Regularity criteria for the topology of algebraic curves and surfaces

In this paper, we consider the problem of analysing the shape of an object defined by polynomial equations in a domain. We describe regularity criteria which allow us to determine the topology of the implicit object in a box from information on the boundary of this box. Such criteria are given for planar and space algebraic curves and for algebraic surfaces. These tests are used in subdivision methods in order to produce a polygonal approximation of the algebraic curves or surfaces, even if it contains singular points. We exploit the representation of polynomials in Bernstein basis to check these criteria and to compute the intersection of edges or facets of the box with these curves or surfaces. Our treatment of singularities exploits results from singularity theory such as an explicit Whitney stratification or the local conic structure around singularities. A few examples illustrate the behavior of the algorithms

Isotopic triangulation of a real algebraic surface

International audienceWe present a new algorithm for computing the topology of a real algebraic surface $S$ in a ball $B$, even in singular cases. We use algorithms for 2D and 3D algebraic curves and show how one can compute a topological complex equivalent to $S$, and even a simplicial complex isotopic to $S$ by exploiting properties of the contour curve of $S$. The correctness proof of the algorithm is based on results from stratification theory. We construct an explicit Whitney stratification of $S$, by resultant computation. Using Thom's isotopy lemma, we show how to deduce the topology of $S$ from a finite number of characteristic points on the surface. An analysis of the complexity of the algorithm and effectiveness issues conclude the paper

Large-Scale Screening of a Targeted Enterococcus faecalis Mutant Library Identifies Envelope Fitness Factors

Spread of antibiotic resistance among bacteria responsible for nosocomial and community-acquired infections urges for novel therapeutic or prophylactic targets and for innovative pathogen-specific antibacterial compounds. Major challenges are posed by opportunistic pathogens belonging to the low GC% Gram-positive bacteria. Among those, Enterococcus faecalis is a leading cause of hospital-acquired infections associated with life-threatening issues and increased hospital costs. To better understand the molecular properties of enterococci that may be required for virulence, and that may explain the emergence of these bacteria in nosocomial infections, we performed the first large-scale functional analysis of E. faecalis V583, the first vancomycin-resistant isolate from a human bloodstream infection. E. faecalis V583 is within the high-risk clonal complex 2 group, which comprises mostly isolates derived from hospital infections worldwide. We conducted broad-range screenings of candidate genes likely involved in host adaptation (e.g., colonization and/or virulence). For this purpose, a library was constructed of targeted insertion mutations in 177 genes encoding putative surface or stress-response factors. Individual mutants were subsequently tested for their i) resistance to oxidative stress, ii) antibiotic resistance, iii) resistance to opsonophagocytosis, iv) adherence to the human colon carcinoma Caco-2 epithelial cells and v) virulence in a surrogate insect model. Our results identified a number of factors that are involved in the interaction between enterococci and their host environments. Their predicted functions highlight the importance of cell envelope glycopolymers in E. faecalis host adaptation. This study provides a valuable genetic database for understanding the steps leading E. faecalis to opportunistic virulence

Community-Level Responses to Iron Availability in Open Ocean Plankton Ecosystems

Predicting responses of plankton to variations in essential nutrients is hampered by limited in situ measurements, a poor understanding of community composition, and the lack of reference gene catalogs for key taxa. Iron is a key driver of plankton dynamics and, therefore, of global biogeochemical cycles and climate. To assess the impact of iron availability on plankton communities, we explored the comprehensive bio-oceanographic and bio-omics data sets from Tara Oceans in the context of the iron products from two state-of-the-art global scale biogeochemical models. We obtained novel information about adaptation and acclimation toward iron in a range of phytoplankton, including picocyanobacteria and diatoms, and identified whole subcommunities covarying with iron. Many of the observed global patterns were recapitulated in the Marquesas archipelago, where frequent plankton blooms are believed to be caused by natural iron fertilization, although they are not captured in large-scale biogeochemical models. This work provides a proof of concept that integrative analyses, spanning from genes to ecosystems and viruses to zooplankton, can disentangle the complexity of plankton communities and can lead to more accurate formulations of resource bioavailability in biogeochemical models, thus improving our understanding of plankton resilience in a changing environment

