Descartes…el regreso

Los computadores se han convertido en una herramienta tecnológica de uso cotidiano para el matemático, en cuanto le ayudan a modelar y a pensar. Ahora es posible comprobar fácilmente una conjetura para apoyar o rechazar hipótesis, por ejemplo, haciendo que el computador lleve a cabo cálculos que de otra forma serían irrealizables. Muy frecuentemente esto se hace interactuando con simulaciones numéricas y/o CAS (Computer Algebra Systems). En esta presentación se mostrará cómo Cabri, originalmente un ambiente computacional desarrollado para interactuar dinámicamente con objetos geométricos es (o puede ser) usado en muchos casos, para realizar tareas que las personas hacían usando sistemas numéricos y/o algebraicos. Expondremos ejemplos ilustrativos donde, operando con objetos matemáticos bajo manipulación directa, Cabri se usa en una forma muy poderosa en álgebra, cálculo, cinemática, mecánica y/o física. La geometría dinámica está basada en la geometría de Euclides, a la cual se agrega el concepto de movimiento y otros principios de diseño como el de continuidad, explicitación del infinito, reversibilidad o ergonomía cognoscitiva, clases de invarianza y muchos otros en los cuales no voy a profundizar. Durante gran parte del desarrollo de la geometría hasta su edad de oro, que podemos considerar data del siglo diecisiete, se ve la geometría como una herramienta para el debate intelectual. Por ejemplo, los elementos de Euclides se constituyeron fundamentalmente en un juego mental sin una perspectiva hacia el aprendizaje o sin la pretensión de hacer de la geometría algo útil; era más una actividad para el espíritu. Sin embargo, aparece en este siglo, el aspecto práctico de la geometría. Para los arquitectos, constructores, físicos, e incluso para los pintores, la geometría tiene gran aplicación. Conocemos por ejemplo el desarrollo de la perspectiva que nació con los problemas planteados por la representación de la naturaleza a los que se enfrentaron los pintores de la época. Pero este desarrollo también tiene algunas limitaciones que frenaron su perfeccionamiento. Entre ellas, mencionaremos limitaciones de tipo teórico como la imposibilidad de ciertas construcciones e igualmente limitaciones de tipo práctico como la mediocridad de la calidad de los trazados. Para ilustrar estas ideas, y a propósito de las construcciones imposibles con regla y compás, quisiera citar algunos ejemplos como el de la cuadratura del círculo, la trisección del ángulo y la duplicación del cubo, entre otros. Estas construcciones son imposibles si nos limitamos al uso de la regla y el compás, pero mostraré cómo es posible realizarlas, con la ayuda de Cabri Géomètre. Realizaremos por ejemplo, la construcción de la trisección del ángulo

Generalized hypercubes and (0,2)-graphs

AbstractA generalized hypercube Qd(S) (S ⊆ {1, 2, …, d}) has {0,1}d as vertex set and two vertices are joined whenever their mutual distance in Qd belongs to S. These graphs have been introduced in (Berrachedi and Mollard, 1996) where the notion mainly investigated there is graph embedding, especially, in the case where the host graph is a hypercube. A simple connected graph G is a (0, 2)-graph if any two vertices have 0 or exactly two common neighbors as introduced in (Mulder, 1980). We give first some results about the structure of generalized hypercubes, and then characterize those of which are (0, 2)-graphs. Using similar construction as in generalized hypercubes, we exhibit a class of (0, 2)-graphs which are not vertex transitive which contradicts again a conjecture of Mulder (1982) on the convexity of interval regular graphs

Identification of novel genes potentially involved in somatic embryogenesis in chicory (Cichorium intybus L.)

