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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 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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Modeling Nonlinear Phenomena

Modeling Nonlinear Phenomena

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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.”…

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"The Origin of Wealth" – Revisited

"The Origin of Wealth" – Revisited

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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…

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Accelerating Change – A Good Read

Accelerating Change – A Good Read

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Writing to you within hours of summer solstice, 2010 – we now have 2 1/2 years (approximately) to the time that has been targeted by multiple cultures as a “pivot point” in human experience. The idea that we are accelerating in our experience on this planet is not new. Right now, this idea is receiving a great deal of attention – too much of which is “acceleration” of emotional content, and not an objective assessment. In this sense, John Smart’s…

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Community Detection in Graphs

Community Detection in Graphs

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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…

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Chapter 2 (Part 3), Sennelart & Blondel – Automatic Discovery of Similar Words

Chapter 2 (Part 3), Sennelart & Blondel – Automatic Discovery of Similar Words

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In Section 2.3, we get to the meat of Sennelart & Blondel’s work, which is a graph-based method for determining similar words, using a dictionary as source. Their method uses a vXv matrix, where each v is a word in the dictionary. They compare their method and results with that of Kleinberg, who proposes a method for determining good Web hubs and authorities, and with the ArcRank and WordNet methods. They test the four methods on four words: disappear, parallelogram,…

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Chapter 2 Review, Continued, Part 2 — "Automatic Discovery of Similar Words"

Chapter 2 Review, Continued, Part 2 — "Automatic Discovery of Similar Words"

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(Direct continuation of yesterday’s post, w/r/t Senellart & Blondel on “Automatic Discovery of Similar Words” in Survey of Text Mining II. I give the references that cite, which I discuss in this post, at the end of the post.) In Chapter 2’s revieww of previous methods and associated literature, Senellart & Blondel start with banal and get progressively more interesting. The one thing I found interesting in the first model that Senellart and Blondel discussed was that the model was…

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"Automatic Discovery of Similar Words" – Chapter 2 in Survey of Text Mining II

"Automatic Discovery of Similar Words" – Chapter 2 in Survey of Text Mining II

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This post begins a review of “Automatic Discovery of Similar Words,” by Pierre Senellart and Vincent D. Blondel, published as Chapter 2 in Berry and Castellanos’ Survey of Text Mining II. This is an excellent and useful chapter, in that it:1) Addresses the broad issue of computational methods for discovering “similar words” (including synonyms, near-synonyms, and thesauri-generating techniques) from large data corpora,2) Illustrates the different leading mathematical methods, giving an excellent overview of the SoA,3) Competently discusses how different methods…

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