A new parallel algorithm for solving large-scale Markov chains

In this paper, we propose a new parallel sparse iterative method (PPSIA) for computing the stationary distribution of large-scale Markov chains. The PPSIA method is based on Markov chain state isolation and aggregation techniques. The parallel method conserves as much as possible the benefits of aggregation, and Gauss–Seidel effects contained in the sequential algorithm (SIA) using a pipelined technique. Both SIA and PPSIA exploit sparse matrix representation in order to solve large-scale Markov chains. Some Markov chains have been tested to compare the performance of SIA, PPSIA algorithms with other techniques such as the power method, and the generalized minimal residual GMRES method. In all the tested models, PPSIA outperforms the other methods and shows a super-linear speed-up.     

Parallel exact sampling and evaluation of Gaussian Markov random fields

Markov chain Monte Carlo algorithms are computationally expensive for large models. Especially, the so-called one-block Metropolis-Hastings (M-H) algorithm demands large computational resources, and parallel computing seems appealing. A parallel one-block M-H algorithm for latent Gaussian Markov random field (GMRF) models is introduced. Important parts of this algorithm are parallel exact sampling and evaluation of GMRFs. Parallelisation is achieved with parallel algorithms from linear algebra for sparse symmetric positive definite matrices. The parallel GMRF sampler is tested for GMRFs on lattices and irregular graphs, and gives both good speed-up and good scalability. The parallel one-block M-H algorithm is used to make inference for a geostatistical GMRF model with a latent spatial field of 31,500 variables.     

基于瓦片算法的并行 QR 分解及其实现

本文介绍了一种基于瓦片算法的稠密矩阵并行 QR 分解及其实现方法。瓦片算法的思想是将完整的矩阵分块,并使每个块内的数据连续存储。各个瓦片块先独立进行分解,其他块接收当前块分解产生的数据,来更新自身块内的矩阵。我们分别实现了串行瓦片算法和并行瓦片算法,采用基于 MPI 和 OpenMP 混合并行编程模型,在“元”超级计算机上验证了该并行算法,并与 PLASMA 软件包进行对比,程序效率和可扩展性优于 PLASMA。 在多个节点上运行时,展现了良好的扩展性。     

三种GPU并行的自适应邻域模拟退火算法

提出了三种新的GPU并行的自适应邻域模拟退火算法,分别是GPU并行的遗传-模拟退火算法,多条马尔可夫链并行的退火算法,基于BLOCK分块的GPU并行模拟退火算法,并通过对GPU端的程序采取合并内存访问,避免bank冲突,归约法等方式进一步提升了性能。实验中选取了11个典型的基准函数,实验结果证明这三种GPU并行退火算法比nonu-SA算法具有更好的精度和更快的收敛速度。     

Estimation of Finite Probabilities via Aggregation of Markov Chains

An aggregated (trivial) chain with fewer number of states than for the initial Markov chain is constructed such that the finite probabilities of aggregated states equal the finite probabilities of the corresponding states of the initial Markov chain. A method is developed for determining the upper and lower estimates of finite probabilities of aggregated states from data defining the initial Markov chain. These estimates are related with the necessary and sufficient conditions for the classical aggregation of Markov chains. An example on computations is given.     

基于BLS聚合签名技术的平行链共识算法优化方案

目前,平行链的每个共识节点均需发送各自的共识交易到主链上以参与共识,这导致大量的共识交易严重占用主链的区块容量,并且浪费手续费。针对上述问题,利用平行链上的共识交易具有共识数据相同签名不同的特点,结合双线性映射技术,提出一种基于BLS聚合签名技术的平行链共识算法优化方案。首先,用共识节点对交易数据进行签名;然后,用平行链各节点通过点对点（P2P）网络在内部广播共识交易并同步消息;最后,由Leader节点统计共识交易,且当共识交易的数量大于2/3时,将对应的BLS签名数据聚合并发送交易聚合签名到主链上进行验证。实验结果表明,所提方案与原始平行链共识算法相比能够有效解决平行链上共识节点重复发送共识交易到主链的问题,在减少对主链存储空间的占用的同时节省交易手续费,只占用主链存储空间4 KB并且只产生一笔0.01比特元（BTY）的交易手续费。     

函数优化问题的一种异步并行模拟退火算法

针对工程中的多极值点复杂函数的优化问题,提出一种完全异步的粗粒度并行模拟退火算法.在一定时间内将一条Markov链分裂成多条Markov链,并结合其他多种改进方法,获得了可扩展的并行效果,提高了算法应用的灵活性.数值计算表明,该方法可显著提高算法的收敛速度.     

