Unrestricted Termination and Non-Termination Arguments for Bit-Vector Programs

Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often restricted to finding linear ranking functions over mathematical integers. This class of functions is insufficient for proving termination of many terminating programs, and furthermore a termination argument for a program operating on mathematical integers does not always lead to a termination argument for the same program operating on fixed-width machine integers. We propose a termination analysis able to generate nonlinear, lexicographic ranking functions and nonlinear recurrence sets that are correct for fixed-width machine arithmetic and floating-point arithmetic Our technique is based on a reduction from program \emph{termination} to second-order \emph{satisfaction}. We provide formulations for termination and non-termination in a fragment of second-order logic with restricted quantification which is decidable over finite domains. The resulted technique is a sound and complete analysis for the termination of finite-state programs with fixed-width integers and IEEE floating-point arithmetic

Model for nucleation in GaAs homoepitaxy derived from first principles

The initial steps of MBE growth of GaAs on beta 2-reconstructed GaAs(001) are investigated by performing total energy and electronic structure calculations using density functional theory and a repeated slab model of the surface. We study the interaction and clustering of adsorbed Ga atoms and the adsorption of As_2 molecules onto Ga atom clusters adsorbed on the surface. The stable nuclei consist of bound pairs of Ga adatoms, which originate either from dimerization or from an indirect interaction mediated through the substrate reconstruction. As_2 adsorption is found to be strongly exothermic on sites with a square array of four Ga dangling bonds. Comparing two scenarios where the first As_2 gets incorporated in the incomplete surface layer, or alternatively in a new added layer, we find the first scenario to be preferable. In summary, the calculations suggest that nucleation of a new atomic layer is most likely on top of those surface regions where a partial filling of trenches in the surface has occurred before.Comment: 8 pages, 14 figures, Submitted to Phys. Rev. B (December 15, 1998). Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Diagnosis delayed: health profile differences between women with undiagnosed polycystic ovary syndrome and those with a clinical diagnosis by age 35 years

STUDY QUESTION: Are reproductive, metabolic or psychological health profiles of women with clinically diagnosed polycystic ovary syndrome (PCOS) different from those with undiagnosed PCOS? SUMMARY ANSWER: Obtaining a clinical diagnosis of PCOS is strongly linked to the experience of fertility problems, but not clinical depression or poor metabolic health, although these were highly prevalent in women with PCOS irrespective of when they were diagnosed. WHAT IS KNOWN ALREADY: PCOS is an endocrine disorder that is relative common, but heterogeneous in presentation. This may impact on the pathways to diagnosis and timely treatment. STUDY DESIGN, SIZE, DURATION: A cross-sectional analysis of a community-based cohort of 974 women, established retrospectively when women were around 30 years of age. PARTICIPANTS/MATERIALS, SETTING, METHODS: In this cohort of women born in Adelaide, South Australia, half of women who met the Rotterdam criteria for PCOS were previously undiagnosed. We compared women with prior clinical diagnosis of PCOS, those diagnosed through participation in this research, and the remainder in the cohort. Sociodemographic characteristics, reproductive, metabolic and psychological health, including medical conditions and medications were considered. Logistic regression was undertaken to identify independent predictors of prior clinical diagnosis. MAIN RESULTS AND THE ROLE OF CHANCE: There were 56 women with a prior clinical diagnosis of PCOS (5.7%) and a further 64 (6.6%) were undiagnosed until study entry. The great majority of women with a prior diagnosis of PCOS reported having had problems with periods (95%) and excess body hair (63%). Corresponding proportions for women undiagnosed until study participation were slightly lower (81% and 45%, respectively). Although the proportion of women attempting or achieving pregnancy was similar across all groups, those with a prior diagnosis of PCOS were four times more likely to have reported difficulties becoming pregnant than those undiagnosed (odds ratio ¼ 4.05, 95% CI 1.74–9.45) and frequently sought medical assistance. Metabolic problems were higher in both PCOS groups compared to women without PCOS. In both PCOS groups, the prevalence of clinical depression was 50% higher than in those with no PCOS (P ¼ 0.021). LIMITATIONS, REASONS FOR CAUTION: The number of women who were diagnosed with PCOS both prior to and during the study limited statistical power available to detect modest differences between the PCOS groups. Some women in the group classified as not having PCOS may have remained undiagnosed, but any bias from this source would contribute to more conservative findings. WIDER IMPLICATIONS OF THE FINDINGS: Findings reinforce the need for early detection of PCOS symptoms from adolescence, ensuring timely diagnosis and appropriate health care. The high prevalence of depression among clinically diagnosed and undiagnosed women with PCOS suggests this is a feature of the condition and supports recent recommendations in the international PCOS guidelines to screen all women with PCOS for depression and anxiety.Renae C. Fernandez, Vivienne M. Moore, Alice R. Rumbold, Melissa J. Whitrow, Jodie C. Avery, and Michael J. Davie

