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Showing papers on "Metric (mathematics) published in 1982"


Journal ArticleDOI
TL;DR: A number of methods for finding the transformation from one metric to another metric are discussed and a new method is presented that combines a number of current methods and recommendations are made.
Abstract: A common problem arises when independent esti mates of item parameters from two separate data sets must be expressed in the same metric This problem is frequently confronted in studies of horizontal and ver tical equating and in studies of item bias This paper discusses a number of methods for finding the appro priate transformation from one metric to another met ric and presents a new method Data are given com paring this new method with a current method, and recommendations are made

676 citations


Proceedings ArticleDOI
01 Jan 1982
TL;DR: The problem of allocating area to modules at the highest level of a top-down decomposition is treated and a theorem of Schoenberg is applied to obtain a good embedding of the module space into the plane.
Abstract: The problem of allocating area to modules at the highest level of a top-down decomposition is treated in this paper. A theorem of Schoenberg is applied to obtain a good embedding of the module space into the plane. The dutch metric is introduced to transform netlist information - if available - into a distance matrix. This metric is flexible enough to enable the user to steer the design in an interactive environment, and rigorous enough to yield results satisfying optimality criterions. The embedding is used to derive the topology of the floorplan in the form of the structure tree of a slicing structure. To store the partial structure tree during the construction a concise and convenient data structure, the shorthand tree, is introduced. For any aspect ratio of the chip a minimum area floorplan can be generated. The paper also shows how wiring space predictions can be incorporated, how varying degrees of module flexibility can be accounted for, and how fixing bonding pad macros affects the procedure.

333 citations


Journal ArticleDOI
TL;DR: The concept of space-time representation in the brain is redefined using tensor network theory and the cerebellum acts as a predictive motor space- time metric which allows the establishment of coincidences of goal-directed movements of limbs inspace-time with external targets.

327 citations



Journal ArticleDOI
TL;DR: A [phi]-entropy functional is defined on the probability space and its Hessian along a direction of the tangent space of the parameter space is taken as the metric, and the distance between two probability distributions is computed as the geodesic distance induced by the metric.

287 citations



01 Jan 1982
TL;DR: In this paper, the authors study the large sample properties of a class of generalized method of moments (GMM) estimators which subsumes many standard econometric estimators, and show how to construct a set of criterion functions with minimizers that converge almost surely to the true parameter vector.
Abstract: IN THIS PAPER we study the large sample properties of a class of generalized method of moments (GMM) estimators which subsumes many standard econometric estimators. To motivate this class, consider an econometric model whose parameter vector we wish to estimate. The model implies a family of orthogonality conditions that embed any economic theoretical restrictions that we wish to impose or test. For example, assumptions that certain equations define projections or that particular variables are predetermined give rise to orthogonality conditions in which expected cross products of unobservable disturbances and functions of observable variables are equated to zero. Heuristically, identification requires at least as many orthogonality conditions as there are coordinates in the parameter vector to be estimated. The unobservable disturbances in the orthogonality conditions can be replaced by an equivalent expression involving the true parameter vector and the observed variables. Using the method of moments, sample estimates of the expected cross products can be computed for any element in an admissible parameter space. A GMM estimator of the true parameter vector is obtained by finding the element of the parameter space that sets linear combinations of the sample cross products as close to zero as possible. In studying strong consistency of GMM estimators, we show how to construct a class of criterion functions with minimizers that converge almost surely to the true parameter vector. The resulting estimators have the interpretation of making the sample versions of the population orthogonality conditions as close as possible to zero according to some metric or measure of distance. We use the metric to index the alternative estimators. This class of estimators includes the nonlinear instrumental variables estimators considered by, among others, Amemiya [1, 2], Jorgenson and Laffont [24], and Gallant [11].2 There the

205 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that invariant measures depend continuously on three types of perturbations: deterministic perturbation, stochastic perturbance, and randomly occuring deterministically occuring perturbant.
Abstract: For a certain class of piecewise monotonic transformations it is shown using a spectral decomposition of the Perron-Frobenius-operator ofT that invariant measures depend continuously on 3 types of perturbations: 1) deterministic perturbations, 2) stochastic perturbations, 3) randomly occuring deterministic perturbations. The topology on the space of perturbed transformations is derived from a metric on the space of Perron-Frobenius-operators.

194 citations


Journal ArticleDOI
TL;DR: A minimization method based on the idea of partitioned updating of the Hessian matrix in the case where the objective function can be decomposed in a sum of convex “element” functions is presented.
Abstract: This paper presents a minimization method based on the idea of partitioned updating of the Hessian matrix in the case where the objective function can be decomposed in a sum of convex "element" functions. This situation occurs in a large class of practical problems including nonlinear finite elements calculations. Some theoretical and algorithmic properties of the update are discussed and encouraging numerical results are presented.