Block sampler and posterior mode estimation for asymmetric stochastic volatility models

A new efficient simulation smoother and disturbance smoother are introduced for asymmetric stochastic volatility models where there exists a correlation between today's return and tomorrow's volatility. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state-space model. The performance of our method is illustrated using two examples: (1) simple asymmetric stochastic volatility model and (2) asymmetric stochastic volatility model with state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable improvement in the mixing property of the Markov chain Monte Carlo chain.     

面向密码流处理器的AES算法软件流水实现方法

针对轮函数在分组密码实现过程中耗时过长的问题,提出了面向可重构密码流处理器（RCSP）的高级加密标准（AES）算法软件流水实现方法。该方法将轮函数操作划分为若干流水段,不同流水段对应不同的并行密码资源,通过并行执行多个轮函数的不同流水段,从而开发指令级并行性提高轮函数执行速度,进而提升分组密码的执行性能。在RCSP的单簇、双簇和四簇运算资源下分析了AES算法的流水线划分过程和软件流水映射方法,实验结果表明,该软件流水实现方法使得单分组或多分组不同数据分块的操作并行执行,不仅能够提升单分组串行执行性能,还能够通过开发分组间的并行性来提高多分组并行执行性能。     

Monte Carlo TD(λ)-methods for the optimal control of discrete-time Markovian jump linear systems

In this paper, we present an iterative technique based on Monte Carlo simulations for deriving the optimal control of the infinite horizon linear regulator problem of discrete-time Markovian jump linear systems for the case in which the transition probability matrix of the Markov chain is not known. We trace a parallel with the theory of TD(λ) algorithms for Markovian decision processes to develop a TD(λ) like algorithm for the optimal control associated to the maximal solution of a set of coupled algebraic Riccati equations (CARE). It is assumed that either there is a sample of past observations of the Markov chain that can be used for the iterative algorithm, or it can be generated through a computer program. Our proofs rely on the spectral radius of the closed loop operators associated to the mean square stability of the system being less than 1.     

基于时空混沌系统的图像分组加密算法

针对一般图像加密算法不能并行化运行的缺陷,提出一种新的基于耦合映象格子（CML）和分组加密技术的图像加密算法。首先对图像一部分进行分组,并迭代混沌系统,产生与图像分组数相同数目的混沌序列。使用混沌序列值与图像分组部分进行混合操作,其操作结果用来对图像另一部分进行加密。所提算法能够并行地实现图像加密,并可用于彩色图像加密。实验表明该加密算法计算简单,易于实现,密钥敏感性强,在安全性和效率上也有很好的表现。     

基于区域扩散机制的无线传感器网络时间同步算法

针对当前无线传感器网络时间同步算法无法满足物联网对于网络实时性的要求,提出了一种基于区域扩散的无线传感器网络时间同步算法。该算法分为两个阶段进行:第一阶段根据生物觅食理论(OFT),按照收益率最高的原理提出一种代言人信息选择算法(SIE)进行区域内时间同步;第二阶段根据时间偏移量最小节点选择区域代言人并在区域之间进行二次同步,同时将同步过程映射到马尔可夫链,提出基于马尔可夫链的代言人加速算法(MarSAA)。理论分析和实验证明,提出的算法具有较好的时间复杂性;并且两阶段算法可以并行进行,相对于传统算法在全网时间同步上具有非常好的性能。     

Lumpable hidden Markov models-model reduction and reducedcomplexity filtering

This paper is concerned with filtering of hidden Markov processes (HMP) which possess (or approximately possess) the property of lumpability. This property is a generalization of the property of lumpability of a Markov chain which has been previously addressed by others. In essence, the property of lumpability means that there is a partition of the (atomic) states of the Markov chain into aggregated sets which act in a similar manner as far as the state dynamics and observation statistics are concerned. We prove necessary and sufficient conditions on the HMP for exact lumpability to hold. For a particular class of hidden Markov models (HMM), namely finite output alphabet models, conditions for lumpability of all HMP representable by a specified HMM are given. The corresponding optimal filter algorithms for the aggregated states are then derived. The paper also describes an approach to efficient suboptimal filtering for HMP which are approximately lumpable. By this we mean that the HMM generating the process may be approximated by a lumpable HMM. This approach involves directly finding a lumped HMM which approximates the original HMM well, in a matrix norm sense. An alternative approach for model reduction based on approximating a given HMM by an exactly lumpable HMM is also derived. This method is based on the alternating convex projections algorithm. Some simulation examples are presented which illustrate the performance of the suboptimal filtering algorithms     

A block-tridiagonal solver with two-level parallelization for finite element-spectral codes

Two-level parallelization is introduced to solve a massive block-tridiagonal matrix system. One-level is used for distributing blocks whose size is as large as the number of block rows due to the spectral basis, and the other level is used for parallelizing in the block row dimension. The purpose of the added parallelization dimension is to retard the saturation of the scaling due to communication overhead and inefficiencies in the single-level parallelization only distributing blocks. As a technique for parallelizing the tridiagonal matrix, the combined method of “Partitioned Thomas method” and “Cyclic Odd–Even Reduction” is implemented in an MPI-Fortran90 based finite element-spectral code (TORIC) that calculates the propagation of electromagnetic waves in a tokamak. The two-level parallel solver using thousands of processors shows more than 5 times improved computation speed with the optimized processor grid compared to the single-level parallel solver under the same conditions. Three-dimensional RF field reconstructions in a tokamak are shown as examples of the physics simulations that have been enabled by this algorithmic advance.     

