Browsed by
Tag: fraction variables

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…

Read More Read More

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…

Read More Read More

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,…

Read More Read More

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…

Read More Read More