Contour estimation via two fidelity computer simulators under limited resources

The utilization of multiple fidelity simulators for the design and analysis of computer experiments has received increased attention in recent years. In this paper, we study the contour estimation problem for complex systems by considering two fidelity simulators. Our goal is to design a methodology of choosing the best suited simulator and input location for each simulation trial so that the overall estimation of the desired contour can be as good as possible under limited simulation resources. The proposed methodology is sequential and based on the construction of Gaussian process surrogate for the output measure of interest. We illustrate the methodology on a canonical queueing system and evaluate its efficiency via a simulation study.     

The extensional ordering of the sequential functionals

We investigate the extensional ordering of the sequential functionals of finite types, with a focus on when the sequential functionals of a given type form a directed complete partial ordering, and on when a finite sequential functional will be the nontrivial least upper bound of an infinite chain of sequential functionals. We offer a full characterization for finite functionals of pure types.     

全函数空间和置换空间的一些性质

In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the property （u） in substitution spaces are obtained.     

Pseudospectral reduction of incompressible two-dimensional turbulence

Spectral reduction was originally formulated entirely in the wavenumber domain as a coarse-grained wavenumber convolution in which bins of modes interact with enhanced coupling coefficients. A Liouville theorem leads to inviscid equipartition solutions when each bin contains the same number of modes. A pseudospectral implementation of spectral reduction which enjoys the efficiency of the fast Fourier transform is described. The model compares well with full pseudospectral simulations of the two-dimensional forced-dissipative energy and enstrophy cascades.     

Numerical experiments with ABS algorithms for linear systems on a parallel machine

Numerical results are obtained on sequential and parallel versions of ABS algorithms for linear systems for both full matrices andq-band matrices. The results using the sequential algorithm on full matrices indicate the superiority of a particular implementation of the symmetric algorithm. The condensed form of the algorithm is well suited for implementation in a parallel environment, and results obtained on the IBM 4381 system favor a synchronous implementation over the asynchronous one. Results are obtained from sequential implementations of theLU, Cholesky, and symmetric algorithms of the ABS class forq-band matrices able to reduce memory storage. A simple parallelization of do-loops for calculating components gives interesting performances.This work has been developed in the framework of a collaboration between IBM-ECSEC, Rome, Italy, and the Department of Mathematics of the University of Bergamo, Bergamo, Italy.The author is grateful to Prof. J. Abaffy (University of Economics, Budapest), Prof. L. Dixon (Hatfield Polytechnic), and Prof. E. Spedicato (Department of Mathematics, University of Bergamo) for useful suggestions.     

Numerical solution of a heat diffusion problem by boundary element methods using the Laplace transform

This paper is concerned with a heat diffusion problem in a half-space which is motivated by the detection of material defects using thermal measurements. This problem is solved by inverting the Laplace transform with respect to time on a contour in the complex plane using an exponentially convergent quadrature rule. This leads to a finite number of time-independent problems, which can be solved in parallel using boundary integral equation methods. We provide a full numerical analysis of this scheme on compact time intervals. Our results are formulated in a way that they can easily be used for other diffusion problems in exterior or interior domains.     

A note on accelerated sequential estimation of the mean of NEF-PVF distributions

The minimum risk point estimation for the mean is addressed for a natural exponential family (NEF) that also has a power variance function (PVF) under a loss function given by the squared error plus linear cost. An appropriate accelerated version of the full purely sequential methodology of Bose and Boukai (1993b, submitted) is proposed along the lines of Mukhopadhyay (1993a, Tech. Report, No. 93-27, Department of Statistics, University of Connecticut) in order to achieve operational savings. The main result provides the asymptotic second-order expansion of the regret function associated with the accelerated sequential estimator of the population mean.     

