18,818 research outputs found

    A Shift Selection Strategy for Parallel Shift-invert Spectrum Slicing in Symmetric Self-consistent Eigenvalue Computation

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    © 2020 ACM. The central importance of large-scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world's largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions that will be explored in future work

    Nonlinear Cosmological Power Spectra in Real and Redshift--Space

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    We present an expression for the nonlinear evolution of the cosmological power spectrum based on following Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in self- gravitating fields. We have extended this analysis into redshift-space and found a solution for the nonlinear, anisotropic redshift-space power spectrum in the limit of plane--parallel redshift distortions. The quadrupole-to- monopole ratio is calculated for the case of power-law initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshift-space distortion parameter, β\beta. The point of zero-crossing of the quadrupole, k0k_0, is found to obey a scaling relation. This model is found to be in agreement with NN-body simulations on scales down to the zero-crossing of the quadrupole, although the wavenumber at zero-crossing is underestimated. These results are applied to the quadrupole--monopole ratio found in the merged QDOT+1.2 Jy IRAS redshift survey. We have estimated that the distortion parameter is constrained to be β>0.5\beta>0.5 at the 95%95 \% level. The local primordial spectral slope is not well constrained, but analysis suggests n2n \approx -2 in the translinear regime. The zero-crossing scale of the quadrupole is k0=0.5±0.1h/Mpck_0=0.5 \pm 0.1 h/Mpc and from this we infer the amplitude of clustering is σ8=0.7±0.05\sigma_8=0.7 \pm 0.05. We suggest that the success of this model is due to nonlinear redshift--space effects arising from infall onto caustics and is not dominated by virialised cluster cores.Comment: 13 pages, uufiles, Latex with 6 postscript figures, submitted to MNRA

    Efficient Information Theoretic Clustering on Discrete Lattices

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    We consider the problem of clustering data that reside on discrete, low dimensional lattices. Canonical examples for this setting are found in image segmentation and key point extraction. Our solution is based on a recent approach to information theoretic clustering where clusters result from an iterative procedure that minimizes a divergence measure. We replace costly processing steps in the original algorithm by means of convolutions. These allow for highly efficient implementations and thus significantly reduce runtime. This paper therefore bridges a gap between machine learning and signal processing.Comment: This paper has been presented at the workshop LWA 201

    Optimizing an Organized Modularity Measure for Topographic Graph Clustering: a Deterministic Annealing Approach

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    This paper proposes an organized generalization of Newman and Girvan's modularity measure for graph clustering. Optimized via a deterministic annealing scheme, this measure produces topologically ordered graph clusterings that lead to faithful and readable graph representations based on clustering induced graphs. Topographic graph clustering provides an alternative to more classical solutions in which a standard graph clustering method is applied to build a simpler graph that is then represented with a graph layout algorithm. A comparative study on four real world graphs ranging from 34 to 1 133 vertices shows the interest of the proposed approach with respect to classical solutions and to self-organizing maps for graphs

    OPTIMIZING LARGE COMBINATIONAL NETWORKS FOR K-LUT BASED FPGA MAPPING

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    Optimizing by partitioning is a central problem in VLSI design automation, addressing circuit’s manufacturability. Circuit partitioning has multiple applications in VLSI design. One of the most common is that of dividing combinational circuits (usually large ones) that will not fit on a single package among a number of packages. Partitioning is of practical importance for k-LUT based FPGA circuit implementation. In this work is presented multilevel a multi-resource partitioning algorithm for partitioning large combinational circuits in order to efficiently use existing and commercially available FPGAs packagestwo-way partitioning, multi-way partitioning, recursive partitioning, flat partitioning, critical path, cutting cones, bottom-up clusters, top-down min-cut
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