160 citations


Journal ArticleDOI
TL;DR: In this paper, a new optimization method is applied to optimal power flow analysis, based on transforming the original problem to that of solving a sequence of linearly constrained subproblems using an augmented Lagrangian type objective function.
Abstract: A new optimization method is applied to optimal power flow analysis. The method is shown to be well suited to large scale (500 buses or more) power systems in that it is computationally efficient and is particularly effective with infeasible starting points. The optimization approach is based on transforming the original problem to that of solving a sequence of linearly constrained subproblems using an augmented Lagrangian type objective function. A fundamental feature of this algorithm (developed by Murtagh and Saunders) is that the solution converges quadratically on the nonlinear power flow constraints, rather than being forced to satisfy the constraints throughout the iterative process. To demonstrate the performance of this algorithm, a set of descent directions, which includes quasi-Newton (variable metric), conjugate directions, and steepest descent, are compared on the basis of convergence and computational effort for a 118 bus and a 600 bus power system.

141 citations


Journal Article
TL;DR: In this article, the stability of the models with respect to perturbations of the metric is investigated, and the spectrum of fluctuations is calculated under certain conditions, the amplitude of the spectrum is sufficient for the formation of galaxies during the hydrodynamic stage after the decay of the polarized vacuum.
Abstract: Small longitudinal quantum fluctuations of the metric in cosmological models with metastable vacuum are considered. A Hamiltonian formalism is constructed and the system of small perturbations quantized. The single-loop corrections are taken into account in the Einstein equations. The stability of the models with respect to perturbations of the metric is investigated. The spectrum of fluctuations of the metric is calculated. Under certain conditions, the amplitude of the spectrum is sufficient for the formation of galaxies during the hydrodynamic stage after the decay of the polarized vacuum.

Journal ArticleDOI
TL;DR: A new method for achieving this goal in an abstract metric space by selecting those models that are closest to an unknown relational description in a database of relational models.

Journal ArticleDOI
TL;DR: In this paper, the authors give conditions sufficient to guarantee that every possible iteration of mappings drawn from {T0,…, TN} converges strongly to a point of the common intersection.

Journal ArticleDOI
TL;DR: In this article, a characterization of one-dimensional subspaces of a normed linear space whose metric projections admit linear selections is given, for the Banach spaces C0(T) and Lp (1 ⩽ p ⌽ ∞).

Journal ArticleDOI
TL;DR: An accurate channel model that allows for splitting, merging, and substitution of symbols is introduced and the best estimate X is obtained by using a dynamic programming search which combines a known search strategy (stack decoding) with a trie structure representation of a dictionary.
Abstract: This paper deals with a method of estimating a correct string X from its noisy version Y produced by a cursive script recognition system. An accurate channel model that allows for splitting, merging, and substitution of symbols is introduced. The best estimate X is obtained by using a dynamic programming search which combines a known search strategy (stack decoding) with a trie structure representation of a dictionary. The computational complexity of the algorithm is derived and compared with that of a method based on the generalized Levenshtein metric. Experimental results with the algorithm on English text based on a dictionary of the 1027 most commonly occurring words are described.

Journal ArticleDOI
TL;DR: In this article, a Fermi normal co-ordinate system is used to describe a gravitational wave in the linear approximation, and the metric tensor is calculated exactly and shown to be a solution ofRμv=0 without the Lorentz condition.
Abstract: SummaryA Fermi normal co-ordinate system is used to describe a gravitational wave in the linear approximation. The metric tensor is calculated exactly and shown to be a solution ofRμv=0 without the «Lorentz condition» taken into account. This result allows for an unambiguous treatment of electromagnetic detectors of gravitational waves.RiassuntoSi usa un sistema di coordinate normali di Fermi per descrivere un’onda gravitazionale nell’approssimazione linearizzata. Si calcola esattamente la metrica e si mostra che è una soluzione diRμv=0 senza prendere in considerazione la «condizione di Lorentz». Questo risultato permette una trattazione non ambigua dei rivelatori elettromagnetici di onde gravitazionali.РезюмеДля описания гравитационной волны в линейном приближении используется система нормальных координат Ферми. Точно вычисляется метрический тензор и показывает, что полученный тензор является решениемRμv=0 без учета «условия Лоренца». Этот результат допускает однозначную трактовку электромагнитных детекторов гравитационных волн.


