine dont la base est fractale, introduit par G. Rauzy dans les annees 1980. Nous decrivons comment une approche decidable pour decrire le bord fractal du domaine et ses proprietes de pavage, permet de s'assurer qu'il s'agit d'un domaine adequat pour un codage du l'automorphisme. La description du bord du domaine permet de decrire ses proprietes topologiques, et de les exploiter dans les differents domaines d'informatique theorique ou les automorphismes et les additions sur un tore apparaissent. Ainsi, en theorie des nombres, nous nous appuyons sur la topologie du domaine pour caracteriser les proprietes des developpements finis ou purement periodiques de rationnels en base non entiere. En geometrie discrete, ces proprietes s'interpretent en termes de conditions pour l'engendrement de plans discrets par des methodes iteratives. La deuxieme classe de systemes concerne les systemes dynamiques de grande echelle en biologie moleculaire. Il s'avere que les donnees et les connaissances sur les modeles de regulations transcriptionnelles dans une cellule sont souvent trop partielles pour leur appliquer les methodes usuellement utilisees pour la modelisation de systemes experimentaux. Dans ce document, nous discutons d'un formalisme (inspire par la dynamique) qui permet d'interpreter les observations en biologie moleculaire, pour aider a la correction de modeles, et, dans le futur, a la mise en place de plans experimentaux. Au vu de la qualite des donnees, les aspects dynamiques sont alors remplaces par des considerations sur les deplacements d'etats stationnaires, et analyser les donnees revient a formaliser puis resoudre des contraintes portant sur des ensembles discrets. Nous montrons ainsi comment aborder les notions de corrections de modeles et de diagnostic de reseaux grande echelle.

https://tel.archives-ouvertes.fr/tel-00358996/document

Analyse de systèmes dynamiques par discrétisation. Exemples d'applications en théorie des nombres et en biologie moléculaire

There is no explicitly known example of a triple (g, a, x), where g ≥ 3 is an integer, a a digit in {0, . . . , g − 1} and x a real algebraic irrational number, for which one can claim that the digit a occurs infinitely often in the g–ary expansion of x. In 1909 and later in 1950, E. Borel considered such questions and suggested that the g–ary expansion of any algebraic irrational number in any base g ≥ 2 satisfies some of the laws that are satisfied by almost all numbers. For instance, the frequency where a given finite sequence of digits occurs should depend only on the base and on the length of the sequence. Hence there is a huge gap between the established theory and the expected state of the art. However, some progress have been made recently, mainly thanks to clever use of the Schmidt’s subspace Theorem. We review some of these results.

/pdf/diophantine-analysis-and-words-37ai6htm4r.pdf

Diophantine analysis and words

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Diophantine analysis and words