Towards sparse matrix operations:graph database approach for power grid computation

The construction of new power systems presents higher requirements for the Power Internet of Things(PIoT)technology.The“source-grid-load-storage”architecture of a new power system requires PIoT to have a stronger multi-source heterogeneous data fusion ability.Native graph databases have great advantages in dealing with multi-source heterogeneous data,which make them suitable for an increasing number of analytical computing tasks.However,only few existing graph database products have native support for matrix operation-related interfaces or functions,resulting in low efficiency when handling matrix calculations that are commonly encountered in power grids.In this paper,the matrix computation process is expressed by a strategy called graph description,which relies on the natural connection between the matrix and structure of the graph.Based on that,we implement matrix operations on graph database,including matrix multiplication,matrix decomposition,etc.Specifically,only the nodes relevant to the computation and their neighbors are concerned in the process,which prunes the influence of zero elements in the matrix and avoids useless iterations compared to the conventional matrix computation.Based on the graph description,a series of power grid computations can be implemented on graph database,which reduces redundant data import and export operations while leveraging the parallel computing capability of graph database.It promotes the efficiency of PIoT when handling multi-source heterogeneous data.An comprehensive experimental study over two different scale power system datasets compares the proposed method with Python and MATLAB baselines.The results reveal the superior performance of our proposed method in both power flow and N-1 contingency computations.

Efficient computation for dynamic responses of systems with time-varying characteristics

Based on Neumman series and epsilon-algorithm, an efficient computation for dynamic responses of systems with arbitrary time-varying characteristics is investigated. Avoiding the calculation for the inverses of the equivalent stiffness matrices in each time step, the computation effort of the proposed method is reduced compared with the full analysis of Newmark method. The validity and applications of the proposed method are illustrated by a 4-DOF spring-mass system with periodical time-varying stiffness properties and a truss structure with arbitrary time-varying lumped mass. It shows that good approximate results can be obtained by the proposed method compared with the responses obtained by the full analysis of Newmark method.

Novel Approach to Data Encryption Based on Matrix Computations

In this paper,we provide a new approach to data encryption using generalized inverses.Encryption is based on the implementation of weighted Moore–Penrose inverse A y MNenxmT over the nx8 constant matrix.The square Hermitian positive definite matrix N8x8 p is the key.The proposed solution represents a very strong key since the number of different variants of positive definite matrices of order 8 is huge.We have provided NIST(National Institute of Standards and Technology)quality assurance tests for a random generated Hermitian matrix(a total of 10 different tests and additional analysis with approximate entropy and random digression).In the additional testing of the quality of the random matrix generated,we can conclude that the results of our analysis satisfy the defined strict requirements.This proposed MP encryption method can be applied effectively in the encryption and decryption of images in multi-party communications.In the experimental part of this paper,we give a comparison of encryption methods between machine learning methods.Machine learning algorithms could be compared by achieved results of classification concentrating on classes.In a comparative analysis,we give results of classifying of advanced encryption standard(AES)algorithm and proposed encryption method based on Moore–Penrose inverse.

Deep Learning Applied to Computational Mechanics:A Comprehensive Review,State of the Art,and the Classics

Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.

Technetium-99m-methylene diphosphonate single photon emission computed tomography/computed tomography combined with prostate-specific antigen/free prostate-specific antigen ratio for bone metastasis of prostate cancer

BACKGROUND Prostate cancer(PC)is one of the most common malignant tumors in men,and bone metastasis is one of its common complications,which seriously affects the quality of life and prognosis of patients.AIM To investigate the diagnostic value of technetium-99m-methylene diphosphonate(99mTc-MDP)single photon emission computed tomography(SPECT)/CT imaging combined with the serum prostate-specific antigen(PSA)/free PSA ratio for PC bone metastasis(PCBM).METHODS One hundred patients with PC who visited the Hospital of Chengdu University of Traditional Chinese Medicine from January 2020 to January 2022 were recruited as the experimental(Exp)group,while 30 patients with benign prostatic lesions(BPLs)were recruited as the control(Ctrl)group.All patients underwent 99mTc-MDP SPECT/CT imaging and serum PSA/fPSA testing.The SPECT/CT imaging results and serum PSA/fPSA ratios of patients were analyzed to evaluate their diagnostic values for PCBM.RESULTS The difference in general information of the patients was not obvious,showing comparability.The two methods showed no visible differences in negative predictive value and sensitivity for patients with PCBM,but had great differences in positive predictive value and specificity(P<0.05).The PSA/fPSA ratio of patients with PC in the Exp group was lower than those with BPLs,and patients with PCBM had a much lower PSA/fPSA ratio than those without PC(P<0.05).The results confirmed that the combined use of 99mTc-MDP SPECT/CT imaging and serum PSA/fPSA ratio achieved a detection rate of 95%for PCBM.CONCLUSION The combination of 99mTc-MDP SPECT/CT and PSA/fPSA ratio is accurate and reliable for the diagnosis of PCBM,which provides an important reference for clinical practice.

