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Rhamidda SL, Girardi-Schappo M, Kinouchi O. Optimal input reverberation and homeostatic self-organization toward the edge of synchronization. CHAOS (WOODBURY, N.Y.) 2024; 34:053127. [PMID: 38767461 DOI: 10.1063/5.0202743] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2024] [Accepted: 04/25/2024] [Indexed: 05/22/2024]
Abstract
Transient or partial synchronization can be used to do computations, although a fully synchronized network is sometimes related to the onset of epileptic seizures. Here, we propose a homeostatic mechanism that is capable of maintaining a neuronal network at the edge of a synchronization transition, thereby avoiding the harmful consequences of a fully synchronized network. We model neurons by maps since they are dynamically richer than integrate-and-fire models and more computationally efficient than conductance-based approaches. We first describe the synchronization phase transition of a dense network of neurons with different tonic spiking frequencies coupled by gap junctions. We show that at the transition critical point, inputs optimally reverberate through the network activity through transient synchronization. Then, we introduce a local homeostatic dynamic in the synaptic coupling and show that it produces a robust self-organization toward the edge of this phase transition. We discuss the potential biological consequences of this self-organization process, such as its relation to the Brain Criticality hypothesis, its input processing capacity, and how its malfunction could lead to pathological synchronization and the onset of seizure-like activity.
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Affiliation(s)
- Sue L Rhamidda
- Departamento de Física, FFCLRP, Universidade de São Paulo, Ribeirão Preto, SP 14040-901, Brazil
| | - Mauricio Girardi-Schappo
- Departamento de Física, Universidade Federal de Santa Catarina, Florianópolis, SC 88040-900, Brazil
| | - Osame Kinouchi
- Departamento de Física, FFCLRP, Universidade de São Paulo, Ribeirão Preto, SP 14040-901, Brazil
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2
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Moraes JT, Trejo EJA, Camargo S, Ferreira SC, Chialvo DR. Self-tuned criticality: Controlling a neuron near its bifurcation point via temporal correlations. Phys Rev E 2023; 107:034204. [PMID: 37072953 DOI: 10.1103/physreve.107.034204] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Accepted: 02/28/2023] [Indexed: 04/20/2023]
Abstract
Previous work showed that the collective activity of large neuronal networks can be tamed to remain near its critical point by a feedback control that maximizes the temporal correlations of the mean-field fluctuations. Since such correlations behave similarly near instabilities across nonlinear dynamical systems, it is expected that the principle should control also low-dimensional dynamical systems exhibiting continuous or discontinuous bifurcations from fixed points to limit cycles. Here we present numerical evidence that the dynamics of a single neuron can be controlled in the vicinity of its bifurcation point. The approach is tested in two models: a two-dimensional generic excitable map and the paradigmatic FitzHugh-Nagumo neuron model. The results show that in both cases, the system can be self-tuned to its bifurcation point by modifying the control parameter according to the first coefficient of the autocorrelation function.
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Affiliation(s)
- Juliane T Moraes
- Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Minas Gerais, Brazil
| | - Eyisto J Aguilar Trejo
- Center for Complex Systems and Brain Sciences (CEMSC3), Instituto de Ciencias Físicas (ICIFI), Universidad Nacional de San Martín, Campus Miguelete, 1650 San Martín, Buenos Aires, Argentina
- Consejo Nacional de Investigaciones Científcas y Tecnológicas (CONICET), 1425 Buenos Aires, Argentina
| | - Sabrina Camargo
- Center for Complex Systems and Brain Sciences (CEMSC3), Instituto de Ciencias Físicas (ICIFI), Universidad Nacional de San Martín, Campus Miguelete, 1650 San Martín, Buenos Aires, Argentina
- Consejo Nacional de Investigaciones Científcas y Tecnológicas (CONICET), 1425 Buenos Aires, Argentina
| | - Silvio C Ferreira
- Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Minas Gerais, Brazil
- National Institute of Science and Technology for Complex Systems, 22290-180 Rio de Janeiro, Brazil
| | - Dante R Chialvo
- Center for Complex Systems and Brain Sciences (CEMSC3), Instituto de Ciencias Físicas (ICIFI), Universidad Nacional de San Martín, Campus Miguelete, 1650 San Martín, Buenos Aires, Argentina
- Consejo Nacional de Investigaciones Científcas y Tecnológicas (CONICET), 1425 Buenos Aires, Argentina
- Mark Kac Center for Complex Systems Research and Institute for Theoretical Physics, Jagiellonian University, 30-348 Kraków, Poland
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3
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Variations of the spontaneous electrical activities of the neuronal networks imposed by the exposure of electromagnetic radiations using computational map-based modeling. J Comput Neurosci 2023; 51:187-200. [PMID: 36539556 DOI: 10.1007/s10827-022-00842-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2022] [Revised: 12/01/2022] [Accepted: 12/04/2022] [Indexed: 01/15/2023]
Abstract
The interaction between neurons in a neuronal network develops spontaneous electrical activities. But the effects of electromagnetic radiation on these activities have not yet been well explored. In this study, a ring of three coupled 1-dimensional Rulkov neurons and the generated electromagnetic field (EMF) are considered to investigate how the spontaneous activities might change regarding the EMF exposure. By employing the bifurcation analysis and time series, a comprehensive view of neuronal behavioral changes due to electromagnetic inductions is provided. The main findings of this study are as follows: 1) When a neuronal network is showing a spontaneous chaotic firing manner (without any external stimuli), a generated magnetic field inhibits this type of behavior. In fact, EMF completely eliminated the chaotic intrinsic behaviors of the neuronal loop. 2) When the network is exhibiting regular period-3 spiking patterns, the generated magnetic field changes its firing pattern to chaotic spiking, which is similar to epileptic seizures. 3) With weak synaptic connections, electromagnetic radiation inhibits and suppresses neuronal activities. 4) If the external magnetic flux has a high amplitude, it can change the shape of the induction current according to its shape 5) when there are weak synaptic connections in the network, a high-frequency external magnetic flux engenders high-frequency fluctuations in the membrane voltages. On the whole, electromagnetic radiation changes the pattern of the spontaneous activities of neuronal networks in the brain according to synaptic strengths and initial states of the neurons.
