Browsed by
Category: Cluster Variation Method

Big Data, Big Graphs, and Graph Theory: Tools and Methods

Big Data, Big Graphs, and Graph Theory: Tools and Methods

Comments 0 Comment

Big Graphs Need Specialized Data Storage and Computational Methods {A Working Blogpost – Notes for research & study} Processing large-scale graph data: A guide to current technology, by Sherif Sakr (ssakr@cse.unsw.edu.au), IBM Developer Works (10 June 2013). Note: Dr. Sherif Sakr is a senior research scientist in the Software Systems Group at National ICT Australia (NICTA), Sydney, Australia. He is also a conjoint senior lecturer in the School of Computer Science and Engineering at University of New South Wales. He…

Read More Read More

Analytic Single-Point Solution for Cluster Variation Method Variables (at x1=x2=0.5)

Analytic Single-Point Solution for Cluster Variation Method Variables (at x1=x2=0.5)

Comments 6 comments

Single-Point Analytic Cluster Variation Method Solution: Solving Set of Three Nonlinear, Coupled Equations The Cluster Variation Method, first introduced by Kikuchi in 1951 (“A theory of cooperative phenomena,” Phys. Rev. 81 (6), 988-1003), provides a means for computing the free energy of a system where the entropy term takes into account distributions of particles into local configurations as well as the distribution into “on/off” binary states. As the equations are more complex, numerical solutions for the cluster variation variables are…

Read More Read More

Community Detection in Graphs

Community Detection in Graphs

Comments 0 Comment

Complexity and Graph Theory: A Brief Note Santo Fortunato has published an interesting and densly rich article, Community Detection in Graphs, in  Complexity (Inter-Wiley). This article is over 100 pages long, it is relatively complete, with numerous references and excellent figures. It is a bit surprising, however, that this extensive discussion misses one of the things that would seem to be most important in discussing graphs, and particularly, clusters within graphs: the stability of these clusters. That is; the theoretical basis for cluster…

Read More Read More

Graph Theory — Becoming "Organizing Framework"

Graph Theory — Becoming "Organizing Framework"

Comments 0 Comment

Something I’ve been noting — both on my own, and in conversations with Jenn Sleeman , who’s in touch with the academic world at UMBC — Graph theory is growing in centrality as a fundamental organizing framework for many current and emerging computational processes. Specifically, anything more complex than a simple “tuple” (RDF or OWL, etc.), needs to be matched against a graph or partial graph. One good “integrative” paper is Understanding Belief Propagation and its Generalizations by J.S. Yedidia,…

Read More Read More