工件的释放时间和加工时间具有一致性的单机在线排序问题研究

工件的释放时间和加工时间具有一致性, 是指释放时间大的工件其加工时间不小于释放时间小的工件的加工时间, 即若$r_{i}\geq r_{j}$, 则$p_{i}\geq p_{j}$。本文在该一致性约束下, 研究最小化最大加权完工时间单机在线排序问题, 和最小化总加权完工时间单机在线排序问题, 并分别设计出$\frac{\sqrt{5}+1}{2}$-竞争的最好可能在线算法。     

稀疏表示及其在人脸识别中的应用

稀疏表示是近年来新兴的一种数据表示方法,是对人类大脑皮层编码机制的模拟。稀疏表示以其良好的鲁棒性、抗干扰能力、可解释性和判别性等优势,广泛应用于模式识别领域。基于稀疏表示的分类器在人脸识别领域取得了令人惊喜的成就,它将训练样本看成字典,寻求测试样本在字典下的最稀疏的表示,即用尽可能少的训练样本的线性组合来重构测试样本。但是经典的基于稀疏表示的分类器没有考虑训练样本的类别信息,以致被选中的训练样本来自许多类,不利于分类,因此基于组稀疏的分类器被提出。组稀疏方法考虑了训练样本的类别相似性,其目的是用尽可能少类别的训练样本来表示测试样本,然而这类方法的缺点是同类的训练样本或者同时被选中或者同时被丢弃。在实际中,人脸受到光照、表情、姿势甚至遮挡等因素的影响,样本之间关系比较复杂,因此最后介绍局部加权组结构稀疏表示方法。该方法尽量用来自于与测试样本相似的类的训练样本和来自测试样本邻域的训练样本来表示测试样本,以减轻不相关类的干扰,并使得表示更稀疏和更具判别性。     

Spatially Weighted Principal Component Analysis for Imaging Classification

The aim of this article is to develop a supervised dimension-reduction framework, called spatially weighted principal component analysis (SWPCA), for high-dimensional imaging classification. Two main challenges in imaging classification are the high dimensionality of the feature space and the complex spatial structure of imaging data. In SWPCA, we introduce two sets of novel weights, including global and local spatial weights, which enable a selective treatment of individual features and incorporation of the spatial structure of imaging data and class label information. We develop an efficient two-stage iterative SWPCA algorithm and its penalized version along with the associated weight determination. We use both simulation studies and real data analysis to evaluate the finite-sample performance of our SWPCA. The results show that SWPCA outperforms several competing principal component analysis (PCA) methods, such as supervised PCA (SPCA), and other competing methods, such as sparse discriminant analysis (SDA).     

一类稀疏约束非线性规划的约束规格

研究一类带有闭凸集约束的稀疏约束非线性规划问题,这类问题在变量选择、模式识别、投资组合等领域具有广泛的应用.首先引进了限制性Slater约束规格的概念,证明了该约束规格强于限制性M-F约束规格,然后在此约束规格成立的条件下,分析了其局部最优解成立的充分和必要条件.最后,对约束集合的两种具体形式,指出限制性Slater约束规格必满足,并给出了一阶必要性条件的具体表达形式.     

A Comparative Study on Dynamic and Static Sparsity Patterns in Parallel Sparse Approximate Inverse Preconditioning

Sparse approximate inverse (SAI) techniques have recently emerged as a new class of parallel preconditioning techniques for solving large sparse linear systems on high performance computers. The choice of the sparsity pattern of the SAI matrix is probably the most important step in constructing an SAI preconditioner. Both dynamic and static sparsity pattern selection approaches have been proposed by researchers. Through a few numerical experiments, we conduct a comparable study on the properties and performance of the SAI preconditioners using the different sparsity patterns for solving some sparse linear systems. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spatial organization in a plant model

In this paper, a spatial plant-wrack model is presented. We find such model has spotted pattern dynamics by using both mathematical analysis and numerical simulations. The obtained results may point that the distribution of the plant in space is self-organized.     

