Balancing conflicting requirements for grid and particle decomposition in continuum-Lagrangian solvers

Load balancing strategies for hybrid solvers that involve grid based partial differential equation solution coupled with particle tracking are presented in this paper. A typical Message Passing Interface (MPI) based parallelization of grid based solves are done using a spatial domain decomposition while particle tracking is primarily done using either of the two techniques. One of the techniques is to distribute the particles to MPI ranks to whose grid they belong to while the other is to share the particles equally among all ranks, irrespective of their spatial location. The former technique provides spatial locality for field interpolation but cannot assure load balance in terms of number of particles, which is achieved by the latter. The two techniques are compared for a case of particle tracking in a homogeneous isotropic turbulence box as well as a turbulent jet case. A strong scaling study is performed to more than 32,000 cores, which results in particle densities representative of anticipated exascale machines. The use of alternative implementations of MPI collectives and efficient load equalization strategies are studied to reduce data communication overheads.     

A multi-dimensional solver for the steady Euler equations

In this paper a numerical algorithm for the solution of the multi-dimensional steady Euler equations in conservative and non-conservative form is presented. Most existing standard and multi-dimensional schemes use flux balances with assumed constant distribution of variables along each cell edge, which interfaces two grid cells. This assumption is believed to be one of the main reasons for the limited advantage gained from multi-dimensional high order discretisations compared to standard one-dimensional ones. The present algorithm is based on the optimisation of polynomials describing the distribution of flow variables in grid cells, where only polynomials that satisfy the Euler equations in the entire grid cell can be selected. The global solution is achieved if all polynomials and by that the flow variables are continuous along edges interfacing neighbouring grid cells. A discrete approximation of a given spatial order is converged if the deviation between polynomial distributions of adjacent grid cells along the interfacing edge of the cells is minimal. Results from the present scheme between first and fifth order spatial accuracy are compared to standard first and second order Roe computations for simple test cases demonstrating the gain in accuracy for a number of sub- and supersonic flow problems.     

A multiobjective spatial fuzzy clustering algorithm for image segmentation

This article describes a multiobjective spatial fuzzy clustering algorithm for image segmentation. To obtain satisfactory segmentation performance for noisy images, the proposed method introduces the non-local spatial information derived from the image into fitness functions which respectively consider the global fuzzy compactness and fuzzy separation among the clusters. After producing the set of non-dominated solutions, the final clustering solution is chosen by a cluster validity index utilizing the non-local spatial information. Moreover, to automatically evolve the number of clusters in the proposed method, a real-coded variable string length technique is used to encode the cluster centers in the chromosomes. The proposed method is applied to synthetic and real images contaminated by noise and compared with k-means, fuzzy c-means, two fuzzy c-means clustering algorithms with spatial information and a multiobjective variable string length genetic fuzzy clustering algorithm. The experimental results show that the proposed method behaves well in evolving the number of clusters and obtaining satisfactory performance on noisy image segmentation.     

Application of the galerkin method to the solution of burgers' equation

The Galerkin method, with an expansion of B-splines is used to solve Burgers' equation from an initial state involving a discontinuity in the space domain.In an initial series of calculations a fixed spatial distribution of knots is used to define the B-splines, and the effect upon accuracy of changes in the order of the spline and the number of terms in the expansion is examined.In a second series of calculations the spatial distribution of knots is varied as the solution advances through time so that an area of fine knot resolution is maintained in the region where the solution of Burgers' equation changes most rapidly. Results of high accuracy are obtained using this method, which avoids the necessity of having a fine resolution knot distribution over the whole spatial domain in order to achieve an accurate solution.     

