On the complexity of computing the kk-restricted edge-connectivity of a graph

The \emph{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph invariant, which can be seen as a generalization of a minimum edge-cut, has been extensively studied from a combinatorial point of view. However, very little is known about the complexity of computing $\lambda_k(G)$. Very recently, in the parameterized complexity community the notion of \emph{good edge separation} of a graph has been defined, which happens to be essentially the same as the $k$-restricted edge-connectivity. Motivated by the relevance of this invariant from both combinatorial and algorithmic points of view, in this article we initiate a systematic study of its computational complexity, with special emphasis on its parameterized complexity for several choices of the parameters. We provide a number of NP-hardness and W[1]-hardness results, as well as FPT-algorithms.Comment: 16 pages, 4 figure

Collecting high-order interactions in an effective pairwise intermolecular potential using the hydrated ion concept: The hydration of Cf3+

This work proposes a new methodology to build interaction potentials between a highly charged metal cation and water molecules. These potentials, which can be used in classical computer simu- lations, have been fitted to reproduce quantum mechanical interaction energies (MP2 and BP86) for a wide range of [M(H2O)n]m+(H2O)l clusters (n going from 6 to 10 and l from 0 to 18). A flexible and polarizable water shell model (Mobile Charge Density of Harmonic Oscillator) has been coupled to the cation-water potential. The simultaneous consideration of poly-hydrated clusters and the polarizability of the interacting particles allows the inclusion of the most important many-body effects in the new polarizable potential. Applications have been centered on the californium, Cf(III) the heaviest actinoid experimentally studied in solution. Two different strategies to select a set of about 2000 structures which are used for the potential building were checked. Monte Carlo simulations of Cf(III)+500 H2O for three of the intermolecular potentials predict an aquaion structure with coordination number close to 8 and average RCf–O in the range 2.43–2.48 Å, whereas the fourth one is closer to 9 with RCf–O = 2.54 Å. Simulated EXAFS spectra derived from the structural Monte Carlo distribution compares fairly well with the available experimental spectrum for the simulations bearing 8 water molecules. An angular distribution similar to that of a square antiprism is found for the octa-coordination.Ministerio de Ciencia e Innovación CTQ2011-2593

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

Acceptability of Male Circumcision for the Prevention of HIV/AIDS in the Dominican Republic

Male circumcision (MC) is an effective strategy to prevent HIV infection in heterosexual men. To our knowledge, there are no studies of the acceptability of this procedure in the Dominican Republic (DR). The main objective of this study was to assess the acceptability of MC to prevent HIV transmission among men ages 18 to 50 years in the Altagracia Province in the Dominican Republic. Because differences in culture and beliefs between Haitians and Dominicans could potentially influence their acceptability of MC, we conducted a comparative analysis based on national origin.A survey was administered to a convenience sample of 368 men. The questionnaire was divided in 3 sections: 1) Background demographics (including national origin), 2) Male circumcision and 3) Sexual health. Stratified and logistic multivariate regression analyses were performed to identify factors associated with the acceptability of MC.The sample consisted of 238 (65%) Dominicans and 130 (35%) Haitian immigrants. Almost all participants were uncircumcised (95%) and about half (52%) were single. The overall acceptability of MC was 29%. The number of men willing to be circumcised increased to 67% after an information session explaining the benefits of the procedure. 74% of men reported that they would be willing to circumcise their sons after hearing that information. In multivariate analysis, Haitian nationality (OR=1.86, 95% CI 1.01-3.41), knowing that circumcision improves hygiene (OR=2.78, 95% CI 1.29-6.0) and not believing that circumcision decreases sexual pleasure (OR=2.18, 95% CI 1.20-3.94) were associated with a higher acceptability of the procedure. Although age was not significantly associated with the willingness to be circumcised in the multivariate analysis, stratified analysis based on national origin suggested that younger Dominicans (<30 years of age) are more likely to accept the procedure when compared to their older counterparts (OR=2.17, 95% CI 1.14-4.12).An important number of sexually active men in the DR may be willing to be circumcised if educational resources detailing the benefits of the procedure are made available. These educational activities would constitute a great opportunity to teach about sexual health and reinforce safe sex practices

Morphology of supported polymer electrolyte ultra-thin films: a numerical study

Morphology of polymer electrolytes membranes (PEM), e.g., Nafion, inside PEM fuel cell catalyst layers has significant impact on the electrochemical activity and transport phenomena that determine cell performance. In those regions, Nafion can be found as an ultra-thin film, coating the catalyst and the catalyst support surfaces. The impact of the hydrophilic/hydrophobic character of these surfaces on the structural formation of the films has not been sufficiently explored yet. Here, we report about Molecular Dynamics simulation investigation of the substrate effects on the ionomer ultra-thin film morphology at different hydration levels. We use a mean-field-like model we introduced in previous publications for the interaction of the hydrated Nafion ionomer with a substrate, characterized by a tunable degree of hydrophilicity. We show that the affinity of the substrate with water plays a crucial role in the molecular rearrangement of the ionomer film, resulting in completely different morphologies. Detailed structural description in different regions of the film shows evidences of strongly heterogeneous behavior. A qualitative discussion of the implications of our observations on the PEMFC catalyst layer performance is finally proposed

Electrospun Polyurethane Fibers for Absorption of Volatile Organic Compounds from Air

Electrospun polyurethane fibers for removal of volatile organic compounds (VOC) from air with rapid VOC absorption and desorption have been developed. Polyurethanes based on 4,4-methylenebis(phenylisocyanate) (MDI) and aliphatic isophorone diisocyanate as the hard segments and butanediol and tetramethylene glycol as the soft segments were electrospun from their solutions in N,N-dimethylformamide to form micrometer-sized fibers. Although activated carbon possessed a many-fold higher surface area than the polyurethane fiber meshes, the sorption capacity of the polyurethane fibers was found to be similar to that of activated carbon specifically designed for vapor adsorption. Furthermore, in contrast to VOC sorption on activated carbon, where complete regeneration of the adsorbent was not possible, the polyurethane fibers demonstrated a completely reversible absorption and desorption, with desorption obtained by a simple purging with nitrogen at room temperature. The fibers possessed a high affinity toward toluene and chloroform, but aliphatic hexane lacked the necessary strong attractive interactions with the polyurethane chains and therefore was less strongly absorbed. The selectivity of the polyurethane fibers toward different vapors, along with the ease of regeneration, makes them attractive materials for VOC filtration.Boeing CompanyNetherlands Organisation for Scientific Research (NWO) (Talent Scholarship

Thermodynamics and dynamics of the formation of spherical lipidic vesicles

We propose a free energy expression accounting for the formation of spherical vesicles from planar lipidic membranes and derive a Fokker-Planck equation for the probability distribution describing the dynamics of vesicle formation. We found that formation may occur as an activated process for small membranes and as a transport process for sufficiently large membranes. We give explicit expressions for the transition rates and the characteristic time of vesicle formation in terms of the relevant physical parameters.Comment: 14pgs, 6 figures, sendo to Jour. Phys. Bio