Parallel sparse linear algebra and application to structural mechanics

The framework of this paper is the parallelization of a plasticity algorithm that uses an implicit method and an incremental approach. More precisely, we will focus on some specific parallel sparse linear algebra algorithms which are the most time-consuming steps to solve efficiently such an engineering application. First, we present a general algorithm which computes an efficient static scheduling of block computations for parallel sparse linear factorization. The associated solver, based on a supernodal fan-in approach, is fully driven by this scheduling. Second, we describe a scalable parallel assembly algorithm based on a distribution of elements induced by the previous distribution for the blocks of the sparse matrix. We give an overview of these algorithms and present performance results on an IBM SP2 for a collection of grid and irregular problems. This revised version was published online in June 2006 with corrections to the Cover Date.     

Circulant Wavelet Preconditioners for Solving Elliptic Differential Equations and Boundary Integral Equations

In this paper is discussed solving an elliptic equation and a boundary integral equation of the second kind by representation of compactly supported wavelets. By using wavelet bases and the Galerkin method for these equations, we obtain a stiff sparse matrix that can be ill-conditioned. Therefore, we have to introduce an operator which maps every sparse matrix to a circulant sparse matrix. This class of circulant matrices is a class of preconditioners in a Banach space. Based on having some properties in the spectral theory for this class of matrices, we conclude that the circulant matrices are a good class of preconditioners for solving these equations. We called them circulant wavelet preconditioners (CWP). Therefore, a class of algorithms is introduced for rapid numerical application.     

Sparse Deep Neural Network for Nonlinear Partial Differential Equations

More competent learning models are demanded for data processing due to increasingly greater amounts of data available in applications. Data that we encounter often have certain embedded sparsity structures. That is, if they are represented in an appropriate basis, their energies can concentrate on a small number of basis functions. This paper is devoted to a numerical study of adaptive approximation of solutions of nonlinear partial differential equations whose solutions may have singularities, by deep neural networks (DNNs) with a sparse regularization with multiple parameters. Noting that DNNs have an intrinsic multi-scale structure which is favorable for adaptive representation of functions, by employing a penalty with multiple parameters, we develop DNNs with a multi-scale sparse regularization (SDNN) for effectively representing functions having certain singularities. We then apply the proposed SDNN to numerical solutions of the Burgers equation and the Schrödinger equation. Numerical examples confirm that solutions generated by the proposed SDNN are sparse and accurate.     

Stable chaos in fluctuation driven neural circuits

We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare mean versus fluctuations driven networks, the former (latter) is realized by considering purely excitatory (inhibitory) sparse neural circuits. In the excitatory case the instabilities of the system can be completely captured by an usual linear stability (Lyapunov) analysis, whereas the inhibitory networks can display the coexistence of linear and nonlinear instabilities. The nonlinear effects are associated to finite amplitude instabilities, which have been characterized in terms of suitable indicators. For inhibitory coupling one observes a transition from chaotic to non chaotic dynamics by decreasing the pulse-width. For sufficiently fast synapses the system, despite showing an erratic evolution, is linearly stable, thus representing a prototypical example of stable chaos.     

A power sparse approximate inverse preconditioning procedure for large sparse linear systems

Motivated by the Cayley–Hamilton theorem, a novel adaptive procedure, called a Power Sparse Approximate Inverse (PSAI) procedure, is proposed that uses a different adaptive sparsity pattern selection approach to constructing a right preconditioner M for the large sparse linear system Ax=b. It determines the sparsity pattern of M dynamically and computes the n independent columns of M that is optimal in the Frobenius norm minimization, subject to the sparsity pattern of M. The PSAI procedure needs a matrix–vector product at each step and updates the solution of a small least squares problem cheaply. To control the sparsity of M and develop a practical PSAI algorithm, two dropping strategies are proposed. The PSAI algorithm can capture an effective approximate sparsity pattern of A^?1 and compute a good sparse approximate inverse M efficiently. Numerical experiments are reported to verify the effectiveness of the PSAI algorithm. Numerical comparisons are made for the PSAI algorithm and the adaptive SPAI algorithm proposed by Grote and Huckle as well as for the PSAI algorithm and three static Sparse Approximate Inverse (SAI) algorithms. The results indicate that the PSAI algorithm is at least comparable to and can be much more effective than the adaptive SPAI algorithm and it often outperforms the static SAI algorithms very considerably and is more robust and practical than the static ones for general problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Solving regression problem with complementary neural networks and an adjusted averaging technique

This research deals with complementary neural networks (CMTNN) for the regression problem. Complementary neural networks consist of a pair of neural networks called truth neural network and falsity neural network, which are trained to predict truth and falsity outputs, respectively. In this paper, a novel adjusted averaging technique is proposed in order to enhance the result obtained from the basic CMTNN. We test our proposed technique based on the classical benchmark problems including housing, concrete compressive strength, and computer hardware data sets from the UCI machine learning repository. We also realize our technique to the porosity prediction problem based on well log data set obtained from practical field data in the oil and gas industry. We found that our proposed technique provides better performance when compared to the traditional CMTNN, backpropagation neural network, and support vector regression with linear, polynomial, and radial basis function kernels.     

