Abstract: One criticism about qualitative research is that it is difficult to generalize findings to settings not studied. To explore this issue, I examine three broad arguments for generalizing from data: sample-to-population extrapolation, analytic generalization, and case-to-case transfer. Qualitative research often uses the last argument, but some efforts have been made to use the first two. I suggest that analytic generalization can be very helpful for qualitative researchers but that sample-to-population extrapolation is not likely to be.

Abstract: Estimation of returns over time, the focus of temporal difference (TD) algorithms, imposes particular constraints on good function approximators or representations. Appropriate generalization between states is determined by how similar their successors are, and representations should follow suit. This paper shows how TD machinery can be used to learn such representations, and illustrates, using a navigation task, the appropriately distributed nature of the result.

Abstract: Meta-analyses should be analytic and deductive. In a review of the state of the science of meta-analysis in the previous volume of Epidemiologic Reviews, a list of definitions and synonyms of meta-analysis was given: "overview, pooling, data pooling, literature synthesis, data synthesis, quantitative synthesis, and quantitative review" (1, p. 154). Indeed, most metaanalyses are more synthetic than analytic: They produce a summary, such as an aggregate relative risk and 95 percent confidence interval, from a set of individual studies and stop there. Such a "meta-synthesis" has an inductive approach, i.e., generalization from a set of particular observations. By contrast, a deductive approach starts with alternative generalizations (hypotheses) and uses particular observations to discriminate among them. The causal hypothesis of primary interest is considered corroborated if competing hypotheses do not stand up to the evidence (2). The words "inductive" and "deductive" here have the meanings used in logic (3). Induction is the inference "If true for A, then true for B" when A is a part, sample, or special case of B. When epidemiologists infer

Abstract: LetM andN be compact riemannian manifolds, andu a stationary harmonic map fromM toN. We prove thatH n−2 (Σ)=0, wheren=dimM and Σ is the singular set ofu. This is a generalization of a result of C. Evans [7], where this is proved in the special caseN is a sphere. We also prove that, ifu is a weakly harmonic map inW 1,n (M, N), thenu is smooth. This extends results of F. Helein for the casen=2, or the caseN is a sphere ([9], [10]).

Abstract: The species problem is one of the oldest controversies in natural history. Its persistence suggests that it is something more than a problem of fact or definition. Considerable light is shed on the species problem when it is viewed as a problem in the representation of the natural system (sensu Griffiths, 1974, Acta Biotheor. 23: 85-131; de Queiroz, 1998, Philos. Sci. 55: 238-259). Just as maps are representations of the earth, and are subject to what is called cartographic generalization, so diagrams of the natural system (evolutionary trees) are representations of the evolutionary chronicle, and are subject to a temporal version of cartographic generalization which may be termed systematic generalization. Cartographic generalization is based on judgements of geographical importance, and systematic generalization is based on judgements of historical importance, judgements expressed in narrative sentences (sensu Danto, 1985, Narration and knowledge, Columbia Univ. Press, New York). At higher systematic levels these narrative sentences are conventional and retrospective, but near the “species” level they become prospective, that is, dependent upon expectations of the future. The truth of prospective narrative sentences is logically indeterminable in the present, and since all the common species concepts depend upon prospective narration, it is impossible for any of them to be applied with precision.

Abstract: Data Envelopment Analysis (DEA) assumes, in most cases, that all inputs and outputs are controlled by the Decision Making Unit (DMU). Inputs and/or outputs that do not conform to this assumption are denoted in DEA asnon-discretionary (ND) factors. Banker and Morey [1986] formulated several variants of DEA models which incorporated ND with ordinary factors. This article extends the Banker and Morey approach for treating nondiscretionary factors in two ways. First, the model is extended to allow for thesimultaneous presence of ND factors in both the input and the output sets. Second, a generalization is offered which, for the first time, enables a quantitative evaluation ofpartially controlled factors. A numerical example is given to illustrate the different models.

Abstract: The problem of constructing Lyapunov functions for a class of nonlinear dynamical systems is considered. The problem is reduced to the construction of a polytope satisfying some conditions. A generalization of the concept of sector condition that it makes possible to evaluate a given nonlinear function by using a set of piecewise-linear functions is proposed. This improvement greatly reduces the conservatism in the stability analysis of nonlinear systems. Two algorithms for constructing such polytopes are proposed, and two examples are shown to demonstrate the usefulness of the results. >

Abstract: In the present paper a model for describing dynamic processes is constructed by combining the common Rasch model with the concept of structurally incomplete designs. This is accomplished by mapping each item on a collection of virtual items, one of which is assumed to be presented to the respondent dependent on the preceding responses and/or the feedback obtained. It is shown that, in the case of subject control, no unique conditional maximum likelihood (CML) estimates exist, whereas marginal maximum likelihood (MML) proves a suitable estimation procedure. A hierarchical family of dynamic models is presented, and it is shown how to test special cases against more general ones. Furthermore, it is shown that the model presented is a generalization of a class of mathematical learning models, known as Luce's beta-model.

