Basic Mathematica

This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several.

The ideas of uncertain variables based on uncertain logics have been introduced and developed for a wide class of uncertain systems. The purpose of this mo- graph is to present basic concepts, definitions and results concerning the uncertain variables and their applications to analysis and decision problems in uncertain systems described by traditional mathematical models and by knowledge rep- sentations. I hope that the book can be useful for graduate students, researchers and all readers working in the field of control and information science. Especially for those interested in the problems of uncertain decision support systems and unc- tain control systems. I wish to express my gratitude to my co-workers from the Institute of Control and Systems Engineering of Wroclaw University of Technology, who assisted in the preparation of the manuscript. My special thanks go to Dr L.Siwek for the valuable remarks and for his work concerning the formatting of the text.

Some of the key mathematical results are stated without proof in order to make the underlying theory accessible to a wider audience. The book assumes a knowledge only of basic calculus, matrix algebra, and elementary statistics. The emphasis is on methods and the analysis of data sets. The logic and tools of model-building for stationary and nonstationary time series are developed in detail and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills in this area.
The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Additional topics include harmonic regression, the Burg and Hannan-Rissanen algorithms, unit roots, regression with ARMA errors, structural models, the EM algorithm, generalized state-space models with applications to time series of count data, exponential smoothing, the Holt-Winters and ARAR forecasting algorithms, transfer function models and intervention analysis. Brief introductions are also given to cointegration and to nonlinear, continuous-time and long-memory models.
The time series package included in the back of the book is a slightly modified version of the package ITSM, published separately as ITSM for Windows, by Springer-Verlag, 1994. It does not handle such large data sets as ITSM for Windows, but like the latter, runs on IBM-PC compatible computers under either DOS or Windows (version 3.1 or later). The programs are all menu-driven so that the reader can immediately apply the techniques in the book to time series data, with a minimal investment of time in the computational and algorithmic aspects of the analysis.

Ever since my days as a student, economists, doctors, physiologists, biologists, and engineers have come to me with queries of a statistical nature. This book is the product of my long interest in practical solutions to such problems. Study of the literature and my own ideas have repeat­ edly led me to improved methods, which will be established here and applied to instructive examples taken from the natural and social sciences. Thus, I hope to help the reader avoid the many fruitless direc­ tions in which I worked at first. The examples are not artificially con­ structed from theoretical considerations but are instead taken from real situations; consequently, many of the examples require detailed explana­ tion. The presentation of the basic mathematical concepts is, I hope, as brief as possible without becoming incomprehensible. Some rather long theoretical arguments have been necessary, but, whenever possible, references for the more difficult proofs have been made to good text­ books already in existence. There would be no point in developing again the mathematical theories which have been presented clearly and in detail by Kolmogorov, Caratheodory, and Cramer.