Browsed by
Category: Entropy

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

Nonextensive Statistical Mechanics – Good Read on Advanced Entropy Formulation

Nonextensive Statistical Mechanics – Good Read on Advanced Entropy Formulation

Comments 0 Comment

Advances in Thinking about Entropy Starting through Tsallis’s book on entropy; Introduction to Nonextensive Statistical Mechanics. This is a fascinating discussion – really, it’s the roots of philosophy; the real “what-is-so” about the world. Which minimally requires a good solid year or two of graduate-level statistical thermodynamics to even start the read. But worth it. There’s some potential applications of this approach to areas in which I’ve worked before; need to mull this over and jig some ideas about to…

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

"Nonadditive Entropy" – An Excellent Review Article

"Nonadditive Entropy" – An Excellent Review Article

Comments 0 Comment

New Advances in Entropy Formulation – “Nonadditive Entropy” Well, chalk it up to being newly returned to the fold – after years of work in knowledge discovery, predictive analysis, neural networks, and sensor fusion, I’m finally returning to my roots and re-invigorating some previous work that involves the Cluster Variation Method. In the course of this, I’ve just learned (as a Janie-come-lately) about the major evolution in thinking about entropy, largely led by Constantino Tsallis. He has an excellent review…

Read More Read More

Gibbs Free Energy, Belief Propagation, and Markov Random Fields

Gibbs Free Energy, Belief Propagation, and Markov Random Fields

Comments 0 Comment

Correspondence Between Free Energy, Belief Propagation, and Markov Random Field Models As a slight digression from previous posts – re-reading the paper by Yedidia et al. on this morning on Understanding Belief Propagation and its Generalizations – which explains the close connection between Belief Propagation (BP) methods and the Bethe approximation (a more generalized version of the simple bistate Ising model that I’ve been using) in statistical thermodynamics. The important point that Yedidia et al. make is that their work…

Read More Read More

"What is X?" – Modeling the Meltdown

"What is X?" – Modeling the Meltdown

Comments 0 Comment

“What is X?” – Modeling the 2008-2009 Financial Systems Meltdown We’re about to start a detailed walkthrough of applying a “simple” statistical thermodynamic model to the Wall Street players in the 2007-2009 timeframe. The two kinds of information that I’ll be joining together for this will be a description of Wall Street dynamics, based largely on Chasing Goldman Sachs (see previous blogposts for link), and the two-state Ising thermodynamic model that I’ve been presenting over the past several posts. The…

Read More Read More

Modeling Nonlinear Phenomena

Modeling Nonlinear Phenomena

Comments 0 Comment

Modeling Nonlinear Phenomena – What is “X”? Many of us grew up hating word problems in algebra. (Some of us found them interesting, sometimes easy, and sometimes fun. We were the minority.) For most of us, even if we understood the mathematical formulas, there was a big “gap” in our understanding and intuition when it came to applying the formulas to some real-world situation. In the problem, we’d be given a set of statements, and then told to find “something.”…

Read More Read More

"The Origin of Wealth" – Revisited

"The Origin of Wealth" – Revisited

Comments 0 Comment

The Origin of Wealth – and Phase Transitions in Complex, Nonlinear Systems Once again, after a nearly two-year hiatus (off by only a week from my first posting on this in May of 2010), I’m getting back to one of my great passions in life – emergent behavior in complex, adaptive systems. And I’m once again starting a discussion/blog-theme referencing Eric Beinhocker’s work, The Origin of Wealth. Since this book was originally published (in 2006), we’ve seen an ongoing series…

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