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Discrete-Time Replicator Equations on Parallel Neural Networks

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Engineering Applications of Neural Networks (EANN 2024)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 2141))

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Abstract

In this paper, we are aiming to propose a novel mathematical model that studies the dynamics of synaptic damage in terms of concentrations of toxic neuropeptides (neurotransmitters) during neurotransmission processes. Our objective is to employ “Wardrop’s first and second principles” within a neural network of the brain. Complete manifestations of Wardrop’s first and second principles within a neural network of the brain are presented through the introduction of two novel concepts: neuropeptide’s (neurotransmitter’s) equilibrium and synapses optimum. In the context of a neural network within the brain, an analogue of the price of anarchy is the price of cognition which is the most unfavorable ratio between the overall impairment caused by toxic neuropeptide’s (neurotransmitter’s) equilibrium in comparison to the optimal state of synapses (synapses optimum). Finally, we also propose an iterative algorithm (neurodynamics) in which the synapses optimum is eventually established during the neurotransmission process. We envision that this mathematical model can serve as a source of motivation to instigate novel experimental and computational research avenues in the fields of artificial neural networks and contemporary neuroscience.

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Authors and Affiliations

  1. College of Engineering and Technology, American University of the Middle East, Egaila, 54200, Kuwait

    Armen Bagdasaryan, Antonios Kalampakas & Mansoor Saburov

Authors
  1. Armen Bagdasaryan
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  2. Antonios Kalampakas
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  3. Mansoor Saburov
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Corresponding author

Correspondence to Antonios Kalampakas .

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Editors and Affiliations

  1. Democritus University of Thrace, Xanthi, Greece

    Lazaros Iliadis

  2. University of Piraeus, Piraeus, Greece

    Ilias Maglogiannis

  3. Democritus University of Thrace, Xanthi, Greece

    Antonios Papaleonidas

  4. University of the West of England, Bristol, UK

    Elias Pimenidis

  5. Teesside University, Middlesbrough, UK

    Chrisina Jayne

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Bagdasaryan, A., Kalampakas, A., Saburov, M. (2024). Discrete-Time Replicator Equations on Parallel Neural Networks. In: Iliadis, L., Maglogiannis, I., Papaleonidas, A., Pimenidis, E., Jayne, C. (eds) Engineering Applications of Neural Networks. EANN 2024. Communications in Computer and Information Science, vol 2141. Springer, Cham. https://doi.org/10.1007/978-3-031-62495-7_37

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  • DOI: https://doi.org/10.1007/978-3-031-62495-7_37

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  • Online ISBN: 978-3-031-62495-7

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