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Mondal A, Mondal A, Aziz-Alaoui MA, Upadhyay RK, Sharma SK, Antonopoulos CG. The generation of diverse traveling pulses and its solution scheme in an excitable slow-fast dynamics. CHAOS (WOODBURY, N.Y.) 2022; 32:083121. [PMID: 36049912 DOI: 10.1063/5.0084606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2022] [Accepted: 07/19/2022] [Indexed: 06/15/2023]
Abstract
In this article, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modeled using the nearest neighbor coupling theory, in which the diffusion part measures the spatial distribution of coupling topology. We derive analytically the conditions for traveling wave profiles that allow the construction of the shape of traveling nerve impulses. The analytical and numerical results are used to explore the nature of propagating pulses. The symmetric or asymmetric nature of traveling pulses is characterized, and the wave velocity is derived as a function of system parameters. Moreover, we present our results for an extended excitable medium by considering a slow-fast biophysical model with a homogeneous, diffusive coupling that can exhibit various traveling pulses. The appearance of series of pulses is an interesting phenomenon from biophysical and dynamical perspective. Varying the perturbation and coupling parameters, we observe the propagation of activities with various amplitude modulations and transition phases of different wave profiles that affect the speed of pulses in certain parameter regimes. We observe different types of traveling pulses, such as envelope solitons and multi-bump solutions, and show how system parameters and coupling play a major role in the formation of different traveling pulses. Finally, we obtain the conditions for stable and unstable plane waves.
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Affiliation(s)
- Arnab Mondal
- Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India
| | - Argha Mondal
- Department of Mathematics, Sidho-Kanho-Birsha University, Purulia 723104, West Bengal, India
| | - M A Aziz-Alaoui
- Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France
| | - Ranjit Kumar Upadhyay
- Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India
| | - Sanjeev Kumar Sharma
- Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India
| | - Chris G Antonopoulos
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom
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Makarov VA, Lobov SA, Shchanikov S, Mikhaylov A, Kazantsev VB. Toward Reflective Spiking Neural Networks Exploiting Memristive Devices. Front Comput Neurosci 2022; 16:859874. [PMID: 35782090 PMCID: PMC9243340 DOI: 10.3389/fncom.2022.859874] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 05/10/2022] [Indexed: 11/29/2022] Open
Abstract
The design of modern convolutional artificial neural networks (ANNs) composed of formal neurons copies the architecture of the visual cortex. Signals proceed through a hierarchy, where receptive fields become increasingly more complex and coding sparse. Nowadays, ANNs outperform humans in controlled pattern recognition tasks yet remain far behind in cognition. In part, it happens due to limited knowledge about the higher echelons of the brain hierarchy, where neurons actively generate predictions about what will happen next, i.e., the information processing jumps from reflex to reflection. In this study, we forecast that spiking neural networks (SNNs) can achieve the next qualitative leap. Reflective SNNs may take advantage of their intrinsic dynamics and mimic complex, not reflex-based, brain actions. They also enable a significant reduction in energy consumption. However, the training of SNNs is a challenging problem, strongly limiting their deployment. We then briefly overview new insights provided by the concept of a high-dimensional brain, which has been put forward to explain the potential power of single neurons in higher brain stations and deep SNN layers. Finally, we discuss the prospect of implementing neural networks in memristive systems. Such systems can densely pack on a chip 2D or 3D arrays of plastic synaptic contacts directly processing analog information. Thus, memristive devices are a good candidate for implementing in-memory and in-sensor computing. Then, memristive SNNs can diverge from the development of ANNs and build their niche, cognitive, or reflective computations.