Bayes theorem,information number and behavior of posteior distributions

Summary According to the sequential decision theory, one is directed to; (i) stop when the posterior distribution, having been successively watched, frist enters the domain in which by stopping he loses less, and then (ii) take that action which gives him the least loss averaged w.r.t. the current posterior distribution (Blackwell-Girshick [1], p. 254). For some reasons we don't know, however, the successive behavior of posterior distribution never draws the full attention of statisticians and probabilists, though some of them have developed the asymptotic theory. As far as the sequential decision theory is concerned, however, the asymptotic behavior tells us nothing, since the stopping rule is only related to finite time. Toe compute the posterior distribution time by time is a laborious task. But to site all possible posterior distributions sometimes facilitates our manipulation of the sequential decision problem. This paper proposes some methods. The Institute of Statistical Mathematics     

Fluid flows around cascades

Flows induced by the small-amplitude and high frequency harmonic oscillations of a cascade of bodies in an unbounded fluid which is otherwise at rest are investigated theoretically. In the theoretical study we separate the flow into inner and outer regions. The flow in the inner region is governed by the Stokes boundary-layer equation. The first-order outer flow is governed by the potential solution which is found by using a conformai mapping technique. The second-order outer flow is governed by the full Navier-Stokes equation and the steady streaming flow has been obtained using a modified central-difference scheme for cascades with square cylinders and flat plates for values of the streaming Reynolds number,R _s , up to 70. These results show a complicated flow structure.     

Period-doubling cascades for large perturbations of Hénon families

The Hénon family has been shown to have period-doubling cascades. We show here that the same occurs for a much larger class: Large perturbations do not destroy cascades. Furthermore, we can classify the period of a cascade in terms of the set of orbits it contains, and count the number of cascades of each period. This class of families extends a general theory explaining why cascades occur [5].     

Berechnung der reibungslosen Strömung für ein vorgegebenes ebenes Schaufelgitter bei hohen Unterschallgeschwindigkeiten

Summary A simple approximation method based onPrandtl-Glauert's rule is given for the calculation of inviscous compressible flow through a two-dimensional cascade. It is applicable to cascades of any solidity and stagger angle with blade sections of small thickness and camber. The calculation of compressible flow for a predetermined cascade at a given Mach number is reduced to the calculation of an ‘associated incompressible flow’ through a cascade having blades of the same blade section, a higher solidity and larger angle of stagger. This associated incompressible cascade flow can be conveniently calculated on the basis of a method disclosed byH. Schlichting [2]. Comparison of some computed pressure distributions along the blade contour reveals satisfactory agreement with measurements in the high-speed cascade wind tunnel of the Deutsche Forschungsanstalt für Luftfahrt (DFL; German Research Centre for Aviation), Brunswick.

---

---

Eine ausführliche Ver?ffentlichung dieser Untersuchungen ist in ?Forschung auf dem Gebiete des Ingenieurwesens?24, 19–28, (1958), erschienen.     

A Bahadur efficiency comparison between one and two sample rank statistics and their sequential rank statistic analogues

One and two sample rank statistics are shown in general to be more efficient in the Bahadur sense than their sequential rank statistic analogues as defined by Mason (1981, Ann. Statist.9 424–436) and Lombard (1981, South African Statist. J.15 129–152), even though the two families of statistics (those based on full ranks and those based on sequential ranks) have the same Pitman efficiency against local alternatives. In the process, general results on large deviation probabilities and laws of large numbers for statistics based on sequential ranks are obtained.     

Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree

The contour tree is an abstraction of a scalar field that encodes the nesting relationships of isosurfaces. We show how to use the contour tree to represent individual contours of a scalar field, how to simplify both the contour tree and the topology of the scalar field, how to compute and store geometric properties for all possible contours in the contour tree, and how to use the simplified contour tree as an interface for exploratory visualization.     

Generalized best choice problem based on the information economics approach

We consider the problem of choosing the ‘best choice’ among a certain number of objects that are presented to a decision-maker in sequential order. Such a sequential selection problem is commonly referred to as the ‘best choice problem’, and its optimal stopping rule has been obtained either via the dynamic programming approach or via the Markovian approach. Based on the theory of information economics, we propose in the paper the third approach to a generalized version of the best choice problem that is intuitively more appealing. Various types of the best choice problem, such as (1) the classical secretary problem, (2) no information group interview problem, and (3) full information best choice problem with a random walk process, are shown to be special cases of the generalized best choice problem. The modelling framework of information economics has potential for building theory that ultimately would produce practical stopping rules.     

