On the Number of Balanced Words of Given Length and Height over a Two-Letter Alphabet

We exhibit a recurrence on the number of discrete line segments joining two integer points in the plane using an encoding of such segments as balanced words of given length and height over the two-letter alphabet $\{0,1\}$. We give generating functions and study the asymptotic behaviour. As a particular case, we focus on the symmetrical discrete segments which are encoded by balanced palindromes.Comment: 24 page

Geometric Palindromic Closure

http://www.boku.ac.at/MATH/udt/vol07/no2/06DomVuillon13-12.pdfInternational audienceWe define, through a set of symmetries, an incremental construction of geometric objects in Z^d. This construction is directed by a word over the alphabet {1,...,d}. These objects are composed of d disjoint components linked by the origin and enjoy the nice property that each component has a central symmetry as well as the global object. This construction may be seen as a geometric palindromic closure. Among other objects, we get a 3 dimensional version of the Rauzy fractal. For the dimension 2, we show that our construction codes the standard discrete lines and is equivalent to the well known palindromic closure in combinatorics on words

On the topology of discrete hyperplanes

https://sites.google.com/site/numeration2012/DamienJamet-abstract.pdf?attredirects=0International audienc

Critical connectedness of thin arithmetical discrete planes

An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully subtractive algorithm. This multidimensional continued fraction algorithm consists, in its linear form, in subtracting the smallest entry to the other ones. We provide a characterization of the discrete planes with critical thickness that have zero intercept and that are $2$-connected. Our tools rely on the notion of dual substitution which is a geometric version of the usual notion of substitution acting on words. We associate with the fully subtractive algorithm a set of substitutions whose incidence matrix is provided by the matrices of the algorithm, and prove that their geometric counterparts generate arithmetic discrete planes.Comment: 18 pages, v2 includes several corrections and is a long version of the DGCI extended abstrac

Palindromic complexity of trees

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.Comment: Submitted to the conference DLT201

Vérification sémantique de spécifications métallurgiques

Projet EURECADans ce document nous présentons d'une part une méthode pour vérifier certaines propriétés sémantiques sur des spécifications décrites par des règles, et d'autre part l'implantation de cette méthode dans un programme appelé Versem. Ce travail a été réalisé à la demande de l'entreprise Sollac qui utilise de telles spécifications pour formaliser des processus de transformation métallurgique

On the Number of Balanced Words of Given Length and Height over a Two-Letter Alphabet

We exhibit a recurrence on the number of discrete line segments joining two integer points in the plane using an encoding of such segments as balanced words of given length and height over the two-letter alphabet $\{0,1\}$. We give generating functions and study the asymptotic behaviour. As a particular case, we focus on the symmetrical discrete segments which are encoded by balanced palindromes

A Generic Solution for Automated Collecting and Integration of Biological Data from Web Sources

Session Posters. Colloque avec actes et comité de lecture. internationale.International audienceWe present here a work dealing with automated collecting and integration of data along a user-defined scenario. Aspects such as query construction, query submission, parsing of returned document, filtering of desired data and storing them in a structured document have been considered as well as the chaining between the various steps of the scenario. Automation of the process allows to refresh the data in a time-saving manner in order to take into account the frequent changes in source contents. A configuration module distinct from the execution module allows to modify the scenario steps according to user preferences and/or source changes

Immunoselection and characterization of a human genomic PPAR binding fragment located within POTE genes

Peroxisome proliferator-activated receptors (PPARs) are ligand-inducible transcription factors and belong to the nuclear hormone receptor superfamily. They form heterodimers with retinoid X receptor (RXR) and bind to specific PPAR-response elements. To identify novel PPAR target genes, we developed an affinity method to isolate human genomic fragments containing binding sites for PPARs. For this, an antibody raised against all PPAR subtypes was used. Immunoselected fragments were amplified and sequenced. One of them, ISF1029, was mapped by BLAT and BLAST searches on different human chromosomes, downstream of several POTE genes. ISF1029 contained three hexamers strongly related to the AGGTCA motif organized according to a DR0/3 motif. The latter was found to bind to PPARΑ in gel mobility shift and supershift assays and to exhibit a downregulation potentiality in transfection experiments under clofibrate treatment. POTE genes were shown to be highly expressed in human Caco-2 colorectal adenocarcinoma cells and downregulated by fenofibrate and 9-cis-retinoic acid, as attested by RT-PCR assays. Microarray analysis confirmed and extended to the human T98-G glioblastoma cells, the downregulation of several POTE genes expression by Wy-14,643, a potent PPARΑ activator. Our data provide new insights about the pleiotropic action of PPARs

Hepatocyte Nuclear Factor 4 Provokes Expression of Epithelial Marker Genes, Acting As a Morphogen in Dedifferentiated Hepatoma Cells

Abstract. We have recently shown that stable expression of an epitope-tagged cDNA of the hepatocyte- enriched transcription factor, hepatocyte nuclear factor (HNF)4, in dedifferentiated rat hepatoma H5 cells is sufficient to provoke reexpression of a set of hepatocyte marker genes. Here, we demonstrate that the effects of HNF4 expression extend to the reestablishment of differentiated epithelial cell morphology and simple epithelial polarity. The acquisition of epithelial morphology occurs in two steps. First, expression of HNF4 results in reexpression of cytokeratin proteins and partial reestablishment of E-cadherin production. Only the transfectants are competent to respond to the synthetic glucocorticoid dexamethasone, which induces the second step of morphogenesis, including formation of the junctional complex and expression of a polarized cell phenotype. Cell fusion experiments revealed that the transfectant cells, which show only partial restoration of E-cadherin expression, produce an extinguisher that is capable of acting in trans to downregulate the E-cadherin gene of well-differentiated hepatoma cells. Bypass of this repression by stable expression of E-cadherin in H5 cells is sufficient to establish some epithelial cell characteristics, implying that the morphogenic potential of HNF4 in hepatic cells acts via activation of the E-cadherin gene. Thus, HNF4 seems to integrate the genetic programs of liver-specific gene expression and epithelial morphogenesis