56,023 research outputs found

    Simplifying Dependent Reductions in the Polyhedral Model

    Full text link
    A Reduction -- an accumulation over a set of values, using an associative and commutative operator -- is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and financial analytics. Contemporary polyhedral-based compilation techniques make it possible to optimize reductions, such as prefix sums, in which each component of the reduction's output potentially shares computation with another component in the reduction. Therefore an optimizing compiler can identify the computation shared between multiple components and generate code that computes the shared computation only once. These techniques, however, do not support reductions that -- when phrased in the language of the polyhedral model -- span multiple dependent statements. In such cases, existing approaches can generate incorrect code that violates the data dependences of the original, unoptimized program. In this work, we identify and formalize the optimization of dependent reductions as an integer bilinear program. We present a heuristic optimization algorithm that uses an affine sequential schedule of the program to determine how to simplfy reductions yet still preserve the program's dependences. We demonstrate that the algorithm provides optimal complexity for a set of benchmark programs from the literature on probabilistic inference algorithms, whose performance critically relies on simplifying these reductions. The complexities for 10 of the 11 programs improve siginifcantly by factors at least of the sizes of the input data, which are in the range of 10410^4 to 10610^6 for typical real application inputs. We also confirm the significance of the improvement by showing speedups in wall-clock time that range from 1.1x1.1\text{x} to over 106x10^6\text{x}

    AdS4 black holes from M-theory

    Full text link
    We consider the BPS conditions of eleven dimensional supergravity, restricted to an appropriate ansatz for black holes in four non-compact directions. Assuming the internal directions to be described by a circle fibration over a K\"ahler manifold and considering the case where the complex structure moduli are frozen, we recast the resulting flow equations in terms of polyforms on this manifold. The result is a set of equations that are in direct correspondence with those of gauged supergravity models in four dimensions consistent with our simplifying assumptions. In view of this correspondence even for internal manifolds that do not correspond to known consistent truncations, we comment on the possibility of obtaining gauged supergravities from reductions on K\"ahler manifolds.Comment: 32 pages, v2: references addes, typos correcte

    Discrete torsion in non-geometric orbifolds and their open-string descendants

    Get PDF
    We discuss some Z_N^L x Z_N^R orbifold compactifications of the type IIB superstring to D= 4,6 dimensions and their type I descendants. Although the Z_N^L x Z_N^R generators act asymmetrically on the chiral string modes, they result into left-right symmetric models that admit sensible unorientable reductions. We carefully work out the phases that appear in the modular transformations of the chiral amplitudes and identify the possibility of introducing discrete torsion. We propose a simplifying ansatz for the construction of the open-string descendants in which the transverse-channel Klein-bottle, annulus and Moebius-strip amplitudes are numerically identical in the proper parametrization of the world-sheet. A simple variant of the ansatz for the Z_2^L x Z_2^R orbifold gives rise to models with supersymmetry breaking in the open-string sector.Comment: 21 pages, Latex, minor typos corrected, references added, version to appear in Nuclear Physics

    The potential impact of a Tier 4 immigration cap on UK and EU-domiciled students’ fees (Current issues note 28)

    Get PDF
    "This note attempts to review the potential financial impact of a reduction in non-EU students on Higher Education Institutions (HEIs) in London. The Government has proposed reducing the number of non-EU students permitted to enter the UK under the Tier 4 student visa entry route. However, any reduction in the number of non-EU students allowed to study in London will have financial impacts for the capital’s HEIs. For the majority of universities non-EU student fees now represent between 10% and 30% of total income. Indeed, fee income from international students is estimated to amount to around £2.4 billion for HEIs in England and Wales. This paper examines one way of assessing the scale of this direct financial impact." - Page 2

    Measuring progress in the costs of bureaucracy : report to the Bureaucracy Review Group

    Get PDF
    • …
    corecore