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Tag: analytic solution

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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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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