Aggregation without Loss of Optimality in Competitive Location Models

In the context of competitive facility location problems demand points often have to be aggregated due to computational intractability. However, usually this spatial aggregation biases the value of the objective function and the optimality of the solution cannot be guaranteed for the original model. We present a preprocessing aggregation method to reduce the number of demand points which prevents this loss of information, and therefore avoids the possible loss of optimality. It is particularly effective in the frequent situation with a large number of demand points and a comparatively low number of potential facility sites, and coverage defined by spatial nearness. It is applicable to any spatial consumer behaviour model of covering type. This aggregation approach is applied in particular to a Competitive Maximal Covering Location Problem and to a recently developed von Stackelberg model. Some empirical results are presented, showing that the approach may be quite effective. This research was partially supported by the projects OZR1067 and SEJ2005-06273ECON.     

Spatially explicit individual-based modeling using a fixed super-individual density

Individual-based models (IBMs) of planktonic microorganisms (e.g., bacterioplankton, phytoplankton) have to simulate large numbers of individuals. Because of computational limitations these models rely on simulating a number of super-individuals that are representative of a larger number of individuals. Using a fixed representative number (the number of individuals one super-individual represents) results in a lower computational resolution (number of super-individuals) at times and in areas of low individual densities, which is undesirable when (a) large temporal and/or spatial gradients exist and (b) variability in state variables or behavior at low densities is important. Various methods exist that fix the number of super-individuals in the global model domain by allowing the representative number to vary in time. Those methods solve the problem introduced by large temporal gradients, but do not address spatial gradients. This paper presents an accounting method that maintains an approximately constant super-individual density in time and space. Each spatial model segment has a local super-individual population that is resampled when the number shrinks or grows outside user-specified bounds, or when the variance of the representative numbers exceeds a user-specified threshold. This local method is compared to a global method and evaluated quantitatively against the analytical solution to an instantaneous input (slug release) into a river, and qualitatively in a biogeochemical phytoplankton model applied to a point source nutrient discharge into a river. Computations are performed using the iAlgae individual-based phytoplankton modeling framework. The applications demonstrate that the local method results in a spatially uniform or density-independent relative error, and it is computationally more efficient at controlling relative error at low densities. However, for the same total number of super-individuals, it is computationally more demanding and therefore less efficient at controlling absolute error. The local method is superior to the global method for the biogeochemical model application, because a significant spatial gradient (front) exists and the dynamics at the low densities affects the model behavior downstream.     

Spatial inference with geometric proportional analogies

We describe an instance-based reasoning solution to a variety of spatial reasoning problems. The solution centers on identifying an isomorphic mapping between labelled graphs that represent some problem data and a known solution instance. We describe a number of spatial reasoning problems that are solved by generating non-deductive inferences, integrating topology with area (and other) features. We report the accuracy of our algorithm on different categories of spatial reasoning tasks from the domain of Geographical Information Science. The generality of our approach is illustrated by also solving geometric proportional (IQ-test type) analogy problems.     

Tensor-based methods for blind spatial signature estimation under arbitrary and unknown source covariance structure

Spatial signature estimation is a problem encountered in several applications in signal processing such as mobile communications, sonar, radar, astronomy and seismology. In this paper, we propose higher-order tensor methods to solve the blind spatial signature estimation problem using planar arrays. By assuming that sources' powers vary between successive time blocks, we recast the spatial and spatiotemporal covariance models for the received data as third-order PARATUCK2 and fourth-order Tucker4 tensor decompositions, respectively. Firstly, by exploiting the multilinear algebraic structure of the proposed tensor models, new iterative algorithms are formulated to blindly estimate the spatial signatures. Secondly, in order to achieve a better spatial resolution, we propose an expanded form of spatial smoothing that returns extra spatial dimensions in comparison with the traditional approaches. Additionally, by exploiting the higher-order structure of the resulting expanded tensor model, a multilinear noise reduction preprocessing step is proposed via higher-order singular value decomposition. We show that the increase on the tensor order provides a more efficient denoising, and consequently a better performance compared to existing spatial smoothing techniques. Finally, a solution based on a multi-stage Khatri–Rao factorization procedure is incorporated as the final stage of our proposed estimators. Our results demonstrate that the proposed tensor methods yield more accurate spatial signature estimates than competing approaches while operating in a challenging scenario where the source covariance structure is unknown and arbitrary (non-diagonal), which is actually the case when sample covariances are computed from a limited number of snapshots.     

