Showing papers on "Generalization published in 1979"

Dynamic choice theory and dynamic programming1

Abstract: Finite horizon sequential decision problems with a "temporal von NeumannMorgenstern utility" criterion are analyzed This criterion, as developed in [7], is a generalization of von Neumann-Morgenstern (expected) utility of the vector of rewards, wherein an individual's preferences concerning the timing of the resolution of uncertainty are taken into account The preference theory underlying this criterion is reviewed and then extended in natural fashion to yield preferences for strategies in sequential decision problems The main result is that value functions for sequential decision problems can be defined by a dynamic programming recursion using the functions which represent the original preferences, and these value functions represent the preferences defined on strategies This permits citation of standard results from the dynamic programming literature, concerning the existence of (memoryless) strategies which are optimal with respect to the given preference relation

Carleson Measure on the Bi-Disc

Abstract: In this paper we discuss a possible generalization of Carleson measure to the bi-disc, and indicate a class of such measures induced by bi-harmonic functions. Let D denote the open unit disc {z I I z I 1, let u(re") = (Pr *f)(0), where P7(0) = (1-r2)/(1-2r cos 0 + r2) is the Poisson kernel. The following theorem is one of the main results in [1].

An Introduction to Forking

Abstract: The notion of forking has been introduced by Shelah, and a full treatment of it will appear in his book on stability [S1]. The principal aim of this paper is to show that it is an easy and natural notion. Consider some well-known examples of ℵ 0 -stable theories: vector spaces over Q , algebraically closed fields, differentially closed fields of characteristic 0; in each of these cases, we have a natural notion of independence: linear, algebraic and differential independence respectively. Forking gives a generalization of these notions. More precisely, if are subsets of some model and c a point of this model, the fact that the type of c over does not fork over means that there are no more relations of dependence between c and than there already existed between c and . In the case of the vector spaces, this means that c is in the space generated by only if it is already in the space generated by . In the case of differentially closed fields, this means that the minimal differential equations of c with coefficient respectively in and have the same order. Of course, these notions of dependence are essential for the study of the above mentioned structures. Forking is no less important for stable theories. A glance at Shelah's book will convince the reader that this is the case. What we have to do is the following. Assuming T stable and given and p a type on , we want to distinguish among the extensions of p to some of them that we shall call the nonforking extensions of p .

A Generalization of the Bayesian Steady Forecasting Model

Abstract: SUMMARY The Bayesian Steady Forecasting model is generalized to a very wide class of processes other than the normal by defining the time series on the decision space. Examples of such processes are presented including a Beta-Binomial process, a Poisson-Gamma process and a Student-t sample distribution steady model. Simple updating relations are given for most of the processes discussed.

On a common generalization of borsuk's and radon's theorem

Abstract: 1. The well-known theorem of RADON [3] says that if A c R a and IAl=>d+2, then there exist B, C c A , B ( ~ C = ~ such that conv BNconv C is not empty. i t is clear that for each finite set A = { a l , ..., a,} in R e with n ~ d + 2 one can find a linear map f : Ra+I-*R a and a set A ' = {a; . . . . , a~}cR a+l such that f ( a ; )=a l i = l , 2, . . . , n and int conv A' is not empty and vert conv A ' = A ' . In view of this fact, Radon ' s theorem can be stated in the following way.

Convergence Results for Schubert’s Method for Solving Sparse Nonlinear Equations

Abstract: Schubert’s method for solving sparse nonlinear equations is an extension of Broyden’s method The zero-nonzero structure defined by the sparse Jacobian is preserved by updating the approximate Jacobian row by row An estimate is presented which permits the extension of the convergence results for Broyden’s method to Schubert’s method The analysis for local and q-superlinear convergence given here includes, as a special case, results in a recent paper by B Lam; this generalization seems theoretically and computationally more satisfying A Kantorovich analysis paralleling one for Broyden’s method is given This leads to a convergence result for linear equations that includes another result by Lam A result by More and Trangenstein is extended to show that a modified Schubert’s method applied to linear equations is globally and q-superlinearly convergent

A Transformational View of Cartography

Abstract: Cartographic transformations are applied to locative geographic data and to substantive geographic data. Conversion between locative aliases are between points, lines, and areas. Substantive transformations occur in map interpolation, filtering, and generalization, and in map reading. The theoretical importance of the inverses is in the study of error propagation effects.

Some Properties of a Generalization of the Richardson Extrapolation Process

Abstract: The Richardson extrapOlation process is generalized to cover a large class of sequences. Error bounds for the approximations are obtained and some convergence theorems for two different limiting processes are given. The results are illustrated by an oscillatory infinite integral.

Some comments on the asymptotic behavior of robust smoothers

Abstract: In curve estimation, running M-estimates are a natural generalization of Kernel-type smoothers (moving averages). We find the rate of convergence that can be expected from these estimates and the leading bias and variance terms. We also explain the effect of twicing for Kernel-type smoothers and give some rationale for its use in robust curve estimation.

