A New Lower Bound on the Maximum Number of Satisfied Clauses in Max-SAT and its Algorithmic Applications

A pair of unit clauses is called conflicting if it is of the form $(x)$, $(\bar{x})$. A CNF formula is unit-conflict free (UCF) if it contains no pair of conflicting unit clauses. Lieberherr and Specker (J. ACM 28, 1981) showed that for each UCF CNF formula with $m$ clauses we can simultaneously satisfy at least \pp m clauses, where \pp =(\sqrt{5}-1)/2. We improve the Lieberherr-Specker bound by showing that for each UCF CNF formula $F$ with $m$ clauses we can find, in polynomial time, a subformula $F'$ with $m'$ clauses such that we can simultaneously satisfy at least \pp m+(1-\pp)m'+(2-3\pp)n"/2 clauses (in $F$), where $n"$ is the number of variables in $F$ which are not in $F'$. We consider two parameterized versions of MAX-SAT, where the parameter is the number of satisfied clauses above the bounds $m/2$ and $m(\sqrt{5}-1)/2$. The former bound is tight for general formulas, and the later is tight for UCF formulas. Mahajan and Raman (J. Algorithms 31, 1999) showed that every instance of the first parameterized problem can be transformed, in polynomial time, into an equivalent one with at most $6k+3$ variables and $10k$ clauses. We improve this to $4k$ variables and $(2\sqrt{5}+4)k$ clauses. Mahajan and Raman conjectured that the second parameterized problem is fixed-parameter tractable (FPT). We show that the problem is indeed FPT by describing a polynomial-time algorithm that transforms any problem instance into an equivalent one with at most $(7+3\sqrt{5})k$ variables. Our results are obtained using our improvement of the Lieberherr-Specker bound above

Asymptotic degeneracy of dyonic N=4 string states and black hole entropy

It is shown that the asymptotic growth of the microscopic degeneracy of BPS dyons in four-dimensional N=4 string theory captures the known corrections to the macroscopic entropy of four-dimensional extremal black holes. These corrections are subleading in the limit of large charges and originate both from the presence of interactions in the effective action quadratic in the Riemann tensor and from non-holomorphic terms. The presence of the non-holomorphic corrections and their contribution to the thermodynamic free energy is discussed. It is pointed out that the expression for the microscopic entropy, written as a function of the dilaton field, is stationary at the horizon by virtue of the attractor equations.Comment: 16 pages Late

Black hole partition functions and duality

The macroscopic entropy and the attractor equations for BPS black holes in four-dimensional N=2 supergravity theories follow from a variational principle for a certain `entropy function'. We present this function in the presence of R^2-interactions and non-holomorphic corrections. The variational principle identifies the entropy as a Legendre transform and this motivates the definition of various partition functions corresponding to different ensembles and a hierarchy of corresponding duality invariant inverse Laplace integral representations for the microscopic degeneracies. Whenever the microscopic degeneracies are known the partition functions can be evaluated directly. This is the case for N=4 heterotic CHL black holes, where we demonstrate that the partition functions are consistent with the results obtained on the macroscopic side for black holes that have a non-vanishing classical area. In this way we confirm the presence of a measure in the duality invariant inverse Laplace integrals. Most, but not all, of these results are obtained in the context of semiclassical approximations. For black holes whose area vanishes classically, there remain discrepancies at the semiclassical level and beyond, the nature of which is not fully understood at present.Comment: 36 pages, Late

A well-balanced scheme for the simulation tool-kit A-MaZe: implementation, tests, and first applications to stellar structure