Fast Matrix Computation Algorithms Based on Rough Attribute Vector Tree Method in RDSS

The concepts of Rough Decision Support System (RDSS) and equivalence matrix are introduced in this paper. Based on a rough attribute vector tree (RAVT) method, two kinds of matrix computation algorithms — Recursive Matrix Computation (RMC) and Parallel Matrix Computation (PMC) are proposed for rules extraction, attributes reduction and data cleaning finished synchronously. The algorithms emphasize the practicability and efficiency of rules generation. A case study of PMC is analyzed, and a comparison experiment of RMC algorithm shows that it is feasible and efficient for data mining and knowledge-discovery in RDSS.

MatDEM-fast matrix computing of the discrete element method

Discrete element method can effectively simulate the discontinuity,inhomogeneity and large deformation and failure of rock and soil.Based on the innovative matrix computing of the discrete element method,the highperformance discrete element software MatDEM may handle millions of elements in one computer,and enables the discrete element simulation at the engineering scale.It supports heat calculation,multi-field and fluidsolid coupling numerical simulations.Furthermore,the software integrates pre-processing,solver,postprocessing,and powerful secondary development,allowing recompiling new discrete element software.The basic principles of the DEM,the implement and development of the MatDEM software,and its applications are introduced in this paper.The software and sample source code are available online(http://matdem.com).

Near Term Hybrid Quantum Computing Solution to the Matrix Riccati Equations

The well-known Riccati differential equations play a key role in many fields,including problems in protein folding,control and stabilization,stochastic control,and cybersecurity(risk analysis and malware propaga-tion).Quantum computer algorithms have the potential to implement faster approximate solutions to the Riccati equations compared with strictly classical algorithms.While systems with many qubits are still under development,there is significant interest in developing algorithms for near-term quantum computers to determine their accuracy and limitations.In this paper,we propose a hybrid quantum-classical algorithm,the Matrix Riccati Solver(MRS).This approach uses a transformation of variables to turn a set of nonlinear differential equation into a set of approximate linear differential equations(i.e.,second order non-constant coefficients)which can in turn be solved using a version of the Harrow-Hassidim-Lloyd(HHL)quantum algorithm for the case of Hermitian matrices.We implement this approach using the Qiskit language and compute near-term results using a 4 qubit IBM Q System quantum computer.Comparisons with classical results and areas for future research are discussed.

Polyhedral Feasible Set Computation of MPC-Based Optimal Control Problems

Feasible sets play an important role in model predictive control(MPC) optimal control problems(OCPs). This paper proposes a multi-parametric programming-based algorithm to compute the feasible set for OCP derived from MPC-based algorithms involving both spectrahedron(represented by linear matrix inequalities) and polyhedral(represented by a set of inequalities) constraints. According to the geometrical meaning of the inner product of vectors, the maximum length of the projection vector from the feasible set to a unit spherical coordinates vector is computed and the optimal solution has been proved to be one of the vertices of the feasible set. After computing the vertices,the convex hull of these vertices is determined which equals the feasible set. The simulation results show that the proposed method is especially efficient for low dimensional feasible set computation and avoids the non-unicity problem of optimizers as well as the memory consumption problem that encountered by projection algorithms.

Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

This paper deals with the fixed-time adaptive time-varying matrix projective synchronization(ATVMPS)of different dimensional chaotic systems(DDCSs)with time delays and unknown parameters.Firstly,to estimate the unknown parameters,adaptive parameter updated laws are designed.Secondly,to realize the fixed-time ATVMPS of the time-delayed DDCSs,an adaptive delay-unrelated controller is designed,where time delays of chaotic systems are known or unknown.Thirdly,some simple fixed-time ATVMPS criteria are deduced,and the rigorous proof is provided by employing the inequality technique and Lyapunov theory.Furthermore,the settling time of fixed-time synchronization(Fix-TS)is obtained,which depends only on controller parameters and system parameters and is independent of the system’s initial states.Finally,simulation examples are presented to validate the theoretical analysis.

