A parallel algorithm for solving the linear complementarity problem

The concept of multitasking mathematical programs is discussed, and an application of multitasking to the multiple-cost-row linear programming problem is considered. Based on this, an algorithm for solving the Linear Complementarity Problem (LCP) in parallel is presented. A variety of computational results are presented using this multitasking approach on the CRAY X-MP/48. These results were obtained for randomly generated LCP's where thenxn dense matrixM has no special properties (hence, the problem is NP-hard). based on these results, an average time performance ofO(n ⁴) is observed.     

Quantum Fourier Transform-Based Arithmetic Logic Unit on a Quantum Processor

This study proposes and construct a primitive quantum arithmetic logic unit (qALU) based on the quantum Fourier transform (QFT). The qALU is capable of performing arithmetic ADD (addition) and logic NAND gate operations. It designs a scalable quantum circuit and presents the circuits for driving ADD and NAND operations on two-input and four-input quantum channels, respectively. By comparing the required number of quantum gates for serial and parallel architectures in executing arithmetic addition, it evaluates the performance. It also execute the proposed quantum Fourier transform-based qALU design on real quantum processor hardware provided by IBM. The results demonstrate that the proposed circuit can perform arithmetic and logic operations with a high success rate. Furthermore, it discusses in detail the potential implementations of the qALU circuit in the field of computer science, highlighting the possibility of constructing a soft-core processor on a quantum processing unit.     

A minimum distance estimator in an imprecise probability model - Computational aspects and applications

The article considers estimating a parameter θ in an imprecise probability model which consists of coherent upper previsions . After the definition of a minimum distance estimator in this setup and a summarization of its main properties, the focus lies on applications. It is shown that approximate minimum distances on the discretized sample space can be calculated by linear programming. After a discussion of some computational aspects, the estimator is applied in a simulation study consisting of two different models. Finally, the estimator is applied on a real data set in a linear regression model.     

Topological structure preserving numerical simulations of dynamical models

This paper brings together two methods producing numerical solutions with a statement of their quality — the nonstandard finite difference method and the method of validated computing. It deals with the construction and the analysis of reliable numerical discretizations of dynamical systems by employing these two techniques. An epidemiological model is used as a model example for their combined application.     

Experiments with a symbolic programming system for complex analysis

The paper reports the results of work on the construction of LISP programs for various symbolic operations in complex analysis, including the evaluation of integrals around closed contours by the use of Cauchy's Theorem. It is concluded that the only difficulty in the way of the preparation of programs for all of the important and useful textbook calculations in complex analysis is that large amounts of fast storage in the computer are needed.     

加权量子搜索算法及其相位匹配条件研究

目前的Grover算法在无序数据库中搜索多个目标时,得到不同目标的几率是相等的,不考虑各个目标重要程度的差异;并且当目标数超过数据库记录总数的四分之一时,搜索到目标的几率迅速下降,当目标数超过记录总数的一半时,算法失效.针对这两个问题,首先提出一种基于加权目标的搜索算法.根据各子目标的重要程度,为每个子目标赋予一个权系数,应用这些权系数将多个子目标表示成一个量子叠加态,这样可使得到每个子目标的几率等于其自身的权系数;其次,提出自适应相位匹配条件,该条件中两次相位旋转的方向相反,大小根据目标量子叠加态和系统初始状态的内积决定.当该内积大于等于((3-√5)/8)^1/2时,至多只需两步搜索,即可以恒等于1的几率得到搜索目标.实验表明,算法及其相位匹配条件是有效的.     

A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, M ≈0.1, in order to mimic incompressible flows. This strategy is widely used for high-order discontinuous Galerkin (DG) discretizations of the compressible Navier-Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to an incompressible formulation. Our contributions to the state of the art are twofold: Firstly, we present a high-performance DG solver for the compressible Navier-Stokes equations based on a highly efficient matrix-free implementation that targets modern cache-based multicore architectures with Flop/Byte ratios significantly larger than 1. The performance results presented in this work focus on the node-level performance, and our results suggest that there is great potential for further performance improvements for current state-of-the-art DG implementations of the compressible Navier-Stokes equations. Secondly, this compressible Navier-Stokes solver is put into perspective by comparing it to an incompressible DG solver that uses the same matrix-free implementation. We discuss algorithmic differences between both solution strategies and present an in-depth numerical investigation of the performance. The considered benchmark test cases are the three-dimensional Taylor-Green vortex problem as a representative of transitional flows and the turbulent channel flow problem as a representative of wall-bounded turbulent flows. The results indicate a clear performance advantage of the incompressible formulation over the compressible one.     

The Application of Fractal Transform and Entropy for Improving Fault Tolerance and Load Balancing in Grid Computing Environments

This paper applies the entropy-based fractal indexing scheme that enables the grid environment for fast indexing and querying. It addresses the issue of fault tolerance and load balancing-based fractal management to make computational grids more effective and reliable. A fractal dimension of a cloud of points gives an estimate of the intrinsic dimensionality of the data in that space. The main drawback of this technique is the long computing time. The main contribution of the suggested work is to investigate the effect of fractal transform by adding R-tree index structure-based entropy to existing grid computing models to obtain a balanced infrastructure with minimal fault. In this regard, the presented work is going to extend the commonly scheduling algorithms that are built based on the physical grid structure to a reduced logical network. The objective of this logical network is to reduce the searching in the grid paths according to arrival time rate and path’s bandwidth with respect to load balance and fault tolerance, respectively. Furthermore, an optimization searching technique is utilized to enhance the grid performance by investigating the optimum number of nodes extracted from the logical grid. The experimental results indicated that the proposed model has better execution time, throughput, makespan, latency, load balancing, and success rate.     

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将理想全二维磁流体(MHD)稳定性数值代码GATO成功移植到HL-2A高性能计算系统,并用其模拟研究了HL-2A装置一次典型弹丸注入实验的等离子体的理想MHD稳定性。利用HL-2A装置第4050次放电的实验数据,应用EFIT代码重建了几个时间片的平衡位形,然后应用GATO代码对每个平衡位形的MHD稳定性进行了计算。通过对结果进行分析比较得出初步结论,由于弹丸注入而造成的反剪切位形的致稳作用,可以提高等离子体的约束性能。