Two linear-time algorithms for computing the minimum length polygon of a digital contour

The Minimum Length Polygon (MLP) is an interesting first order approximation of a digital contour. For instance, the convexity of the MLP is characteristic of the digital convexity of the shape, its perimeter is a good estimate of the perimeter of the digitized shape. We present here two novel equivalent definitions of MLP, one arithmetic, one combinatorial, and both definitions lead to two different linear time algorithms to compute them. This paper extends the work presented in Provençal and Lachaud (2009) [26], by detailing the algorithms and providing full proofs. It includes also a comparative experimental evaluation of both algorithms showing that the combinatorial algorithm is about 5 times faster than the other. We also checked the multigrid convergence of the length estimator based on the MLP.     

A block Arnoldi-type contour integral spectral projection method for solving generalized eigenvalue problems

For generalized eigenvalue problems, we consider computing all eigenvalues located in a certain region and their corresponding eigenvectors. Recently, contour integral spectral projection methods have been proposed for solving such problems. In this study, from the analysis of the relationship between the contour integral spectral projection and the Krylov subspace, we conclude that the Rayleigh–Ritz-type of the contour integral spectral projection method is mathematically equivalent to the Arnoldi method with the projected vectors obtained from the contour integration. By this Arnoldi-based interpretation, we then propose a block Arnoldi-type contour integral spectral projection method for solving the eigenvalue problem.     

An axiomatic semantics for nested concurrency

We give transformation rules for the concurrent parts of Hoare's language CSP, transforming concurrent CSP programs into nondeterministic, sequential programs.On the basis of these transformations we define an axiomatic semantics for CSP with nested concurrency.This axiomatic system includes a rule for binary, associative process composition, enabling modular verification dealing with parts of concurrent systems as well as full programs.The proof system is fully abstract, in the sense that the internal structure of processes is irrelevant in the specification inasmuch it is not externally observable.An outline of a verification of a recursive, concurrent sorter is given as an example.     

A scenario for the creation of chaotic attractors in Chua’s system

We investigate a scenario for the creation of irregular chaotic attractors in Chua’s system. We show that irregular attractors in Chua’s system are created by those and only those mechanisms that characterize Lorenz, Rössler, and other dissipative nonlinear systems described by ordinary differential equations. These mechanisms include cascades of Feigenbaum period doubling bifurcations, subharmonic cascades of cycle bifurcations in Sharkovskii’s order, and homoclinic cascades of bifurcations.     

Limit theorems for generalized sequential rank statistics

Summary A general class of statistics based on sequential ranks is introduced. Under suitable regularity conditions, an almost sure representation and invariance principle are established for this class. In particular, it is shown that these statistics can obey invariance principles that are radically different from those obeyed by the usual full rank statistics.Research supported by the CSIR and the University of South AfricaResearch supported by the University of Delaware Research Foundation, Grant #8325530015     

Application in Aerohydrodynamics of the Solution of an Inverse Boundary Value Problem for Analytic Functions

We consider a modified inverse boundary value problem of aerohydrodynamics in which it is required to find the shape of an airfoil streamlined by a potential flow of an incompressible nonviscous fluid, when the distribution of the velocity potential on one section of the airfoil is given as a function of the abscissa, while, on other sections of the airfoil, as a function of the ordinate of the point. The velocity of the undisturbed flow streamlining the sought-for airfoil is determined in the process of solving the problem. It is shown that, under rather general conditions on the initially set functions, the sought-for contour is closed unlike the inverse problem in the case when, on the unknown contour, the velocity distribution is given as a function of the arc abscissa of the contour point. We also consider the case when, on the entire desired contour, the distribution of the velocity potential is given as a function of one and the same Cartesian coordinate of the contour point.