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Analysis of Observed Chaotic Data
A clear and systematic treatment of time series of data, regular and chaotic, found in nonlinear systems. The text leads readers 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. It 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 modern mathematical tools for investigating chaotic behaviour to uncover properties of physical systems, requiring knowledge of dynamical systems at the advanced undergraduate level and some knowledge of Fourier transforms and other signal processing methods.
Studies in Mathematical Physics
Some of the articles in this collection give up-to-date accounts of areas in mathematical physics to which Valentine Bargmann made pioneering contributions. The others treat a selection of the most interesting current topics in the field. The contributions include both reviews and original results. Contents: The Inverse r-Squared Force (Henry D. I. Abarbanel; Certain Hilbert Spaces of Analytic Functions Associated with the Heisenberg Group (Donald Babbitt); Lower Bound for the Ground State Energy of the Schrodinger Equation Using the Sharp Form of Young's Inequality (John F. Barnes, Herm Jan Brascamp, and Elliott II. Lieb); Alternative Theories of Gravitation (Peter G. Bergmann; )Generalized...
Isaac Abarbanel's Stance Toward Tradition
Winner of the 2002 Nauchman Sokol-Mollie Halberstadt Prize in Biblical/Rabbinic Scholarship presented by the Canadian Jewish Book Awards Finalist, 2002 Scholarship Morris J. and Betty Kaplun Award presented by the National Jewish Book Council Financier and courtier to the kings of Portugal, Spain, and Italy and Spanish Jewry's foremost representative at court at the time of its 1492 expulsion, Isaac Abarbanel was also Judaism's leading scholar at the turn of the sixteenth century. His work has had a profound influence on both his contemporaries and later thinkers, Jewish and Christian. Isaac Abarbanel's Stance Toward Tradition is the first full-length study of Abarbanel in half a century. Th...
The Cortex and the Critical Point
How the cerebral cortex operates near a critical phase transition point for optimum performance. Individual neurons have limited computational powers, but when they work together, it is almost like magic. Firing synchronously and then breaking off to improvise by themselves, they can be paradoxically both independent and interdependent. This happens near the critical point: when neurons are poised between a phase where activity is damped and a phase where it is amplified, where information processing is optimized, and complex emergent activity patterns arise. The claim that neurons in the cortex work best when they operate near the critical point is known as the criticality hypothesis. In th...