Journal ArticleDOI
TL;DR: It is suggested that, for a specific theory dealing with a specific set of research questions, metric multidimensional scaling, modified in certain important ways, provides useful results obtainable either only with great difficulty or not at all by nonmetric means.
Abstract: Although the first multidimensional (MDS) scaling algorithms developed were metric algorithms (Torgerson, 1958), the development of nonmetric methods (Shepard, 1966) led to a rapia and nearly complete abandonment of the metric procedures in favor of these newer algorithms. Recently, however, there has been a resurgence of interest in metric algorithms, particularly within the field of human communication research, where the use of metric procedures predominates. In order to understand this reversion to what many psychometricians believe to be an outdated technique it is necessary to understand the difficulties and philosophy which led to the increased interest in metric scaling. While there is little doubt that the development of nonmetric multidimensional scaling algorithms represents a great advance in the methods available to the contemporary social scientist, there exist some areas of inquiry in which the metric scaling routines may offer certain advantages. This article discusses one such case, familiar to communication researchers in particular. The reader should understand at the outset that this article is not an argument against the use of nonmetric scaling, but rather a suggestion that, for a specific theory dealing with a specific set of research questions, metric multidimensional scaling, modified in certain important ways, provides useful results obtainable either only with great difficulty or not at all by nonmetric means.

01 Jun 1982
TL;DR: In this paper, a number of methods for finding the appro priate transformation from one metric to another metric is discussed and a new method is presented, and data are given for comparing this new method with a current method.
Abstract: A common problem arises when independent esti mates of item parameters from two separate data sets must be expressed in the same metric. This problem is frequently confronted in studies of horizontal and ver tical equating and in studies of item bias. This paper discusses a number of methods for finding the appro priate transformation from one metric to another met ric and presents a new method. Data are given com paring this new method with a current method, and recommendations are made.


Journal ArticleDOI
TL;DR: In this article, a Kerr-like metric is obtained by means of a complex coordinate transformation in the Brans-Dicke theory, which is obtained through a complex-coordinate transformation.
Abstract: A Kerr‐like metric is obtained by means of a complex coordinate transformation in the Brans–Dicke theory.

Journal ArticleDOI
TL;DR: In this article, the authors explore the feasibility of using period laws in questions pertaining to particle topology and show that the topology of microphysical structures can be tested on their one-, two-, and three-connectedness with the help of three period laws.
Abstract: The following is an exploratory investigation into the viability of using period laws in questions pertaining to particle topology. Since the macro-micro distinction in physics is a metric-related notion, metric independence is taken to be the key to whether or not such laws can be extrapolated into the microphysical realm. The topology of microphysical structures can then be tested on their one-, two-, and three-connectedness with the help of three period laws. The partly qualitative topological information obtained by these metric-free criteria is then resubmitted to a process of metric adaptation for further quantitative answers.

Journal ArticleDOI
C.J.S Clarke1
TL;DR: In this paper, it was shown that unique timelike geodesies exist provided only that the Riemann tensor and the first derivatives of the metric are bounded, and that a space-time can be extended subject to the Holder continuity of the tensor.

Proceedings ArticleDOI
George E. Heidorn1
16 Jun 1982
TL;DR: In this article, a metric that can be easily computed during either bottom-up or top-down construction of a parse tree for ranking the desirability of alternative parses is presented.
Abstract: This brief paper, which is itself an extended abstract for a forthcoming paper, describes a metric that can be easily computed during either bottom-up or top-down construction of a parse tree for ranking the desirability of alternative parses. In its simplest form, the metric tends to prefer trees in which constituents are pushed as far down as possible, but by appropriate modification of a constant in the formula other behavior can be obtained also. This paper includes in introduction to the EPISTLE system being developed at IBM Research and a discussion of the results of using this metric with that system.

Journal ArticleDOI
TL;DR: In this article, the coagulation-fragmentation equation describes geodesic motion in an infinite-dimensional space with a symmetric affine connection but no metric in general.
Abstract: The coagulation-fragmentation equation describes geodesic motion in an infinite-dimensional space. This space has a symmetric affine connection but no metric in general. Some advantages of the new approach are indicated.

Journal ArticleDOI
TL;DR: A modified upper bound for the Lee metric is derived and is used to prove a nonexistence theorem for perfect Lee codes over large alphabets.
Abstract: The classical Elias bound for the Lee metric is weak when the size of the alphabet is larger than the minimum distance. A modified upper bound which is also strong for large alphabets is derived. This bound then is used to prove a nonexistence theorem for perfect Lee codes over large alphabets.