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The Single Most Important Equation for Brain-Computer Information Interfaces

The Single Most Important Equation for Brain-Computer Information Interfaces

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The Kullback-Leibler Divergence Equation for Brain-Computer Information Interfaces The Kullback-Leibler equation is arguably the best place for starting our thoughts about information theory as applied to Brain-Computer Interfaces (BCIs), or Brain-Computer Information Interfaces (BCIIs). The Kullback-Leibler equation is given as: We seek to express how well our model of reality matches the real system. Or, just as usefully, we seek to express the information-difference when we have two different models for the same underlying real phenomena or data. The K-L…

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Biologically-Based Multisensor Fusion for Brain-Computer Interfaces

Biologically-Based Multisensor Fusion for Brain-Computer Interfaces

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Multisensor Fusion for Brain-Computer Interfaces (BCIs) More than 25 years ago, sensor fusion was identified as a militarily critical technology. (See blog post describing role of sensor fusion for Navy air traffic control.) Since that time, both our knowledge of – and the importance of – sensor fusion has grown substantially. Groundbreaking work by Barry Stein and M. Alex Meredith, at the Bowman Grey School of Medicine at Wake Forrest University, elucidated the specific mechanisms of biological sensor fusion in…

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Statistical Mechanics – Neural Ensembles

Statistical Mechanics – Neural Ensembles

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Statistical Mechanics and Equilibrium Properties – Small Neural Ensembles Statistical Mechanics of Small Neural Ensembles – Commentary on Tkačik et al. In a series of related articles, Gašper Tkačik et al. (see references below) investigated small (10-120) groups of neurons in the salamander retina, with the purpose of estimating entropy and other statistical mechanics properties. They provide the following interesting results: Simple scheme for entropy estimation in undersampled region (1), given that only a small fraction of possible states can…

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Statistical Mechanics, Neural Domains, and Big Data

Statistical Mechanics, Neural Domains, and Big Data

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How Neural Domain Activation and Statistical Mechanics Model Interactions in Large Data Corpora (Big Data) I was enthralled. I could read for only a few pages at a time, I was so overwhelmed with the insights that this book provided. And I was about twenty-five years old at the time. I had just discovered this book while browsing the stacks as a graduate student at Arizona State (ASU). The book was The Mindful Brain: Cortical Organization and the Group-Selective Theory…

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Why Nonadditive Entropy Is Important for Big Data Corpora Combinations

Why Nonadditive Entropy Is Important for Big Data Corpora Combinations

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Non-Additive Entropy – A Crucial Predictive Analysis Measure for Data Mining in Multiple Large Data Corpora Statistical mechanics has an important role to play in big data analytics. Up until now, there has been almost no understanding of how statistical mechanics provides both practical value and a theoretic framework for data analysis and even predictive intelligence (sometimes called predictive analysis). This blogpost focuses on a related – and crucially important – issue: How can we determine the value of combining…

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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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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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