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Affiliation(s)
- Valeri A. Makarov
- Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Madrid, Spain
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- *Correspondence: Valeri A. Makarov,
| | - Sergey A. Lobov
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia
- Center For Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
| | - Sergey Shchanikov
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Department of Information Technologies, Vladimir State University, Vladimir, Russia
| | - Alexey Mikhaylov
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Viktor B. Kazantsev
- Department of Neurotechnologies, Research Institute of Physics and Technology, Laboratory of Stochastic Multistable Systems, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis, Russia
- Center For Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, Kaliningrad, Russia
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Lobov SA, Zharinov AI, Makarov VA, Kazantsev VB. Spatial Memory in a Spiking Neural Network with Robot Embodiment. SENSORS 2021; 21:s21082678. [PMID: 33920246 PMCID: PMC8070389 DOI: 10.3390/s21082678] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/19/2021] [Revised: 04/06/2021] [Accepted: 04/07/2021] [Indexed: 11/16/2022]
Abstract
Cognitive maps and spatial memory are fundamental paradigms of brain functioning. Here, we present a spiking neural network (SNN) capable of generating an internal representation of the external environment and implementing spatial memory. The SNN initially has a non-specific architecture, which is then shaped by Hebbian-type synaptic plasticity. The network receives stimuli at specific loci, while the memory retrieval operates as a functional SNN response in the form of population bursts. The SNN function is explored through its embodiment in a robot moving in an arena with safe and dangerous zones. We propose a measure of the global network memory using the synaptic vector field approach to validate results and calculate information characteristics, including learning curves. We show that after training, the SNN can effectively control the robot’s cognitive behavior, allowing it to avoid dangerous regions in the arena. However, the learning is not perfect. The robot eventually visits dangerous areas. Such behavior, also observed in animals, enables relearning in time-evolving environments. If a dangerous zone moves into another place, the SNN remaps positive and negative areas, allowing escaping the catastrophic interference phenomenon known for some AI architectures. Thus, the robot adapts to changing world.
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Affiliation(s)
- Sergey A. Lobov
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., 603950 Nizhny Novgorod, Russia; (A.I.Z.); (V.A.M.); (V.B.K.)
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 1 Universitetskaya Str., 420500 Innopolis, Russia
- Center For Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, 14 Nevsky Str., 236016 Kaliningrad, Russia
- Correspondence:
| | - Alexey I. Zharinov
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., 603950 Nizhny Novgorod, Russia; (A.I.Z.); (V.A.M.); (V.B.K.)
| | - Valeri A. Makarov
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., 603950 Nizhny Novgorod, Russia; (A.I.Z.); (V.A.M.); (V.B.K.)
- Instituto de Matemática Interdisciplinar, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Victor B. Kazantsev
- Neurotechnology Department, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., 603950 Nizhny Novgorod, Russia; (A.I.Z.); (V.A.M.); (V.B.K.)
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 1 Universitetskaya Str., 420500 Innopolis, Russia
- Center For Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, 14 Nevsky Str., 236016 Kaliningrad, Russia
- Lab of Neurocybernetics, Russian State Scientific Center for Robotics and Technical Cybernetics, 21 Tikhoretsky Ave., St., 194064 Petersburg, Russia
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Tankou Tagne AS, Takembo CN, Ben-Bolie HG, Owona Ateba P. Localized nonlinear excitations in diffusive memristor-based neuronal networks. PLoS One 2019; 14:e0214989. [PMID: 31163037 PMCID: PMC6548494 DOI: 10.1371/journal.pone.0214989] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2018] [Accepted: 03/25/2019] [Indexed: 12/02/2022] Open
Abstract
We extend the existing ordinary differential equations modeling neural electrical activity to include the memory effect of electromagnetic induction through magnetic flux, used to describe time varying electromagnetic field. Through the multi-scale expansion in the semi-discrete approximation, we show that the neural network dynamical equations can be governed by the complex Ginzburg-Landau equation. The analytical and numerical envelop soliton of this equation are reported. The results obtained suggest the possibility of collective information processing and sharing in the nervous system, operating in both the spatial and temporal domains in the form of localized modulated waves. The effects of memristive synaptic electromagnetic induction coupling and perturbation on the modulated action potential dynamics examined. Large electromagnetic induction coupling strength may contribute to signal block as the amplitude of modulated waves are observed to decrease. This could help in the development of a chemical brain anaesthesia for some brain pathologies.
