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Mathematical Modeling of Neuronal Logic, Memory and Clocking Circuits

Lynch, Stephen and Borresen, Jon and Roach, Paul and Kotter, Mark and Slevin, Mark (2020) Mathematical Modeling of Neuronal Logic, Memory and Clocking Circuits. International Journal of Bifurcation and Chaos, 30 (01). p. 2050003. ISSN 0218-1274

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Abstract

The differential equations used to model biological neurons and the chemical kinetics involved in synaptic excitation and inhibition have been well-established for a number of decades. For the first time, this paper presents mathematical and computational models of a neuronal binary oscillator half-adder, a neuronal Set-Reset (SR) flip-flop and a simple neuronal clocking circuit, which have all been shown to be noise resistant. In modern computers, the half-adder is the basic component to perform logic, the SR flip-flop is used to store memory and clocking circuits are used to synchronize components in parts of the computer. These novel circuits will provide the world with neuronal assays that can measure the functionality of the neurons and hence provide more information than is available with current technology. The authors are not proposing to build conventional computers with these components (they would be too slow to be practical) but the simple circuits could be used to measure the functionality of diseased circuits which are subjected to certain drugs. Neurological conditions research into Alzheimer’s disease, epilepsy and Parkinson’s disease, for example, would all benefit from this research. These assays for neuronal degradation could have major implications for the National Center for the Replacement, Refinement and Reduction of Animals in Research — otherwise known as the NC3R agenda.

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