Showing papers on "Generalization published in 1985"
TL;DR: Recursive input-output models for non-linear multivariate discrete-time systems are derived, and sufficient conditions for their existence are defined.
Abstract: Recursive input-output models for non-linear multivariate discrete-time systems are derived, and sufficient conditions for their existence are defined. The paper is divided into two parts. The first part introduces and defines concepts such as Nerode realization, multistructural forms and results from differential geometry which are then used to derive a recursive input-output model for multivariable deterministic non-linear systems. The second part introduces several examples, compares the derived model with other representations and extends the results to create prediction error or innovation input-output models for non-linear stochastic systems. These latter models are the generalization of the multivariable ARM AX models for linear systems and are referred to as NARMAX or Non-linear AutoRegressive Moving Average models with exogenous inputs.
1,198 citations
217 citations
TL;DR: A generalization of Newmark's time marching integration scheme, called the β-m method, which provides a gcneral single-step scheme applicable to any set of initial value problems and which unifies old and new methods.
Abstract: Introduced herein is a generalization of Newmark's time marching integration scheme, called the β-m method. Like the SSpj method (introduced in Parts 1 and 2 of this series), the β-m method provides a gcneral single-step scheme applicable to any set of initial value problems. The method is specialized by specifying the method order m along with rn integration parameters, β0, β1, …, βm−1. For a particular choice of m, the integration parameters provide a subfamily of methods which control accuracy and stability, as well as offering options for explicit or implicit algorithms. For the most part, attention is focused on the application to structural dynamic equations. Most well-known methods (e.g. Newmark, Wilson, Houbolt, etc.) are shown to be special cases within the β-m family. Hence, one computationally efficient and surprisingly simple algorithm unifies old and new methods. Stability and accuracy analyses are presented for method orders m = 2, 3 and 4 to determine optimal parameters for implicit and explicit schemes, along with numerical verification.
211 citations
TL;DR: This paper presents inclusion-exclusion bounds and compares them with disjoint subset bounds and is based on a generalization of Abraham's recursive disjointed products.
Abstract: The reliability literature has recently introduced several multistate models. This paper discusses reliability bounds in the most general of these models. It presents inclusion-exclusion bounds and compares them with disjoint subset bounds. The later bounds are based on a generalization of Abraham's recursive disjoint products.
211 citations
TL;DR: In this article, a generalization of the conventional method of McKelvey and Zavoina (1975) is proposed, which eliminates the assumption of constant category thresholds for the oidinal latent index and instead the thresholds are assumed to be linear functions of obtained exogenous variables whose values are observation specific.
Abstract: Probit models for the analysis of oidinal qualitative vaiiables are discussed. A generalization of the conventional method of McKelvey and Zavoina (1975) is proposed. Ihe geneial model entails the elimination of the assumption of constant category thresholds for the oidinal latent index. Instead the thresholds are assumed to be linear functions of obseived exogenous vaiiables whose values aie observation specific. A few typical examples aie discussed and the details of maximum likelihood estimation of the general model aie given. Ihe method is applied to an analysis of the bond ratings of electric utilities and is thereby shown to be computationally efficient and conducive to hypothesis tests that are precluded by conventional methods.
150 citations
01 Jan 1985
TL;DR: In this paper, the authors describe experiments utilizing base lines of perceptually selected critical points to evaluate three common line-generalization algorithms: nth-point elimination, a perpendicular routine, and the Douglas algorithm.
Abstract: Line generalization, used to reduce scale in mapping, caricatures an original line by retaining points essential to its shape—called characteristic, or critical, points—and discarding others. This study describes experiments utilizing base lines of perceptually selected critical points to evaluate three common line-generalization algorithms: nth-point elimination, a perpendicular routine, and the Douglas algorithm. Base-line correspondence to computer generalizations was measured by graphical overlay, areal offset, commonly held points, and mean number of times respondents judged particular points to be critical. Visual comparison of an original line and its computer generalization followed. The Douglas algorithm's line generalizations proved more faithful to original lines than those of perpendicular point selection and nth-point elimination.
110 citations
TL;DR: In this article, a generalization of the Godunov-based method for solving conservation laws is proposed, which can be applied for arbitrarily large time steps and is easy to implement and may also be useful in other contexts, such as mesh refinement or shock tracking.