同态明文-密文矩阵运算及其应用

支持单指令多数据操作的同态加密方案能有效提高密文计算的均摊效率,但密文结构导致矩阵运算复杂度高。在许多应用中,采用明文-密文矩阵操作可以在确保安全的同时实现隐私计算。基于此,提出一个适用于任意维数的明文-密文矩阵乘法方案。该方案通过明文矩阵编码和密文矩阵维数变换等步骤计算得到密文结果。与已知最好的Jiang等所提的密文方阵乘法算法相比,所提方案支持任意维数的矩阵乘法,并支持矩阵连乘;理论分析和实验结果均表明,所提方案具有更低的密文旋转复杂度和更高的计算效率。将所提方案应用在隐私保护的贝叶斯分类器中,能以更高安全参数和更少计算时间完成分类任务。

用于有界噪声时变矩阵计算的终端零化神经网络

为提升零化神经网络(ZNN)求解时变矩阵计算问题时的收敛性能,提出一种具有抗噪能力的终端零化神经网络(TZNN)及其对数加速形式(LA-TZNN)。对误差动态的终态吸引性展开分析,结果表明所提网络在受到有界噪声干扰时仍能在固定时间内使误差归零,其中LA-TZNN可实现对数调节时间稳定,收敛速度相较于TZNN更快。考虑到实际情况中初始误差有界,给出半全局意义上的调节时间上界,并通过设置可调参数,使网络实现预定义时间稳定。将2种模型应用于时变矩阵求逆和PUMA560机械臂重复运动规划问题,仿真结果验证了所提方法相较于传统ZNN设计,调节时间更短,收敛精度更高,并能够有效抑制有界噪声干扰。

CT大重建矩阵联合重建算法对肺结节的诊断价值

目的探讨CT大重建矩阵1024×1024联合Karl迭代重建算法对肺结节的诊断价值。资料与方法前瞻性收集2021年10月—2022年5月于大连医科大学附属第一医院行胸部CT检查的500例患者,对CT扫描图像原始数据进行分组重建。A组采用常规512×512矩阵结合Karl 5级重建;B组采用1024×1024大重建矩阵结合不同等级Karl算法重建,获得B1(Karl 6)、B2(Karl 7)、B3(Karl 8)、B4(Karl 9)4个亚组。测量主动脉弓上方的气管腔内(气管区)及左肺上叶无血管区(肺实质)的CT值和噪声值,计算信噪比。由2位医师评价A、B组肺部总体图像质量。比较B组中图像质量最佳亚组与A组病灶显示情况,依据手术病理结果,分析诊断效能。结果B组组内随Karl等级升高,气管和肺实质标准差值逐渐下降,信噪比逐渐升高(F=675.002~2020.903,P<0.05)。B组各项主观评分均高于A组(Z=-15.361~-6.465,P<0.05),B4组主观评分最高。A组和B4组部分实性结节(≤3 mm)和实性结节(6.1 mm~≤3 cm)显示清晰度差异无统计学意义(Z=-2.000、-0.378,P>0.05);与A组相比,B4组结节显示清晰率提升12%~100%;胸膜凹陷征显示差异无统计学意义(χ^(2)=2.143,P>0.05)。以43例手术病理结果为诊断金标准,B4组诊断准确度为65.12%,优于A组的41.86%(χ^(2)=4.674,P<0.05)。结论大重建矩阵联合Karl算法可以获得较好的图像质量,有利于诊断肺结节。

面向GPU的地形遮蔽探测并行算法

地形遮蔽算法在军事、民航和气象分析等领域有广泛应用。随着仿真规模的扩大、仿真结果实时性要求越来越高,传统计算模型俨然不能满足当下的实时性要求。为解决这一不足,实现了在统一计算设备架构(CUDA)并行计算平台上的地形遮蔽探测算法,解决了仿真计算速度慢的问题。在CPU端将雷达探测区域内离散采样点的高程数据矩阵化,进而提升高程值在并行化计算中的读取速度。针对雷达仿真计算参数对线程分配方式进行优化,采用循环对比方式对地形遮蔽角的计算进行并行加速。采用设备端线程同步和数据交替传输技术,确保计算结果一致性和最大化利用GPU端计算资源。采用多模式并行化计算模式,使用多线程并行化计算和单线程串行化计算来支撑GPU端计算资源不足时的退化计算,从而保证计算的高可用。实验结果表明,相较于i7-12700H CPU在仿真粒度为3 600条探测波束下的地形遮蔽串行计算和多线程并行计算,在3060 Laptop GPU下分别获取了48倍和17倍加速,为仿真实时性提供了有效的工程解决方案。

基于矩阵乘积态的有限纠缠量子傅里叶变换模拟

与经典计算不同,在量子计算中量子比特可以处于叠加态,多个量子比特之间还可以形成纠缠态。表示n个量子比特组成的量子态需要存储2^(n)个振幅,这种指数级的存储开销使得大规模的量子模拟难以进行。然而当量子态的纠缠程度有限时,使用矩阵乘积态表示量子态仅需要线性的空间复杂度,可以扩大模拟的规模。使用HIP-Clang语言,基于CPU+DCU的异构编程模型,使用矩阵乘积态表示量子态,对量子傅里叶变换进行模拟。结合矩阵乘积态的特点,对量子傅里叶变换线路进行分析,减少模拟实现时不必要的张量缩并运算与正交化构建。对模拟过程中的张量缩并进行分析,使用TTGT算法完成张量缩并运算,同时利用DCU的并行处理能力来提高效率。对模拟结果进行分析,分别通过振幅误差与半经典Draper量子加法器的结果验证了模拟的正确性。对模拟规模进行分析,当量子态的纠缠熵最大时,使用16 GB的内存空间最多只能模拟24位的量子态,而当量子态内部纠缠程度较低时,可以对上百位的量子态进行量子傅里叶变换模拟。

