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

Evolution of the Cluster Correlation Function

We study the evolution of the cluster correlation function and its richness-dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with \Omega_m = 0.3 and, for comparison, a tilted \Omega_m = 1 model, TSCDM, are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high redshift clusters are clustered more strongly (in comoving scale) than low redshift clusters of the same mass. The increased correlations with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation-scale versus cluster mean separation relation, R_0 - d, is found to be, remarkably, independent of redshift to z <~ 2 for LCDM and z <~ 1 for TCDM (for a fixed correlation function slope and cluster mass within a fixed comoving radius). The non-evolving R_0 - d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters so that the R_0 - d relation remains essentially unchanged. The evolution of the R_0 - d relation from z ~ 0 to z ~ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ~ 0 and provide precise determination of cosmological parameters.Comment: AASTeX, 15 pages, including 5 figures, accepted version for publication in ApJ, vol.603, March 200

The Amplitude of Mass Fluctuations

We determine the linear amplitude of mass fluctuations in the universe, sigma_8, from the abundance of massive clusters at redshifts z=0.5 to 0.8. The evolution of massive clusters depends exponentially on the amplitude of mass fluctuations and thus provides a powerful measure of this important cosmological parameter. The relatively high abundance of massive clusters observed at z>0.5, and the relatively slow evolution of their abundance with time, suggest a high amplitude of mass fluctuations: sigma_8=0.9 +-10% for Omega_m=0.4, increasing slightly to sigma_8=0.95 for Omega_m=0.25 and sigma_8=1.0 for Omega_m=0.1 (flat CDM models). We use the cluster abundance observed at z=0.5 to 0.8 to derive a normalization relation from the high-redshift clusters, which is only weakly dependent on Omega_m: sigma_8*Omega_m^0.14 = 0.78 +-0.08. When combined with recent constraints from the present-day cluster mass function (sigma_8*Omega_m^0.6=0.33 +-0.03) we find sigma_8=0.98 +-0.1 and Omega_m=0.17 +-0.05. Low sigma_8 values (<0.7) are unlikely; they produce an order of magnitude fewer massive clusters than observed.Comment: 12 pages including 3 figures; updated to match published versio

The symbiotic star CH Cygni. III. A precessing radio jet

VLA, MERLIN and Hubble Space Telescope imaging observations of the extended regions of the symbiotic system CH Cygni are analysed. These extensions are evidence of a strong collimation mechanism, probably an accretion disk surrounding the hot component of the system. Over 16 years (between 1985 and 2001) the general trend is that these jets are seen to precess. Fitting a simple ballistic model of matter ejection to the geometry of the extended regions suggests a period of 6520 +/- 150 days, with a precession cone opening angle of 35 +/- 1 degrees. This period is of the same order as that proposed for the orbital period of the outer giant in the system, suggesting a possible link between the two. Anomalous knots in the emission, not explained by the simple model, are believed to be the result of older, slower moving ejecta, or possibly jet material that has become disrupted through sideways interaction with the surrounding medium.Comment: 9 pages, 4 figure

Chandra detection of extended X-ray emission from the recurrent nova RS Ophiuchi

Radio, infrared, and optical observations of the 2006 eruption of the symbiotic recurrent nova RS Ophiuchi (RS Oph) showed that the explosion produced non-spherical ejecta. Some of this ejected material was in the form of bipolar jets to the east and west of the central source. Here we describe Xray observations taken with the Chandra X-ray Observatory one and a half years after the beginning of the outburst that reveal narrow, extended structure with a position angle of approximately 300 degrees (east of north). Although the orientation of the extended feature in the X-ray image is consistent with the readout direction of the CCD detector, extensive testing suggests that the feature is not an artifact. Assuming it is not an instrumental effect, the extended X-ray structure shows hot plasma stretching more than 1,900 AU from the central binary (taking a distance of 1.6 kpc). The X-ray emission is elongated in the northwest direction - in line with the extended infrared emission and some minor features in the published radio image. It is less consistent with the orientation of the radio jets and the main bipolar optical structure. Most of the photons in the extended X-ray structure have energies of less than 0.8 keV. If the extended X-ray feature was produced when the nova explosion occurred, then its 1".2 length as of 2007 August implies that it expanded at an average rate of more than 2 mas/d, which corresponds to a flow speed of greater than 6,000 km/s (d/1.6 kpc) in the plane of the sky. This expansion rate is similar to the earliest measured expansion rates for the radio jets.Comment: accepted in Ap