Parallel, iterative solution of sparse linear systems: Models and architectures

A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication. The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed

A model of asynchronous iterative algorithms for solving large, sparse, linear systems

Solving large, sparse, linear systems of equations is one of the fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. This model is then analyzed to determine the expected intertask data transfer and task computational complexity as functions of the number of tasks. Based on the analysis, recommendations for task partitioning are made. These recommendations are a function of the sparseness of the linear system, its structure (i.e., randomly sparse or banded), and dimension

Stencils and problem partitionings: Their influence on the performance of multiple processor systems

Given a discretization stencil, partitioning the problem domain is an important first step for the efficient solution of partial differential equations on multiple processor systems. Partitions are derived that minimize interprocessor communication when the number of processors is known a priori and each domain partition is assigned to a different processor. This partitioning technique uses the stencil structure to select appropriate partition shapes. For square problem domains, it is shown that non-standard partitions (e.g., hexagons) are frequently preferable to the standard square partitions for a variety of commonly used stencils. This investigation is concluded with a formalization of the relationship between partition shape, stencil structure, and architecture, allowing selection of optimal partitions for a variety of parallel systems

Propagation and organization in lattice random media

We show that a signal can propagate in a particular direction through a model random medium regardless of the precise state of the medium. As a prototype, we consider a point particle moving on a one-dimensional lattice whose sites are occupied by scatterers with the following properties: (i) the state of each site is defined by its spin (up or down); (ii) the particle arriving at a site is scattered forward (backward) if the spin is up (down); (iii) the state of the site is modified by the passage of the particle, i.e. the spin of the site where a scattering has taken place, flips ($\uparrow \Leftrightarrow \downarrow$). We consider one dimensional and triangular lattices, for which we give a microscopic description of the dynamics, prove the propagation of a particle through the scatterers, and compute analytically its statistical properties. In particular we prove that, in one dimension, the average propagation velocity is $= 1/(3-2q)$, with $q$ the probability that a site has a spin $\uparrow$, and, in the triangular lattice, the average propagation velocity is independent of the scatterers distribution: $= 1/8$. In both cases, the origin of the propagation is a blocking mechanism, restricting the motion of the particle in the direction opposite to the ultimate propagation direction, and there is a specific re-organization of the spins after the passage of the particle. A detailed mathematical analysis of this phenomenon is, to the best of our knowledge, presented here for the first time.Comment: 30 pages, 15 separate figures (in PostScript); submitted to J. Stat. Phy

Thermodynamic properties of extremely diluted symmetric Q-Ising neural networks

Using the replica-symmetric mean-field theory approach the thermodynamic and retrieval properties of extremely diluted {\it symmetric} $Q$-Ising neural networks are studied. In particular, capacity-gain parameter and capacity-temperature phase diagrams are derived for $Q=3, 4$ and $Q=\infty$. The zero-temperature results are compared with those obtained from a study of the dynamics of the model. Furthermore, the de Almeida-Thouless line is determined. Where appropriate, the difference with other $Q$-Ising architectures is outlined.Comment: 16 pages Latex including 6 eps-figures. Corrections, also in most of the figures have been mad

Detecting solar axions using Earth's magnetic field

We show that solar axion conversion to photons in the Earth's magnetosphere can produce an x-ray flux, with average energy \sim 4 keV, which is measurable on the dark side of the Earth. The smallness of the Earth's magnetic field is compensated by a large magnetized volume. For axion masses < 10^{-4} eV, a low-Earth-orbit x-ray detector with an effective area of 10^4 cm^2, pointed at the solar core, can probe the photon-axion coupling down to 10^{-11} GeV^{-1}, in one year. Thus, the sensitivity of this new approach will be an order of magnitude beyond current laboratory limits.Comment: 3 pages, 1 figure, typos corrected, references adde

Evidence that Gamma-ray Burst 130702A Exploded in a Dwarf Satellite of a Massive Galaxy

GRB 130702A is a nearby long-duration gamma-ray burst (LGRB) discovered by the Fermi satellite whose associated afterglow was detected by the Palomar Transient Factory. Subsequent photometric and spectroscopic monitoring has identified a coincident broad-lined Type Ic supernova (SN), and nebular emission detected near the explosion site is consistent with a redshift of z=0.145. The SN-GRB exploded at an offset of ~7.6" from the center of an inclined r=18.1 mag red disk-dominated galaxy, and ~0.6" from the center of a much fainter r=23 mag object. We obtained Keck-II DEIMOS spectra of the two objects and find a 2{\sigma} upper limit on their line-of-sight velocity offset of ~<60 km/s. If we project the SN-GRB coordinates onto the plane of the inclined massive disk galaxy, the explosion would have a ~61+-10 kpc offset, or ~6 times the galaxy's half-light radius. This large estimated nuclear offset suggests that the faint source is not a star-forming region of the massive red galaxy but is instead a dwarf galaxy. The star-formation rate of the dwarf galaxy is ~0.05 solar masses per year, and we place an upper limit on its oxygen abundance of 12 + log(O/H) < 8.16 dex. The identification of an LGRB in a dwarf satellite of a massive, metal-rich primary galaxy suggests that recent detections of LGRBs spatially coincident with metal-rich galaxies may be, in some cases, superpositions.Comment: Accepted by ApJ 8/14/13, minor modification

Evaluation of the capture efficiency and size selectivity of four pot types in the prospective fishery for North Pacific giant octopus (Enteroctopus dofleini)

Over 230 metric tons of octopus is harvested as bycatch annually in Alaskan trawl, long-line, and pot fisheries. An expanding market has fostered interest in the development of a directed fishery for North Pacific giant octopus (Enteroctopus dofleini). To investigate the potential for fishery development we examined the efficacy of four different pot types for capture of this species. During two surveys in Kachemak Bay, Alaska, strings of 16 –20 sablefish, Korean hair crab, shrimp, and Kodiak wooden lair pots were set at depths ranging between 62 and 390 meters. Catch per-unit-of-ef for t estimates were highest for sablefish and lair pots. Sablefish pots caught significantly heavier North Pacific giant octopuses but also produced the highest bycatch of commercially important species, such as halibut (Hippoglossus stenolepis), Pacific cod (Gadus macrocephalus), and Tanner crab (Chionoecetes bairdi)

Transport Properties of a spinon Fermi surface coupled to a U(1) gauge field

With the organic compound $\kappa$-(BEDT-TTF)$_2$-Cu$_2$(CN)$_3$ in mind, we consider a spin liquid system where a spinon Fermi surface is coupled to a U(1) gauge field. Using the non-equilibrium Green's function formalism, we derive the Quantum Boltzmann Equation (QBE) for this system. In this system, however, one cannot a priori assume the existence of Landau quasiparticles. We show that even without this assumption one can still derive a linearized equation for a generalized distribution function. We show that the divergence of the effective mass and of the finite temperature self-energy do not enter these transport coefficients and thus they are well-defined. Moreover, using a variational method, we calculate the temperature dependence of the spin resistivity and thermal conductivity of this system.Comment: 12 page