A discrete dynamics approach to sparse calculation and applied in ontology science

ABSTRACT

In the era of big data, with the increase of data processing information and the increase of data complexity, higher requirements are put on the tools and algorithms of data processing. As a tool for structured information representation, ontology has been used in engineering fields such as chemistry, biology, pharmacy, and materials. As a dynamic structure, the increasing concepts contributes to a gradual increase of a single ontology. In order to solve the problem of computational complexity decreasing in the procedure of similarity calculating, the techniques of dimensionality reduction and sparse computing are applied to ontology learning. This article presents discrete dynamics approach showing several tricks on applying the sparse computing method to ontology learning, and verify its efficiency through experiments.     

PowerNet: Efficient Representations of Polynomials and Smooth Functions by Deep Neural Networks with Rectified Power Units

Deep neural network with rectified linear units (ReLU) is getting more and more popular recently. However, the derivatives of the function represented by a ReLU network are not continuous, which limit the usage of ReLU network to situations only when smoothness is not required. In this paper, we construct deep neural networks with rectified power units (RePU), which can give better approximations for smooth functions. Optimal algorithms are proposed to explicitly build neural networks with sparsely connected RePUs, which we call PowerNets, to represent polynomials with no approximation error. For general smooth functions, we first project the function to their polynomial approximations, then use the proposed algorithms to construct corresponding PowerNets. Thus, the error of best polynomial approximation provides an upper bound of the best RePU network approximation error. For smooth functions in higher dimensional Sobolev spaces, we use fast spectral transforms for tensor-product grid and sparse grid discretization to get polynomial approximations. Our constructive algorithms show clearly a close connection between spectral methods and deep neural networks: PowerNets with $n$ hidden layers can exactly represent polynomials up to degree $s^n$, where $s$ is the power of RePUs. The proposed PowerNets have potential applications in the situations where high-accuracy is desired or smoothness is required.     

利用分片贪婪算法求解分片稀疏恢复问题

在实际应用中,有一些信号是具有分片的结构的.本文我们提出一种分片正交匹配追踪算法(P\_OMP)来求解分片稀疏恢复问题,旨在保护分片信号中的分片结构(或者小尺度非零元).P\_OMP算法是基于CoSaMP和OMMP算法的思想上延伸出的一种针对分片稀疏问题的贪婪算法. P\_OMP算法不仅仅具有OMP算法的优势,还能够在比CoSaMP方法更松弛的条件下得到同样的误差下降速率.进一步,P\_OMP~算法在保护分片稀疏信号的尺度细节信息上表现的更好.数值实验表明相比于CoSaMP, OMP, OMMP和BP算法, P\_OMP算法在分片稀疏恢复上更有效更稳定.     

Using spatial games to model dynamic evolutionary systems

Modelling the dynamics of evolutionary competing species on a physical grid is a challenging modelling problem. This paper presents a novel modelling approach for synthesizing evolutionary dynamics of competing species using a spatial game perspective. This modelling approach describes the movement of players (‘species’ in our context) across a lattice. The model is based on a payoff function which controls the move likelihood and direction of the players (‘predators’ and ‘preys’). Using simulated results, the paper provides a comparison between the spatial game model and an existing predator-prey dynamic model. Finally, a case study is performed to illustrate the application of this formalism and validate the model.     

基于Spectral Tetris算法的框架的最佳稀疏性

当信号维数较大时,使用稀疏框架分解信号就能减少大量的加法和乘法运算,所以,研究稀疏框架很有意义.本文介绍有限框架的稀疏性,并研究基于Spectral Tetris算法构造的框架的稀疏性.首先,给出基于Spectral Tetris算法的框架的最佳稀疏性;其次,得到基于Spectral Tetris算法的可剖分紧框架的最佳稀疏性.     

