A Unifying Splitting Framework

International audienceAVATAR is an elegant and effective way to split clauses in a saturation prover using a SAT solver. But is it refutationally complete? And how does it relate to other splitting architectures? To answer these questions, we present a unifying framework that extends a saturation calculus (e.g., superposition) with splitting and embeds the result in a prover guided by a SAT solver. The framework also allows us to study locking, a subsumption-like mechanism based on the current propositional model. Various architectures are instances of the framework, including AVATAR, labeled splitting, and SMT with quantifiers

Superposition for Full Higher-order Logic

International audienceWe recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free $\lambda$-superposition and superposition for first-order logic with interpreted Booleans. Stepping on these stones, we finally reach a sound and refutationally complete calculus for higher-order logic with polymorphism, extensionality, Hilbert choice, and Henkin semantics. In addition to the complexity of combining the calculus’s two predecessors, new challenges arise from the interplay between $\lambda$-terms and Booleans. Our implementation in Zipperposition outperforms all other higher-order theorem provers and is on a par with an earlier, pragmatic prototype of Booleans in Zipperposition

The Conserved nhaAR Operon Is Drastically Divergent between B2 and Non-B2 Escherichia coli and Is Involved in Extra-Intestinal Virulence

The Escherichia coli species is divided in phylogenetic groups that differ in their virulence and commensal distribution. Strains belonging to the B2 group are involved in extra-intestinal pathologies but also appear to be more prevalent as commensals among human occidental populations. To investigate the genetic specificities of B2 sub-group, we used 128 sequenced genomes and identified genes of the core genome that showed marked difference between B2 and non-B2 genomes. We focused on the gene and its surrounding region with the strongest divergence between B2 and non-B2, the antiporter gene nhaA. This gene is part of the nhaAR operon, which is in the core genome but flanked by mobile regions, and is involved in growth at high pH and high sodium concentrations. Consistently, we found that a panel of non-B2 strains grew faster than B2 at high pH and high sodium concentrations. However, we could not identify differences in expression of the nhaAR operon using fluorescence reporter plasmids. Furthermore, the operon deletion had no differential impact between B2 and non-B2 strains, and did not result in a fitness modification in a murine model of gut colonization. Nevertheless, sequence analysis and experiments in a murine model of septicemia revealed that recombination in nhaA among B2 strains was observed in strains with low virulence. Finally, nhaA and nhaAR operon deletions drastically decreased virulence in one B2 strain. This effect of nhaAR deletion appeared to be stronger than deletion of all pathogenicity islands. Thus, a population genetic approach allowed us to identify an operon in the core genome without strong effect in commensalism but with an important role in extra-intestinal virulence, a landmark of the B2 strains

Superposition with Lambdas

We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $\beta\eta$-equivalence classes of $\lambda$-terms and rely on higher-order unification to achieve refutational completeness. We implemented the calculus in the Zipperposition prover and evaluated it on TPTP and Isabelle benchmarks. The results suggest that superposition is a suitable basis for higher-order reasoning

Superposition with Lambdas

We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on βη-equivalence classes of λ-terms and rely on higher-order unification to achieve refutational completeness. We implemented the calculus in the Zipperposition prover and evaluated it on TPTP and Isabelle benchmarks. The results suggest that superposition is a suitable basis for higher-order reasoning

Efficiency and accuracy of GPU-parallelized Fourier spectral methods for solving phase-field models

Phase-field models are widely employed to simulate microstructure evolution during processes such as solidification or heat treatment. The resulting partial differential equations, often strongly coupled together, may be solved by a broad range of numerical methods, but this often results in a high computational cost, which calls for advanced numerical methods to accelerate their resolution. Here, we quantitatively test the efficiency and accuracy of semi-implicit Fourier spectral-based methods, implemented in Python programming language and parallelized on a graphics processing unit (GPU), for solving a phase-field model coupling Cahn-Hilliard and Allen-Cahn equations. We compare computational performance and accuracy with a standard explicit finite difference (FD) implementation with similar GPU parallelization on the same hardware. For a similar spatial discretization, the semi-implicit Fourier spectral (FS) solvers outperform the FD resolution as soon as the time step can be taken 5 to 6 times higher than afforded for the stability of the FD scheme. The accuracy of the FS methods also remains excellent even for coarse grids, while that of FD deteriorates significantly. Therefore, for an equivalent level of accuracy, semi-implicit FS methods severely outperform explicit FD, by up to 4 orders of magnitude, as they allow much coarser spatial and temporal discretization

