Fractal Dimensions of Networks
暫譯: 網絡的分形維度
Eric Rosenberg
- 出版商: Springer
- 出版日期: 2021-07-08
- 售價: $3,010
- 貴賓價: 9.5 折 $2,860
- 語言: 英文
- 頁數: 524
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3030431711
- ISBN-13: 9783030431716
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商品描述
Current interest in fractal dimensions of networks is the result of more than a century of previous research on dimensions. Fractal Dimensions of Networks ties the theory and methods for computing fractal dimensions of networks to the "classic" theory of dimensions of geometric objects.
The goal of the book is to provide a unified treatment of fractal dimensions of sets and networks. Since almost all of the major concepts in fractal dimensions originated in the study of sets, the book achieves this goal by first clearly presenting, with an abundance of examples and illustrations, the theory and algorithms for sets, and then showing how the theory and algorithms have been applied to networks. Thus, the book presents the classical theory and algorithms for the box counting dimension for sets, and then presents the box counting dimension for networks. All the major fractal dimensions are studied, e.g., the correlation dimension, the information dimension, the Hausdorff dimension, the multifractal spectrum, as well as many lesser known dimensions. Algorithm descriptions are accompanied by worked examples, many applications of the methods are presented, and many exercises, ranging in difficulty from easy to research level, are included.
商品描述(中文翻譯)
目前對於網絡的分形維度的興趣是基於超過一世紀以來對維度的研究結果。《網絡的分形維度》將計算網絡分形維度的理論和方法與幾何物體的「經典」維度理論相結合。
本書的目標是提供對集合和網絡的分形維度的統一處理。由於幾乎所有主要的分形維度概念都源於集合的研究，本書首先通過大量的例子和插圖清晰地呈現集合的理論和算法，然後展示這些理論和算法如何應用於網絡。因此，本書介紹了集合的盒子計數維度的經典理論和算法，然後介紹網絡的盒子計數維度。所有主要的分形維度都被研究，例如，相關維度、信息維度、Hausdorff維度、多重分形譜，以及許多不太知名的維度。算法描述附有實例，展示了許多方法的應用，並包含了從簡單到研究級別的多個練習題。
作者簡介
Eric Rosenberg has taught undergraduate and graduate courses in modelling and optimization at Princeton University, New Jersey Institute of Technology, and Rutgers University. He recently retired from AT&T Labs in Middletown, New Jersey, and has joined the faculty of Georgian Court University in Lakewood, New Jersey.
He received a B.A. in Mathematics from Oberlin College and a Ph.D. in Operations Research from Stanford University, and has authored or co-authored 19 patents and has published in the areas of convex analysis and nonlinearly constrained optimization, computer aided design of integrated circuits and printed wire boards, telecommunications network design and routing, and fractal dimensions of networks.
Dr. Rosenberg is the author of A Primer of Multicast Routing, and A Survey of Fractal Dimensions of Networks, both published by Springer.
New research and applications relating to fractal dimensions of networks can be sent to Dr. Rosenberg at FractalDimensionsOfNetworks@gmail.com.
作者簡介(中文翻譯)
埃瑞克·羅森伯格（Eric Rosenberg）曾在普林斯頓大學、新澤西理工學院和羅格斯大學教授建模與優化的本科及研究生課程。他最近從新澤西州米德敦的AT&T實驗室退休，並加入新澤西州萊克伍德的喬治亞法院大學（Georgian Court University）任教。
他在奧伯林學院獲得數學學士學位，並在史丹佛大學獲得運籌學博士學位，擁有19項專利的著作或共同著作，並在凸分析、非線性約束優化、集成電路和印刷電路板的計算機輔助設計、電信網絡設計與路由以及網絡的分形維度等領域發表過論文。
羅森伯格博士是《多播路由入門》（A Primer of Multicast Routing）和《網絡的分形維度調查》（A Survey of Fractal Dimensions of Networks）的作者，這兩本書均由施普林格（Springer）出版。
有關網絡分形維度的新研究和應用可以發送至羅森伯格博士的電子郵件：FractalDimensionsOfNetworks@gmail.com。
