Large Number Of Points Research Articles

Reply to our discussants

Let us begin by thanking our eight discussants. It is an unexpected blessing to have received careful and extensive consideration from such a constructive and fair-minded group. Our reaction to their comments is perhaps better understood with some autobiographical perspective. As is probably evident to any reader, we are not econometricians. This is not to offer an excuse for any shortcomings of our work, but to explain that it was motivated by interests somewhat different than the typical interests of econometricians. We are both applied monetary/macroeconomists, and one of us is particularly interested in the philosophical and methodological problems of empirical economics. We have both done applied work on causal inference in macroeconomics, using concepts and techniques substantially different from those that originate in the work of Clive Granger. In our causal investigations, we have used LSE specification procedures. Our experience has been, contrary to our initial expectation, that the validity of these procedures, which we took to be fairly well established, was more often questioned by referees than was the validity of the causal methodologies that we proposed, and which we regarded as novel. We were faced with a dual problem: on the one hand convincing referees and editors that our applied work made sense; and, on the other hand, assuaging the doubts that were naturally raised in our own minds by intelligent critics. Thus, while we had a natural predisposition towards the LSE approach, we believe that we were genuinely ready to acknowledge whatever results we obtained. Interestingly, while LSE econometricians have generally greeted our paper enthusiastically, opponents of the LSE approach often see the results that we report—even taken at face value—as lending little comfort to LSE practitioners. The key thing to remember is that our goal was not to provide a generalized tool for specification search, but to ask whether it worked in a case in which we thought the LSE approach should work, if it could ever work at all. The five commentaries raise a large number of points. We will not attempt to address them all. Rather, in the remainder of the reply, we would like to consider only some of the larger themes.

Changes of snow cover thickness measured by conventional mass balance methods and by global positioning system surveying

The most labour‐intensive and time‐consuming part of many mass balance programmes is the acquisition of snow depth data. The standard technique, which involves probing the snow cover at intervals along a series of profiles, generally by an individual on skis, may involve more than 300 discrete measurements along a total of more than 20 km of profiling at a single glacier. Kinematic surveying with a global positioning system (GPS) in differential mode provides much more information about changes of glacier surface level and snow thickness between surveys. The positions of a large number of points can be fixed in a relatively short time by GPS surveying, and the technique is usable in adverse weather conditions. With real‐time kinematic GPS surveying, it is possible to return to the same positions (longitude, latitude) during successive field programmes, and a previously followed route can be retraced precisely. GPS surveying facilitates the production of accurate glacier maps for mass balance programmes. Data obtained by snow depth probing and GPS surveying in 1995 at Austre Okstindbreen, the largest glacier of the Okstindan area, Norway (66°N), indicate that repeated GPS surveys are likely to provide a large amount of information on withinyear and between‐year changes of surface topography and are not subject to the errors in mass balance calculations which arise from probing snow depths along selected profiles. Kinematic GPS surveying of several glaciers within an area would overcome the difficulties arising when mass balance studies are confined to a single glacier within a particular area.

VESH: A VERTICAL ENERGY SURFACE HOPPING PROCEDURE FOR DETERMINING STABLE ISOMERS OF POLYATOMIC MOLECULAR SYSTEMS

We describe a heuristic algorithmic procedure by which a large number of points of minimal energy in configuration space of a polyatomic molecular system (isomers) can be determined. Making use of the intrinsic electronic structure energy scheme of the molecular system, the procedure is initiated from an arbitrary starting configuration and progresses via successive vertical spin, and/or charge state shifts with interposed optimization steps. In this systematic way, a great manifold of stable isomers not only on the ground state potential energy surface but also on excited spin and charge state surfaces can be located. The efficiency and computational practicability of the procedure has been tested on various examples. In these cases, the global minima have been found. Results for singlet and triplet states of the system P 4 are presented in detail.

