This book develops a clear and systematic treatment of time series of data, regular and chaotic, that one finds in observations of nonlinear systems. The reader is led from measurements of one or more variables through the steps of building models of the source as a dynamical system, classifying the source by its dynamical characteristics, and finally predicting and controlling the dynamical system. The text examines methods for separating the signal of physical interest from contamination by unwanted noise, and for investigating the phase space of the chaotic signal and its properties. The emphasis throughout is on the use of the modern mathematical tools for investigating chaotic behavior to uncover properties of physical systems. The methods require knowledge of dynamical systems at the advanced undergraduate level and some knowledge of Fourier transforms and other signal processing methods. The toolkit developed in the book will provide the reader with efficient and effective methods for analyzing signals from nonlinear sources; these methods are applicable to problems of control, communication, and prediction in a wide variety of systems encountered in physics, chemistry, biology, and geophysics.

Through the development of an exact path integral for use in transferring information from observations to a model of the observed system, the author provides a general framework for the discussion of model building and evaluation across disciplines. Through many illustrative examples drawn from models in neuroscience, geosciences, and nonlinear electrical circuits, the concepts are exemplified in detail. Practical numerical methods for approximate evaluations of the path integral are explored, and their use in designing experiments and determining a model's consistency with observations is explored.

The ocean has entranced mankind for as long as we have gazed upon it, traversed it, dived into it, and studied it. It remains ever changing and seemingly never changing. Each wave that progresses through the. imme diate surf zone on every coast is strikingly different, yet the waves come again and again, as if never to end. The seasons come with essential reg ularity, and. yet each is individual-whatever did happen to that year of the normal rainfall or tidal behavior? This fascination with the currents of the ocean has always had a most immediate practical aspect: shipping, transportation, commerce, and war have depended upon our knowledge, when we had it, and floundered on our surprising ignorance more often than we wish to reflect. These important practical issues have commanded attention from commercial, academic, and military research scientists and engineers from the earliest era of organized scientific investigation. The matter of direct and insistent investigation was from the outset the behavior of ocean currents with long time scales; namely, those varying on annual or at least seasonal cycles. Planning for all the named enterprises depended, as they still do, of course, on the ability to predict with some certainty this class of phenomena. That ability, as with most physical sci ence, is predicated on a firm basis of observational fact to establish what, amorig the myriad of mathematical possibilities, is chosen by Nature as her expression of fact."

Through the development of an exact path integral for use in transferring information from observations to a model of the observed system, the author provides a general framework for the discussion of model building and evaluation across disciplines. Through many illustrative examples drawn from models in neuroscience, geosciences, and nonlinear electrical circuits, the concepts are exemplified in detail. Practical numerical methods for approximate evaluations of the path integral are explored, and their use in designing experiments and determining a model's consistency with observations is explored.

And Characteristics On Judaism, Past, Present, Future.

And Characteristics On Judaism, Past, Present, Future.

And Characteristics On Judaism, Past, Present, Future.