<p>Abstract</p> <p>Background</p> <p>In our laboratory we use cultured chicory (<it>Cichorium intybus</it>) explants as a model to investigate cell reactivation and somatic embryogenesis and have produced 2 chicory genotypes (K59, C15) sharing a similar genetic background. K59 is a responsive genotype (embryogenic) capable of undergoing complete cell reactivation <it>i.e</it>. cell de- and re-differentiation leading to somatic embryogenesis (SE), whereas C15 is a non-responsive genotype (non-embryogenic) and is unable to undergo SE. Previous studies <abbrgrp><abbr bid="B1">1</abbr></abbrgrp> showed that the use of the β-D-glucosyl Yariv reagent (β-GlcY) that specifically binds arabinogalactan-proteins (AGPs) blocked somatic embryo production in chicory root explants. This observation indicates that β-GlcY is a useful tool for investigating somatic embryogenesis (SE) in chicory. In addition, a putative AGP (DT212818) encoding gene was previously found to be significantly up-regulated in the embryogenic K59 chicory genotype as compared to the non-embryogenic C15 genotype suggesting that this AGP could be involved in chicory re-differentiation <abbrgrp><abbr bid="B2">2</abbr></abbrgrp>. In order to improve our understanding of the molecular and cellular regulation underlying SE in chicory, we undertook a detailed cytological study of cell reactivation events in K59 and C15 genotypes, and used microarray profiling to compare gene expression in these 2 genotypes. In addition we also used β-GlcY to block SE in order to identify genes potentially involved in this process.</p> <p>Results</p> <p>Microscopy confirmed that only the K59, but not the C15 genotype underwent complete cell reactivation leading to SE formation. β-GlcY-treatment of explants blocked <it>in vitro </it>SE induction, but not cell reactivation, and induced cell wall modifications. Microarray analyses revealed that 78 genes were differentially expressed between induced K59 and C15 genotypes. The expression profiles of 19 genes were modified by β-GlcY-treatment. Eight genes were both differentially expressed between K59 and C15 genotypes during SE induction and transcriptionally affected by β-GlcY-treatment: <it>AGP </it>(DT212818), <it>26 S proteasome AAA ATPase subunit 6 </it>(<it>RPT6</it>), <it>remorin </it>(<it>REM</it>), <it>metallothionein-1 </it>(<it>MT1</it>), two non-specific lipid transfer proteins genes (<it>SDI-9 and DEA1</it>), <it>3-hydroxy-3-methylglutaryl-CoA reductase </it>(<it>HMG-CoA reductase</it>), and <it>snakin 2 </it>(<it>SN2</it>). These results suggest that the 8 genes, including the previously-identified <it>AGP </it>gene (DT212818), could be involved in cell fate determination events leading to SE commitment in chicory.</p> <p>Conclusion</p> <p>The use of two different chicory genotypes differing in their responsiveness to SE induction, together with β-GlcY-treatment represented an efficient tool to discriminate cell reactivation from the SE morphogenetic pathway. Such an approach, together with microarray analyses, permitted us to identify several putative key genes related to the SE morphogenetic pathway in chicory.</p

Projet INCOME : INfrastructure de gestion de COntexte Multi-Echelle pour l'Internet des Objets

International audienceCet article donne un aperçu du projet de recherche INCOME financé par l'Agence Nationale de la Recherche française en décrivant la fiche d'identité du projet, ses principaux enjeux scientifiques ainsi que les premiers résultats obtenus

Gestion de contexte multi-échelle pour l'Internet des objets

Cet article présente une architecture logicielle de gestion de contexte multi-échelle pour l'Internet des objets. Nous présentons d'abord quelques défis spécifiques auxquels est confrontée cette nouvelle génération d'intergiciels, tels que la communication répartie en modes push et pull, la sensibilité multi-échelle, et la réponse à des exigences et des garanties de qualité de l'information de contexte et de respect de la vie privée. Nous donnons ensuite la vision du projet INCOME pour répondre à ces défis en fournissant une infrastructure répartie de gestion de contexte et en assurant son déploiement de manière autonomique

The Influence of Number and Timing of Pregnancies on Breast Cancer Risk for Women With BRCA1 or BRCA2 Mutations