What's the Story

What's the Story

Computing the correlation dimension on a network of workstations

SUMMARY We present a parallel algorithm for computing the correlation dimension (D2) from a time series generated by a dynamic system, using the method of correlation integrals, which essentially requires the computation of distances among a set of points in the state space. The parallelization is suitable for coarse-grained multiprocessor systems with distributed memory and is carried out using a virtually shared memory model. The algorithm simultaneously gives all the correlation integrals at various state space dimensions needed to estimate the D2. Two versions are discussed: the first computes all distances between points; the second computes only distances less than a fixed, and employs a boxassisted approach and linked lists for an efficient search of neighbouring points. The algorithms, coded in Fortran 77, are tested on a heterogeneous network of workstations consisting of various DEC Alphas of different powers, interconnected by Ethernet; the Network Linda parallel environment is used. A detailed analysis of performance is carried out using the generalization of speed-up and efficiency for heterogeneous systems. The algorithms are fully asynchronous and so intrinsically balanced. In almost all the situations they provide a unitary efficiency. The second version greatly reduces the computational work, thus making it possible to tackle D2 estimation even for medium and high-dimensional systems, where an extremely large number of points is involved. The algorithms can also be employed in other applicative contexts requiring the efficient computation of distances among a large set of points. The method proposed for the analysis of performance can be applied to similar problems. ©1998 John Wiley & Sons, Ltd.

Videogrammetric Methods in Velocimetry

Photogrammetry has been successfully applied in surveying and mapping for a long time. New imaging techniques, digital data acquisition and storage and powerful computing facilities transformed photogrammetry into videogrammetry, a technique applied in many fields for precise and reliable position measurements. Two applications of videogrammetry in fluid mechanics are presented in this article. Both are at their present stage of development suited for three-dimensional velocity measurements in liquids. One is based on tracking particles seeded in the liquid by using three to four synchronized video-cameras (PTV). It allows one to determine accurately the velocity vectors at a large number of points inside a thick observation volume and also to follow the trajectories of these particles for sufficiently long time periods. It is especially well suited for Lagrangian measurements in flows. The other tracks small three-dimensional patterns in flows of liquids tagged by fluorescent dye (LIFV). The three-dimensional Laser Induced Fluorescence images needed are obtained by sweeping rapidly a thin laser-light sheet with simultaneous imaging using a high speed solid-state camera. The method yields the shift and deformations of the liquid volumes associated with these patterns and allows one to determine velocity vectors and their derivatives simultaneously and accurately at a large number of points inside the observation volume. This review article includes 100 references.

An Experimental Investigation of the Velocity and Temperature Fields of Cold Jets Injected Into a Hot Crossflow

It is shown here by dimensional analysis that the near-wall flow field of an effusion-cooled combustor can be scaled if the Reynolds, Mach, and Prandtl numbers and the temperature and velocity ratios are kept constant. It is also demonstrated that a practical model experiment can be designed, which fulfills all the scaling laws. A test rig meeting these requirements has been designed, built and tested. The experimental conditions have been chosen to correspond to the conditions usually met in a real effusion-cooled combustion chamber. One geometric configuration has been investigated. This consists of one transverse row of holes drilled with a 30 deg angle to the wall through which the cooling air enters a cross-flowing mainstream. The mean values of all three velocity components and the three normal fluctuating Reynolds stresses as well as the mean temperature have been measured in a large number of points surrounding the central injection hole. Experiments were carried out for jet-to-mainstream density ratios of 1.2 and 1.8. The results indicate that realistic density ratios are necessary to provide data directly applicable to effusion-cooling design.

A framework for non-contact measurement and analysis of NURBS surfaces

The paper presents an implementation of a methodology for reliable and feasible dimensional measurement of engineering components containing free-form surfaces. Two main requirements had to be satisfied. First, a large number of points had to be accurately measured. Secondly, the set of corresponding points on the nominal model had to be computed within a reasonable time. The first aspect was satisfied by adopting a non-contact measurement technique based on laser triangulation. High accuracy was achieved through software prealignment for precise component localisation and through appropriate measurement planning, both based on the CAD model. Determination of the corresponding nominal points was solved by best-fitting. Significant speed improvements were achieved through an implementation of the iterative closest point algorithm, based on a dual representation of the surface. The nominal surface is defined using NURBS entities and its approximation is determined as a polyhedral mesh. A sampling criterion for complex surfaces was derived and implemented, producing encouraging results. Validity of the proposed approach is supported by experiments and by simulation studies involving real engineering components.

