Community structure in industrial SAT instances

Modern SAT solvers have experienced a remarkable progress on solving industrial instances. It is believed that most of these successful techniques exploit the underlying structure of industrial instances. Recently, there have been some attempts to analyze the structure of industrial SAT instances in terms of complex networks, with the aim of explaining the success of SAT solving techniques, and possibly improving them. In this paper, we study the community structure, or modularity, of industrial SAT instances. In a graph with clear community structure, or high modularity, we can find a partition of its nodes into communities such that most edges connect variables of the same community. Representing SAT instances as graphs, we show that most application benchmarks are characterized by a high modularity. On the contrary, random SAT instances are closer to the classical Erdös-Rényi random graph model, where no structure can be observed. We also analyze how this structure evolves by the effects of the execution of a CDCL SAT solver, and observe that new clauses learned by the solver during the search contribute to destroy the original structure of the formula. Motivated by this observation, we finally present an application that exploits the community structure to detect relevant learned clauses, and we show that detecting these clauses results in an improvement on the performance of the SAT solver. Empirically, we observe that this improves the performance of several SAT solvers on industrial SAT formulas, especially on satisfiable instances.Peer ReviewedPostprint (published version

Stroke prevalence among the Spanish elderly: an analysis based on screening surveys

BACKGROUND: This study sought to describe stroke prevalence in Spanish elderly populations and compare it against that of other European countries. METHODS: We identified screening surveys -both published and unpublished- in Spanish populations, which fulfilled specific quality requirements and targeted prevalence of stroke in populations aged 70 years and over. Surveys covering seven geographically different populations with prevalence years in the period 1991–2002 were selected, and the respective authors were then asked to provide descriptions of the methodology and raw age-specific data by completing a questionnaire. In addition, five reported screening surveys in European populations furnished useful data for comparison purposes. Prevalence data were combined, using direct adjustment and logistic regression. RESULTS: The overall study population, resident in central and north-eastern Spain, totalled 10,647 persons and yielded 715 cases. Age-adjusted prevalences, using the European standard population, were 7.3% for men, 5.6% for women, and 6.4% for both sexes. Prevalence was significantly lower in women, OR 0.79 95% CI 0.68–0.93, increased with age, particularly among women, and displayed a threefold spatial variation with statistically significant differences. Prevalences were highest, 8.7%, in suburban, and lowest, 3.8%, in rural populations. Compared to pooled Spanish populations, statistically significant differences were seen in eight Italian populations, OR 1.39 95%CI (1.18–1.64), and in Kungsholmen, Sweden, OR 0.40 95%CI (0.27–0.58). CONCLUSION: Prevalence in central and north-eastern Spain is higher in males and in suburban areas, and displays a threefold geographic variation, with women constituting the majority of elderly stroke sufferers. Compared to reported European data, stroke prevalence in Spain can be said to be medium and presents similar age- and sex-specific traits

A genome-wide association study identifies risk alleles in plasminogen and P4HA2 associated with giant cell arteritis

Giant cell arteritis (GCA) is the most common form of vasculitis in individuals older than 50 years in Western countries. To shed light onto the genetic background influencing susceptibility for GCA, we performed a genome-wide association screening in a well-powered study cohort. After imputation, 1,844,133 genetic variants were analysed in 2,134 cases and 9,125 unaffected controls from ten independent populations of European ancestry. Our data confirmed HLA class II as the strongest associated region (independent signals: rs9268905, P = 1.94E-54, per-allele OR = 1.79; and rs9275592, P = 1.14E-40, OR = 2.08). Additionally, PLG and P4HA2 were identified as GCA risk genes at the genome-wide level of significance (rs4252134, P = 1.23E-10, OR = 1.28; and rs128738, P = 4.60E-09, OR = 1.32, respectively). Interestingly, we observed that the association peaks overlapped with different regulatory elements related to cell types and tissues involved in the pathophysiology of GCA. PLG and P4HA2 are involved in vascular remodelling and angiogenesis, suggesting a high relevance of these processes for the pathogenic mechanisms underlying this type of vasculitis

A Large-Scale Genetic Analysis Reveals a Strong Contribution of the HLA Class II Region to Giant Cell Arteritis Susceptibility