Abstract: A generalization of Godunov–s method for solving systems of conservation laws is proposed which can be applied for arbitrarily large time steps. Interactions of waves from neighboring Riemann problems are handled in an approximate but conservative manner that is exact for linear problems. For nonlinear systems it is found that better accuracy and sharper resolution of discontinuities is often obtained with Courant numbers somewhat larger than those allowed in Godunov's method. We explore the reasons for this behavior and, more generally, the effects of approximating wave interactions linearly. This linearization is easy to implement and may also be useful in other contexts, such as mesh refinement or shock tracking. A large time step generalization of the random choice method is also mentioned.
105 citations
98 citations
TL;DR: A generalization of the cube-connected cycles of Preparata and Vuillemin is described which retains the symmetry of these architectures while allowing for constructions of greater density and of arbitrary degree.
Abstract: A generalization of the cube-connected cycles of Preparata and Vuillemin is described which retains the symmetry of these architectures while allowing for constructions of greater density and of arbitrary degree. These constructions are of a type known as Cayley graphs, and their analysis is greatly facilitated by the applicability of methods from abstract algebra.
84 citations
TL;DR: In this paper, a technique for determining derivatives (fluxes or stresses) from finite element solutions is developed, which is a generalization to higher dimensions of a procedure known to give highly accurate results in one dimension.
80 citations
TL;DR: In this article, a generalization of the compound matrix method is presented to deal with eigenvalue and boundary-value problems involving unstable systems of ordinary differential equations, and a simple equivalence relation exists between the compounds of the solution matrices of the eigen value problems and their adjoints, and this relation can be exploited to simplify the calculation of the adjoint eigenfunctions.
TL;DR: On etablit quelques resultats lies a l'integralite de B. Jessen pour les fonctions convexes as mentioned in this paper, which is the integralite of B.
TL;DR: In this paper, a generalization of the familiar mesh point technique for numerical approximation of functions is presented, and high accuracy and very rapid convergence may be obtained by thoughtful choice of the reference function chosen for interpolation between the mesh points.
Abstract: A generalization of the familiar mesh point technique for numerical approximation of functions is presented. High accuracy and very rapid convergence may be obtained by thoughtful choice of the reference function chosen for interpolation between the mesh points. In particular, derivative operators are represented by highly nonlocal matrices; but this is no drawback when one has computing machines to perform the algebraic manipulations. Some examples are given from familiar quantum mechanical problems.
TL;DR: Implications for peak shift, selection of analytical level, and identification of the behavioral unit are discussed, as well as factors that may determine the acceptability of the quantal interpretation.
Abstract: This paper is a selective review of research that addresses the validity of two interpretations of stimulus generalization. One interpretation, referred to as the descriptive stimulus-control interpretation, proposes that during stimulus generalization a continuous relation exists between stimulus and response dimensions. The other interpretation, referred to as the quantal interpretation, proposes that a stimulus-response relation functions as a unit that may or may not occur. From the latter viewpoint, the continuity typically obtained during generalization tests is deemed to be artifactual and to result from averaging across multiple controlling stimulus-response relations. Studies examining the contribution of these multiple relations to generalization gradients are reviewed. With few exceptions, the quantal interpretation appears to better characterize the results of these studies. Implications for peak shift, selection of analytical level, and identification of the behavioral unit are discussed, as well as factors that may determine the acceptability of the quantal interpretation.
01 May 1985
TL;DR: The natural reductive homogeneous spaces have been studied by a number of authors as a natural generalization of Riemannian symmetric spaces, including D'Atri and Ziller as discussed by the authors, who proved that all naturally reductive spaces are spaces with volume-preserving local geodesic symmetries.
Abstract: Naturally reductive homogeneous spaces have been studied by a number of authors as a natural generalization of Riemannian symmetric spaces. A general theory with many examples was well-developed by D'Atri and Ziller[3]. D'Atri and Nickerson have proved that all naturally reductive spaces are spaces with volume-preserving local geodesic symmetries (see [1] and [2]).
TL;DR: This paper looks at the need for categorizing numeric data and several methods for doing so, and focuses on the use of generalization-based memory, a memory organization where actual examples are stored along with generalizations, which leads to a generalized-based categorization algorithm.
TL;DR: In this paper, a probabilistic Rasch model is advocated for brand-attribute measurements which replace ubiquitous mean ratings, and the usefulness of this model is then extended by showing that distinct latent processes, one extreme value and the other logistic, imply common probability structures for both its classical form and the generalization developed here.
Abstract: A probabilistic Rasch model is advocated for brand-attribute measurements which replace ubiquitous mean ratings. The usefulness of this model is then extended by showing that distinct latent processes, one extreme value and the other logistic, imply common probability structures for both its classical form and the generalization developed here. If given data reject the classical structure, an extended analysis is carried out in which logistic coefficients are estimated for the general model. These values are then used in a generalized-least-squares GLS procedure for estimating and testing the brand-attribute locations. An illustrative multiattribute analysis is given in which logistic coefficients and locations are found for 16 soft drinks on the continua of preference, sweetness, and fizziness.