A robust digital image watermarking technique using lifting wavelet transform and firefly algorithm

In this paper, an optimized and robust digital image watermarking technique based on lifting wavelet transform (LWT) and firefly algorithm is proposed. LWT is newer and faster generation of former wavelet transforms and firefly algorithm is an efficient optimizing algorithms. In current technique, base image decomposed by LWT into 4 sub bands then the first sub band separated into non overlapping blocks. After that blocks are sorted in order of descending based on standard derivation of each block. Selecting suitable blocks for special embedding process seems to be an optimization problem due to existence of a trade-off between imperceptibility and robustness. Firefly algorithm used to solve this trade-off while selecting primary blocks causes high robustness and low imperceptibility and vice versa. For improving security, Arnold transform applied to watermark and achieved scrambled image bits used as condition for embedding process. The proposed technique evaluated by variety of attacks like additive noise, average filter, median filter, sharpening filter and some other geometric and non-geometric attacks and experimental results showed its good imperceptibility and high robustness.     

基于边缘块的线段提取方法

为了解决传统直线提取算法中由于梯度信息孤立而造成检测效果不理想的问题,本文提出结合边缘块的连通域信息进行边缘连接的直线提取方法.首先提取图像边缘图,利用边缘点的连通域,建立边缘点标注模型,进行边缘块搜索.然后用邻接矩阵统计边缘块之间的位置信息,采用深度优先搜素算法,得到初始路径.最后利用直线的几何特征作为路径筛选条件,...     

分级的混合模式布局算法

针对混合模式的布局问题提出一种分级的自动布局算法.所谓混合模式就是标准单元和宏模块相结合的布局模式.该算法在模块级和单元级两个层次上完成布局.在模块级上,首先将所有随机单元划分成若干软模块,然后采用基于序列对(sequence pair,简称SP)的方法完成模块布局;在单元级上,首先对每个软模块内部采用二次规划的布局算法进行布局,然后在全芯片范围内对布局进行改善,最后采用一种基于最小割(min-cut)和枚举相结合的快速详细布局算法完成最终布局.在一组标准单元数和宏模块数不同的电路上对该算法进行了验证,效果是令人满意的.     

Computing bounds for the performance indices of quasi-lumpablestochastic well-formed nets

Structural symmetries in stochastic well-formed colored Petri nets (SWN's) lead to behavioral symmetries that can be exploited by using the symbolic reachability graph (SRG) construction algorithm. The SRC allows one to compute an aggregated reachability graph (RG) and a “lumped” continuous time Markov chain (CTMC) that contain all the information needed to study the qualitative properties and the performance of the modeled system, respectively. Some models exhibit qualitative behavioral symmetries that are not completely reflected at the CTMC level. We call them quasi-lumpable SWN models. In these cases, exact performance indices can be obtained by avoiding the aggregation of those markings that are qualitatively, but not quantitatively, equivalent. An alternative approach consists of aggregating all the qualitatively equivalent states and computing approximated performance indices. In this paper, a technique is proposed to compute bounds on the performance of SWN models of this kind, using the results we have presented elsewhere. The technique is based on the Courtois and Semal bounded aggregation method     

基于局部最优分析的纺织品瑕疵检测方法

针对复杂的含有周期变化图案的纺织品瑕疵检测,提出改进Markov随机场模型的无监督纺织品瑕疵检测方法.应用随机场实现周期性纺织品图像的瑕疵检测,利用Markov邻域特性,综合判断瑕疵区域.结合周期图像分割,确定Markov随机场最小图像块计算单元,降低算法的计算复杂度.在随机场势函数定义中,综合考虑相邻图像块的差异特性,结合Markov随机场的全局性判断瑕疵点的位置.引入模糊相似关系矩阵概念,求解改进后的模型参数,使所有图像块的局部能量达到最优.实验表明,文中方法对样本的查全率较高.     

循环分块在MPI程序设计中的应用研究

提出了循环分块在MPI系统中的块分配方案———列组分配方案,并给出了在不同并行体系结构下依据列组分配方案计算块分配大小的算法。实验表明算法计算出的块分配方法对于发挥循环流水并行的效率有着较好的作用。