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Category: Cluster Variation Method

Brain Networks and the Cluster Variation Method: Testing a Scale-Free Model

Brain Networks and the Cluster Variation Method: Testing a Scale-Free Model

Surprising Result Modeling a Simple Scale-Free Brain Network Using the Cluster Variation Method One of the primary research thrusts that I suggested in my recent paper, The Cluster Variation Method: A Primer for Neuroscientists, was that we could use the 2-D Cluster Variation Method (CVM) to model distribution of configuration variables in different brain network topologies. Specifically, I was expecting that the h-value (which measures the interaction enthalpy strength between nodes in a 2-D CVM grid) would change in a…

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The Cluster Variation Method: A Primer for Neuroscientists

The Cluster Variation Method: A Primer for Neuroscientists

Single-Parameter Analytic Solution for Modeling Local Pattern Distributions The cluster variation method (CVM) offers a means for the characterization of both 1-D and 2-D local pattern distributions. The paper referenced at the end of this post provides neuroscientists and BCI researchers with a CVM tutorial that will help them to understand how the CVM statistical thermodynamics formulation can model 1-D and 2-D pattern distributions expressing structural and functional dynamics in the brain. The equilibrium distribution of local patterns, or configuration…

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The 1-D Cluster Variation Method (CVM) – Simple Application

The 1-D Cluster Variation Method (CVM) – Simple Application

The 1-D Cluster Variation Method – Application to Text Mining and Data Mining There are three particularly good reasons for us to look at the Cluster Variation Method (CVM) as an alternative means of understanding the information in a system: The CVM captures local pattern distributions (for an equilibrium state), When the system is made up of equal numbers of units in each of two states, and the enthalpy for each state is the same (the simple unit activation energy…

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Statistical Mechanics, Neural Domains, and Big Data

Statistical Mechanics, Neural Domains, and Big Data

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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Visualizing Variables with the 2-D Cluster Variation Method

Visualizing Variables with the 2-D Cluster Variation Method

Cluster Variation Method – 2-D Case – Configuration Variables, Entropy and Free Energy Following the previous blog on the 1-D Cluster Variation Method, I illustrate here a micro-ensemble for the 2-D Cluster Variation Method, consisting of the original single zigzag chain of only ten units (see previous post), with three additional layers added, as shown in the following Figure 1. In Figure 1, we again have an equilibrium distribution of fraction variables z(i). Note that, as with the 1-D case,…

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Visualizing Configuration Variables with the 1-D Cluster Variation Method

Visualizing Configuration Variables with the 1-D Cluster Variation Method

Cluster Variation Method – 1-D Case – Configuration Variables, Entropy and Free Energy We construct a micro-system consisting of a single zigzag chain of only eight units, as shown in the following Figure 1. (Note that the additional textured units, with a dashed border, to the right illustrate a wrap-around effect, giving full horizontal nearest-neighbor connectivity.) In Figure 1, we have the equilibrium distribution of fraction variables z(i). Note that the weighting coefficients for z(2) = z(5) = 2, whereas…

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Why Nonadditive Entropy Is Important for Big Data Corpora Combinations

Why Nonadditive Entropy Is Important for Big Data Corpora Combinations

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). In a separate White Paper (link to be provided), I identify – for the first time – how statistical mechanics,…

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

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

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…

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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)

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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Community Detection in Graphs

Community Detection in Graphs

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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