Inner product computation for sparse iterative solvers on\ud distributed supercomputer

Recent years have witnessed that iterative Krylov methods without re-designing are not suitable for distribute supercomputers because of intensive global communications. It is well accepted that re-engineering Krylov methods for prescribed computer architecture is necessary and important to achieve higher performance and scalability. The paper focuses on simple and practical ways to re-organize Krylov methods and improve their performance for current heterogeneous distributed supercomputers. In construct with most of current software development of Krylov methods which usually focuses on efficient matrix vector multiplications, the paper focuses on the way to compute inner products on supercomputers and explains why inner product computation on current heterogeneous distributed supercomputers is crucial for scalable Krylov methods. Communication complexity analysis shows that how the inner product computation can be the bottleneck of performance of (inner) product-type iterative solvers on distributed supercomputers due to global communications. Principles of reducing such global communications are discussed. The importance of minimizing communications is demonstrated by experiments using up to 900 processors. The experiments were carried on a Dawning 5000A, one of the fastest and earliest heterogeneous supercomputers in the world. Both the analysis and experiments indicates that inner product computation is very likely to be the most challenging kernel for inner product-based iterative solvers to achieve exascale

Minimizing synchronizations in sparse iterative solvers for distributed supercomputers

Eliminating synchronizations is one of the important techniques related to minimizing communications for modern high performance computing. This paper discusses principles of reducing communications due to global synchronizations in sparse iterative solvers on distributed supercomputers. We demonstrates how to minimizing global synchronizations by rescheduling a typical Krylov subspace method. The benefit of minimizing synchronizations is shown in theoretical analysis and is verified by numerical experiments using up to 900 processors. The experiments also show the communication complexity for some structured sparse matrix vector multiplications and global communications in the underlying supercomputers are in the order P1/2.5 and P4/5 respectively, where P is the number of processors and the experiments were carried on a Dawning 5000A

Risk, cohabitation and marriage

This paper introduces imperfect information,learning,and risk aversion in a two sided matching model.The modelprovides a theoreticalframework for the com- monly occurring phenomenon of cohabitation followed by marriage,and is con- sistent with empirical findings on these institutions.The paper has three major results.First,individuals set higher standards for marriage than for cohabitation. When the true worth of a cohabiting partner is revealed,some cohabiting unions are converted into marriage while others are not.Second,individuals cohabit within classes.Third,the premium that compensates individuals for the higher risk involved in marriage over a cohabiting partnership is derived.This premium can be decomposed into two parts.The first part is a function of the individual ’s level of risk aversion,while the second part is a function of the di difference in risk between marriage and cohabitation.

Fast Monte Carlo Simulation for Patient-specific CT/CBCT Imaging Dose Calculation

Recently, X-ray imaging dose from computed tomography (CT) or cone beam CT (CBCT) scans has become a serious concern. Patient-specific imaging dose calculation has been proposed for the purpose of dose management. While Monte Carlo (MC) dose calculation can be quite accurate for this purpose, it suffers from low computational efficiency. In response to this problem, we have successfully developed a MC dose calculation package, gCTD, on GPU architecture under the NVIDIA CUDA platform for fast and accurate estimation of the x-ray imaging dose received by a patient during a CT or CBCT scan. Techniques have been developed particularly for the GPU architecture to achieve high computational efficiency. Dose calculations using CBCT scanning geometry in a homogeneous water phantom and a heterogeneous Zubal head phantom have shown good agreement between gCTD and EGSnrc, indicating the accuracy of our code. In terms of improved efficiency, it is found that gCTD attains a speed-up of ~400 times in the homogeneous water phantom and ~76.6 times in the Zubal phantom compared to EGSnrc. As for absolute computation time, imaging dose calculation for the Zubal phantom can be accomplished in ~17 sec with the average relative standard deviation of 0.4%. Though our gCTD code has been developed and tested in the context of CBCT scans, with simple modification of geometry it can be used for assessing imaging dose in CT scans as well.Comment: 18 pages, 7 figures, and 1 tabl

Value encoding in the globus pallidus: fMRI reveals an interaction effect between reward and dopamine drive

The external part of the globus pallidus (GPe) is a core nucleus of the basal ganglia (BG) whose activity is disrupted under conditions of low dopamine release, as in Parkinson's disease. Current models assume decreased dopamine release in the dorsal striatum results in deactivation of dorsal GPe, which in turn affects motor expression via a regulatory effect on other nuclei of the BG. However, recent studies in healthy and pathological animal models have reported neural dynamics that do not match with this view of the GPe as a relay in the BG circuit. Thus, the computational role of the GPe in the BG is still to be determined. We previously proposed a neural model that revisits the functions of the nuclei of the BG, and this model predicts that GPe encodes values which are amplified under a condition of low striatal dopaminergic drive. To test this prediction, we used an fMRI paradigm involving a within-subject placebo-controlled design, using the dopamine antagonist risperidone, wherein healthy volunteers performed a motor selection and maintenance task under low and high reward conditions. ROI-based fMRI analysis revealed an interaction between reward and dopamine drive manipulations, with increased BOLD activity in GPe in a high compared to low reward condition, and under risperidone compared to placebo. These results confirm the core prediction of our computational model, and provide a new perspective on neural dynamics in the BG and their effects on motor selection and cognitive disorders

Ground-State Entanglement in Interacting Bosonic Graphs

We consider a collection of bosonic modes corresponding to the vertices of a graph $\Gamma.$ Quantum tunneling can occur only along the edges of $\Gamma$ and a local self-interaction term is present. Quantum entanglement of one vertex with respect the rest of the graph is analyzed in the ground-state of the system as a function of the tunneling amplitude $\tau.$ The topology of $\Gamma$ plays a major role in determining the tunneling amplitude $\tau^*$ which leads to the maximum ground-state entanglement. Whereas in most of the cases one finds the intuitively expected result $\tau^*=\infty$ we show that it there exists a family of graphs for which the optimal value of$\tau$ is pushed down to a finite value. We also show that, for complete graphs, our bi-partite entanglement provides useful insights in the analysis of the cross-over between insulating and superfluid ground statesComment: 5 pages (LaTeX) 5 eps figures include

Six-dimensional weak-strong simulations of head-on beam-beam compensation in RHIC

To compensate the large beam-beam tune spread and beam-beam resonance driving terms in the polarized proton operation in the Relativistic Heavy Ion Collider (RHIC), we will introduce a low-energy DC electron beam into each ring to collide head-on with the opposing proton beam. The device to provide the electron beam is called an electron lens. In this article, using a 6-D weak-strong-beam-beam interaction simulation model, we investigate the effects of head-on beam-beam compensation with electron lenses on the proton beam dynamics in the RHIC 250 GeV polarized proton operation. This article is abridged from the published article [1].Comment: 5 pages, contribution to the ICFA Mini-Workshop on Beam-Beam Effects in Hadron Colliders, CERN, Geneva, Switzerland, 18-22 Mar 201

An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations