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. 2020 Oct 29;22(11):1231.
doi: 10.3390/e22111231.

Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach

Carlos Islas  1 , Pablo Padilla  2 , Marco Antonio Prado  1   2
Affiliations

Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach

Carlos Islas et al. Entropy (Basel). .

Abstract

We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge-Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge-Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray's law in this context.

Keywords: Monge–Ampère equation; Murray’s law; informational entropy; neuronal branching structures; neuroscience; optimal transport; variational calculus.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Numerical solution of the linearization of the Monge-Ampère equation including growth. Branching occurs when there is the concentration of the solution, the morphogen, above a certain threshold (the color code stands for standard heat maps: red, high; blue, low). This simulation was provided by Jorge Castillo-Medina and developed in COMSOL. For more details, the reader is referred to [21] and the references therein.
Figure 2
Figure 2
A similar simulation as in the previous figure with a different growth rate. Notice the different branching structure. Simulation performed by J. Castillo as well; see also [21].
Figure 3
Figure 3
The figure shows schematically the geometric configuration when branching occurs on a plane. Illustration after [33] by the authors.
See this image and copyright information in PMC

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