01 Nov 1985
TL;DR: Projection pursuit regression is generalized to multivariate responses by viewing classification as a special case, and this generalization serves to extend classification and discriminant analysis via the projection pursuit approach.
Abstract: : Projection pursuit regression is generalized to multivariate responses. By viewing classification as a special case, this generalization serves to extend classification and discriminant analysis via the projection pursuit approach.
TL;DR: This theorem generalizes a theorem which gives a solution for the problem without the condition and gives a necessary and sufficient condition for the uniqueness of the solution in the KKL theorem.
Abstract: LetA be a set ofk-subsets of {1,...,n} with[Figure not available: see fulltext.]. We determine the minimal cardinality of thel-shadow ofA. This theorem generalizes a theorem of Kruskal [10], Katona [8], Lindstrom [11] and other which gives a solution for the problem without the condition[Figure not available: see fulltext.]. Furthermore we give a necessary and sufficient condition for the uniqueness of the solution in the KKL theorem.
TL;DR: In this paper, a generalization of the identity of dimensionless regular-zation is proposed, which is used to divide the complete set of dimensionally (and analytically) regularized Feynman integrals with one external momentum into classes of equal integrals, and also for calculating some of them.
Abstract: A generalization of the identity of dimensionless regular-zation is proposed. The generalization is used to divide the complete set of dimensionally (and analytically) regularized Feynman integrals with one external momentum into classes of equal integrals, and also for calculating some of them. A nontrivial symmetry of the propagator integrals is revealed, on the basis of which a complete system of functional equations for determining two-loop integrals is derived. Possible generalizations of these equations are discussed.
TL;DR: In this paper, the authors investigated the class of orthonormal bases in L 2 (0, 1) with respect to which all quasi-martingales become integrable in the sense of non-causal integration.
Abstract: We will investigate the problem of characterizing the class of such orthonormal bases inL
2([0, 1]) with respect to which all quasi-martingales become integrable in the sense of noncausal integration. As an application of the results, we will show that the integral of noncausal type is a natural generalization of symmetric integrals.
TL;DR: A unique factorization theory for labelled combinatorial objects is developed and applied to enumerate several families of objects, including certain families of set partitions, permutations, graphs, and collections of subintervals of [1, n].
TL;DR: In this article, a generalization of Sylvester's identity on determinants is proved by elimination techniques, and some inequalities for determinants of totally positive or positive definite matrices are derived.
Proceedings Article•
18 Aug 1985TL;DR: A program which simulates the discovery of the wave theory of sound, using several kinds of inductive inference that are triggered in the context of problem solving, which produces new concepts by combining existing concepts, represented as frame-like clusters of production rules.
Abstract: This paper describes a program which simulates the discovery of the wave theory of sound, using several kinds of inductive inference that are triggered in the context of problem solving. The most novel of these is conceptual combination, which produces new concepts by combining existing concepts, represented as frame-like clusters of production rules. Combined concepts are not a linear amalgam of existing ones, since the conflicting expectations of the rules in the donor concepts must be resolved by a set of top-down and bottom-up procedures. The theoretical concept of a sound wave is produced by conceptual combination. The rule that sound consists of waves is produced by applications of other kinds of inductive inference: generalization and abduction.
TL;DR: In this article, a multivariate generalization of Shaked's bivariate families which are dependent by total positivity (DTP) is introduced, and some interrelationships and inequalities are generalized.
Abstract: A multivariate generalization of Shaked's bivariate families which are dependent by total positivity (DTP) is introduced. Some interrelationships and inequalities are generalized. Monotonicity properties of conditional hazard rate and mean residual life functions of some multivariate DTP families are investigated. Relationships with other positive dependence concepts are given.
TL;DR: In this paper, a generalized selfduality condition for 4 p dimensions (p = 2,3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 28) was proposed.
TL;DR: A number of different approaches for empirically defining a geograhic market are explored in this article, and it is demonstrated that the rest proposed by Horowitz, and even a generalization of it,provide conflicting and inconsistent results.
Abstract: A number of different approaches for empirically defining a geograhic market are explored in this paper. It is demonstrated that the rest proposed by Horowitz, and even a generalization of it,provide conflicting and inconsistent results. Correlation analysis, while appealing in its simplicity, has the potential for providing misleading results. Finally, the notion of causality as applied here, seems to be a promising approach to the issue.