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Quotient Space Based Problem Solving

RRP $237.99

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Quotient Space Based Problem Solving provides an in-depth treatment of hierarchical problem solving, computational complexity, and the principles and applications of multi-granular computing, including inference, information fusing, planning, and heuristic search. Drawing upon years of academic research and using numerous examples and illustrative applications, the authors, Ling Zhang and Bo Zhang provide a unique guide to computerized problem solving and granular computing. This book is a valuable guide to graduate students, research fellows, and academics specializing in artificial intelligence or concerned with computerized problem solving and granular computing. It explains the theory of hierarchical problem solving, its computational complexity, and discusses the principle and applications of multi-granular computing. It describes a human-like, theoretical framework using quotient space theory, that will be of interest to researchers in artificial intelligence. It provides many applications and examples in the engineering and computer science area. It includes complete coverage of planning, heuristic search and coverage of strictly mathematical models.

Ill-posed Problems

RRP $50.00

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Recent years have been characterized by the increasing amountofpublications in the field ofso-called ill-posed problems. This is easilyunderstandable because we observe the rapid progress of a relatively young branch ofmathematics, ofwhich the first results date back to about 30 years ago. By now, impressive results have been achieved both in the theory ofsolving ill-posed problems and in the applicationsofalgorithms using modem computers. To mention just one field, one can name the computer tomography which could not possibly have been developed without modem tools for solving ill-posed problems. When writing this book, the authors tried to define the place and role of ill- posed problems in modem mathematics. In a few words, we define the theory of ill-posed problems as the theory of approximating functions with approximately given arguments in functional spaces. The difference between well-posed and ill- posed problems is concerned with the fact that the latter are associated with discontinuous functions. This approach is followed by the authors throughout the whole book. We hope that the theoretical results will be of interest to researchers working in approximation theory and functional analysis. As for particular algorithms for solving ill-posed problems, the authors paid general attention to the principles ofconstructing such algorithms as the methods for approximating discontinuous functions with approximately specified arguments. In this way it proved possible to define the limits of applicability of regularization techniques.

Multilevel Modeling Of Social Problems

RRP $903.99

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Uniquely focusing on intersections of social problems, multilevel statistical modeling, and causality; the substantively and methodologically integrated chapters of this book clarify basic strategies for developing and testing multilevel linear models (MLMs), and drawing casual inferences from such models. These models are also referred to as hierarchical linear models (HLMs) or mixed models. The statistical modeling of multilevel data structures enables researchers to combine contextual and longitudinal analyses appropriately. But researchers working on social problems seldom apply these methods, even though the topics they are studying and the empirical data call for their use. By applying multilevel modeling to hierarchical data structures, this book illustrates how the use of these methods can facilitate social problems research and the formulation of social policies. It gives the reader access to working data sets, computer code, and analytic techniques, while at the same time carefully discussing issues of causality in such models. This book innovatively: *Develops procedures for studying social, economic, and human development. * Uses typologies to group (i.e., classify or nest) the level of random macro-level factors. * Estimates models with Poisson, binomial, and Gaussian end points using SAS's generalized linear mixed models (GLIMMIX) procedure. * Selects appropriate covariance structures for generalized linear mixed models. * Applies difference-in-differences study designs in the multilevel modeling of intervention studies. *Calculates propensity scores by applying Firth logistic regression to Goldberger-corrected data. * Uses the Kenward-Rogers correction in mixed models of repeated measures. * Explicates differences between associational and causal analysis of multilevel models. * Consolidates research findings via meta-analysis and methodological critique. *Develops criteria for assessing a study's validity and zone of causality. Because of its social problems focus, clarity of exposition, and use of state-of-the-art procedures; policy researchers, methodologists, and applied statisticians in the social sciences (specifically, sociology, social psychology, political science, education, and public health) will find this book of great interest. It can be used as a primary text in courses on multilevel modeling or as a primer for more advanced texts.

How To Think Like A Computer Programmer

RRP $327.99

The Problem Of Estimation

RRP $18.99

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As Reviewed by Irving Fisher

Mr. Walsh is the author of "The Measurement of General Exchange Value," one of the chief classics on the subject of index numbers. The present book is partly a condensation of "The Measurement of General Exchange Value," and partly an extension of its ideas to other problems than that of index numbers.

Nevertheless the chief interest in the present volume centers, I think, in the author's discussion of index numbers. It is largely taken up with a discussion of the geometric mean as contrasted with other means.

Mr. Walsh has delved deep in the lore to be found in libraries on the subject and has unearthed an interesting old discussion of Galileo on "the problem of estimation."

Mr. Walsh begins his book by giving the arguments of Galileo and his opponent, which are very entertaining. This old problem reads "if a horse worth 100 pounds is estimated by one person at 1000 and by another at 10, which of these two estimates is the less erroneous, or are they equally erroneous?" According to one view 10 is much nearer the truth (100) than is 1000, the difference in the first case being 90 and in the second, 900. According to another view they are equally distant, one being 10 times as large and the other 10 times as little! Galileo took the latter view and Walsh approves.

In the part devoted to index numbers, Walsh (page 102) confirms my views expressed in the March Number of the Quarterly Publications of the American Statistical Association on the best formula for an index number although his method of arriving at the result is quite different from my own. It is interesting to observe that Allyn Young of Harvard in the August number of the Quarterly Journal of Economics in an article entitled "The Measurement of Changes of the General Price Level," has reached the same result from a different angle.

Walsh's argument is largely that the formula in question comes nearest to satisfying Westergaard's test, that is the so-called circular test that any index number should, if calculated from one year to another and from the second to a third and so on in a chain, give the same result as though calculated directly from the original base to the last year.

In my forthcoming book on Index Numbers, to be published by the Pollak Foundation for Economic Research, I propose to show that, while index numbers which come near to satisfying Westergaard's test are better than those which fall far short of satisfying it, nevertheless there is an irreducible minimum of discrepancy which is not only inevitable in good index numbers but commendable. Much of Walsh's work in index numbers has been in the search for a formula which will completely fulfill Westergaard's test. The truth is that no such formula exists; at least not one which has different weights for each year to year comparison.

But the search for such fulfillment, while in vain in the sense of being unsuccessful in its object, has nevertheless not been fruitless; for Walsh has laid secure foundations in this subject, which he was enabled to lay by virtue of his search for the impossible.


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