Abstract: A category can contain either an infinite or limited number of stimuli. Categories with an infinite number of stimuli have been called open-ended; they contain stimuli that are physically similar. Categories with a limited number of stimuli include functional classes and equivalence classes; they contain stimuli that are physically disparate. The processes of equivalence class formation and primary generalization acting in combination yield a category containing stimuli that are physically similar as well as those that are physically disparate. Such a category is called a generalized equivalence class. A response trained to one member of such a class transfers to all remaining members of that class, yielding a generalized functional class. The extension of equivalence classes through generalization is predicted from primary generalization gradients obtained before class formation. Generalized equivalence classes and generalized functional classes bring together the study of stimulus equivalence and open-ended categories. They also provide a plausible account of the establishment of complex categories observed in natural settings.

Abstract: Let R be a ring and M a right R-module. The module M is a CS-module or satifies (C1) if every submodule is essential in a direct summand of M. In this note we investigate two generalizations of CS-modules.

Abstract: Explanation-based generalization (EBG) is a powerful approach to concept formation in which a justifiable concept definition is acquired from a single training example and an underlying theory of how the example is an instance of the concept. Soar is an attempt to build a general cognitive architecture combining general learning, problem solving, and memory capabilities. It includes an independently developed learning mechanism, called chunking, that is similar to but not the same as explanation-based generalization. In this article we clarify the relationship between the explanation-based generalization framework and the Soar/chunking combination by showing how the EBG framework maps onto Soar, how several EBG conceptformation tasks are implemented in Soar, and how the Soar approach suggests answers to some of the outstanding issues in explanation-based generalization.

Abstract: This chapter discusses the generalization of causal relationships and offers an applied, meta-analytical approach.

Abstract: There are currently several types of constructive, (or growth), algorithms available for training a feed-forward neural network. This paper describes and explains the main ones, using a fundamental approach to the multi-layer perceptron problem-solving mechanisms. The claimed convergence properties of the algorithms are verified using just two mapping theorems, which consequently enables all the algorithms to be unified under a basic mechanism. The algorithms are compared and contrasted and the deficiencies of some highlighted. The fundamental reasons for the actual success of these algorithms are extracted, and used to suggest where they might most fruitfully be applied. A suspicion that they are not a panacea for all current neural network difficulties, and that one must somewhere along the line pay for the learning efficiency they promise, is developed into an argument that their generalization abilities will lie on average below that of back-propagation.

Abstract: An approximate analytical solution of the problem of attenuation and distance-dependent resolution effects in single photon emission tomography is presented for the case of a uniform absorbing medium. The algorithm obtained is a generalization of the Bellini and co-workers formula correcting for the single attenuation effect and is derived by means of Fourier transforms only. The method has been validated on mathematical phantoms as well as on physical data.

Abstract: The paper refers to problems of handling various types of uncertainty in the rough set approach to analysis of information systems. Besides ambiguity resulting from a limited discernibility of objects, we consider uncertainty caused by: discretization of quantitative attributes, imprecise descriptors, unknown descriptors, or multiple descriptors. A special way of modelling the first three types of uncertainty using fuzzy sets, boils them down to the fourth type, i.e. multiple descriptors. So, the generalization of the rough set approach consists in handling the case of multiple descriptors.

Abstract: A generalization of the binary algorithm for operation at ‘word level” by using a new concept of ‘modular conjugates” computes the GCD of multiprecision integers two times faster than Lehmer–Euclid method. Most importantly, however, the new algorithm is suitable for systolic parallelization, in ‘least-significant digits jirst” pipelined manner and for aggregation with other systolic algorithms for the arithmetic of multiprecision rational numbers.

Abstract: This article presents a quantitative model of adaptation-level (AL) effects on stimulus generalization and integrates results from single stimulus, go-no-go, and choice discrimination training paradigms. The model accurately predicts (a) the gradualness of the shift in responding during the course of asymmetrical generalization testing, (b) the relation between the degree of asymmetry and the amount of shift, (c) the effect of overrepresenting certain stimuli during testing, and (d) the effect of varying the amount of training. With the discrimination training paradigms the effects of the degree of separation between the training stimuli (TSs) and of the relative frequency of their presentation during training and subsequent generalization testing are consistent with an extension of the basic model. Finally, new research is described affirming the applicability of the AL model to several infrahuman species

Abstract: © Foundation Compositio Mathematica, 1993, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Abstract: The purpose of this paper is to investigate an extension of ? theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed ? and absolute stability theory. In particular, it is shown that the upper bounds for mixed ? are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered.

Abstract: A rule of thumb for obtaining good generalization in systems trained by examples is that one should use the smallest system that will fit the data Unfortunately, it usually is not obvious what size is best; a system that is too small will not be able to learn the data while one that is just big enough may learn very slowly and be very sensitive to initial conditions and learning parameters This paper is a survey of neural network pruning algorithms The approach taken by the methods described here is to train a network that is larger than necessary and then remove the parts that are not needed >

Abstract: We consider a bivariate Pareto distribution, as a generalization of the Lindley-Singpurwalla model, by incorporating the influence of the operating conditions on a two-component dependent system. The properties of the model and its applications to reliability analysis are discussed. © 1993 John Wiley & Sons, Inc.

Abstract: © Foundation Compositio Mathematica, 1993, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.