Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.

A transputer-based extended hypercube

The Extended Hypercube is a new approach in multiprocessor architectures, which reduces the communication burden on the processor elements. We propose a scheme for implementing such an architecture using INMOS transputers as the processor and controller elements to achieve a very high computation to communication ratio.

Composite Performance and Reliability Analysis for Hypercube Systems

In this paper we propose a novel technique to model and ana¿ lyze the performability of parallel and distributed architectures using GSPN-reward models.

Load balancing algorithms for an extended hypercube

Reduction of the execution time of a job through equitable distribution of work load among the processors in a distributed system is the goal of load balancing. Performance of static and dynamic load balancing algorithms for the extended hypercube, is discussed. Threshold algorithms are very well-known algorithms for dynamic load balancing in distributed systems. An extension of the threshold algorithm, called the multilevel threshold algorithm, has been proposed. The hierarchical interconnection network of the extended hypercube is suitable for implementing the proposed algorithm. The new algorithm has been implemented on a transputer-based system and the performance of the algorithm for an extended hypercube is compared with those for mesh and binary hypercube networks

Influence of Spatial Variability on Pavement Responses Using Latin Hypercube Sampling on Two-Dimensional Random Fields

Although uncertainties in material properties have been addressed in the design of flexible pavements, most current modeling techniques assume that pavement layers are homogeneous. The paper addresses the influence of the spatial variability of the resilient moduli of pavement layers by evaluating the effect of the variance and correlation length on the pavement responses to loading. The integration of the spatially varying log-normal random field with the finite-difference method has been achieved through an exponential autocorrelation function. The variation in the correlation length was found to have a marginal effect on the mean values of the critical strains and a noticeable effect on the standard deviation which decreases with decreases in correlation length. This reduction in the variance arises because of the spatial averaging phenomenon over the softer and stiffer zones generated because of spatial variability. The increase in the mean value of critical strains with decreasing correlation length, although minor, illustrates that pavement performance is adversely affected by the presence of spatially varying layers. The study also confirmed that the higher the variability in the pavement layer moduli, introduced through a higher value of coefficient of variation (COV), the higher the variability in the pavement response. The study concludes that ignoring spatial variability by modeling the pavement layers as homogeneous that have very short correlation lengths can result in the underestimation of the critical strains and thus an inaccurate assessment of the pavement performance. (C) 2014 American Society of Civil Engineers.

Latin hypercube sampling used in the calculation of the fracture probability

The paper proposes Latin hypercube sampling combined with the stratified sampling of variance reduction technique to calculate accurate fracture probability. In the compound sampling, the number of simulations is relatively small and the calculation error is satisfactory.

Continuous dynamical systems that realize discrete optimization on the hypercube

We study the problem of finding a local minimum of a multilinear function E over the discrete set {0,1}n. The search is achieved by a gradient-like system in [0,1]n with cost function E. Under mild restrictions on the metric, the stable attractors of the gradient-like system are shown to produce solutions of the problem, even when they are not in the vicinity of the discrete set {0,1}n. Moreover, the gradient-like system connects with interior point methods for linear programming and with the analog neural network studied by Vidyasagar (IEEE Trans. Automat. Control 40 (8) (1995) 1359), in the same context. © 2004 Elsevier B.V. All rights reserved.

On the maximal connected component of hypercube with faulty vertices

In evaluating an interconnection network, it is indispensable to estimate the size of the maximal connected components of the underlying graph when the network begins to lose processors. Hypercube is one of the most popular interconnection networks. This article addresses the maximal connected components of an n -dimensional cube with faulty processors. We first prove that an n -cube with a set F of at most 2n - 3 failing processors has a component of size greater than or equal to2(n) - \F\ - 1. We then prove that an n -cube with a set F of at most 3n - 6 missing processors has a component of size greater than or equal to2(n) - \F\ - 2.

On the maximal connected component of hypercube with faulty vertices (II)

evaluating the fault tolerance of an interconnection network, it is essential to estimate the size of a maximal connected component of the network at the presence of faulty processors. Hypercube is one of the most popular interconnection networks. In this paper, we prove that for ngreater than or equal to6, an n-dimensional cube with a set F of at most (4n-10) failing processors has a component of size greater than or equal to2"-\F-3. This result demonstrates the superiority of hypercube in terms of the fault tolerance.

On the maximal connected component of a hypercube with faulty vertices III

Hypercube is one of the most popular topologies for connecting processors in multicomputer systems. In this paper we address the maximum order of a connected component in a faulty cube. The results established include several known conclusions as special cases. We conclude that the hypercube structure is resilient as it includes a large connected component in the presence of large number of faulty vertices.

Case-based system: Indexing and retrieval with fuzzy hypercube

In some applications with case-based system, the attributes available for indexing are better described as linguistic variables instead of receiving numerical treatment. In these applications, the concept of fuzzy hypercube can be applied to give a geometrical interpretation of similarities among cases. This paper presents an approach that uses geometrical properties of fuzzy hypercube space to make indexing and retrieval processes of cases.

Incorporating priorities for waiting customers in the hypercube queuing model with application to an emergency medical service system in Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Spin glasses on the hypercube

We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the nontrivial problem of generating these lattices. Afterward, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are the following: i the dynamics is ruled by an infinite number of time sectors, ii the aging dynamics consists of the growth of coherent domains with a nonvanishing surface-volume ratio, and iii the propagator in Fourier space follows the p4 law. We study as well the finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well.