Holonomy, quantum mechanics and the signal-tuned Gabor approach to the striate cortex

José R. A. Torreão ()
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José R. A. Torreão: Instituto de Computação, Universidade Federal Fluminense, Niterói RJ 24210-346, Brazil

International Journal of Modern Physics C (IJMPC), 2016, vol. 27, issue 08, 1-15

Abstract: It has been suggested that an appeal to holographic and quantum properties will be ultimately required for the understanding of higher brain functions. On the other hand, successful quantum-like approaches to cognitive and behavioral processes bear witness to the usefulness of quantum prescriptions as applied to the analysis of complex non-quantum systems. Here, we show that the signal-tuned Gabor approach for modeling cortical neurons, although not based on quantum assumptions, also admits a quantum-like interpretation. Recently, the equation of motion for the signal-tuned complex cell response has been derived and proven equivalent to the Schrödinger equation for a dissipative quantum system whose solutions come under two guises: as plane-wave and Airy-packet responses. By interpreting the squared magnitude of the plane-wave solution as a probability density, in accordance with the quantum mechanics prescription, we arrive at a Poisson spiking probability — a common model of neuronal response — while spike propagation can be described by the Airy-packet solution. The signal-tuned approach is also proven consistent with holonomic brain theories, as it is based on Gabor functions which provide a holographic representation of the cell’s input, in the sense that any restricted subset of these functions still allows stimulus reconstruction.

Keywords: Quantum-like approaches; holographic representations; Schrödinger equation; signal-tuned Gabor approach; visual cortex (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0129183116500893

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