Parameterized Complexity of Equitable Coloring

A graph on $n$ vertices is equitably $k$-colorable if it is $k$-colorable and every color is used either $\left\lfloor n/k \right\rfloor$ or $\left\lceil n/k \right\rceil$ times. Such a problem appears to be considerably harder than vertex coloring, being $\mathsf{NP\text{-}Complete}$ even for cographs and interval graphs. In this work, we prove that it is $\mathsf{W[1]\text{-}Hard}$ for block graphs and for disjoint union of split graphs when parameterized by the number of colors; and $\mathsf{W[1]\text{-}Hard}$ for $K_{1,4}$-free interval graphs when parameterized by treewidth, number of colors and maximum degree, generalizing a result by Fellows et al. (2014) through a much simpler reduction. Using a previous result due to Dominique de Werra (1985), we establish a dichotomy for the complexity of equitable coloring of chordal graphs based on the size of the largest induced star. Finally, we show that \textsc{equitable coloring} is $\mathsf{FPT}$ when parameterized by the treewidth of the complement graph

On the Computational Complexity of the Strong Geodetic Recognition Problem

A strong geodetic set of a graph~$G=(V,E)$ is a vertex set~$S \subseteq V(G)$ in which it is possible to cover all the remaining vertices of~$V(G) \setminus S$ by assigning a unique shortest path between each vertex pair of~$S$. In the Strong Geodetic problem (SG) a graph~$G$ and a positive integer~$k$ are given as input and one has to decide whether~$G$ has a strong geodetic set of cardinality at most~$k$. This problem is known to be NP-hard for general graphs. In this work we introduce the Strong Geodetic Recognition problem (SGR), which consists in determining whether even a given vertex set~$S \subseteq V(G)$ is strong geodetic. We demonstrate that this version is NP-complete. We investigate and compare the computational complexity of both decision problems restricted to some graph classes, deriving polynomial-time algorithms, NP-completeness proofs, and initial parameterized complexity results, including an answer to an open question in the literature for the complexity of SG for chordal graphs

Against the Odds: Hybrid Zones between Mangrove Killifish Species with Different Mating Systems

Different mating systems are expected to affect the extent and direction of hybridization. Due to the different levels of sexual conflict, the weak inbreeder/strong outbreeder (WISO) hypothesis predicts that gametes from self-incompatible (SI) species should outcompete gametes from self-compatible (SC) ones. However, other factors such as timing of selfing and unilateral incompatibilities may also play a role on the direction of hybridization. In addition, differential mating opportunities provided by different mating systems are also expected to affect the direction of introgression in hybrid zones involving outcrossers and selfers. Here, we explored these hypotheses with a unique case of recent hybridization between two mangrove killifish species with different mating systems, Kryptolebias ocellatus (obligately outcrossing) and K. hermaphroditus (predominantly self-fertilizing) in two hybrid zones in southeast Brazil. Hybridization rates were relatively high (~20%), representing the first example of natural hybridization between species with different mating systems in vertebrates. All F1 individuals were sired by the selfing species. Backcrossing was small, but mostly asymmetrical with the SI parental species, suggesting pattern commonly observed in plant hybrid zones with different mating systems. Our findings shed light on how contrasting mating systems may affect the direction and extent of gene flow between sympatric species, ultimately affecting the evolution and maintenance of hybrid zones

Para o estudo da evolução do ensino e da formação em administração educacional em Portugal

Estudos sobre a evolução do ensino de disciplinas, na formação de professores em Portugal, são recentes. O controle burocrático centralizado reteve as dimensões do controle político-administrativo. De certo modo, protegeu a esfera educativa das influências modernizantes, do capitalismo industrial e das lógicas mercantis e gerencialistas. Defendeu a educação do domínio político, da intervenção de movimentos sociais, das propagandas de ideais democráticos e da cidadania. A utilização da designação "Administração educacional" ilustra as dificuldades sentidas, ao longo dos últimos anos, em termos da construção acadêmica de uma área, seja pela falta de tradição, seja pelos antecedentes históricos.In Portugal, studies about the evolution of disciplines teaching in the teachers formation are recent. The centralized bureaucratic control has held back the dimensions of politic administrative control. In a certain way, it has protected the education against the new-fashioned influences, manufacturing capitalism, and mercantile and managerial logics. This centralized bureaucratic control has also profected the education against the politic dominion, the intervention of social movements, the advertising of democratic ideals, and against the citizenship. The use of the term "Educational administration" shows the difficulties met by the searchers along the latest years, since there is no tradiction nor historic antecedence

ESR observations of paramagnetic centers in intrinsic hydrogenated microcrystalline silicon

Paramagnetic centers in hydrogenated microcrystalline silicon, µc-Si:H have been studied using dark and light-induced electron-spin resonance (ESR). In dark ESR measurements only one center is observed. The g values obtained empirically from powder-pattern line-shape simulations are g=2.0096 and g'=2.0031. We suggest that this center may be due to defects in the crystalline phase. During illumination at low temperatures, an additional ESR signal appears. This signal is best described by two powder patterns indicating the presence of two centers. One center is asymmetric (gi=1.999, g'=1.996), while the other is characterized by large, unresolved broadening such that unique g values cannot be obtained. The average g value for this center is 1.998. The light-induced signal, which we interpret as coming from carriers trapped in the band tails at the crystalline grain boundaries, remains for at least several minutes after the light is turned off. Although the time scales of the decay curves are very different for two samples prepared by different techniques, both decays can be fitted using the assumption of recombination due to distant pairs of electrons and holes trapped in localized band-tail states