Optimal General Matchings

Given a graph $G=(V,E)$ and for each vertex $v \in V$ a subset $B(v)$ of the set $\{0,1,\ldots, d_G(v)\}$, where $d_G(v)$ denotes the degree of vertex $v$ in the graph $G$, a $B$-factor of $G$ is any set $F \subseteq E$ such that $d_F(v) \in B(v)$ for each vertex $v$, where $d_F(v)$ denotes the number of edges of $F$ incident to $v$. The general factor problem asks the existence of a $B$-factor in a given graph. A set $B(v)$ is said to have a {\em gap of length} $p$ if there exists a natural number $k \in B(v)$ such that $k+1, \ldots, k+p \notin B(v)$ and $k+p+1 \in B(v)$. Without any restrictions the general factor problem is NP-complete. However, if no set $B(v)$ contains a gap of length greater than $1$, then the problem can be solved in polynomial time and Cornuejols \cite{Cor} presented an algorithm for finding a $B$-factor, if it exists. In this paper we consider a weighted version of the general factor problem, in which each edge has a nonnegative weight and we are interested in finding a $B$-factor of maximum (or minimum) weight. In particular, this version comprises the minimum/maximum cardinality variant of the general factor problem, where we want to find a $B$-factor having a minimum/maximum number of edges. We present an algorithm for the maximum/minimum weight $B$-factor for the case when no set $B(v)$ contains a gap of length greater than $1$. This also yields the first polynomial time algorithm for the maximum/minimum cardinality $B$-factor for this case

Constraint satisfaction parameterized by solution size

In the constraint satisfaction problem (CSP) corresponding to a constraint language (i.e., a set of relations) $\Gamma$, the goal is to find an assignment of values to variables so that a given set of constraints specified by relations from $\Gamma$ is satisfied. The complexity of this problem has received substantial amount of attention in the past decade. In this paper we study the fixed-parameter tractability of constraint satisfaction problems parameterized by the size of the solution in the following sense: one of the possible values, say 0, is "free," and the number of variables allowed to take other, "expensive," values is restricted. A size constraint requires that exactly $k$ variables take nonzero values. We also study a more refined version of this restriction: a global cardinality constraint prescribes how many variables have to be assigned each particular value. We study the parameterized complexity of these types of CSPs where the parameter is the required number $k$ of nonzero variables. As special cases, we can obtain natural and well-studied parameterized problems such as Independent Set, Vertex Cover, d-Hitting Set, Biclique, etc. In the case of constraint languages closed under substitution of constants, we give a complete characterization of the fixed-parameter tractable cases of CSPs with size constraints, and we show that all the remaining problems are W[1]-hard. For CSPs with cardinality constraints, we obtain a similar classification, but for some of the problems we are only able to show that they are Biclique-hard. The exact parameterized complexity of the Biclique problem is a notorious open problem, although it is believed to be W[1]-hard.Comment: To appear in SICOMP. Conference version in ICALP 201

Does Kin Recognition and Sib-Mating Avoidance Limit the Risk of Genetic Incompatibility in a Parasitic Wasp?

Background: When some combinations of maternal and paternal alleles have a detrimental effect on offspring fitness, females should be able to choose mates on the basis of their genetic compatibility. In numerous Hymenoptera, the sex of an individual depends of the allelic combination at a specific locus (single-locus Complementary Sex Determination), and in most of these species individuals that are homozygous at this sexual locus develop into diploid males with zero fitness. Methods and Findings: In this paper, we tested the hypothesis of genetic incompatibility avoidance by investigating sibmating avoidance in the solitary wasp parasitoid, Venturia canescens. In the context of mate choice we show, for the first time in a non-social hymenopteran species, that females can avoid mating with their brothers through kin recognition. In ‘‘no-choice’ ’ tests, the probability a female will mate with an unrelated male is twice as high as the chance of her mating with her brothers. In contrast, in choice tests in small test arenas, no kin discrimination effect was observed. Further experiments with male extracts demonstrate that chemical cues emanating from related males influence the acceptance rate of unrelated males. Conclusions: Our results are compatible with the genetic incompatibility hypothesis. They suggest that the female wasps recognize sibs on the basis of a chemical signature carried or emitted by males possibly using a ‘‘self-referent phenotyp

Wood Utilization Is Dependent on Catalase Activities in the Filamentous Fungus Podospora anserina

Catalases are enzymes that play critical roles in protecting cells against the toxic effects of hydrogen peroxide. They are implicated in various physiological and pathological conditions but some of their functions remain unclear. In order to decipher the role(s) of catalases during the life cycle of Podospora anserina, we analyzed the role of the four monofunctional catalases and one bifunctional catalase-peroxidase genes present in its genome. The five genes were deleted and the phenotypes of each single and all multiple mutants were investigated. Intriguingly, although the genes are differently expressed during the life cycle, catalase activity is dispensable during both vegetative growth and sexual reproduction in laboratory conditions. Catalases are also not essential for cellulose or fatty acid assimilation. In contrast, they are strictly required for efficient utilization of more complex biomass like wood shavings by allowing growth in the presence of lignin. The secreted CATB and cytosolic CAT2 are the major catalases implicated in peroxide resistance, while CAT2 is the major player during complex biomass assimilation. Our results suggest that P. anserina produces external H2O2 to assimilate complex biomass and that catalases are necessary to protect the cells during this process. In addition, the phenotypes of strains lacking only one catalase gene suggest that a decrease of catalase activity improves the capacity of the fungus to degrade complex biomass

Les femmes et la pauvreté : histoires de familles, histoires d’emplois ?

La situation socio-économique des femmes s’explique, d’une part, par leur présence plus ou moins soutenue sur le marché de l’emploi et, d’autre part, par leur histoire de famille, c’est-à-dire par les types de ménages auxquels elles appartiennent au cours de leur vie. Union libre, présence d’enfants, mariage, autant d’éléments qui déterminent largement le niveau de vie des femmes et, partant, leurs risques de vivre sous le seuil de pauvreté. Par ailleurs, les interruptions de carrière des femmes semblent pénalisantes, quoique de façon variable selon les différentes histoires de familles.The women socio-economic status can be explained, on the one hand, by their more or less constant presence in the working place and, on the other hand, by their family history, that is to say, the different types of household to which they belong during their life. Free union, children, marriage, are as many elements which largely influence women standards of living and, therefore, the risks of living below the poverty line. Furthermore, career interruptions seem to be penalizing for women, in one way or another, according to their family history.La situación socio-económica de las mujeres se explica, por una parte, por su presencia más o menos contínua en el mercado del empleo, y, por otra, por su historia familiar, por los tipos de hogares a los que pertenecen durante su vida. Unión libre, presencia de hijos, matrimonio: todos ellos son elementos que determinan en gran parte el nivel de vida y los riesgos que confrontan de vivir bajo el nivel de pobreza. Las interrupciones de carrera de las mujeres son también elementos de penalización, aunque de impacto variable según sus historias de familia