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 $\ell\sim200$ 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 $\rho\approx0.4$ or greater for $\ell<20$ and $f_{\mathrm{sky}}\geq0.5$, dropping to $\rho\approx0.2$ for $30<\ell<200$. (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 $\leq \ell \leq$110 is $0.3_{-0.2}^{+0.3}$. 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

Supersymmetry Breaking and Moduli Stabilization with Anomalous U(1) Gauge Symmetry

We examine the effects of anomalous U(1)_A gauge symmetry on soft supersymmetry breaking terms while incorporating the stabilization of the modulus-axion multiplet responsible for the Green-Schwarz (GS) anomaly cancellation mechanism. In case of the KKLT stabilization of the GS modulus, soft terms are determined by the GS modulus mediation, the anomaly mediation and the U(1)_A mediation which are generically comparable to each other, thereby yielding the mirage mediation pattern of superparticle masses at low energy scale. Independently of the mechanism of moduli stabilization and supersymmetry breaking, the U(1)_A D-term potential can not be an uplifting potential for de Sitter vacuum when the gravitino mass is smaller than the Planck scale by many orders of magnitude. We also discuss some features of the supersymmetry breaking by red-shifted anti-brane which is a key element of the KKLT moduli stabilization.Comment: 32 pages; references are adde