Propriétés Quantitatives des Singularités des Variétés Algébriques Réelles

I plan to publish articles based on this thesis which will streamline the proofs, and may extend and complete the resultsThe introduction (section 1) presents the general subject-matter of the thesis: the quantitative measurement of the geometric properties of real algebraic varieties, and especially their triangulation. Section 2 explains a fast and certified subdivision procedure triangulating an algebraic plane curve. The mathematical tools are the topological degree, and the Bernstein's polynomial basis. Section 3 is a copy of an article explaining the subdivision method for smooth surfaces in Rn. It includes a complexity analysis. Section 4 presents a quantitative version of Thom-Mather's topological triviality for singular semi-algebraic maps. Stem from it: A “metrically stable” version of the local conic structure theorem and of the existence of a “Milnor tube” around strata. A triangulation algorithm based on Vorono˘i partitions (not completely implementable because the effective estimation of transversality is not completely detailed). Section 5 is a copy of an article published in 2008 on a sweeping method to compute the topology of singular surfaces in R3. It is based on Thom-Mathers theorem. Section 6 presents a bound on the generic number of connected components in an affine section of a real analytic germ in terms of the multiplicity and of the dimension of the ambient space. The bound does not always apply and counter-examples are given in that case.L'introduction (section 1) introduit la probl´ematique g´en´erale de la th`ese: la mesure quantitative des propri´et´es g´eom´etriques des vari´et´es alg´ebriques et particuli`erement leur triangulation. La section 2 explique une proc´edure de subdivision rapide et certifi´ee triangulant une courbe alg´ebrique r´eelle plane. Les outils math´ematiques sont le degr´e topologique, la base des polynˆomes de Bernstein. La section 3 est une copie d'un article expliquant la m´ethode de subdivision pour les surfaces lisses dans Rn. Elle comporte une analyse de complexit´e. La section 4 pr´esente une version quantitative du th´eor`eme de trivialit´e topologique de Thom-Mather pour des applications semi-alg´ebriques non lisses. Il en d´ecoule: une version “m´etriquement stable” du th´eor`eme de structure conique local et de l'existence d'un “tube de Milnor” autour des strates. Un algorithme de triangulation utilisant des partitions de Vorono˘i (sa mise en place n'est pas compl`ete car l'estimation effective de la transversalit´e n'est pas compl`etement trait´e). La section 5 est une copie d'un article paru en 2008 sur une m´ethode de balayage pour calculer la topologie d'une surface singuli`ere de R3. Elle repose sur l'utilisation du th´eor`eme de Thom-Mather. La section 6 pr´esente une borne sur le nombre g´en´erique de composantes connexes dans une section d'un germe analytique r´eel par un espace affine en fonction de la multiplicit´e et de la dimension de l'espace. La borne ne s'applique pas toujours et des contre-examples sont donn´es

Propriétés Quantitatives des Singularités des Variétés Algébriques Réelles

I plan to publish articles based on this thesis which will streamline the proofs, and may extend and complete the resultsThe introduction (section 1) presents the general subject-matter of the thesis: the quantitative measurement of the geometric properties of real algebraic varieties, and especially their triangulation. Section 2 explains a fast and certified subdivision procedure triangulating an algebraic plane curve. The mathematical tools are the topological degree, and the Bernstein's polynomial basis. Section 3 is a copy of an article explaining the subdivision method for smooth surfaces in Rn. It includes a complexity analysis. Section 4 presents a quantitative version of Thom-Mather's topological triviality for singular semi-algebraic maps. Stem from it: A “metrically stable” version of the local conic structure theorem and of the existence of a “Milnor tube” around strata. A triangulation algorithm based on Vorono˘i partitions (not completely implementable because the effective estimation of transversality is not completely detailed). Section 5 is a copy of an article published in 2008 on a sweeping method to compute the topology of singular surfaces in R3. It is based on Thom-Mathers theorem. Section 6 presents a bound on the generic number of connected components in an affine section of a real analytic germ in terms of the multiplicity and of the dimension of the ambient space. The bound does not always apply and counter-examples are given in that case.L'introduction (section 1) introduit la probl´ematique g´en´erale de la th`ese: la mesure quantitative des propri´et´es g´eom´etriques des vari´et´es alg´ebriques et particuli`erement leur triangulation. La section 2 explique une proc´edure de subdivision rapide et certifi´ee triangulant une courbe alg´ebrique r´eelle plane. Les outils math´ematiques sont le degr´e topologique, la base des polynˆomes de Bernstein. La section 3 est une copie d'un article expliquant la m´ethode de subdivision pour les surfaces lisses dans Rn. Elle comporte une analyse de complexit´e. La section 4 pr´esente une version quantitative du th´eor`eme de trivialit´e topologique de Thom-Mather pour des applications semi-alg´ebriques non lisses. Il en d´ecoule: une version “m´etriquement stable” du th´eor`eme de structure conique local et de l'existence d'un “tube de Milnor” autour des strates. Un algorithme de triangulation utilisant des partitions de Vorono˘i (sa mise en place n'est pas compl`ete car l'estimation effective de la transversalit´e n'est pas compl`etement trait´e). La section 5 est une copie d'un article paru en 2008 sur une m´ethode de balayage pour calculer la topologie d'une surface singuli`ere de R3. Elle repose sur l'utilisation du th´eor`eme de Thom-Mather. La section 6 pr´esente une borne sur le nombre g´en´erique de composantes connexes dans une section d'un germe analytique r´eel par un espace affine en fonction de la multiplicit´e et de la dimension de l'espace. La borne ne s'applique pas toujours et des contre-examples sont donn´es

C57BL/6 congenic mouse NRAS Q61K melanoma cell lines are highly sensitive to the combination of Mek and Akt inhibitors in vitro and in vivo

International audienceRAS is frequently mutated in various tumors and known to be difficult to target. NRASQ61K/R are the second most frequent mutations found in human skin melanoma after BRAFV600E . Aside from surgery, various approaches, including targeted therapies, immunotherapies, and combination therapies, are used to treat patients carrying NRAS mutations, but they are inefficient. Here, we established mouse NRASQ61K melanoma cell lines and genetically derived isografts (GDIs) from Tyr::NRASQ61K mouse melanoma that can be used in vitro and in vivo in an immune-competent environment (C57BL/6) to test and discover novel therapies. We characterized these cell lines at the cellular, molecular, and oncogenic levels and show that NRASQ61K melanoma is highly sensitive to the combination of Mek and Akt inhibitors. This preclinical model shows much potential for the screening of novel therapeutic strategies for patients harboring NRAS mutations that have limited therapeutic options and resulted in poor prognoses