Comparison of adaptive multiple phenotype association tests using summary statistics in genome-wide association studies

Genome-wide association studies have been successful mapping loci for individual phenotypes, but few studies have comprehensively interrogated evidence of shared genetic effects across multiple phenotypes simultaneously. Statistical methods have been proposed for analyzing multiple phenotypes using summary statistics, which enables studies of shared genetic effects while avoiding challenges associated with individual-level data sharing. Adaptive tests have been developed to maintain power against multiple alternative hypotheses because the most powerful single-alternative test depends on the underlying structure of the associations between the multiple phenotypes and a single nucleotide polymorphism (SNP). Here we compare the performance of six such adaptive tests: two adaptive sum of powered scores (aSPU) tests, the unified score association test (metaUSAT), the adaptive test in a mixed-models framework (mixAda) and two principal-component-based adaptive tests (PCAQ and PCO). Our simulations highlight practical challenges that arise when multivariate distributions of phenotypes do not satisfy assumptions of multivariate normality. Previous reports in this context focus on low minor allele count (MAC) and omit the aSPU test, which relies less than other methods on asymptotic and distributional assumptions. When these assumptions are not satisfied, particularly when MAC is low and/or phenotype covariance matrices are singular or nearly singular, aSPU better preserves type I error, sometimes at the cost of decreased power. We illustrate this trade-off with multiple phenotype analyses of six quantitative electrocardiogram traits in the Population Architecture using Genomics and Epidemiology (PAGE) study

Benchmark Test Calculation of a Four-Nucleon Bound State

In the past, several efficient methods have been developed to solve the Schroedinger equation for four-nucleon bound states accurately. These are the Faddeev-Yakubovsky, the coupled-rearrangement-channel Gaussian-basis variational, the stochastic variational, the hyperspherical variational, the Green's function Monte Carlo, the no-core shell model and the effective interaction hyperspherical harmonic methods. In this article we compare the energy eigenvalue results and some wave function properties using the realistic AV8' NN interaction. The results of all schemes agree very well showing the high accuracy of our present ability to calculate the four-nucleon bound state.Comment: 17 pages, 1 figure

Ancestry-specific associations identified in genome-wide combined-phenotype study of red blood cell traits emphasize benefits of diversity in genomics

Background: Quantitative red blood cell (RBC) traits are highly polygenic clinically relevant traits, with approximately 500 reported GWAS loci. The majority of RBC trait GWAS have been performed in European- or East Asian-ancestry populations, despite evidence that rare or ancestry-specific variation contributes substantially to RBC trait heritability. Recently developed combined-phenotype methods which leverage genetic trait correlation to improve statistical power have not yet been applied to these traits. Here we leveraged correlation of seven quantitative RBC traits in performing a combined-phenotype analysis in a multi-ethnic study population. Results: We used the adaptive sum of powered scores (aSPU) test to assess combined-phenotype associations between ~ 21 million SNPs and seven RBC traits in a multi-ethnic population (maximum n = 67,885 participants; 24% African American, 30% Hispanic/Latino, and 43% European American; 76% female). Thirty-nine loci in our multi-ethnic population contained at least one significant association signal (p 5%) across all ancestral populations. Nineteen additional independent association signals were identified at seven known loci (HFE, KIT, HBS1L/MYB, CITED2/FILNC1, ABO, HBA1/2, and PLIN4/5). For example, the HBA1/2 locus contained 14 conditionally independent association signals, 11 of which were previously unreported and are specific to African and Amerindian ancestries. One variant in this region was common in all ancestries, but exhibited a narrower LD block in African Americans than European Americans or Hispanics/Latinos. GTEx eQTL analysis of all independent lead SNPs yielded 31 significant associations in relevant tissues, over half of which were not at the gene immediately proximal to the lead SNP. Conclusion: This work identified seven loci containing multiple independent association signals for RBC traits using a combined-phenotype approach, which may improve discovery in genetically correlated traits. Highly complex genetic architecture at the HBA1/2 locus was only revealed by the inclusion of African Americans and Hispanics/Latinos, underscoring the continued importance of expanding large GWAS to include ancestrally diverse populations. © 2020 The Author(s)

