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Fractal-Based Point Processes
Steven Bradley Lowen
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Description for Fractal-Based Point Processes
Hardcover. This book addresses the systematic analysis, modeling, and synthesis of integrated fractal and fractal-rate point processes in a rigorous but useful manner. Fractal and fractal-rate point processes exhibit both the scaling properties of fractals, and the discrete nature of random point processes. Series: Wiley Series in Probability and Statistics. Num Pages: 626 pages, Illustrations. BIC Classification: PBMX. Category: (P) Professional & Vocational. Dimension: 242 x 167 x 39. Weight in Grams: 1034.
An integrated approach to fractals and point processes
This publication provides a complete and integrated presentation of the fields of fractals and point processes, from definitions and measures to analysis and estimation. The authors skillfully demonstrate how fractal-based point processes, established as the intersection of these two fields, are tremendously useful for representing and describing a wide variety of diverse phenomena in the physical and biological sciences. Topics range from information-packet arrivals on a computer network to action-potential occurrences in a neural preparation.
The authors begin with concrete and key examples of fractals and point processes, followed by an introduction to fractals and chaos. Point processes are defined, and a collection of characterizing measures are presented. With the concepts of fractals and point processes thoroughly explored, the authors move on to integrate the two fields of study. Mathematical formulations for several important fractal-based point-process families are provided, as well as an explanation of how various operations modify such processes. The authors also examine analysis and estimation techniques suitable for these processes. Finally, computer network traffic, an important application used to illustrate the various approaches and models set forth in earlier chapters, is discussed.
Throughout the presentation, readers are exposed to a number of important applications that are examined with the aid of a set of point processes drawn from biological signals and computer network traffic. Problems are provided at the end of each chapter allowing readers to put their newfound knowledge into practice, and all solutions are provided in an appendix. An accompanying Web site features links to supplementary materials and tools to assist with data analysis and simulation.
With its focus on applications and numerous solved problem sets, this is an excellent graduate-level text for courses in such diverse fields as statistics, physics, engineering, computer science, psychology, and neuroscience.
This publication provides a complete and integrated presentation of the fields of fractals and point processes, from definitions and measures to analysis and estimation. The authors skillfully demonstrate how fractal-based point processes, established as the intersection of these two fields, are tremendously useful for representing and describing a wide variety of diverse phenomena in the physical and biological sciences. Topics range from information-packet arrivals on a computer network to action-potential occurrences in a neural preparation.
The authors begin with concrete and key examples of fractals and point processes, followed by an introduction to fractals and chaos. Point processes are defined, and a collection of characterizing measures are presented. With the concepts of fractals and point processes thoroughly explored, the authors move on to integrate the two fields of study. Mathematical formulations for several important fractal-based point-process families are provided, as well as an explanation of how various operations modify such processes. The authors also examine analysis and estimation techniques suitable for these processes. Finally, computer network traffic, an important application used to illustrate the various approaches and models set forth in earlier chapters, is discussed.
Throughout the presentation, readers are exposed to a number of important applications that are examined with the aid of a set of point processes drawn from biological signals and computer network traffic. Problems are provided at the end of each chapter allowing readers to put their newfound knowledge into practice, and all solutions are provided in an appendix. An accompanying Web site features links to supplementary materials and tools to assist with data analysis and simulation.
With its focus on applications and numerous solved problem sets, this is an excellent graduate-level text for courses in such diverse fields as statistics, physics, engineering, computer science, psychology, and neuroscience.
Product Details
Format
Hardback
Publication date
2005
Publisher
John Wiley & Sons Inc United States
Number of pages
626
Condition
New
Series
Wiley Series in Probability and Statistics
Number of Pages
626
Place of Publication
, United States
ISBN
9780471383765
SKU
V9780471383765
Shipping Time
Usually ships in 7 to 11 working days
Ref
99-50
About Steven Bradley Lowen
STEVEN BRADLEY LOWEN, PHD, is Assistant Professor of Psychiatry at Harvard Medical School and is affiliated with the Brain Imaging Center at McLean Hospital in Belmont, Massachusetts. He received a BS degree from Yale University and MS and PhD degrees from Columbia University. MALVIN CARL TEICH, PHD, is Professor in the Departments of Electrical and Computer Engineering; Biomedical Engineering; and Physics at Boston University; as well as Professor Emeritus at Columbia University. He received SB, MS, and PhD degrees from the Massachusetts Institute of Technology, Stanford University, and Cornell University, respectively.
Reviews for Fractal-Based Point Processes
"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)