2,176 research outputs found

    The computation of previously inaccessible digits of π<sup>2</sup> and Catalan's constant

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    We recently concluded a very large mathematical calculation, uncovering objects that until recently were widely considered to be forever inaccessible to computation. Our computations stem from the “BBP” formula for π, which was discovered in 1997 using a computer program implementing the “PSLQ” integer relation algorithm. This formula has the remarkable property that it permits one to directly calculate binary digits of π, beginning at an arbitrary position d, without needing to calculate any of the first d - 1 digits. Since 1997 numerous other BBP-type formulas have been discovered for various mathematical constants, including formulas for π² (both in binary and ternary bases) and for Catalan’s constant. In this article we describe the computation of base-64 digits of π², base-729 digits of π², and base-4096 digits of Catalan’s constant, in each case beginning at the ten trillionth place, computations that involved a total of approximately 1:549 x 1019 floating-point operations. We also discuss connections between BBP-type formulas and the age-old unsolved questions of whether and why constants such as π; π²; log 2, and Catalan’s constant have “random” digits

    Benchmark based on application signature to analyze and predict their behavior

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    Currently, there are benchmark sets that measure the performance of HPC systems under specific computing and communication properties. These benchmarks represent the kernels of applications that measure specific hardware components. If the user’s application is not represented by any benchmark, it is not possible to obtain an equivalent performance metric. In this work, we propose a benchmark based on the signature of an MPI application obtained by the PAS2P method. PAS2P creates the application signature in order to predict the execution time, which we believe will be very adjusted in relation to the execution time of the full application. The signature has two performance qualities: the bounded time to execute it (a benchmark property) and the quality of prediction. Therefore, we propose to extend the signature by giving the benchmark capacities such as the efficiency of the application over the HPC system. The performance metrics will be performed by the benchmark proposed. The experimentation validates our proposal with an average error of prediction close to 7%.Instituto de Investigación en Informátic

    A 2D algorithm with asymmetric workload for the UPC conjugate gradient method

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    This is a post-peer-review, pre-copyedit version of an article published in Journal of Supercomputing. The final authenticated version is available online at: https://doi.org/10.1007/s11227-014-1300-0[Abstract] This paper examines four different strategies, each one with its own data distribution, for implementing the parallel conjugate gradient (CG) method and how they impact communication and overall performance. Firstly, typical 1D and 2D distributions of the matrix involved in CG computations are considered. Then, a new 2D version of the CG method with asymmetric workload, based on leaving some threads idle during part of the computation to reduce communication, is proposed. The four strategies are independent of sparse storage schemes and are implemented using Unified Parallel C (UPC), a Partitioned Global Address Space (PGAS) language. The strategies are evaluated on two different platforms through a set of matrices that exhibit distinct sparse patterns, demonstrating that our asymmetric proposal outperforms the others except for one matrix on one platform.Ministerio de EconomĂ­a y Competitividad; TIN2013-42148-PXunta de Galicia; GRC2013/055United States. Department of Energy; DEAC03-76SF0009

    Genome-wide association study of male sexual orientation

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    Family and twin studies suggest that genes play a role in male sexual orientation. We conducted a genome-wide association study (GWAS) of male sexual orientation on a primarily European ancestry sample of 1,077 homosexual men and 1,231 heterosexual men using Affymetrix single nucleotide polymorphism (SNP) arrays. We identified several SNPs with p < 10 -5 , including regions of multiple supporting SNPs on chromosomes 13 (minimum p = 7.5 Ă— 10 -7 ) and 14 (p = 4.7 Ă— 10 -7 ). The genes nearest to these peaks have functions plausibly relevant to the development of sexual orientation. On chromosome 13, SLITRK6 is a neurodevelopmental gene mostly expressed in the diencephalon, which contains a region previously reported as differing in size in men by sexual orientation. On chromosome 14, TSHR genetic variants in intron 1 could conceivably help explain past findings relating familial atypical thyroid function and male homosexuality. Furthermore, skewed X chromosome inactivation has been found in the thyroid condition, Graves' disease, as well as in mothers of homosexual men. On pericentromeric chromosome 8 within our previously reported linkage peak, we found support (p = 4.1 Ă— 10 -3 ) for a SNP association previously reported (rs77013977, p = 7.1 Ă— 10 -8 ), with the combined analysis yielding p = 6.7 Ă— 10 -9 , i.e., a genome-wide significant association

    Genetic and Environmental Influences on Female Sexual Orientation, Childhood Gender Typicality and Adult Gender Identity

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    Background: Human sexual orientation is influenced by genetic and non-shared environmental factors as are two important psychological correlates – childhood gender typicality (CGT) and adult gender identity (AGI). However, researchers have been unable to resolve the genetic and non-genetic components that contribute to the covariation between these traits, particularly in women. Methodology/Principal Findings: Here we performed a multivariate genetic analysis in a large sample of British female twins (N = 4,426) who completed a questionnaire assessing sexual attraction, CGT and AGI. Univariate genetic models indicated modest genetic influences on sexual attraction (25%), AGI (11%) and CGT (31%). For the multivariate analyses, a common pathway model best fitted the data. Conclusions/Significance: This indicated that a single latent variable influenced by a genetic component and common nonshared environmental component explained the association between the three traits but there was substantial measurement error. These findings highlight common developmental factors affecting differences in sexual orientation
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