On the Performance Prediction of BLAS-based Tensor Contractions

Tensor operations are surging as the computational building blocks for a variety of scientific simulations and the development of high-performance kernels for such operations is known to be a challenging task. While for operations on one- and two-dimensional tensors there exist standardized interfaces and highly-optimized libraries (BLAS), for higher dimensional tensors neither standards nor highly-tuned implementations exist yet. In this paper, we consider contractions between two tensors of arbitrary dimensionality and take on the challenge of generating high-performance implementations by resorting to sequences of BLAS kernels. The approach consists in breaking the contraction down into operations that only involve matrices or vectors. Since in general there are many alternative ways of decomposing a contraction, we are able to methodically derive a large family of algorithms. The main contribution of this paper is a systematic methodology to accurately identify the fastest algorithms in the bunch, without executing them. The goal is instead accomplished with the help of a set of cache-aware micro-benchmarks for the underlying BLAS kernels. The predictions we construct from such benchmarks allow us to reliably single out the best-performing algorithms in a tiny fraction of the time taken by the direct execution of the algorithms.Comment: Submitted to PMBS1

Periastron Advance in Spinning Black Hole Binaries: Gravitational Self-Force from Numerical Relativity

We study the general relativistic periastron advance in spinning black hole binaries on quasi-circular orbits, with spins aligned or anti-aligned with the orbital angular momentum, using numerical-relativity simulations, the post-Newtonian approximation, and black hole perturbation theory. By imposing a symmetry by exchange of the bodies' labels, we devise an improved version of the perturbative result, and use it as the leading term of a new type of expansion in powers of the symmetric mass ratio. This allows us to measure, for the first time, the gravitational self-force effect on the periastron advance of a non-spinning particle orbiting a Kerr black hole of mass M and spin S = -0.5 M^2, down to separations of order 9M. Comparing the predictions of our improved perturbative expansion with the exact results from numerical simulations of equal-mass and equal-spin binaries, we find a remarkable agreement over a wide range of spins and orbital separations.Comment: 18 pages, 12 figures; matches version to appear in Phys. Rev.

The Statistical Mechanics of Horizons and Black Hole Thermodynamics

Although we know that black holes are characterized by a temperature and an entropy, we do not yet have a satisfactory microscopic ``statistical mechanical'' explanation for black hole thermodynamics. I describe a new approach that attributes the thermodynamic properties to ``would-be gauge'' degrees of freedom that become dynamical on the horizon. For the (2+1)-dimensional black hole, this approach gives the correct entropy. (Talk given at the Pacific Conference on Gravitation and Cosmology, Seoul, February 1996.)Comment: 11 pages, LaTe

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many non-linear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary's orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.Comment: 109 pages, 1 figure; this version is an update of the Living Review article originally published in 2002; available on-line at http://www.livingreviews.org

2.5PN kick from black-hole binaries in circular orbit: Nonspinning case

Using the Multipolar post-Minskowskian formalism, we compute the linear momentum flux from black-hole binaries in circular orbits and having no spins. The total linear momentum flux contains various types of instantaneous (which are functions of the retarded time) and hereditary (which depends on the dynamics of the binary in the past) terms both of which are analytically computed. In addition to the inspiral contribution, we use a simple model of plunge to compute the kick or recoil accumulated during this phase.Comment: To appear in Proceedings of "Relativity and Gravitation - 100 Years after Einstein in Prague" Ed. J. Bicak (2013

Factors associated with grade progression in pancreatic neuroendocrine tumors.

Grade progression of well-differentiated pancreatic neuroendocrine tumors (panNETs) can occur over time, with G1/2 to G3 being the most clinically relevant form. Here, we conducted a retrospective cohort study of 66 patients with initially G1/2 panNET (median initial Ki67, 4.6%). Patients were followed up for a median 6.8 years and had a median of two metachronous tumor biopsies over their disease course. 34.8% of patients underwent any form of grade progression, including G1 to G2/3 and G2 to G3, while 24.2% demonstrated G1/2 to G3 grade progression. Over a median 2.3 years, G1/2 to G3 grade progressors experienced a median Ki67 change of +27.0% (range, +6.4 to +48.7%). Subsequent biopsies showing progression to G3 had a median Ki67 value of 31.0% (range, 21.0-60.0%) and were more often performed following suspicious clinical behavior (75.0%) rather than routinely at the time of scheduled procedure/surgery (25.0%). Similar to prior studies, G1/2 to G3 grade progressors had worse overall survival from the time of metastatic disease (median, 4.8 years vs not reached for stably G1/2 disease; P = 0.002). Heavier pretreatment and heterogeneity or lack of uptake on somatostatin receptor imaging was independently associated with progression to G3. In the largest study of metachronous panNET biopsies to date, our findings show that baseline biopsies suggesting G1/2 disease may not accurately reflect future disease status, highlighting the possible limitations of using archived tissue to stratify patients into trials and/or choose future therapy. Additional work is needed to better understand the impact of prior therapies on grade progression and how to identify which lesions to best follow up for repeat biopsy

Exploring new physics frontiers through numerical relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology

Two binary stars gravitational waves - homotopy perturbation method

Homotopy perturbation is one of the newest methods for numerical analysis of deferential equations. We have used for solving wave equation around a black hole. Our conclusions have this method far reaching consequences for comparison of theoritical physics and experimental physics.Comment: The manuscript considers the important problem of solve equation wave around a black hole. We have solved that by using Homotopy perturbation methods. Homotopy perturbation is one of the newest methods for numerical analysis of deferential equations. Our conclusions have far reaching consequences for comparison of theoritical physics and experimental physic

Global Chromatin Architecture Reflects Pluripotency and Lineage Commitment in the Early Mouse Embryo

An open chromatin architecture devoid of compact chromatin is thought to be associated with pluripotency in embryonic stem cells. Establishing this distinct epigenetic state may also be required for somatic cell reprogramming. However, there has been little direct examination of global structural domains of chromatin during the founding and loss of pluripotency that occurs in preimplantation mouse development. Here, we used electron spectroscopic imaging to examine large-scale chromatin structural changes during the transition from one-cell to early postimplantation stage embryos. In one-cell embryos chromatin was extensively dispersed with no noticeable accumulation at the nuclear envelope. Major changes were observed from one-cell to two-cell stage embryos, where chromatin became confined to discrete blocks of compaction and with an increased concentration at the nuclear envelope. In eight-cell embryos and pluripotent epiblast cells, chromatin was primarily distributed as an extended meshwork of uncompacted fibres and was indistinguishable from chromatin organization in embryonic stem cells. In contrast, lineage-committed trophectoderm and primitive endoderm cells, and the stem cell lines derived from these tissues, displayed higher levels of chromatin compaction, suggesting an association between developmental potential and chromatin organisation. We examined this association in vivo and found that deletion of Oct4, a factor required for pluripotency, caused the formation of large blocks of compact chromatin in putative epiblast cells. Together, these studies show that an open chromatin architecture is established in the embryonic lineages during development and is sufficient to distinguish pluripotent cells from tissue-restricted progenitor cells