This is the final version. Available on open access from EDP Sciences via the DOI in this recordCharacterizing stellar convection in multiple dimensions is a topic at the forefront of stellar astrophysics. Numerical simulations are an essential tool for this task. We present an extension of the existing numerical tool-kit A-MaZe that enables such simulations of stratified flows in a gravitational field. The finite-volume based, cell-centered, and time-explicit hydrodynamics solver of A-MaZe was extended such that the scheme is now well-balanced in both momentum and energy. The algorithm maintains an initially static balance between gravity and pressure to machine precision. Quasi-stationary convection in slab-geometry preserves gas energy (internal plus kinetic) on average despite strong local up- and down-drafts. By contrast, a more standard numerical scheme is demonstrated to result in substantial gains of energy within a short time on purely numerical grounds. The test is further used to point out the role of dimensionality, viscosity, and Rayleigh number for compressible convection. Applications to a young sun in 2D and 3D, covering a part of the inner radiative zone as well as the outer convective zone, demonstrate that the scheme meets its initial design goal. Comparison with results obtained for a physically identical setup with a time-implicit code show qualitative agreement.European Research Council (ERC)French National Program for High Energies PNH

The Impact of Fission on R-Process Calculations

We have performed r-process calculations in neutron star mergers (NSM) and jets of magnetohydrodynamically driven (MHD) supernovae. In these very neutron-rich environments the fission model of heavy nuclei has an impact on the shape of the final abundance distribution and the second r-process peak in particular. We have studied the effect of different fission fragment mass distribution models in calculations of low-Ye ejecta, ranging from a simple parametrization to extensive statistical treatments (ABLA07). The r-process path ends when it reaches an area in the nuclear chart where fission dominates over further neutron captures. The position of this point is determined by the fission barriers and the neutron separation energies of the nuclei involved. As these values both depend on the choice of the nuclear mass model, so does the r-process path. Here we present calculations using the FRDM (Finite Range Droplet Model) and the ETFSI (Extended Thomas Fermi with Strutinsky Integral) mass model with the related TF and ETFSI fission barrier predictions. Utilizing sophisticated fission fragment distribution leads to a highly improved abundance distribution.Peer reviewe

Gravitational waves from supernova matter

We have performed a set of 11 three-dimensional magnetohydrodynamical core collapse supernova simulations in order to investigate the dependencies of the gravitational wave signal on the progenitor's initial conditions. We study the effects of the initial central angular velocity and different variants of neutrino transport. Our models are started up from a 15 solar mass progenitor and incorporate an effective general relativistic gravitational potential and a finite temperature nuclear equation of state. Furthermore, the electron flavour neutrino transport is tracked by efficient algorithms for the radiative transfer of massless fermions. We find that non- and slowly rotating models show gravitational wave emission due to prompt- and lepton driven convection that reveals details about the hydrodynamical state of the fluid inside the protoneutron stars. Furthermore we show that protoneutron stars can become dynamically unstable to rotational instabilities at T/|W| values as low as ~2 % at core bounce. We point out that the inclusion of deleptonization during the postbounce phase is very important for the quantitative GW prediction, as it enhances the absolute values of the gravitational wave trains up to a factor of ten with respect to a lepton-conserving treatment.Comment: 10 pages, 6 figures, accepted, to be published in a Classical and Quantum Gravity special issue for MICRA200

Salmonella enterica serotype Virchow associated with human infections in Switzerland: 2004-2009