International audienceBACKGROUND:Full-term pregnancy (FTP) is associated with a reduced breast cancer (BC) risk over time, but women are at increased BC risk in the immediate years following an FTP. No large prospective studies, however, have examined whether the number and timing of pregnancies are associated with BC risk for BRCA1 and BRCA2 mutation carriers.METHODS:Using weighted and time-varying Cox proportional hazards models, we investigated whether reproductive events are associated with BC risk for mutation carriers using a retrospective cohort (5707 BRCA1 and 3525 BRCA2 mutation carriers) and a prospective cohort (2276 BRCA1 and 1610 BRCA2 mutation carriers), separately for each cohort and the combined prospective and retrospective cohort.RESULTS:For BRCA1 mutation carriers, there was no overall association with parity compared with nulliparity (combined hazard ratio [HRc] = 0.99, 95% confidence interval [CI] = 0.83 to 1.18). Relative to being uniparous, an increased number of FTPs was associated with decreased BC risk (HRc = 0.79, 95% CI = 0.69 to 0.91; HRc = 0.70, 95% CI = 0.59 to 0.82; HRc = 0.50, 95% CI = 0.40 to 0.63, for 2, 3, and ≥4 FTPs, respectively, P trend < .0001) and increasing duration of breastfeeding was associated with decreased BC risk (combined cohort P trend = .0003). Relative to being nulliparous, uniparous BRCA1 mutation carriers were at increased BC risk in the prospective analysis (prospective hazard ration [HRp] = 1.69, 95% CI = 1.09 to 2.62). For BRCA2 mutation carriers, being parous was associated with a 30% increase in BC risk (HRc = 1.33, 95% CI = 1.05 to 1.69), and there was no apparent decrease in risk associated with multiparity except for having at least 4 FTPs vs. 1 FTP (HRc = 0.72, 95% CI = 0.54 to 0.98).CONCLUSIONS:These findings suggest differential associations with parity between BRCA1 and BRCA2 mutation carriers with higher risk for uniparous BRCA1 carriers and parous BRCA2 carriers

Correction to: Risk-reducing salpingo-oophorectomy, natural menopause, and breast cancer risk: an international prospective cohort of BRCA1 and BRCA2 mutation carriers.

After publication of the original article [1], we were notified that columns in Table 2 were erroneously displayed

The Influence of Number and Timing of Pregnancies on Breast Cancer Risk for Women With BRCA1 or BRCA2 Mutations

Background: Full-term pregnancy (FTP) is associated with a reduced breast cancer (BC) risk over time, but women are at increased BC risk in the immediate years following an FTP. No large prospective studies, however, have examined whether the number and timing of pregnancies are associated with BC risk for BRCA1 and BRCA2 mutation carriers. Methods: Using weighted and time-varying Cox proportional hazards models, we investigated whether reproductive events are associated with BC risk for mutation carriers using a retrospective cohort (5707 BRCA1 and 3525 BRCA2 mutation carriers) and a prospective cohort (2276 BRCA1 and 1610 BRCA2 mutation carriers), separately for each cohort and the combined prospective and retrospective cohort. Results: For BRCA1 mutation carriers, there was no overall association with parity compared with nulliparity (combined hazard ratio [HRc] ¼ 0.99, 95% confidence interval [CI] ¼ 0.83 to 1.18). Relative to being uniparous, an increased number of FTPs was associated with decreased BC risk (HRc¼ 0.79, 95% CI ¼ 0.69 to 0.91; HRc¼ 0.70, 95% CI ¼ 0.59 to 0.82; HRc¼ 0.50, 95% CI ¼ 0.40 to 0.63, for 2, 3, and 4 FTPs, respectively, Ptrend < .0001) and increasing duration of breastfeeding was associated with decreased BC risk (combined cohort Ptrend ¼ .0003). Relative to being nulliparous, uniparous BRCA1 mutation carriers were at increased BC risk in the prospective analysis (prospective hazard ration [HRp] ¼ 1.69, 95% CI ¼ 1.09 to 2.62). For BRCA2 mutation carriers, being parous was associated with a 30% increase in BC risk (HRc ¼ 1.33, 95% CI ¼ 1.05 to 1.69), and there was no apparent decrease in risk associated with multiparity except for having at least 4 FTPs vs. 1 FTP (HRc¼ 0.72, 95% CI ¼ 0.54 to 0.98). Conclusions: These findings suggest differential associations with parity between BRCA1 and BRCA2 mutation carriers with higher risk for uniparous BRCA1 carriers and parous BRCA2 carriers