Scheduling optimization of parallel linear algebra algorithms using Supervised Learning

Linear algebra algorithms are used widely in a variety of domains, e.g machine learning, numerical physics and video games graphics. For all these applications, loop-level parallelism is required to achieve high performance. However, finding the optimal way to schedule the workload between threads is a non-trivial problem because it depends on the structure of the algorithm being parallelized and the hardware the executable is run on. In the realm of Asynchronous Many Task runtime systems, a key aspect of the scheduling problem is predicting the proper chunk-size, where the chunk-size is defined as the number of iterations of a for-loop assigned to a thread as one task. In this paper, we study the applications of supervised learning models to predict the chunk-size which yields maximum performance on multiple parallel linear algebra operations using the HPX backend of Blaze's linear algebra library. More precisely, we generate our training and tests sets by measuring performance of the application with different chunk-sizes for multiple linear algebra operations; vector-addition, matrix-vector-multiplication, matrix-matrix addition and matrix-matrix-multiplication. We compare the use of logistic regression, neural networks and decision trees with a newly developed decision tree based model in order to predict the optimal value for chunk-size. Our results show that classical decision trees and our custom decision tree model are able to forecast a chunk-size which results in good performance for the linear algebra operations.Comment: Accepted at HPCML1

Bogoliubov modes of a dipolar condensate in a cylindrical trap

The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation

The optical depth of the Universe to ultrahigh energy cosmic ray scattering in the magnetized large scale structure

This paper provides an analytical description of the transport of ultrahigh energy cosmic rays in an inhomogeneously magnetized intergalactic medium. This latter is modeled as a collection of magnetized scattering centers such as radio cocoons, magnetized galactic winds, clusters or magnetized filaments of large scale structure, with negligible magnetic fields in between. Magnetic deflection is no longer a continuous process, it is rather dominated by scattering events. We study the interaction between high energy cosmic rays and the scattering agents. We then compute the optical depth of the Universe to cosmic ray scattering and discuss the phenomological consequences for various source scenarios. For typical parameters of the scattering centers, the optical depth is greater than unity at 5x10^{19}eV, but the total angular deflection is smaller than unity. One important consequence of this scenario is the possibility that the last scattering center encountered by a cosmic ray be mistaken with the source of this cosmic ray. In particular, we suggest that part of the correlation recently reported by the Pierre Auger Observatory may be affected by such delusion: this experiment may be observing in part the last scattering surface of ultrahigh energy cosmic rays rather than their source population. Since the optical depth falls rapidly with increasing energy, one should probe the arrival directions of the highest energy events beyond 10^{20}eV on an event by event basis to circumvent this effect.Comment: version to appear in PRD; substantial improvements: extended introduction, sections added on angular images and on direction dependent effects with sky maps of optical depth, enlarged discussion of Auger results (conclusions unchanged); 27 pages, 9 figure

On The Origin of Very High Energy Cosmic Rays

We discuss the most recent developments in our understanding of the acceleration and propagation of cosmic rays up to the highest energies. In particular we specialize our discussion to three issues: 1) developments in the theory of particle acceleration at shock waves; 2) the transition from galactic to extragalactic cosmic rays; 3) implications of up-to-date observations for the origin of ultra high energy cosmic rays (UHECRs).Comment: Invited Review Article to appear in Modern Physics Letters A, Review Sectio

Static and Dry Friction due to Multiscale Surface Roughness

It is shown on the basis of scaling arguments that a disordered interface between two elastic solids will quite generally exhibit static and "dry friction" (i.e., kinetic friction which does not vanish as the sliding velocity approaches zero), because of Tomlinson model instabilities that occur for small length scale asperities. This provides a possible explanation for why static and "dry" friction are virtually always observed, and superlubricity almost never occurs