Oracle空间关系处理能力扩充的研究与实现

针对传统GIS基于客户端的空间关系处理的不足,文章提出了将空间关系处理放在数据库管理系统（DBMS）中实现的解决方案,并扩充了Oracle的空间关系处理能力。文章首先分析和研究了在DBMS中实现空间关系处理必须具备的条件;然后,对Oracle提供的基于对象机制的空间关系处理解决方案——Oracle Spatial进行了深入的分析和研究;考虑到目前的GIS系统大多采用Oracle RDBMS来存储管理空间数据,文章最后重点研究了如何利用Oracle的扩展机制在传统的Oracle RDBMS中实现空间关系处理,并给出了具体实现。     

Three-dimensional static analysis,of a spatially loaded planar rigid-jointed plexus frame

An exact matrix solution for the static analysis of a multi-storey and multi-column rectangular rigid-jointed plexus frame, subjected to a general spatial loading, is presented. Since the obtained closed-form formulae, giving all the structure redundants, include matrices of maximum dimensions mn × mn (where m = number of storeys and n = number of columns), the proposed methodology is more convenient compared to other existing methods, because it requires less memory space and computer coding. Also, a numerical application demonstrates the correctness and the potentialities of the method. In addition, this solution technique may become a useful guideline for the further investigation of three-dimensional frame structures.     

Spatial branch-and-bound algorithm for MIQCPs featuring multiparametric disaggregation

Spatial branch-and-bound (B&B) is widely used for the global optimization of non-convex problems. It basically works by iteratively reducing the domain of the variables so that tighter relaxations can be achieved that ultimately converge to the global optimal solution. Recent developments for bilinear problems have brought us piecewise relaxation techniques that can prove optimality for a sufficiently large number of partitions and hence avoid spatial B&B altogether. Of these, normalized multiparametric disaggregation (NMDT) exhibits a good performance due to the logarithmic increase in the number of binary variables with the number of partitions. We now propose to integrate NMDT with spatial B&B for solving mixed-integer quadratically constrained minimization problems. Optimality-based bound tightening is also part of the algorithm so as to compute tight lower bounds in every step of the search and reduce the number of nodes to explore. Through the solution of a set of benchmark problems from the literature, it is shown that the new global optimization algorithm can potentially lead to orders of magnitude reduction in optimality gap when compared to commercial solvers BARON and GloMIQO.     

K-means Iterative Fisher (KIF) unsupervised clustering algorithm applied to image texture segmentation

The K-means Iterative Fisher (KIF) algorithm is a robust, unsupervised clustering algorithm applied here to the problem of image texture segmentation. The KIF algorithm involves two steps. First, K-means is applied. Second, the K-means class assignments are used to estimate parameters required for a Fisher linear discriminant (FLD). The FLD is applied iteratively to improve the solution. This combined K-means and iterative FLD is referred to as the KIF algorithm. Two KIF implementations are presented: a mixture resolving approach is extended to an unsupervised binary hierarchical approach. The same binary hierarchical KIF algorithm is used to properly segment images even though the number of classes, the class spatial boundaries, and the number of samples per class vary. The binary hierarchical KIF algorithm is fully unsupervised, requires no a priori knowledge of the number of classes, is a non-parametric solution, and is computationally efficient compared to other methods used for clustering in image texture segmentation solutions. This unsupervised methodology is demonstrated to be an improvement over other published texture segmentation results using a wide variety of test imagery. Gabor filters and co-occurrence probabilities are used as texture features.     

