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### A brief overview of network algorithms

Fan Chung Graham
2006 Journal of computer and system sciences (Print)
A first step is to take advantage of the relationships among the data and to form an information network. The Web crawler views the Web as a graph with Web pages as nodes and hyperlinks as edges.  ...  Since then, the spectral analysis of the Web graph has become an active subfield. There is a great deal of interplay between spectral methods and probabilistic techniques.  ...

### Ranking via Arrow-Debreu Equilibrium [article]

Ye Du
2009 arXiv   pre-print
First of all, we show that the ranking vector of PageRank or Invariant method is precisely the equilibrium of a special Cobb-Douglas market.  ...  In this paper, we establish a connection between ranking theory and general equilibrium theory.  ...  Acknowledgements I would like to thank Xiaotie Deng, Romesh Saigal, Yaoyun Shi and Michael Wellman to read the preliminary version of this paper and provide valuable suggestions.  ...

### Verifying Nash Equilibria in PageRank Games on Undirected Web Graphs [chapter]

David Avis, Kazuo Iwama, Daichi Paku
2011 Lecture Notes in Computer Science
We study the problem of determining whether the given graph represents a Nash equilibrium or not.  ...  We give an O(n 2 ) time algorithm for a tree, and a parametric O(2 k n 4 ) time algorithm for general graphs, where k is the maximum vertex degree in any biconnected component of the graph.  ...  Introduction A PageRank value is assigned to each web page according to the stationary distribution of an α-random walk on the web graph.  ...

### Algebraic graph statics

T. Van Mele, P. Block
2014 Computer-Aided Design
Using graph theoretical properties of reciprocal graphs, the geometrical relation between the form and force diagrams used in graphic statics is written algebraically.  ...  These formulations have been found to be equivalent to the equilibrium equations used in matrix analysis of planar, self-stressed structural systems.  ...  This is the case if, for example, the form graph represents an equilibrium system in an infeasible configuration.  ...

### A HISTORY OF THE STUDY OF ECOLOGICAL NETWORKS [chapter]

Louis-Félix Bersier
2007 Biological Networks
My apologies to all whose contributions could not be tackled in the Chapter. This research was supported by a Swiss NSF grant (3100A0-113843).  ...  grateful to all colleagues and friends who helped me to sharpen my ideas about community ecology, to all field ecologists involved in data collection presented here, and to Russell Naisbit for revising the  ...  Figure 11 . 11 Interactions in a food-web in an equilibrium and a non-equilibrium context (Michalski and Arditi 1995) (132).  ...

### Reputation Games for Undirected Graphs [article]

David Avis, Kazuo Iwama, Daichi Paku
2012 arXiv   pre-print
We study the problem of determining whether the given graph represents a Nash equilibrium or not in this model.  ...  Sheldon originally introduced network reputation games to investigate the self-interested behavior of web authors who want to maximize their PageRank on a directed web graph by choosing their outlinks  ...  PageRank is a value that is assigned to each web page according to the stationary distribution of an α-random walk on the web graph.  ...

### On the α-Sensitivity of Nash Equilibria in PageRank-Based Network Reputation Games [chapter]

Wei Chen, Shang-Hua Teng, Yajun Wang, Yuan Zhou
2009 Lecture Notes in Computer Science
They show that a positive answer to the question would imply that all Nash equilibria in the PageRank game must satisfy some strong algebraic symmetry, a property rarely satisfied by real web graphs.  ...  They pose an open question in [10] asking whether all Nash equilibria in the PageRank game are insensitive to the restart probability α of the PageRank algorithm.  ...  Note that we define G n,m as an undirected graph for the simplicity of presentation. This is because each Nash equilibrium is bidirectional.  ...

### Of the matrics of the equilibrium of the rod formation system based on the principle the duality of the problems of structures mechanics

2019 MATEC Web of Conferences
The topological structure of the model is set using the graph and the accompanying incidence matrix.  ...  The formation of the equilibrium matrix of the core system in the matrix form is based on the use of the mechanical model of the system obtained by its discretization.  ...  If linear displacements of nodes are redesignated The construction of the frame graph, the schemes of concentrated bending deformations, as well as the formation of the incidence matrices accompanying  ...

