110,544 research outputs found
Scalable Task-Based Algorithm for Multiplication of Block-Rank-Sparse Matrices
A task-based formulation of Scalable Universal Matrix Multiplication
Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is
applied to the multiplication of hierarchy-free, rank-structured matrices that
appear in the domain of quantum chemistry (QC). The novel features of our
formulation are: (1) concurrent scheduling of multiple SUMMA iterations, and
(2) fine-grained task-based composition. These features make it tolerant of the
load imbalance due to the irregular matrix structure and eliminate all
artifactual sources of global synchronization.Scalability of iterative
computation of square-root inverse of block-rank-sparse QC matrices is
demonstrated; for full-rank (dense) matrices the performance of our SUMMA
formulation usually exceeds that of the state-of-the-art dense MM
implementations (ScaLAPACK and Cyclops Tensor Framework).Comment: 8 pages, 6 figures, accepted to IA3 2015. arXiv admin note: text
overlap with arXiv:1504.0504
Symmetry groups, semidefinite programs, and sums of squares
We investigate the representation of symmetric polynomials as a sum of
squares. Since this task is solved using semidefinite programming tools we
explore the geometric, algebraic, and computational implications of the
presence of discrete symmetries in semidefinite programs. It is shown that
symmetry exploitation allows a significant reduction in both matrix size and
number of decision variables. This result is applied to semidefinite programs
arising from the computation of sum of squares decompositions for multivariate
polynomials. The results, reinterpreted from an invariant-theoretic viewpoint,
provide a novel representation of a class of nonnegative symmetric polynomials.
The main theorem states that an invariant sum of squares polynomial is a sum of
inner products of pairs of matrices, whose entries are invariant polynomials.
In these pairs, one of the matrices is computed based on the real irreducible
representations of the group, and the other is a sum of squares matrix. The
reduction techniques enable the numerical solution of large-scale instances,
otherwise computationally infeasible to solve.Comment: 38 pages, submitte
Polarized galactic synchrotron and dust emission and their correlation
We present an analysis of the level of polarized dust and synchrotron
emission using the WMAP9 and Planck data. The primary goal of this study is to
inform the assessment of foreground contamination in the cosmic microwave
background (CMB) measurements below from 23 to 353 GHz. We
compute angular power spectra as a function of sky cut based on the Planck 353
GHz polarization maps. Our primary findings are the following. (1) There is a
spatial correlation between the dust emission as measured by Planck at 353 GHz
and the synchrotron emission as measured by WMAP at 23 GHz with
or greater for and ,
dropping to for . (2) A simple foreground model
with dust, synchrotron, and their correlation fits well to all possible cross
spectra formed with the WMAP and Planck 353 GHz data given the current
uncertainties. (3) In the 50 cleanest region of the polarized dust map, the
ratio of synchrotron to dust amplitudes at 90 GHz for 50 110 is
. Smaller regions of sky can be cleaner although the
uncertainties in our knowledge of synchrotron emission are larger. A
high-sensitivity measurement of synchrotron below 90 GHz will be important for
understanding all the components of foreground emission near 90 GHz.Comment: 10 pages, 8 figures; Published in JCAP. Source masks updated, minor
change
A Critique of the Odious Debt Doctrine
Choi and Posner indicate that it is unclear whether the doctrine will improve the welfare of the population that might be subject to a dictatorship in terms of the odious debt doctrine. The traditional backward-looking defense of the odious debt doctrine, which suggests that the doctrine is costless because it releases a suffering population from an unjust debt, is seriously incomplete. Although in specific cases the benefits of loan sanctions may exceed the costs, the defenders of the doctrine have not made the empirical case that the net benefits are sufficiently high in the aggregate as to warrant routine application of loan sanctions to odious dictators. Therefore, in the absence of such a showing, there is no reason to think that the odious debt doctrine would be a desirable rule of international law
The Gaugino Code
Gauginos might play a crucial role in the search for supersymmetry at the
Large Hadron Collider (LHC). Mass predictions for gauginos are rather robust
and often related to the values of the gauge couplings. We analyse the ratios
of gaugino masses in the LHC energy range for various schemes of supersymmetry
breakdown and mediation. Three distinct mass patterns emerge.Comment: 42 pages, Latex; a discussion of deflected anomaly mediation added,
references adde
CP violation at one loop in the polarization-independent chargino production in e+e- collisions
Recently Osland and Vereshagin noticed, based on sample calculations of some
box diagrams, that in unpolarised e+e- collisions CP-odd effects in the
non-diagonal chargino-pair production process are generated at one-loop. Here
we perform a full one-loop analysis of these effects and point out that in some
cases the neglected vertex and self-energy contributions may play a dominant
role. We also show that CP asymmetries in chargino production are sensitive not
only to the phase of mu parameter in the chargino sector but also to the phase
of stop trilinear coupling A_t.Comment: 14 pages, 5 figure
p-Wave Resonant Bose Gas: A Finite-Momentum Spinor Superfluid
We show that a degenerate gas of two-species bosonic atoms interacting
through a p-wave Feshbach resonance (as realized in, e.g., a 85Rb-87Rb mixture)
exhibits a finite-momentum atomic-molecular superfluid (AMSF), sandwiched by a
molecular p-wave (orbital spinor) superfluid and by an s-wave atomic superfluid
at large negative and positive detunings, respectively. The magnetic field can
be used to tune the modulation wave vector of the AMSF state, as well as to
drive quantum phase transitions in this rich system.Comment: updated version published in PRL, with minor typos correcte
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