Hybrid ab Initio Quantum Mechanics/Molecular Mechanics Calculations of Free Energy Surfaces for Enzymatic Reactions: The Nucleophilic Attack in Subtilisin

An effective approach for ab initio calculations of activation free energies of enzymatic reactions is developed and examined. This approach uses an empirical valence bond (EVB) potential surface as a reference potential for evaluating the free energies of a hybrid ab initio quantum mechanics/molecular mechanics (QM(ai)/MM) potential surface. This procedure involves an automated calibration of the EVB potential using gas-phase ab initio calculations. In addition, strategies for treating the contact region of QM and MM atoms as well as enzyme and solvent environments are developed. Two levels of ab initio calculations are used in studying the QM atoms: the HF/4-31G method, which allows calculations on a large number of points while still giving accurate results, and the MP2/6-31+G* approach. The QM(ai)/MM method is implemented and examined by simulating the nucleophilic attack step in the catalytic reaction of subtilisin. It is found that the use of the EVB potential as a reference allows one to obtain th...

An analytical representation of the ground potential energy surface (2A′) of the H+Cl2→HCl+Cl and Cl+HCl→HCl+Cl reactions, based on ab initio calculations

In this work we have studied at an ab initio level the lowest 2A′ potential energy surface (PES) of the HCl2 system. This PES is involved in the H(2S)+Cl2(X 1Σg+)→HCl(X 1Σ+)+Cl(2P) and Cl(2P)+HCl(X 1Σ+)→HCl(X 1Σ+)+Cl(2P) gas phase elementary chemical reactions. The former reaction is an important chemical laser while the second one is the most frequently used prototype of heavy–light–heavy reaction. A large number of points on the 2A′ PES have been calculated at the PUMP2/6-311G(3d2 f,3p2d) ab initio level. The ab initio calculations show the existence of two angular transition states with negligible or very small barriers to collinearity. This and other properties of the PES are in agreement with previous studies. An analytical expression based on a many-body expansion has been used to obtain a satisfactory fit of the 740 ab initio points calculated, with a root-mean-square deviation within the range of the estimated ab initio method error margin. This analytical representation of the 2A′ PES has been used to evaluate the variational transition state theory thermal rate constants of the above-mentioned reactions, including also the Cl+DCl reaction, and quite good agreement has been obtained when comparing with experimental results. The analytical PES obtained in this work is suitable for use in studies on the kinetics and dynamics of the HCl2 system.

Estimation of a spatial tree-influence model using iterative optimization

A method is described that aims at quantifying and modeling single tree spatial effects on forest ecosystem characteristics within complex stand structures. The procedure is based on iterative optimization techniques and it utilizes spatially explicit data of tree stand structure and the environmental variable(s) of interest. The method can be applied to estimate the effects of tree neighborhoods on the distribution of environmental variables, both abiotic (e.g. availability of various growth resources) and biotic (e.g. growth rate or plant community composition affected by the competition for resources). The method was tested in a 9 ha plot of mapped boreal Pinus sylvestris forest. First, known tree influence functions were used to simulate values of a hypothetical tree influence potential at a large number of points ( n=688) in the forest. Then, the ability of the iterative optimization method to estimate or reconstruct these a priori known influence functions of trees was tested. The method was successful in estimating the form of the tree influence functions, and when the estimated functions were used to predict the tree influence potential in the same points within the forest, the correlation between the `real' and predicted values was high ( r=0.99). Secondly, the method was used to examine the effect of trees on two measured ecosystem characteristics, namely humus layer thickness and canopy coverage, the latter having been quantified with the LAI-2000 canopy analyzer. The spatial autocorrelation pattern of these two variables was also examined. These analyses showed that the spatial pattern of humus layer thickness could not be explained satisfactorily by tree influences, because this variable was finer than tree-scale variability. However, the results suggest that in their vicinity the largest trees (dbh 40–50 cm) have a strong positive effect on humus layer thickness. The method was successful in predicting the measured canopy coverage for the measurement points in the forest ( r=0.69). The iterative optimization method presented provides a way to examine whether, and to what extent, the spatial pattern of a given ecosystem characteristic in a forest is regulated by distance-dependent spatial influences of individual trees. The method also makes it possible to derive models to describe the influence of individual trees of different sizes. Knowledge of these small-scale influence domain effects of trees on ecosystem characteristics is useful in revealing the effect of the tree community on the spatial organization of forest ecosystem structure.