FUSE Observations of the HD Molecule toward HD 73882

The Lyman and Werner band systems of deuterated molecular hydrogen (HD) occur in the far UV range below 1200 A. The high sensitivity of the FUSE mission can give access, at moderate resolution, to hot stars shining through translucent clouds, in the hope of observing molecular cores in which deuterium is essentially in the form of HD. Thus, the measurement of the HD/H2 ratio may become a new powerful tool to evaluate the deuterium abundance, D/H, in the interstellar medium. We report here on the detection of HD toward the high extinction star HD 73882 [E(B-V)=0.72]. A preliminary analysis is presented.Comment: 4 pages + 4 .ps figures. This paper will appear in a special issue of Astrophysical Journal Letters devoted to the first scientific results from the FUSE missio

Enhancement of tissue lesion depth by dual wavelength irradiation with the Nd-YAG/KTP laser: Perspectives for laser prostatectomy

The Nd-YAG/KTP laser coagulates and vaporizes prostate tissue. The objective of this study was to investigate the combined effects of both wavelengths and to determine the irradiation parameters allowing the largest lesion volume. Chicken breast tissue was irradiated ex vivo. Consecutive 1064 and 532 nm Nd-YAG/KTP laser irradiations were performed for different combinations (30 W/10 W, 20 W/20 W, 10 W/30 W) with variable total fluence (1200 J, 2400 J, 3600 J) and compared to isofluent single wavelengths at 40 W irradiation. The depths, diameters and volumes of the total lesion as well as the vaporization effects of the 532 nm wavelength on normal and on priorly coagulated tissue were analysed. Maximum total lesion depths (p< 0.001) were found under combined Nd-YAG/KTP (20 W/20 W) irradiation conditions. Ablation efficacy of the 532 nm wavelength was reduced after prior 1064 nm irradiation, but crater depths were increased. Dual wavelength irradiation with the Nd-YAG/KTP laser induces a specific denaturation process. This may represent a new approach to increase the depth of coagulation necrosis, and thus the treated volume, thereby improving long-term result

An Ultra-High-Resolution Survey of the Interstellar ^7Li-to-^6Li Isotope Ratio in the Solar Neighborhood

In an effort to probe the extent of variations in the interstellar ^7Li/^6Li ratio seen previously, ultra-high-resolution (R ~ 360,000), high signal-to-noise spectra of stars in the Perseus OB2 and Scorpius OB2 Associations were obtained. These measurements confirm our earlier findings of an interstellar ^7Li/^6Li ratio of about 2 toward o Per, the value predicted from models of Galactic cosmic ray spallation reactions. Observations of other nearby stars yield limits consistent with the isotopic ratio ~ 12 seen in carbonaceous chondrite meteorites. If this ratio originally represented the gas toward o Per, then to decrease the original isotope ratio to its current value an order of magnitude increase in the Li abundance is expected, but is not seen. The elemental K/Li ratio is not unusual, although Li and K are formed via different nucleosynthetic pathways. Several proposals to account for the low ^7Li/^6Li ratio were considered, but none seems satisfactory. Analysis of the Li and K abundances from our survey highlighted two sight lines where depletion effects are prevalent. There is evidence for enhanced depletion toward X Per, since both abundances are lower by a factor of 4 when compared to other sight lines. Moreover, a smaller Li/H abundance is observed toward 20 Aql, but the K/H abundance is normal, suggesting enhanced Li depletion (relative to K) in this direction. Our results suggest that the ^7Li/^6Li ratio has not changed significantly during the last 4.5 billion years and that a ratio ~ 12 represents most gas in the solar neighborhood. In addition, there appears to be a constant stellar contribution of ^7Li, indicating that one or two processes dominate its production in the Galaxy.Comment: 54 pages, accepted for publication in the Astrophysical Journa

The Corley-Jacobson dispersion relation and trans-Planckian inflation

In this Letter we study the dependence of the spectrum of fluctuations in inflationary cosmology on possible effects of trans-Planckian physics, using the Corley/Jacobson dispersion relations as an example. We compare the methods used in previous work [1] with the WKB approximation, give a new exact analytical result, and study the dependence of the spectrum obtained using the approximate method of Ref. [1] on the choice of the matching time between different time intervals. We also comment on recent work subsequent to Ref. [1] on the trans-Planckian problem for inflationary cosmology.Comment: 6 pages, Revtex