Embedding multi-dimensional meshes into twisted cubes

The twisted cube is an important variant of the most popular hypercube network for parallel processing. In this paper, we consider the problem of embedding multi-dimensional meshes into twisted cubes in a systematic way. We present a recursive method for embedding a family of disjoint multi-dimensional meshes into a twisted cube with dilation 1 and expansion 1. We also prove that a single multi-dimensional mesh can be embedded into a twisted cube with dilation 2 and expansion 1. Our work extends some previously known results.     

Tests and Proofs

This special issue collects current advances in the ongoing attempt to obtain synergies from the combination of Tests and Proofs.     

Direct raycasting of unstructured cell-centered data by discontinuity Roe-average computation

In the field of computational fluid dynamics (CFD), the upwind finite volume method (FVM) is widely applied to solve 3D flows with discontinuity phenomena (e.g., shock waves). It produces unstructured data at the center of each cell (cell-centered data) with the flow discontinuity constraint on the inner-face between face-neighboring cells. For visualization, existing approaches with interpolation usually pre-extrapolate cell-centered data into cell-vertexed data (data values given at cell vertices) and only handle cell-vertexed data during actual rendering, which unconsciously depress the rendering accuracy and violate the discontinuity constraint. In this paper, we propose a novel method to visualize cell-centered data directly avoiding extrapolation and keep the discontinuity in the rendering data on the framework of multi-pass raycasting. During resampling, the field is reconstructed using the original cell-centered data value and the cell-gradient estimated by Green–Gauss theorem. To keep the discontinuity, we reconstruct the field at an inner-face resampled point using both the face-adjacencies and get two discontinuous field values. Then the field is obtained by computing Roe-average of the two. The analysis and experiments demonstrate that our approach gains a high-accuracy reconstruction and leads to a high-quality image.     

Optimal Error Estimates of the Legendre Tau Method for Second-Order Differential Equations

In this paper, we prove that the Legendre tau method has the optimal rate of convergence in L ²-norm, H ¹-norm and H ²-norm for one-dimensional second-order steady differential equations with three kinds of boundary conditions and in C([0,T];L ²(I))-norm for the corresponding evolution equation with the Dirichlet boundary condition. For the generalized Burgers equation, we develop a Legendre tau-Chebyshev collocation method, which can also be optimally convergent in C([0,T];L ²(I))-norm. Finally, we give some numerical examples.     

Fast and highly scalable parallel computations for fundamental matrix problems on distributed memory systems

We present fast and highly scalable parallel computations for a number of important and fundamental matrix problems on distributed memory systems (DMS). These problems include matrix multiplication, matrix chain product, and computing the powers, the inverse, the characteristic polynomial, the determinant, the rank, the Krylov matrix, and an LU- and a QR-factorization of a matrix, and solving linear systems of equations. Our highly scalable parallel computations for these problems are based on a highly scalable implementation of the fastest sequential matrix multiplication algorithm on DMS. We show that compared with the best known parallel time complexities on parallel random access machines (PRAM), the most powerful but unrealistic shared memory model of parallel computing, our parallel matrix computations achieve the same speeds on distributed memory parallel computers (DMPC), and have an extra polylog factor in the time complexities on DMS with hypercubic networks. Furthermore, our parallel matrix computations are fully scalable on DMPC and highly scalable over a wide range of system size on DMS with hypercubic networks. Such fast (in terms of parallel time complexity) and highly scalable (in terms of our definition of scalability) parallel matrix computations were rarely seen before on any distributed memory systems.     

Sliding Mode Control with Adaptive Fuzzy Dead-Zone Compensation of an Electro-hydraulic Servo-System

Electro-hydraulic servo-systems are widely employed in industrial applications such as robotic manipulators, active suspensions, precision machine tools and aerospace systems. They provide many advantages over electric motors, including high force to weight ratio, fast response time and compact size. However, precise control of electro-hydraulic systems, due to their inherent nonlinear characteristics, cannot be easily obtained with conventional linear controllers. Most flow control valves can also exhibit some hard nonlinearities such as dead-zone due to valve spool overlap. This work describes the development of an adaptive fuzzy sliding mode controller for an electro-hydraulic system with unknown dead-zone. The boundedness and convergence properties of the closed-loop signals are proven using Lyapunov stability theory and Barbalat’s lemma. Numerical results are presented in order to demonstrate the control system performance.     

Infinitesimal Perturbation Analysis in Networks of Stochastic Flow Models: General Framework and Case Study of Tandem Networks with Flow Control

This paper presents a general algorithmic framework for computing the IPA derivatives of sample performance functions defined on networks of fluid queues. The underlying network-model consists of bi-layered hybrid dynamical systems with continuous-time dynamics at the lower layer and discrete-event dynamics at the upper layer. The linearized system, computed from the sample path via a discrete-event process, yields fairly simple algorithms for the IPA derivatives. As an application-example, the paper discusses loss and workload performance functions in a tandem network with congestion control, subjected to signal delays.     

Do organisational and environmental factors moderate the effects of Internet-based interorganisational systems on firm performance?

We developed a model of the relationships among several organisational, interorganisational and technological factors, the adoption of Internet-based interorganisational systems (IBIS) and various measures of firm performance. We used structural equation modelling to empirically test these relationships. The findings showed that adopting IBIS indirectly improves the operational performance of firms through business process performance. The positive effect on financial performance of adopting IBIS is not direct, but through the mediating effects of operational performance and business process performance. We also utilised multiple group analysis to test some of the model relationships across firms using several organisational and environmental factors as moderators. The organisational factors tested are firm type, age and ownership type. The environmental factors consisted of dynamism, complexity and hostility. We found that the organisational factors are significant moderators and that complexity and hostility are not significant moderators. However, the effects of dynamism as a moderator are less clear.