BIM 空间关系数据的云存储与检索方法研究

随着工程项目体量的增大,模型中存在的空间关系更加复杂多样化,现有的建筑 信息模型(BIM)数据存储和检索方式无法满足使用要求。为了提高 BIM 中大量空间关系数据的 存储和检索效率,通过集成 BIM 与云计算技术,提出了一种 BIM 分布式负载均衡集群方案, 在此基础上利用弹性搜索框架(Elastic Search)和图数据库Neo4j实现了IFC空间关系数据的云存 储和检索,为海量 BIM 空间关系数据提供一种高效快速的云存储和检索方法。     

基于边缘增强与光谱特性保持的Pan-sharpening融合模型

为生成兼具高光谱质量与高空间质量的融合图像,本文提出了一种新的Pan-sharpening变分融合模型.通过拟合退化后的全色（Panchromatic,Pan）波段图像与低分辨率多光谱（Multispectral,MS）波段图像间的线性关系得到各波段MS图像的权重系数,计算从Pan图像抽取的空间细节;基于全色波段图像的梯度定义加权函数,增强了图像的强梯度边缘并对因噪声而引入的虚假边缘进行了抑制,有效地保持了全色波段图像中目标的几何结构;基于MS波段传感器的调制传输函数定义低通滤波器,自适应地限制注入空间细节的数量,显著降低了融合MS图像的光谱失真;针对Pan-sharpening模型的不适定性问题,引入L1正则化能量项,保证了数值解的稳定性.采用Split Bregman数值方法求解能量泛函的最优解,提高了算法的计算效率.QuickBird、IKONOS和GeoEye-1数据集上的实验结果表明,模型的综合融合性能优于MTF-CON、AWLP、SparseFI、TVR和MTF-Variational等算法.     

Determination of Aircraft Orientation for a Vision-Based System Using Artificial Neural Networks

An algorithm for real-time estimation of 3-D orientation of an aircraft, given its monocular, binary image from an arbitrary viewing direction is presented. This being an inverse problem, we attempt to provide an approximate but a fast solution using the artificial neural network technique. A set of spatial moments (scale, translation, and planar rotation invariant) is used as features to characterize different views of the aircraft, which corresponds to the feature space representation of the aircraft. A new neural network topology is suggested in order to solve the resulting functional approximation problem for the input (feature vector)-output (viewing direction) relationship. The feature space is partitioned into a number of subsets using a Kohonen clustering algorithm to express the complex relationship into a number of simpler ones. Separate multi-layer perceptrons (MLP) are then trained to capture the functional relations that exist between each class of feature vectors and the corresponding target orientation. This approach is shown to give better results when compared to those obtained with a single MLP trained for the entire feature space.     

Classification of Spatial Properties for Spatial Allocation Modeling

Given a set of spatial units, such as land parcels and grid cells, how to allocate subsets of it to activities of interest while satisfying certain criteria? Such a decision process is here called spatial allocation. Though many problems of spatial allocation share this generic construct, each may have a quite unique set of criteria and interpret even the same criteria in its own way. Such diversity makes it difficult to model spatial allocation problems in unambiguous terms that are amenable to algorithmic solution. This paper proposes a classification scheme for spatial properties that helps to address a variety of spatial properties in establishing spatial allocation criteria. The implication of the paper is that a number of spatial properties and spatial allocation criteria can be decomposed into a few kinds of primitive spatial properties and their relations.     

Post-buckling analysis of spatial structures by vector iteration methods

The present study is concerned with the application of two vector iteration methods in the investigation of the large deflection behavior of spatial structures. The dynamic relaxation and the first order conjugate gradient belong to this category of methods which do not require the computation or formulation of any tangent stiffness matrix. The convergence to the solution is achieved by using only vectorial quantities and no stiffness matrix is required in its overall assembled form. In an effort to evaluate the merits of the methods, extensive numerical studies were carried out on a number of selected structural systems. The advantages of using these vector iteration methods, in tracing the post-buckling behavior of spatial structures, are demonstrated.     