Multi-ethnic genome-wide association study of decomposed cardioelectric phenotypes illustrates strategies to identify and characterize evidence of shared genetic effects for complex traits

Background: We examined how expanding electrocardiographic trait genome-wide association studies to include ancestrally diverse populations, prioritize more precise phenotypic measures, and evaluate evidence for shared genetic effects enabled the detection and characterization of loci. Methods: We decomposed 10 seconds, 12-lead electrocardiograms from 34 668 multi-ethnic participants (15% Black; 30% Hispanic/Latino) into 6 contiguous, physiologically distinct (P wave, PR segment, QRS interval, ST segment, T wave, and TP segment) and 2 composite, conventional (PR interval and QT interval) interval scale traits and conducted multivariable-adjusted, trait-specific univariate genome-wide association studies using 1000-G imputed single-nucleotide polymorphisms. Evidence of shared genetic effects was evaluated by aggregating meta-analyzed univariate results across the 6 continuous electrocardiographic traits using the combined phenotype adaptive sum of powered scores test. Results: We identified 6 novels (CD36, PITX2, EMB, ZNF592, YPEL2, and BC043580) and 87 known loci (adaptive sum of powered score test P<5×10-9). Lead single-nucleotide polymorphism rs3211938 at CD36 was common in Blacks (minor allele frequency=10%), near monomorphic in European Americans, and had effects on the QT interval and TP segment that ranked among the largest reported to date for common variants. The other 5 novel loci were observed when evaluating the contiguous but not the composite electrocardiographic traits. Combined phenotype testing did not identify novel electrocardiographic loci unapparent using traditional univariate approaches, although this approach did assist with the characterization of known loci. Conclusions: Despite including one-third as many participants as published electrocardiographic trait genome-wide association studies, our study identified 6 novel loci, emphasizing the importance of ancestral diversity and phenotype resolution in this era of ever-growing genome-wide association studies

Multi-ethnic genome-wide association analyses of white blood cell and platelet traits in the Population Architecture using Genomics and Epidemiology (PAGE) study

Background: Circulating white blood cell and platelet traits are clinically linked to various disease outcomes and differ across individuals and ancestry groups. Genetic factors play an important role in determining these traits and many loci have been identified. However, most of these findings were identified in populations of European ancestry (EA), with African Americans (AA), Hispanics/Latinos (HL), and other races/ethnicities being severely underrepresented. Results: We performed ancestry-combined and ancestry-specific genome-wide association studies (GWAS) for white blood cell and platelet traits in the ancestrally diverse Population Architecture using Genomics and Epidemiology (PAGE) Study, including 16,201 AA, 21,347 HL, and 27,236 EA participants. We identified six novel findings at suggestive significance (P < 5E-8), which need confirmation, and independent signals at six previously established regions at genome-wide significance (P < 2E-9). We confirmed multiple previously reported genome-wide significant variants in the single variant association analysis and multiple genes using PrediXcan. Evaluation of loci reported from a Euro-centric GWAS indicated attenuation of effect estimates in AA and HL compared to EA populations. Conclusions: Our results highlighted the potential to identify ancestry-specific and ancestry-agnostic variants in participants with diverse backgrounds and advocate for continued efforts in improving inclusion of racially/ethnically diverse populations in genetic association studies for complex traits