1024×1024重建矩阵结合迭代重建算法在胃部CT血管成像中的应用

目的 探究1 024×1 024重建矩阵结合迭代重建(Karl)算法在胃部血管及肿瘤供血动脉CT血管成像中的应用价值。资料与方法 前瞻性收集大连医科大学附属第一医院2022年3—6月行胃部CT血管成像的胃部肿瘤患者30例,对CT扫描图像原始数据进行分组重建。A组采用常规512×512矩阵结合Karl 5级重建;B组采用1 024×1 024大重建矩阵结合不同等级Karl算法重建,分为B1(Karl 5)、B2(Karl 7)及B3(Karl 9)3个亚组。在轴位图像上测量胃左动脉起始部的腹主动脉、腹腔干、脾动脉、肝动脉及同层面腹壁皮下脂肪组织的CT值和SD值,计算信噪比(SNR)、对比噪声比(CNR)。由2名观察者采用5分法评估各组图像质量。结果 2名观察者主观评价一致性较好(Kappa=0.782~0.789,P<0.05),B1~B3组图像主观评分均优于A组,B2组得分最高(二维评分:χ^(2)=27.309、24.250;三维评分:χ^(2)=21.964、21.294;P均<0.05),30例患者中25例见胃动脉系统参与肿瘤供血,B2组各血管的清晰显示率均优于A组;A与B1、B2组各血管CT值差异无统计学意义(t=-1.918~2.720,P>0.05),B2组较A组血管SD值、SNR、CNR和背景噪声值,除腹主动脉SD、肝动脉CNR外差异均无统计学意义(t=-5.909~5.768,P>0.05);B1~3组图像随着Karl算法等级提高,SD值逐渐降低(F=2.881~27.109,P<0.05),SNR、CNR逐渐升高(F=3.612~12.149,P<0.05)。结论 1 024×1 024重建矩阵结合Karl 7级算法可以改善图像质量,增强胃部微细血管及肿瘤供血动脉分支的显示效果,在临床上有很好的应用价值。

石墨烯增强金属基复合材料界面研究进展

金属基复合材料是由高强度增强相与金属基体组成,因具备优良的综合性能,在各领域内展现出广阔的应用潜力。与常规增强相不同,石墨烯是一种由碳原子以sp^(2)杂化轨道组成六角呈蜂巢状晶格的二维碳纳米材料,因其独特的结构而具有优异的电学、力学、热学和光学等特性。石墨烯增强金属基复合材料已经成为先进复合材料领域的研究热点,而对于金属基复合材料,其综合性能与界面的结构和性质关联密切。从近年来石墨烯增强金属基复合材料界面微观组织及理论研究出发,对常见石墨烯增强金属基复合材料体系的界面结构及力学性能进行总结,同时总结计算机模拟手段在分析界面结构、界面结合强度以及界面微观断裂机制等方面的进展,为设计和优化金属基复合材料界面提供理论依据。

New criterion for delay-dependent absolute stability of Lurie system with interval time-varying delay

The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities （LMIs）. By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.

高性能稀疏矩阵向量乘的程序设计综述

稀疏矩阵向量乘(SpMV)广泛应用于科学计算、图计算、数据分析等领域,是自现代计算机诞生以来经久不衰且挑战依旧的研究热点。本文系统回顾了20世纪70年代以来稀疏矩阵向量乘程序设计的发展脉络和各阶段的代表性工作;分析比较了这一领域4条技术路线,即人工程序设计、自动调优器、稀疏编译器和自动程序设计器,在当今的流行方法;并在此基础上对高性能稀疏矩阵向量乘程序设计的研究趋势做出预测,力图给学习者和研究者带来有益的知识与启示。

高模量镁基材料实验和集成计算研究进展

镁合金由于低密度、高比强度、高阻尼以及良好的导热性等突出优点,广泛应用于航空航天领域,但其低弹性模量限制了其在大型薄壁构件中的可靠应用。本文针对如何提高镁基材料模量性能的问题,简介影响合金模量的主要因素,比较相关计算模型如等应力应变模型、混合定律、Halpin-Tsai模型以及两相复合材料模型的优缺点和适用范围,概括镁基材料模量性能研究的现状与进展,梳理镁基材料模量提升的两大途径以及性能提升机理。基于集成计算材料工程,提出了原子-晶格尺度类高模量铝合金开发和机器学习辅助优化实验设计的高强度高模量镁基材料集成开发策略。