Optimal Relay Assignment and Power Allocation for Cooperative Communications

Cooperative communication for wireless networks has gained a lot of recent interest due to its ability to mitigate fading with exploration of spatial diversity. In this paper, we study a joint optimization problem of jointly considering transmission mode selection, relay assignment and power allocation to maximize the capacity of the network through cooperative wireless communications. This problem is much more challenging than relay assignment considered in literature work which simply targets to maximize the transmission capacity for a single transmission pair. We formulate the problem as a variation of the maximum weight matching problem where the weight is a function over power values which must meet power constraints (VMWMC). Although VMWMC is a non-convex problem whose complexity increases exponentially with the number of relay nodes, we show that the duality gap of VMWMC is virtual zero. Based on this result, we propose a solution using Lagrange dual decomposition to reduce the computation complexity. We do simulations to evaluate the performance of the proposed solution. The results show that our solution can achieve maximum network capacity with much less computation time compared with exhaustive search, and our solution outperforms existing sub-optimal solutions that can only achieve much lower network capacity.     

Performance of local search heuristics on scheduling a class of pipelined multiprocessor tasks

This paper presents the evaluation of the solution quality of heuristic algorithms developed for scheduling multiprocessor tasks for a class of multiprocessor architectures designed to exploit temporal and spatial parallelism simultaneously. More specifically, we deal with multi-level or partitionable architectures where MIMD parallelism and multiprogramming support are the two main characteristics of the system. We investigate scheduling a number of pipelined multiprocessor tasks with arbitrary processing times and arbitrary processor requirements in this system. The scheduling problem consists of two interrelated sub-problems, which are finding a sequence of pipelined multiprocessor tasks on a processor and finding a proper mapping of tasks to the processors that are already being sequenced. For the solution of the second problem, various techniques are available. However, the problem remains of generating a feasible sequence for the pipelined operations. We employed three well-known local search heuristic algorithms that are known to be robust methods applicable to various optimization problems. These are Simulated Annealing, Tabu Search, and Genetic Algorithms. We then conduct computational experiments and evaluate the reduction achieved in completion time by each heuristic. We have also compared the results with well-known simple list-based heuristics.     

结合基因表达式编程与空间模糊聚类的图像分割

目的 针对模糊C-均值聚类图像分割方法存在的对初始值敏感及抗噪性能差的问题,提出一种结合基因表达式编程与空间模糊聚类的图像分割方法。方法 首先,利用基因表达式编程算法对图像进行初次分割,即将聚类中心编码成染色体,通过适应度评价引导搜索获得优化的聚类中心;然后在隶属度计算中引入空间函数,以初次分割结果作为初始值,使用空间模糊聚类对图像进行二次分割。结果 对加噪的合成图像和Berkeley图像的分割实验显示,本文方法在聚类划分系数（VPC）、聚类划分熵（VPE）和峰值信噪比（PSNR）等评价指标上总体性能优于经典的模糊C-均值聚类和空间模糊C-均值聚类分割算法,其中VPC值平均高出0.062 4和0.061 1,VPE值平均降低0.117 0和0.101 1,而PSNR值平均提升了约13.312 1 dB和3.308 4 dB;在对Berkeley图像库中的6幅图片的分割实验显示,本文方法对图像分割的VPC值均在0.93以上,相比两种对比方法平均提高0.157 6和0.013 3,VPE值保持在0.1附近,均低于对比方法,PSNR值平均提高2.896 3 dB和1.934 4 dB;在多目标分割实验上,随着聚类数目增加,3种方法的分割性能均有下降,但本文方法性能曲线最为平缓,受聚类数目的影响最小。虽然本文方法所需的运行时间略有增加,但求解所需的迭代次数却极大地减少。结论 本文提出的图像分割方法具有很强的抗噪性、更高的分割精度和稳定性,适用于需要更精确结果、对时间要求不高的分割场景。