BACKGROUND: Salmonellosis is one of the most important foodborne diseases and a major threat to public health. Salmonella serotype Virchow ranks among the top five serovars in Europe. METHOD: A total of 153 strains isolated from different patients from 2004 through 2009 in Switzerland were further characterized by (i) assessing phenotypic antibiotic resistance profiles using the disk diffusion method and (ii) by genotyping using pulsed-field gel electrophoresis (PFGE) after macrorestriction with XbaI in order to evaluate strain relationship. RESULTS: The relative frequency of S. Virchow among other Salmonella serovars varied between 4th to 8th rank. The annual incidence ranged from 0.45/100'000 in 2004 to 0.40/100'000 in 2009. A total of 48 strains (32%) were resistant to one to 3 antimicrobials, 54 strains (36%) displayed resistance patterns to more than three antibiotics. No trend was identifiable over the years 2004 to 2009. We found a high prevalence (62%) of nalidixic acid resistant strains, suggesting an equally high rate of decreased fluoroqionolone susceptibility, whereas intermediate resistance to ciprofloxacin was negligible. Two strains were extended spectrum β-lactamase (ESBL) producers. Analysis of PFGE patterns uncovered a predominant cluster (similarity coefficient above 80%) consisting of 104 of the 153 strains. CONCLUSION: The worldwide increase of antibiotic resistances in Salmonella is an emerging public health problem. For Switzerland, no clear trend is identifiable over the years 2004 to 2009 for S. Virchow. Antimicrobial susceptibility and resistance profiles varied considerably within this period. Nevertheless, the situation in Switzerland coincided with findings in other European countries. Genotyping results of this strain collection revealed no evidence for an undetected outbreak within this time period

Like Will to Like: Abundances of Closely Related Species Can Predict Susceptibility to Intestinal Colonization by Pathogenic and Commensal Bacteria

The intestinal ecosystem is formed by a complex, yet highly characteristic microbial community. The parameters defining whether this community permits invasion of a new bacterial species are unclear. In particular, inhibition of enteropathogen infection by the gut microbiota ( = colonization resistance) is poorly understood. To analyze the mechanisms of microbiota-mediated protection from Salmonella enterica induced enterocolitis, we used a mouse infection model and large scale high-throughput pyrosequencing. In contrast to conventional mice (CON), mice with a gut microbiota of low complexity (LCM) were highly susceptible to S. enterica induced colonization and enterocolitis. Colonization resistance was partially restored in LCM-animals by co-housing with conventional mice for 21 days (LCMcon21). 16S rRNA sequence analysis comparing LCM, LCMcon21 and CON gut microbiota revealed that gut microbiota complexity increased upon conventionalization and correlated with increased resistance to S. enterica infection. Comparative microbiota analysis of mice with varying degrees of colonization resistance allowed us to identify intestinal ecosystem characteristics associated with susceptibility to S. enterica infection. Moreover, this system enabled us to gain further insights into the general principles of gut ecosystem invasion by non-pathogenic, commensal bacteria. Mice harboring high commensal E. coli densities were more susceptible to S. enterica induced gut inflammation. Similarly, mice with high titers of Lactobacilli were more efficiently colonized by a commensal Lactobacillus reuteri RR strain after oral inoculation. Upon examination of 16S rRNA sequence data from 9 CON mice we found that closely related phylotypes generally display significantly correlated abundances (co-occurrence), more so than distantly related phylotypes. Thus, in essence, the presence of closely related species can increase the chance of invasion of newly incoming species into the gut ecosystem. We provide evidence that this principle might be of general validity for invasion of bacteria in preformed gut ecosystems. This might be of relevance for human enteropathogen infections as well as therapeutic use of probiotic commensal bacteria

Salmonella-Induced Mucosal Lectin RegIIIβ Kills Competing Gut Microbiota

Intestinal inflammation induces alterations of the gut microbiota and promotes overgrowth of the enteric pathogen Salmonella enterica by largely unknown mechanisms. Here, we identified a host factor involved in this process. Specifically, the C-type lectin RegIIIβ is strongly upregulated during mucosal infection and released into the gut lumen. In vitro, RegIIIβ kills diverse commensal gut bacteria but not Salmonella enterica subspecies I serovar Typhimurium (S. Typhimurium). Protection of the pathogen was attributable to its specific cell envelope structure. Co-infection experiments with an avirulent S. Typhimurium mutant and a RegIIIβ-sensitive commensal E. coli strain demonstrated that feeding of RegIIIβ was sufficient for suppressing commensals in the absence of all other changes inflicted by mucosal disease. These data suggest that RegIIIβ production by the host can promote S. Typhimurium infection by eliminating inhibitory gut microbiota