Some exceptional electrovac type D metrics with cosmological constant

Abstract: We investigate all type D solutions of the Einstein–Maxwell equations (with cosmological constant) such that the Debever–Penrose vectors are aligned along the two eigenvectors of the electromagnetic field, in the special case when a direct generalization of the Goldberg–Sachs theorem is not possible. A solution is found which admits no Killing vectors. We also present an extension of the Golberg–Sachs theorem valid for type D metrics.

An analysis of generalization as a search problem

Abstract: The problem of concept learning, or forming a general description of a class of objects given a set of examples and non-examples, is viewed here as a search problem. Existing programs that generalize from examples are characterized in terms of the classes of search strategies that they employ. Several classes of search strategies are then analyzed and compared in terms of their relative capabilities and computational complexities.

The pebbling problem is complete in polynomial space

Abstract: We examine a pebbling problem which has been used to study the storage requirements of various models of computation. Sethi has shown this problem to be NP-hard and Lingas has shown a generalization to be P-space complete. We prove the original problem P-space complete by employing a modification of Lingas's proof. The pebbling problem is one of the few examples of a P-space complete problem not exhibiting any obvious quantifier alternation.

Convex/stochastic programming and multilocation inventory problems

Abstract: This paper examines a convex programming problem that arises in several contexts. In particular, the formulation was motivated by a generalization of the stochastic multilocation problem of inventory theory. The formulation also subsumes some “active” models of stochastic programming. A qualititative analysis of the problem is presented and it is shown that optimal policies have a certain geometric form. Properties of the optimal policy and of the optimal value function are described.

Power consumption and gas capacity of self‐inducting turbo aerators

Abstract: A theoretical and experimental analysis of self-inducting turbo aerator performance was carried out based on the theory of water jet injector operation. It was shown that the aerator's injection coefficient is completely determined by only two dimensionless groups, CH and EuG, between which there is a single valued dependence on whose basis generalization of experimental data is possible. An analytical expression for the optimality criterion or aerator performance index, accounting for aerator gas capacity, power consumption, and submergence, has been obtained in terms of CH and EuG with only one adjustable parameter. From the above two dependencies, a methodology was developed for determining optimal operating conditions, by means of which all the data necessary for the optimal design can be obtained from the results of bench scale experiment.

On the theory of moving average graduation

Abstract: In this paper a new criterion for judging the properties of moving averages is given, and moving averages which are optimal according to this criterion under general assumptions are derived. For the standard case where the observations are uncorrelated and have equal variance, our optimal moving averages generalize two well-known optimal moving averages: The minimum-variance and the minimum-Rz moving averages. This case is given some particular attention in the theoretical discussion, and some Monte Carlo experiments throw further light on it. These investigations indicate that our generalization is of practical as well as theoretical interest. The paper also contains the result that Spencer's 21-term moving average is approximately equal to the corresponding minimum-R 5 moving average.

A Class of New Methods for Congressional Apportionment

Abstract: This paper develops a class of new methods for congressional apportionment by building upon and extending the recent work done by M. L. Balinski and H. P. Young. The class, which also includes the Balinski–Young Quota Method, consists of all apportionment methods satisfying two basic criteria (satisfying quota and house monotonicity) articulated by Balinski and Young. The class is defined for both the pure apportionment problem and the apportionment problem with minimum requirements. In the latter case, a new generalization of lower quota is presented, which differs from Balinski and Young’s generalization. Finally, reasons are given for rejecting the Balinski–Young Quota Method and preferring instead one of the new methods in the class.

A Study of Some Factors Affecting Generalization of Language Training

Abstract: Two related experiments examined generalization across contexts involving different sentence forms when selected grammatical features were trained within a single syntactic context. Results obtaine...

A class of functions synthesized from a finite number of examples and a lisp program scheme

Abstract: We define a class of functions that can be synthesized from example problems. The algorithmic representation of these functions is the interpretation of a given scheme. The instantiation of the scheme variables is realized by a new method which uses pattern matching then if necessary generalization and further pattern matching. One can compute the number of examples necessary to characterize in a unique way a function of this class.

Generalized quantum spins, coherent states, and Lieb inequalities

Abstract: A mathematical generalization of the concept of quantum spin is constructed in which the role of the symmetry groupO3 is replaced byOv (ν=2,3,4, ...). The notion of spin direction is replaced by a point on the manifold of oriented planes in ℝv. The theory of coherent states is developed, and it is shown that the natural generalizations of Lieb's formulae connecting quantum spins and classical configuration space hold true. This leads to the Lieb inequalities [1] and with it to the limit theorems as the quantum spinl approaches infinity. The critical step in the proofs is the validity of the appropriate generalization of the Wigner-Eckart theorem.