Convolutional solutions of partial difference equations

A significant part of the theory of one-dimensional linear shift-invariant systems is based on the concept of weighting function (or impulse response): the output is the convolution of the weighting function with the input. This paper introduces the concept of linear translation-invariant systems and uses this notion in studying impulse response, z-transforms, and transfer functions for multidimensional systems.     

Multidimensional ARKN methods for general oscillatory second-order initial value problems

Based on B-series theory, the order conditions of the multidimensional ARKN methods are presented for the general multi-frequency and multidimensional oscillatory second-order initial value problems by Wu et al. (2009). These multidimensional ARKN methods exactly integrate the multi-frequency and multidimensional unperturbed oscillators. In this paper, we pay attention to the analysis of the concrete multidimensional ARKN methods for the general multi-frequency oscillatory second-order initial value problems whose right-hand side functions depend on both  y$y$and  y^′$y^{\prime }$ (the class of physical problems which fall within its scope is broader). Numerical experiments are carried out to show that the new multidimensional ARKN methods are more efficient compared with some well-known methods for dealing with the oscillatory problems in the scientific literature.     

Kokkos: Enabling manycore performance portability through polymorphic memory access patterns

The manycore revolution can be characterized by increasing thread counts, decreasing memory per thread, and diversity of continually evolving manycore architectures. High performance computing (HPC) applications and libraries must exploit increasingly finer levels of parallelism within their codes to sustain scalability on these devices. A major obstacle to performance portability is the diverse and conflicting set of constraints on memory access patterns across devices. Contemporary portable programming models address manycore parallelism (e.g., OpenMP, OpenACC, OpenCL) but fail to address memory access patterns. The Kokkos C++ library enables applications and domain libraries to achieve performance portability on diverse manycore architectures by unifying abstractions for both fine-grain data parallelism and memory access patterns. In this paper we describe Kokkos’ abstractions, summarize its application programmer interface (API), present performance results for unit-test kernels and mini-applications, and outline an incremental strategy for migrating legacy C++ codes to Kokkos. The Kokkos library is under active research and development to incorporate capabilities from new generations of manycore architectures, and to address a growing list of applications and domain libraries.     

电子商务模式的多维分类体系研究

电子商务模式的开展是实现电子商务应用的重要问题之一.为充分探讨电子商务模式的体系建立,在总结已有成果基础上,本文基于电子商务模式的分类讨论十大类基本的电子商务模式,分析构建多维电子商务模式分类体系.     

高校统考课程成绩数据仓库的建立与应用

通过分析高校统考课程成绩对高校教学进行分析决策的重要价值,以计算机基础统考课程成绩为实例,建立一个基于高校统考课程成绩的数据仓库模型。该成绩数据仓库不仅综合分析学生的总得分,而且将试卷难度和题型得分也做深入分析,分析结果不仅能让教学管理者了解到学生成绩波动趋势,而且可以更详细地知道成绩波动的原因所在,从而能帮助教学管理者更加科学快速地做出有效的决策,最终达到提高教学水平的目的。     

A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization

New challenges in engineering design lead to multiobjective (multicriteria) problems. In this context, the Pareto front supplies a set of solutions where the designer (decision-maker) has to look for the best choice according to his preferences. Visualization techniques often play a key role in helping decision-makers, but they have important restrictions for more than two-dimensional Pareto fronts. In this work, a new graphical representation, called Level Diagrams, for n-dimensional Pareto front analysis is proposed. Level Diagrams consists of representing each objective and design parameter on separate diagrams. This new technique is based on two key points: classification of Pareto front points according to their proximity to ideal points measured with a specific norm of normalized objectives (several norms can be used); and synchronization of objective and parameter diagrams. Some of the new possibilities for analyzing Pareto fronts are shown. Additionally, in order to introduce designer preferences, Level Diagrams can be coloured, so establishing a visual representation of preferences that can help the decision-maker. Finally, an example of a robust control design is presented - a benchmark proposed at the American Control Conference. This design is set as a six-dimensional multiobjective problem.     

Analysis of Two-Dimensional Non-Rigid Shapes

Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major problems in the analysis of non-rigid shapes: similarity, partial similarity, and correspondence. We present an axiomatic construction of similarity criteria for deformation-invariant shape comparison, based on intrinsic geometric properties of the shapes, and show that such criteria are related to the Gromov-Hausdorff distance. Next, we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole, and present a construction of set-valued distances, based on the notion of Pareto optimality. Finally, we show that the correspondence between non-rigid shapes can be obtained as a byproduct of the non-rigid similarity problem. As a numerical framework, we use the generalized multidimensional scaling (GMDS) method, which is the numerical core of the three problems addressed in this paper.     

Hard multidimensional multiple choice knapsack problems, an empirical study

Recent advances in algorithms for the multidimensional multiple choice knapsack problems have enabled us to solve rather large problem instances. However, these algorithms are evaluated with very limited benchmark instances. In this study, we propose new methods to systematically generate comprehensive benchmark instances. Some instances with special correlation properties between parameters are found to be several orders of magnitude harder than those currently used for benchmarking the algorithms. Experiments on an existing exact algorithm and two generic solvers show that instances whose weights are uncorrelated with the profits are easier compared with weakly or strongly correlated cases. Instances with classes containing similar set of profits for items and with weights strongly correlated to the profits are the hardest among all instance groups investigated. These hard instances deserve further study and understanding their properties may shed light to better algorithms.     

Global and robust formation-shape stabilization of relative sensing networks

This paper proposes a simple, distributed algorithm that achieves global stabilization of formations for relative sensing networks in arbitrary dimensions with fixed topology. Assuming the network runs an initialization procedure to equally orient all agent reference frames, convergence to the desired formation shape is guaranteed even in partially asynchronous settings. We characterize the algorithm robustness against several sources of errors: link failures, measurement errors, and frame initialization errors. The technical approach combines algebraic graph theory, multidimensional scaling, and distributed linear iterations.