### Hubs, authorities, and communities

Jon M. Kleinberg
1999 ACM Computing Surveys
Only a few years ago, the World Wide Web was known just to a small research community; it is hard to remember that the voluminous content we see on the WWW, expanding by an estimated million pages each  ...  The Web has become the most visible manifestation of a new medium: a global, populist hypertext.  ...  Acknowledgments The author is supported in part by an Alfred P.  ...

### Using the Web to Improve Computer-Aided Instruction in Economics

Joseph I. Daniel
1999 Journal of Economic Education
See Leuthold (1998a) for an example of a Web-based application of Mathematica to microeconomics and Leuthold (1998b) for an example of the interactive use of an Excel spreadsheet in a Web-based application  ...  The competitive equilibrium model in Figure 4 is an example of a programmable model that uses the parameters specified in Table 3 .  ...  I particularly liked the graphing program, which permits the graphing of economics functions based on common utility and production functions.  ...

### Using the Web to Improve Computer-Aided Instruction in Economics

Joseph I. Daniel
1999 Journal of Economic Education
See Leuthold (1998a) for an example of a Web-based application of Mathematica to microeconomics and Leuthold (1998b) for an example of the interactive use of an Excel spreadsheet in a Web-based application  ...  The competitive equilibrium model in Figure 4 is an example of a programmable model that uses the parameters specified in Table 3 .  ...  I particularly liked the graphing program, which permits the graphing of economics functions based on common utility and production functions.  ...

### PageRank, HITS and a Unified Framework for Link Analysis [chapter]

Chris Ding, Xiaofeng He, Parry Husbands, Hongyuan Zha, Horst Simon
2003 Proceedings of the 2003 SIAM International Conference on Data Mining
The ranking framework contains a large algorithm space; HITS and PageRank are two extreme ends in this space.  ...  HITS emphasizes mutual reinforcement between authority and hub webpages, while PageRank emphasizes hyperlink weight normalization and web surfing based on random walk models.  ...  This work is supported by the U.S. Department of Energy (Office of Science, Office of Laboratory Policy and Infrastructure through LDRD) under contract DE-AC03-76SF00098.  ...

### PageRank, HITS and a unified framework for link analysis

Chris Ding, Xiaofeng He, Parry Husbands, Hongyuan Zha, Horst D. Simon
2002 Proceedings of the 25th annual international ACM SIGIR conference on Research and development in information retrieval - SIGIR '02
The ranking framework contains a large algorithm space; HITS and PageRank are two extreme ends in this space.  ...  HITS emphasizes mutual reinforcement between authority and hub webpages, while PageRank emphasizes hyperlink weight normalization and web surfing based on random walk models.  ...  This work is supported by the U.S. Department of Energy (Office of Science, Office of Laboratory Policy and Infrastructure through LDRD) under contract DE-AC03-76SF00098.  ...

### PageRank, HITS and a unified framework for link analysis

Chris Ding, Xiaofeng He, Parry Husbands, Hongyuan Zha, Horst D. Simon
2002 Proceedings of the 25th annual international ACM SIGIR conference on Research and development in information retrieval - SIGIR '02
The ranking framework contains a large algorithm space; HITS and PageRank are two extreme ends in this space.  ...  HITS emphasizes mutual reinforcement between authority and hub webpages, while PageRank emphasizes hyperlink weight normalization and web surfing based on random walk models.  ...  This work is supported by the U.S. Department of Energy (Office of Science, Office of Laboratory Policy and Infrastructure through LDRD) under contract DE-AC03-76SF00098.  ...

### NUPACK: Analysis and design of nucleic acid systems

Joseph N. Zadeh, Conrad D. Steenberg, Justin S. Bois, Brian R. Wolfe, Marshall B. Pierce, Asif R. Khan, Robert M. Dirks, Niles A. Pierce
2010 Journal of Computational Chemistry
The NUPACK web server (http://www.nupack.org) currently enables: • Analysis: thermodynamic analysis of dilute solutions of interacting nucleic acid strands. • Design: sequence design for complexes of nucleic  ...  acid strands intended to adopt a target secondary structure at equilibrium. • Utilities: evaluation, display, and annotation of equilibrium properties of a complex of nucleic acid strands.  ...  Utilities The Utilities page allows users to evaluate, display, and annotate the equilibrium properties of an ordered complex.  ...
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