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Chaos Solitons & Fractals

A model of biological neuron with terminal chaos and quantum-like features

Elio Conte, Gianpaolo Pierri, Antonio Federici, Leonardo Mendolicchio, Joseph P. Zbilut

Published Apr 18, 2006• 29 citations
Publisher
DOI
10.1016/j.chaos.2005.08.211

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A wide spectrum of social, biological, physical, chemical and computational systems have been investigated by the tools and techniques from the field of Dynamical Systems Theory to formalize the behaviour in time and quantify and qualify the parametric variations of those systems. In Biology in particular, studies have shown that learning neuron maximization can occur in specific dynamics conditions where information processing is optimized. This it may be expected that some of those conditions can be recognized and used in artificial models. This work studies the quantum artificial neuron weightless qRAM behavior, from the design iteration models - taking into account the physical and mathematical conditions of quantum computing that restricts the extraction of information at every time step - to its parametric analysis where converging behaviors, damped or oscillatory, are detailed. Tools of dynamical systems like orbits diagram and time series qualitatively illustrate its temporal variability. The main contribution of this work is to detail the neuron qRAM behavior so that the results can be used within the machine learning area, coupled with larger systems to achieve maximum learning tasks. As result, we propose a novel dynamical neuron model, named Quadratic Extraction Model (QEM), we perfom parametric studies of the existing models where underdamped, overdamped and undamped behaviour are encountered, and we present apresentation of a neuron configuration inside a quantum architecture with chaos behaviour. A quantitative measure model to compare dynamics orbits was also proposed.
We study biologically ‘orchestrated’ coherent quantum processes in collections of protein microtubules of brain neurons, which correlate with, and regulate, neuronal synaptic and membrane activity. In this situation the continuous Schrodinger evolution of each such process terminates in accordance with the specific Diosi–Penrose (DP) scheme of ‘objective reduction’ (‘OR’) of the quantum state. This orchestrated OR activity (‘Orch OR’) is taken to result in moments of conscious awareness and/or choice. We analyze Orch OR in light of advances and developments in quantum physics, computational neuroscience and quantum biology. Much attention is also devoted to the ‘beat frequencies’ of faster microtubule vibrations as a possible source of the observed electroencephalographic (‘EEG’) correlates of consciousness. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.