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Point Processes Based on Fractals
Malvin and Steven Bradley Lowen Teich, Carl
OVERVIEW
A combined method for studying point processes and fractals
From definitions and measurements to analysis and estimation, this book offers a thorough and comprehensive introduction to the domains of fractals and point processes. The authors expertly illustrate the great utility of fractal-based point processes, which are recognized as the nexus of these two domains, in the representation and description of a vast array of different phenomena in the biological and physical sciences. Information packet arrivals on a computer network and action-potential events in a neural preparation are among the topics covered.
The writers give an overview of chaos and fractals after providing important and tangible examples of point processes and fractals. A number of defining metrics are provided along with a definition of point processes. After thoroughly examining the ideas of point processes and fractals, the writers proceed to merge the two disciplines. An explanation of how different operations affect such processes is given, along with mathematical formulations for a number of significant fractal-based point-process families. The authors also look at estimating and analysis methods that work well for these procedures. The final topic covered is computer network traffic, a crucial application that serves to highlight the many strategies and models presented in previous chapters.
Using a collection of point processes derived from computer network traffic and biological signals, readers are introduced to several significant applications during the presentation. Each chapter concludes with problems that let readers apply what they have learned, and all of the answers are included in an appendix. Links to further resources and tools to help with data analysis and simulation can be found on an associated website.
This is a great graduate-level work for courses in a variety of subjects, including statistics, physics, engineering, computer science, psychology, and neuroscience, because of its emphasis on applications and large number of solved problem sets.
CONCERNING THE AUTHOR
Harvard Medical School Assistant Professor of Psychiatry Steven Bradley Lowen, PHD, is connected to McLean Hospital’s Brain Imaging Center in Belmont, Massachusetts. Yale University awarded him a bachelor’s degree, and Columbia University awarded him an MS and a PhD.
MALVIN CARL TEICH, PHD, is a professor at Boston University in the fields of physics, biomedical engineering, and electrical and computer engineering. He is also a professor emeritus at Columbia University. Stanford University, Cornell University, and the Massachusetts Institute of Technology awarded him SB, MS, and PhD degrees, respectively.
TABLE OF CONTENTS
Preface.
List of Figures.
List of Tables.
Authors.
1. Introduction.
2. Scaling, Fractals, and Chaos.
3. Point Processes: Definition and Measures.
4. Point Processes: Examples.
5. Fractal and Fractal-Rate Point Processes.
6. Processes Based on Fractional Brownian Motion.
7. Fractal Renewal Processes.
8. Processes Based on the Alternating Fractal Renewal Process.
9. Fractal Shot Noise.
10. Fractal-Shot-Noise-Driven Point Processes.
11. Operations.
12. Analysis and Estimation.
13. Computer Network Traffic.
Appendix A: Derivations.
Appendix B: Problem Solutions.
Appendix C: List of Symbols.
Bibliography.
Author Index.
Subject Index.
REVIEWS
“The style of text is practical and informal with a distinct engineering approach.” (Zentralblatt Math)
“It is apparent that the authors are truly at home in their field…will certainly prove valuable to scientists working in many distinct fields.” (Journal of the American Statistical Association, March 2007)
“…an excellent exposition of a cutting-edge topic, and will be extremely valuable as a textbook and for scientists in diverse fields, including astronomy.” (Technometrics, February 2007)
“…a very well-written monograph on its subject…” (Computing Reviews.com, August 10, 2006)
“….a valuable resource and a quarry of many concrete results from real life.” (Mathematical Reviews, 2006f)