Approximation and Simulation of the Distributions of Scan Statistics for Poisson Processes in Higher Dimensions

Given a Poisson process in two or three dimensions, we are interested in the scan statistic, i.e. the largest number of points contained in a translate of a fixed scanning set restricted to lie inside a rectangular area. The distribution of the scan statistic is accurately approximated for rectangular scanning sets, using a technique that is also extended to higher dimensions. The accuracy of the approximation is checked through simulation.

Construction of two-step Runge-Kutta methods of high order for ordinary differential equations

The construction of two-step Runge-Kutta methods of order p and stage order q=p with stability polynomial given in advance is described. This polynomial is chosen to have a large interval of absolute stability for explicit methods and to be A-stable and L-stable for implicit methods. After satisfying the order and stage order conditions the remaining free parameters are computed by minimizing the sum of squares of the difference between the stability function of the method and a given polynomial at a sufficiently large number of points in the complex plane.

Datailed surveying and mapping of plant communities on featureless terrain

AbstractA system of detailed vegetation mapping has been developed for use on undulating terrain where there is a complex mosaic of soil types, drainage characteristics and plant communities and where topography is such that it is impossible to locate a position by reference solely to a map grid reference point, for example hill/moorland grazings, sand dunes and mud flats. The system involved using electronic surveying equipment to locate accurately, in terms of National Grid coordinates and altitude, a large number of points over the area to be surveyed for which vegetation types were identified and recorded. The merged location and vegetation data set for individual points were imported into a geographic information system (GIS) to map ‘point’ vegetation data accurately. The GIS was then used to create regions around points (voronoi) using Delaunay triangulation to produce a vegetation map. Altitude information was used within the GIS to produce a contour map of the surveyed area.Vegetation was classified into communities of the British National Vegetation Classification and, although it does not describe all the variants within communities/sub‐communities fully, extra information for individual point locations was stored in tables within the GIS. This information was readily accessed by using the mouse cursor to highlight a point and reveal a window containing all the tabulated information for that point.This methodology was used to produce a reliable map that accurately positioned and mapped previously unmarked landscape features, new boundaries/fences, vegetation types and contours. This facility could be used for a variety of experimental, planning and consultancy applications including botanical survey work, grazing behaviour studies, conservation, land use planning and management.

Analysis, Synthesis, and Estimation of Fractal-Rate Stochastic Point Processes

Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs) provide useful models for describing a broad range of diverse phenomena, including electron transport in amorphous semiconductors, computer-network traffic, and sequences of neuronal action potentials. A particularly useful statistic of these processes is the fractal exponent α, which may be estimated for any FSPP or FRSPP by using a variety of statistical methods. Simulated FSPPs and FRSPPs consistently exhibit bias in this fractal exponent, however, rendering the study and analysis of these processes non-trivial. In this paper, we examine the synthesis and estimation of FRSPPs by carrying out a systematic series of simulations for several different types of FRSPP over a range of design values for α. The discrepancy between the desired and achieved values of α is shown to arise from finite data size and from the character of the point-process generation mechanism. In the context of point-process simulation, reduction of this discrepancy requires generating data sets with either a large number of points, or with low jitter in the generation of the points. In the context of fractal data analysis, the results presented here suggest caution when interpreting fractal exponents estimated from experimental data sets.

An automated method for navigation assessment for Earth survey sensors using island targets

An automated method has been developed for performing navigation assessment on satellite-based Earth sensor data. The method utilizes islands as targets which can be readily located in the sensor data and identified with reference locations. The essential elements are an algorithm for classifying the sensor data according to source, a reference catalogue of island locations, and a robust pattern-matching algorithm for island identification. The algorithms were developed and tested for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), an ocean colour sensor. This method will allow navigation error statistics to be automatically generated for large numbers of points, supporting analysis over large spatial and temporal ranges.

A Least-Squares Approach to the Practical Use of the Hole Method in Photoelasticity

The use of a small circular hole in elastostatic photoelasticity to determine the stress tensor for any two-dimensional general loading situation is well known. The original application required fringe-order information at four points on the boundary, on opposite sides, along the axes of symmetry or principal stress directions. Later, to obtain greater precision, it was adapted so that fringe information inside the field could be used. This led to the also limited use of fringe-order information from four points at 1.4 and two times the radius of the hole, along the principal axes of symmetry. More recent work has even allowed the use of fringe-order information, at a fixed radius, anywhere along the two principal axes of symmetry. The greatest limitation of all of these approaches is that the majority of the fringe-order information that is available, away. from the axes of symmetry, is not utilized at all. The current work presents a least-squares approach to the hole method that allows the simultaneous use of information anywhere and at any radial distance from the center of the hole inside the stress field. The objectives of this paper are: to apply the use of the least-squares approach to the hole method in photoelasticity; and, to show the consistent and practical application of this least-squares approach to the hole method. The achievement of this last objective permits the use of the values of specimen birefringence at a large number of points, taken from anywhere in the field around the hole.

