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Author: AJMaren

Nonextensive Statistical Mechanics – Good Read on Advanced Entropy Formulation

Nonextensive Statistical Mechanics – Good Read on Advanced Entropy Formulation

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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…

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Modeling the Future: Tools from Complex Systems

Modeling the Future: Tools from Complex Systems

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2012 and Beyond: Tools for Predicting the Next Sixty Years Is the world coming to an end on Dec. 21st, 2012, or not? Very likely, not. We’ll still wake up in the morning, in the same beds in which we went to sleep in the night before. We’ll still walk out to our cars, or get to our Metro stations, on time. And we’ll likely stop for the same “cup of joe” on the way to work. But will our…

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Good Read on Modeling Social Emergent Phenomena – But Still Not There Yet!

Good Read on Modeling Social Emergent Phenomena – But Still Not There Yet!

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Philip Ball – Critical Mass The most important thing we can do right now – given the huge changes ahead of us – both in society, the world, and technology – is to get some sort of “handle” on what’s coming up. By that, I mean a good set of models. And as a result, I’m on a search for good models. Those that I know, those that are new. Those that make sense, and those that don’t. (We need…

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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)

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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…

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"Nonadditive Entropy" – An Excellent Review Article

"Nonadditive Entropy" – An Excellent Review Article

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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…

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Modeling Trends in Long-Term IT as a Phase Transition

Modeling Trends in Long-Term IT as a Phase Transition

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The most reasonable model for our faster-than-exponential growth in long-term IT trends is that of a phase transition. At a second-order phase transition, the heat capacity becomes discontinuous. The heat capacity image is provided courtesy of a wikipedia site on heat capacity transition(s). L. Witthauer and M. Diertele present a number of excellent computations in graphical form in their paper The Phase Transition of the 2D-Ising Model. There is another interesting article by B. Derrida & D. Stauffer in Europhysics…

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Going Beyond Moore’s Law

Going Beyond Moore’s Law

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Super-Exponential Long-Term Trends in Information Technology Interesting read for the day: Super-exponential long-term trends in Information Technology by B. Nagy, J.D. Farmer, J.E. Trancik, & J.P. Gonzales, shows that which Kurzeil suggested in his earlier work on “technology singularities” is true: We are experiencing faster-than-exponential growth within the information technology area. Nagy et al. are careful to point out that their work indicates a “mathematical singularity,” not to be confused with the more broadly-sweeping notion of a “technological singularity” discussed…

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Gibbs Free Energy, Belief Propagation, and Markov Random Fields

Gibbs Free Energy, Belief Propagation, and Markov Random Fields

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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…

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What Makes a Metastable State Happen?

What Makes a Metastable State Happen?

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Metastable States – the Meltdown Precursors I’ve just read a recent column by JL, one of the editors from Taipan Daily. He states, in his column “There Will Be Blood in Europe”: Stepping back a bit: What is so frightening right now, not just in Europe but China and America and Japan too, is the presence of fraud-fueled “Lehman 2.0” catalysts threatening to explode. One could say that the 2008 financial crisis was the mother of all wake-up calls. But…

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"What is X?" – Modeling the Meltdown

"What is X?" – Modeling the Meltdown

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“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…

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