Grain growth competition and formation of grain boundaries during solidification of hcp alloys

Grain growth competition during directional solidification of a polycrystal with hexagonal (hcp) symmetry (Mg-1wt%Gd alloy) is studied by phase-field modeling, exploring the effect of the temperature gradient G on the resulting grain boundary (GB) orientation selection. Results show that selection mechanisms and scaling laws derived for cubic (fcc, bcc) crystals also apply to hcp materials (within their basal plane), provided a re-estimation of fitting parameters and re-scaling to account for the sixfold symmetry. While grain growth competition remains stochastic with rare events of unexpected elimination or side-branching along the developing GBs, we also confirm an overall transition from a geometrical limit to a favorably oriented grain limit behavior with an increase of thermal gradient within the dendritic regime, and the progressive alignment of dendrites and GBs toward the temperature gradient direction with an increase of G during the dendritic-to-cellular morphological transition. Comparisons with original thin-sample directional solidification experiments show a qualitative agreement with PF results, yet with notable discrepancies, which nonetheless can be explained based on the stochastic variability of selected GB orientations, and the statistically limited experimental sample size. Overall, our results extend the understanding of GB formation and grain growth competition during solidification of hcp materials, and the effect of thermal conditions, nonetheless concluding on the challenges of extending the current studies to three dimensions, and the need for much broader (statistically significant) data sets of GB orientation selected under well-identified solidification conditions

Efficacy and toxicity of intravenous iron in a mouse model of critical care anemia

OBJECTIVE: Anemia is common in critically ill patients, due to inflammation and blood loss. Anemia can be associated with iron deficiency and low serum hepcidin levels. However, iron administration in this setting remains controversial because of its potential toxicity, including oxidative stress induction and sepsis facilitation. The objective of this work was to determine the efficacy and toxicity of iron administration using a mouse model mimicking critical care anemia as well as a model of acute septicemia. DESIGN: Prospective, randomized, open label controlled animal study. SETTING: University-based research laboratory. SUBJECTS: C57BL/6 and OF1 mice. INTERVENTIONS: Intraperitoneal injection of zymosan inducing generalized inflammation in C57BL/6 mice, followed in our full model by repeated phlebotomies. A dose equivalent to 15 mg/kg of ferric carboxymaltose was injected intravenously on day 5. To assess the toxicity of iron in a septicemia model, OF1 mice were simultaneously injected with iron and different Escherichia coli strains. MEASUREMENTS AND MAIN RESULTS: To investigate the effect of iron on oxidative stress, we measured reactive oxygen species production in the blood using luminol-amplified chemiluminescence and superoxide dismutase 2 messenger RNA levels in the liver. These markers of oxidative stress were increased after iron administration in control mice but not in zymosan-treated mice. Liver catalase messenger RNA levels decreased in iron-treated control mice. Iron administration was not associated with increased mortality in the septicemia model or in the generalized inflammation model. Iron increased hemoglobin levels in mice fed with a low iron diet and subjected to phlebotomies and zymosan 2 wks after treatment administration. CONCLUSIONS: Adverse effects of intravenous iron supplementation by ferric carboxymaltose seem to be minimal in our animal models. Furthermore, iron appears to be effective in correcting anemia, despite inflammation. Studies of efficacy and safety of iron in critically ill patients are warranted

BARRANCO DE AZUAJE [Material gráfico]

ADQUIRIDA POR EL COLECCIONISTA EN LAS PALMAS DE G.C.FOTO POSTAL DE "FUENTE DE AZUAJE. MOYA. GRAN CANARIA, LAS PALMAS" (COLOREADA)Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte. Subdirección General de Coordinación Bibliotecaria, 201