Improving Performance of Iterative Methods by Lossy Checkponting

Iterative methods are commonly used approaches to solve large, sparse linear systems, which are fundamental operations for many modern scientific simulations. When the large-scale iterative methods are running with a large number of ranks in parallel, they have to checkpoint the dynamic variables periodically in case of unavoidable fail-stop errors, requiring fast I/O systems and large storage space. To this end, significantly reducing the checkpointing overhead is critical to improving the overall performance of iterative methods. Our contribution is fourfold. (1) We propose a novel lossy checkpointing scheme that can significantly improve the checkpointing performance of iterative methods by leveraging lossy compressors. (2) We formulate a lossy checkpointing performance model and derive theoretically an upper bound for the extra number of iterations caused by the distortion of data in lossy checkpoints, in order to guarantee the performance improvement under the lossy checkpointing scheme. (3) We analyze the impact of lossy checkpointing (i.e., extra number of iterations caused by lossy checkpointing files) for multiple types of iterative methods. (4)We evaluate the lossy checkpointing scheme with optimal checkpointing intervals on a high-performance computing environment with 2,048 cores, using a well-known scientific computation package PETSc and a state-of-the-art checkpoint/restart toolkit. Experiments show that our optimized lossy checkpointing scheme can significantly reduce the fault tolerance overhead for iterative methods by 23%~70% compared with traditional checkpointing and 20%~58% compared with lossless-compressed checkpointing, in the presence of system failures.Comment: 14 pages, 10 figures, HPDC'1

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Robert T. Barrett is associate dean and professor of management, School of Business, Francis Marion University, Florence, SC 29501-0547. Robert E. Pugh is Eugene A. Fallon Jr., professor of management and associate professor, School of Business, Francis Marion University, Florence, SC 29501-0547

An algebraic interpretation of the Wheeler-DeWitt equation

We make a direct connection between the construction of three dimensional topological state sums from tensor categories and three dimensional quantum gravity by noting that the discrete version of the Wheeler-DeWitt equation is exactly the pentagon for the associator of the tensor category, the Biedenharn-Elliott identity. A crucial role is played by an asymptotic formula relating 6j-symbols to rotation matrices given by Edmonds.Comment: 10 pages, amstex, uses epsf.tex. New version has improved presentatio

Distinct Quantum States Can Be Compatible with a Single State of Reality

Perhaps the quantum state represents information about reality, and not reality directly. Wave function collapse is then possibly no more mysterious than a Bayesian update of a probability distribution given new data. We consider models for quantum systems with measurement outcomes determined by an underlying physical state of the system but where several quantum states are consistent with a single underlying state---i.e., probability distributions for distinct quantum states overlap. Significantly, we demonstrate by example that additional assumptions are always necessary to rule out such a model.Comment: 5 pages, 2 figure

Fine-Scale Variations in Eucritic Pyroxene FeO/MnO: Process vs. Provenance.

Most asteroidal igneous rocks are eucrite-like basalts and gabbros, composed mostly of ferroan low- and high-Ca pyroxenes and calcic plagioclase, plus smaller amounts of silica (most commonly tridymite), ilmenite, chromite, troilite, Ca-phosphate, metal and sometimes ferroan olivine. Eucrite-like mafic rocks are fragments of the crusts of differentiated asteroids, and most are likely from 4 Vesta

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Canonical path integral measures for Holst and Plebanski gravity. I. Reduced Phase Space Derivation

An important aspect in defining a path integral quantum theory is the determination of the correct measure. For interacting theories and theories with constraints, this is non-trivial, and is normally not the heuristic "Lebesgue measure" usually used. There have been many determinations of a measure for gravity in the literature, but none for the Palatini or Holst formulations of gravity. Furthermore, the relations between different resulting measures for different formulations of gravity are usually not discussed. In this paper we use the reduced phase technique in order to derive the path-integral measure for the Palatini and Holst formulation of gravity, which is different from the Lebesgue measure up to local measure factors which depend on the spacetime volume element and spatial volume element. From this path integral for the Holst formulation of GR we can also give a new derivation of the Plebanski path integral and discover a discrepancy with the result due to Buffenoir, Henneaux, Noui and Roche (BHNR) whose origin we resolve. This paper is the first in a series that aims at better understanding the relation between canonical LQG and the spin foam approach.Comment: 27 pages, minor correction

Optically Pumped NMR Measurements of the Electron Spin Polarization in GaAs Quantum Wells near Landau Level Filling Factor nu=1/3

The Knight shift of Ga-71 nuclei is measured in two different electron-doped multiple quantum well samples using optically pumped NMR. These data are the first direct measurements of the electron spin polarization, P(nu,T)=/max, near nu=1/3. The P(T) data at nu=1/3 probe the neutral spin-flip excitations of a fractional quantum Hall ferromagnet. In addition, the saturated P(nu) drops on either side of nu=1/3, even in a Btot=12 Tesla field. The observed depolarization is quite small, consistent with an average of about 0.1 spin-flips per quasihole (or quasiparticle), a value which does not appear to be explicable by the current theoretical understanding of the FQHE near nu=1/3.Comment: 4 pages (REVTEX), 5 eps figures embedded in text; minor changes, published versio

Simple model for quantum general relativity from loop quantum gravity

New progress in loop gravity has lead to a simple model of `general-covariant quantum field theory'. I sum up the definition of the model in self-contained form, in terms accessible to those outside the subfield. I emphasize its formulation as a generalized topological quantum field theory with an infinite number of degrees of freedom, and its relation to lattice theory. I list the indications supporting the conjecture that the model is related to general relativity and UV finite.Comment: 8 pages, 3 figure