Separation Dynamics of Strap-On Boosters in the Atmosphere

Thedynamicsassociated with thejettisoning ofa strap-onboosterfrom theparentlaunch vehicle isinvestigated. The present analysis accounts for experimental aerodynamics of separation utilizing a two-step method that employs a wind tunnel in a problem-solving mode. The e rst step consists of collecting wind-tunnel test results at a large number of points in the multidimensional space of independent variables. A suitable approach for surface e tting to the data leads to empirical models of the aerodynamic behavior, which are used in numerical simulations to design the appropriate separation system. The suitability of this design is examined, as a second step, through extensivesimulationsusingthewindtunnelasahardwaresubroutinetogenerateaerodynamicforcesandmoments. Two strap-on booster cone gurations are used for illustration.

Stochastic analysis of concentration measurements in the transport experiment at Twin Lake Site

A procedure to identify the parameters characterizing flow and transport in heterogeneous aquifers with the aid of concentration measurements in tracer field experiments is developed. Unlike previous studies, which employed the measured plume spatial moments at different times and their theoretical expressions, we rely here on breakthrough curves and temporal moments in order to analyze the field tests at Chalk River Site. In these experiments, breakthrough curves of a radioactive tracer were measured continuously at a large number of points in parallel control planes. We derive theoretical expressions of the temporal moments of the breakthrough curves by the same Lagrangian approach that was used previously for spatial moment. We assume a stationary random velocity field of constant mean and relate it to the axisymmetric log conductivity covariance by a first‐order approximation in the variance, with neglect of the effect of pore‐scale dispersion. The final theoretical results relate the temporal moments to U (the mean velocity), σY2 (the log conductivity variance), IYh (the horizontal integral scale), and b(e) (a function of the anisotropy ratio e=IYυ/IYh). By assuming ergodicity, we identify the temporal moments at the Chalk River Site experiment from measured breakthrough curves. With the aid of the theoretical results and by a best fit we could estimate U, σY2, IYh, and IYh/b(e). An attempt to identify the vertical and transverse integral scales from temporal‐spatial moments in the control planes was not successful. We took advantage of the dense measurements of breakthrough curves along vertical transects (at intervals of 1 cm) in order to identify the experimental concentration two‐point covariance. We derived a simplified theoretical expression for its dependence on the log conductivity vertical integral scale IYυ, which was identified by a best fit with experimental results. This procedure, applied for the first time to analysis of field tests, led to the identification of the estimates of σY2 and IYh, as well as of their variances of estimation.

Measuring-sequence planning by the nearest neighbour method and the refinement method

This paper focuses on the measurement, using a coordinate measuring machine (CMM), of the shape of a workpiece made up of geometric elements. It explores how a CMM can complete the whole measuring process with an optimised measuring sequence to reduce measuring time, after a CAD/CAM software system has planned the number and positions of the measurement points. In this paper, the nearest neighbour method and the refinement method are proposed to plan the measuring sequence. The nearest neighbour method uses individual element faces as the subject of planning. It takes the position closest to the starting point as the initial measuring face, and then gradually completes the sequence of all points. It arranges the sequence of measurement points on the initial measurement face by means of the nearest neighbour method as described in the aforementioned algorithm. It calculates the distance between the final point on the initial measurement face and all of the unmeasured points on the other faces. The point with the shortest distance between the final point on the initial measurement face and all of the unmeasured points on the other faces is selected as the next measurement point and the measurement face of this selected point is considered as the next initial measurement face. It determines whether all of the faces and measurement points are completely planned. The refinement method does not distinguish among element faces, but treats all planning points as the goal. The method is often used to handle the measurement-sequence problem where a large area and a large number of points are involved. The CAD/CAM software and power of calculation and analytical capability of the system can quickly obtain a suitable measuring sequence.