الصفحة 1
الصفحة 1
Ergodic Dynamics : From Basic Theory to Applications
This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author offers readers an approachable entry-point to the dynamics of ergodic systems. Modern and classical applications complement the theory on topics ranging from financial fraud to virus dynamics, offering numerous avenues for further inquiry. Starting with several simple examples of dynamical systems, the book begins by establishing the basics of measurable dynamical systems, attractors, and the ergodic theorems. From here, chapters are modular and can be selected according to interest. Highlights include the Perron–Frobenius theorem, which is presented with proof and applications that include Google PageRank. An in-depth exploration of invariant measures includes ratio sets and type III measurable dynamical systems using the von Neumann factor classification. Topological and measure theoretic entropy are illustrated and compared in detail, with an algorithmic application of entropy used to study the papillomavirus genome. A chapter on complex dynamics introduces Julia sets and proves their ergodicity for certain maps. Cellular automata are explored as a series of case studies in one and two dimensions, including Conway’s Game of Life and latent infections of HIV. Other chapters discuss mixing properties, shift spaces, and toral automorphisms.
Algorithms and Models for the Web-Graph ; 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007, Proceedings
The book address a wide variety of topics related to the study of the Web-graph such as random graph models for the Web-graph, PageRank analysis and computation, decentralized search, local partitioning algorithms,and traceroute sampling. The Web-graph has been the focal point of a tremendous amount of research for more than a decade. The view of the Web as a graph has great practical importance and has also generated much interesting theoretical work.
Algorithms and Models for the Web-Graph ; 4th International Workshop, WAW 2006, Banff, Canada, November 30 - December 1, 2006. Revised Papers
his book constitutes the revised papers of the Fourth International Workshop on Algorithms and Models for the Web-Graph, WAW 2006, held in Banff, Canada, November 30 - December 1, 2006.