A Bayesian network model for spatial event surveillance

Methods for spatial cluster detection attempt to locate spatial subregions of some larger region where the count of some occurrences is higher than expected. Event surveillance consists of monitoring a region in order to detect emerging patterns that are indicative of some event of interest. In spatial event surveillance, we search for emerging patterns in spatial subregions.A well-known method for spatial cluster detection is Kulldorff’s [M. Kulldorff, A spatial scan statistic, Communications in Statistics: Theory and Methods 26 (6) (1997)] spatial scan statistic, which directly analyzes the counts of occurrences in the subregions. Neill et al. [D.B. Neill, A.W. Moore, G.F. Cooper, A Bayesian spatial scan statistic, Advances in Neural Information Processing Systems (NIPS) 18 (2005)] developed a Bayesian spatial scan statistic called BSS, which also directly analyzes the counts.We developed a new Bayesian-network-based spatial scan statistic, called BNetScan, which models the relationships among the events of interest and the observable events using a Bayesian network. BNetScan is an entity-based Bayesian network that models the underlying state and observable variables for each individual in a population.We compared the performance of BNetScan to Kulldorff’s spatial scan statistic and BSS using simulated outbreaks of influenza and cryptosporidiosis injected into real Emergency Department data from Allegheny County, Pennsylvania. It is an open question whether we can obtain acceptable results using a Bayesian network if the probability distributions in the network do not closely reflect reality, and thus, we examined the robustness of BNetScan relative to the probability distributions used to generate the data in the experiments. Our results indicate that BNetScan outperforms the other methods and its performance is robust relative to the probability distribution that is used to generate the data.     

Beamforming and Interference Cancellation for Capacity Gain in Mobile Networks

The growth of wireless communication continues. There is a demand for more user capacity from new subscribers and new services such as wireless internet. In order to meet these expectations new and improved technology must be developed. A way to increase the capacity of an existing mobile radio network is to exploit the spatial domain in an efficient way. An antenna array adds spatial domain selectivity in order to improve the Carrier-to-Interference ratio (C/I) as well as Signal-to-Noise Ratio (SNR). An adaptive antenna array can further improve the Carrier-to-Interference ratio (C/I) by suppressing interfering signals and steer a beam towards the user. The suggested scheme is a combination of a beamformer and an interference canceller.The proposed structure is a circular array consisting of K omni-directional elements and combines fixed beamforming with interference cancelling. The fixed beamformers use a weight matrix to form multiple beams. The interference cancelling stage suppresses undesired signals, leaking into the desired beam.The desired signal is filtered out by the fixed beamforming structure. Due to the side-lobes, interfering signals will also be present in this beam. Two alternative strategies were chosen to cancel these interferers; use the other beamformer outputs as inputs to an adaptive interference canceller; or regenerate the outputs from the other beamformer outputs and generate clean signals which are used as inputs to adaptive interference cancellers.Resulting beamformer patterns as well as interference cancellation simulation results are presented. Two different methods have been used to design the beamformer weights, Least Square (LS) and minimax optimisation. In the minimax optimisation a semi-infinite linear programming approach was used. Although the optimisation plays an essential role in the performance of the beamformer, this paper is focused on the application rather then the optimisation methods.     

Spatial Lasso With Applications to GIS Model Selection

Geographic information systems (GIS) organize spatial data in multiple two-dimensional arrays called layers. In many applications, a response of interest is observed on a set of sites in the landscape, and it is of interest to build a regression model from the GIS layers to predict the response at unsampled sites. Model selection in this context then consists not only of selecting appropriate layers, but also of choosing appropriate neighborhoods within those layers. We formalize this problem as a linear model and propose the use of Lasso to simultaneously select variables, choose neighborhoods, and estimate parameters. Spatially dependent errors are accounted for using generalized least squares and spatial smoothness in selected coefficients is incorporated through use of a priori spatial covariance structure. This leads to a modification of the Lasso procedure, called spatial Lasso. The spatial Lasso can be implemented by a fast algorithm and it performs well in numerical examples, including an application to prediction of soil moisture. The methodology is also extended to generalized linear models. Supplemental materials including R computer code and data analyzed in this article are available online.