56,023 research outputs found
Simplifying Dependent Reductions in the Polyhedral Model
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 to
for typical real application inputs. We also confirm the significance of
the improvement by showing speedups in wall-clock time that range from
to over
AdS4 black holes from M-theory
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
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)
"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 ÂŁ2.4 billion for HEIs in England and Wales.
This paper examines one way of assessing the scale of this direct financial impact." - Page 2
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