We conducted a large-scale genetic analysis on giant cell arteritis (GCA), a polygenic immune-mediated vasculitis. A case-control cohort, comprising 1,651 case subjects with GCA and 15,306 unrelated control subjects from six different countries of European ancestry, was genotyped by the Immunochip array. We also imputed HLA data with a previously validated imputation method to perform a more comprehensive analysis of this genomic region. The strongest association signals were observed in the HLA region, with rs477515 representing the highest peak (p = 4.05 × 10−40, OR = 1.73). A multivariate model including class II amino acids of HLA-DRβ1 and HLA-DQα1 and one class I amino acid of HLA-B explained most of the HLA association with GCA, consistent with previously reported associations of classical HLA alleles like HLA-DRB1∗04. An omnibus test on polymorphic amino acid positions highlighted DRβ1 13 (p = 4.08 × 10−43) and HLA-DQα1 47 (p = 4.02 × 10−46), 56, and 76 (both p = 1.84 × 10−45) as relevant positions for disease susceptibility. Outside the HLA region, the most significant loci included PTPN22 (rs2476601, p = 1.73 × 10−6, OR = 1.38), LRRC32 (rs10160518, p = 4.39 × 10−6, OR = 1.20), and REL (rs115674477, p = 1.10 × 10−5, OR = 1.63). Our study provides evidence of a strong contribution of HLA class I and II molecules to susceptibility to GCA. In the non-HLA region, we confirmed a key role for the functional PTPN22 rs2476601 variant and proposed other putative risk loci for GCA involved in Th1, Th17, and Treg cell function

Heterogeneous contributions of change in population distribution of body mass index to change in obesity and underweight NCD Risk Factor Collaboration (NCD-RisC)

From 1985 to 2016, the prevalence of underweight decreased, and that of obesity and severe obesity increased, in most regions, with significant variation in the magnitude of these changes across regions. We investigated how much change in mean body mass index (BMI) explains changes in the prevalence of underweight, obesity, and severe obesity in different regions using data from 2896 population-based studies with 187 million participants. Changes in the prevalence of underweight and total obesity, and to a lesser extent severe obesity, are largely driven by shifts in the distribution of BMI, with smaller contributions from changes in the shape of the distribution. In East and Southeast Asia and sub-Saharan Africa, the underweight tail of the BMI distribution was left behind as the distribution shifted. There is a need for policies that address all forms of malnutrition by making healthy foods accessible and affordable, while restricting unhealthy foods through fiscal and regulatory restrictions

A new algorithm for Weighted Partial MaxSAT

We present and implement a Weighted Partial MaxSAT solver based on successive calls to a SAT solver. We prove the correctness of our algorithm and compare our solver with other Weighted Partial MaxSAT solvers.Peer Reviewe

A new algorithm for Weighted Partial MaxSAT

We present and implement a Weighted Partial MaxSAT solver based on successive calls to a SAT solver. We prove the correctness of our algorithm and compare our solver with other Weighted Partial MaxSAT solvers.Peer ReviewedPostprint (published version

A new algorithm for Weighted Partial MaxSAT

We present and implement a Weighted Partial MaxSAT solver based on successive calls to a SAT solver. We prove the correctness of our algorithm and compare our solver with other Weighted Partial MaxSAT solvers.Peer Reviewe

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Towards industrial-like random SAT instances

We focus on the random generation of SAT instances that have computational properties that are similar to real-world instances. It is known that industrial instances, even with a great number of variables, can be solved by a clever solver in a reasonable amount of time. This is not possible, in general, with classical randomly generated instances. We provide different generation models of SAT instances, extending the uniform and regular 3-CNF models. They are based on the use of non-uniform probability distributions to select variables. Our last model also uses a mechanism to produce clauses of different lengths as in industrial instances. We show the existence of the phase transition phenomena for our models and we study the hardness of the generated instances as a function of the parameters of the probability distributions. We prove that, with these parameters we can adjust the difficulty of the problems in the phase transition point. We measure hardness in terms of the performance of different solvers. We show how these models will allow us to generate random instances similar to industrial instances, of interest for testing purposes