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Affiliation(s)
- A. S. Tankou Tagne
- Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, Cameroon
| | - C. N. Takembo
- Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, Cameroon
- * E-mail:
| | - H. G. Ben-Bolie
- Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, Cameroon
| | - P. Owona Ateba
- Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, Cameroon
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Zhang J, Osan R. Analytically tractable studies of traveling waves of activity in integrate-and-fire neural networks. Phys Rev E 2016; 93:052228. [PMID: 27300901 DOI: 10.1103/physreve.93.052228] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2015] [Indexed: 11/07/2022]
Abstract
In contrast to other large-scale network models for propagation of electrical activity in neural tissue that have no analytical solutions for their dynamics, we show that for a specific class of integrate and fire neural networks the acceleration depends quadratically on the instantaneous speed of the activity propagation. We use this property to analytically compute the network spike dynamics and to highlight the emergence of a natural time scale for the evolution of the traveling waves. These results allow us to examine other applications of this model such as the effect that a nonconductive gap of tissue has on further activity propagation. Furthermore we show that activity propagation also depends on local conditions for other more general connectivity functions, by converting the evolution equations for network dynamics into a low-dimensional system of ordinary differential equations. This approach greatly enhances our intuition into the mechanisms of the traveling waves evolution and significantly reduces the simulation time for this class of models.
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Affiliation(s)
- Jie Zhang
- Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA
| | - Remus Osan
- Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA.,Neuroscience Institute, Georgia State University, Atlanta, Georgia 30093, USA
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Moukam Kakmeni FM, Inack EM, Yamakou EM. Localized nonlinear excitations in diffusive Hindmarsh-Rose neural networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052919. [PMID: 25353873 DOI: 10.1103/physreve.89.052919] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2014] [Indexed: 06/04/2023]
Abstract
We study localized nonlinear excitations in diffusive Hindmarsh-Rose neural networks. We show that the Hindmarsh-Rose model can be reduced to a modified Complex Ginzburg-Landau equation through the application of a perturbation technique. We equally report on the presence of envelop solitons of the nerve impulse in this neural network. From the biological point of view, this result suggests that neurons can participate in a collective processing of information, a relevant part of which is shared over all neurons but not concentrated at the single neuron level. By employing the standard linear stability analysis, the growth rate of the modulational instability is derived as a function of the wave number and systems parameters.
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Affiliation(s)
- F M Moukam Kakmeni
- Complex Systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea-Cameroon
| | - E M Inack
- Complex Systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea-Cameroon
| | - E M Yamakou
- Complex Systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea-Cameroon
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Single-neuron criticality optimizes analog dendritic computation. Sci Rep 2013; 3:3222. [PMID: 24226045 PMCID: PMC3827605 DOI: 10.1038/srep03222] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2013] [Accepted: 10/30/2013] [Indexed: 11/08/2022] Open
Abstract
Active dendritic branchlets enable the propagation of dendritic spikes, whose computational functions remain an open question. Here we propose a concrete function to the active channels in large dendritic trees. Modelling the input-output response of large active dendritic arbors subjected to complex spatio-temporal inputs and exhibiting non-stereotyped dendritic spikes, we find that the dendritic arbor can undergo a continuous phase transition from a quiescent to an active state, thereby exhibiting spontaneous and self-sustained localized activity as suggested by experiments. Analogously to the critical brain hypothesis, which states that neuronal networks self-organize near criticality to take advantage of its specific properties, here we propose that neurons with large dendritic arbors optimize their capacity to distinguish incoming stimuli at the critical state. We suggest that "computation at the edge of a phase transition" is more compatible with the view that dendritic arbors perform an analog rather than a digital dendritic computation.
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