On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers

Concussion knowledge and experience among Welsh amateur rugby union coaches and referees

Background Rugby union is a collision sport where participants are at high risk of sustaining a concussion. In settings where there is little qualified medical supervision, certain stakeholders (eg, coaches and officials) should possess sufficient knowledge in regard to the recognition and management of concussion. Aim The aim of this study was to assess the knowledge and experience of various aspects of concussion among coaches and referees involved in Welsh amateur rugby union. Methods A questionnaire was distributed to 1843 coaches and 420 referees. Results A total of 333 coaches and 283 referees completed the questionnaire (18% and 68% response rates, respectively). Participants exhibited greater knowledge of concussion symptom recognition relative to knowledge of both the consequences of concussion and associated return-to-play protocols, both of which could be considered poor. There were no differences in knowledge levels between coaches and referees or between participants with or without a history of concussion. Two-thirds of participants incorrectly believed that headgear could prevent concussion, and nearly 30% of coaches reported having witnessed other coaches allowing a potentially concussed player to continue playing. Conclusions Identification of several misconceptions indicates that concussion management within Welsh amateur rugby union needs to be improved, warranting a multi-faceted educational intervention

Accurate masses and radii of normal stars: modern results and applications

This paper presents and discusses a critical compilation of accurate, fundamental determinations of stellar masses and radii. We have identified 95 detached binary systems containing 190 stars (94 eclipsing systems, and alpha Centauri) that satisfy our criterion that the mass and radius of both stars be known to 3% or better. To these we add interstellar reddening, effective temperature, metal abundance, rotational velocity and apsidal motion determinations when available, and we compute a number of other physical parameters, notably luminosity and distance. We discuss the use of this information for testing models of stellar evolution. The amount and quality of the data also allow us to analyse the tidal evolution of the systems in considerable depth, testing prescriptions of rotational synchronisation and orbital circularisation in greater detail than possible before. The new data also enable us to derive empirical calibrations of M and R for single (post-) main-sequence stars above 0.6 M(Sun). Simple, polynomial functions of T(eff), log g and [Fe/H] yield M and R with errors of 6% and 3%, respectively. Excellent agreement is found with independent determinations for host stars of transiting extrasolar planets, and good agreement with determinations of M and R from stellar models as constrained by trigonometric parallaxes and spectroscopic values of T(eff) and [Fe/H]. Finally, we list a set of 23 interferometric binaries with masses known to better than 3%, but without fundamental radius determinations (except alpha Aur). We discuss the prospects for improving these and other stellar parameters in the near future.Comment: 56 pages including figures and tables. To appear in The Astronomy and Astrophysics Review. Ascii versions of the tables will appear in the online version of the articl

Hip and spine bone mineral density are greater in master sprinters, but not endurance runners compared with non-athletic controls

Summary: We examined bone density in older athletes and controls. Sprinters had greater hip and spine bone density than endurance athletes and controls, whereas values were similar in the latter two groups. These results could not be explained by differences in impact, muscle size or power between sprint and endurance athletes. Purpose: We examined the relationship between prolonged participation in regular sprint or endurance running and skeletal health at key clinical sites in older age, and the factors responsible for any associations which we observed. Methods: We recruited 38 master sprint runners (28 males, 10 females, mean age 71 ± 7 years), 149 master endurance runners (111 males, 38 females, mean age 70 ± 6 years) and 59 non-athletic controls (29 males, 30 females, mean age 74 ± 5 years). Dual X-ray absorptiometry was used to assess hip and spine bone mineral density (BMD), body composition (lean and fat mass), whilst jump power was assessed with jumping mechanography. In athletes, vertical impacts were recorded over 7 days from a waist-worn accelerometer, and details of starting age, age-graded performance and training hours were recorded. Results: In ANOVA models adjusted for sex, age, height, body composition, and jump power, sprinter hip BMD was 10 and 14% greater than that of endurance runners and controls respectively. Sprinter spine BMD was also greater than that of both endurance runners and controls. There were no differences in hip or spine BMD between endurance runners and controls. Stepwise regression showed only discipline (sprint/endurance), sex, and age as predictors of athlete spine BMD, whilst these variables and starting age were predictive of hip BMD. Conclusions: Regular running is associated with greater BMD at the fracture-prone hip and spine sites in master sprinters but not endurance runners. These benefits cannot be explained by indicators of mechanical loading measured in this study including vertical impacts, body composition or muscular output

Dynamics of Disks and Warps

This chapter reviews theoretical work on the stellar dynamics of galaxy disks. All the known collective global instabilities are identified, and their mechanisms described in terms of local wave mechanics. A detailed discussion of warps and other bending waves is also given. The structure of bars in galaxies, and their effect on galaxy evolution, is now reasonably well understood, but there is still no convincing explanation for their origin and frequency. Spiral patterns have long presented a special challenge, and ideas and recent developments are reviewed. Other topics include scattering of disk stars and the survival of thin disks.Comment: Chapter accepted to appear in Planets, Stars and Stellar Systems, vol 5, ed G. Gilmore. 32 pages, 17 figures. Includes minor corrections made in proofs. Uses emulateapj.st

Fine-mapping of prostate cancer susceptibility loci in a large meta-analysis identifies candidate causal variants.

Prostate cancer is a polygenic disease with a large heritable component. A number of common, low-penetrance prostate cancer risk loci have been identified through GWAS. Here we apply the Bayesian multivariate variable selection algorithm JAM to fine-map 84 prostate cancer susceptibility loci, using summary data from a large European ancestry meta-analysis. We observe evidence for multiple independent signals at 12 regions and 99 risk signals overall. Only 15 original GWAS tag SNPs remain among the catalogue of candidate variants identified; the remainder are replaced by more likely candidates. Biological annotation of our credible set of variants indicates significant enrichment within promoter and enhancer elements, and transcription factor-binding sites, including AR, ERG and FOXA1. In 40 regions at least one variant is colocalised with an eQTL in prostate cancer tissue. The refined set of candidate variants substantially increase the proportion of familial relative risk explained by these known susceptibility regions, which highlights the importance of fine-mapping studies and has implications for clinical risk profiling