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Bahramian A, Ramadoss J, Nazarimehr F, Rajagopal K, Jafari S, Hussain I. A simple one-dimensional map-based model of spiking neurons with wide ranges of firing rates and complexities. J Theor Biol 2022; 539:111062. [DOI: 10.1016/j.jtbi.2022.111062] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Revised: 02/01/2022] [Accepted: 02/08/2022] [Indexed: 11/25/2022]
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5
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Rajagopal K, He S, Duraisamy P, Karthikeyan A. Spiral waves in a hybrid discrete excitable media with electromagnetic flux coupling. CHAOS (WOODBURY, N.Y.) 2021; 31:113132. [PMID: 34881596 DOI: 10.1063/5.0066157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Accepted: 10/27/2021] [Indexed: 06/13/2023]
Abstract
Though there are many neuron models based on differential equations, the complexity in realizing them into digital circuits is still a challenge. Hence, many new discrete neuron models have been recently proposed, which can be easily implemented in digital circuits. We consider the well-known FitzHugh-Nagumo model and derive the discrete version of the model considering the sigmoid type of recovery variable and electromagnetic flux coupling. We show the various time series plots confirming the existence of periodic and chaotic bursting as in differential equation type neuron models. Also, we have used the bifurcation plots, Lyapunov exponents, and frequency bifurcations to investigate the dynamics of the proposed discrete neuron model. Different topologies of networks like single, two, and three layers are considered to analyze the wave propagation phenomenon in the network. We introduce the concept of using energy levels of nodes to study the spiral wave existence and compare them with the spatiotemporal snapshots. Interestingly, the energy plots clearly show that when the energy level of nodes is different and distributed, the occurrence of the spiral waves is identified in the network.
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Affiliation(s)
- Karthikeyan Rajagopal
- Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - Shaobo He
- School of Physics and Electronics, Central South University, Changsha 410083, China
| | - Prakash Duraisamy
- Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - Anitha Karthikeyan
- Department of Electronics and Communication Engineering, Prathyusha Engineering College, Chennai 602025, India
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6
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Girardi-Schappo M, Fadaie F, Lee HM, Caldairou B, Sziklas V, Crane J, Bernhardt BC, Bernasconi A, Bernasconi N. Altered communication dynamics reflect cognitive deficits in temporal lobe epilepsy. Epilepsia 2021; 62:1022-1033. [PMID: 33705572 DOI: 10.1111/epi.16864] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2020] [Revised: 02/15/2021] [Accepted: 02/15/2021] [Indexed: 12/23/2022]
Abstract
OBJECTIVE Although temporal lobe epilepsy (TLE) is recognized as a system-level disorder, little work has investigated pathoconnectomics from a dynamic perspective. By leveraging computational simulations that quantify patterns of information flow across the connectome, we tested the hypothesis that network communication is abnormal in this condition, studied the interplay between hippocampal- and network-level disease effects, and assessed associations with cognition. METHODS We simulated signal spreading via a linear threshold model that temporally evolves on a structural graph derived from diffusion-weighted magnetic resonance imaging (MRI), comparing a homogeneous group of 31 patients with histologically proven hippocampal sclerosis to 31 age- and sex-matched healthy controls. We evaluated the modulatory effects of structural alterations of the neocortex and hippocampus on network dynamics. Furthermore, multivariate statistics addressed the relationship with cognitive parameters. RESULTS We observed a slowing of in- and out-spreading times across multiple areas bilaterally, indexing delayed information flow, with the strongest effects in ipsilateral frontotemporal regions, thalamus, and hippocampus. Effects were markedly reduced when controlling for hippocampal volume but not cortical thickness, underscoring the central role of the hippocampus in whole-brain disease expression. Multivariate analysis associated slower spreading time in frontoparietal, limbic, default mode, and subcortical networks with impairment across tasks tapping into sensorimotor, executive, memory, and verbal abilities. SIGNIFICANCE Moving beyond descriptions of static topology toward the formulation of brain dynamics, our work provides novel insight into structurally mediated network dysfunction and demonstrates that altered whole-brain communication dynamics contribute to common cognitive difficulties in TLE.
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Affiliation(s)
- Mauricio Girardi-Schappo
- Neuroimaging of Epilepsy Laboratory, McConnell Brain Imaging Center, Montreal Neurological Institute and Hospital, McGill University, Montreal, QC, Canada
| | - Fatemeh Fadaie
- Neuroimaging of Epilepsy Laboratory, McConnell Brain Imaging Center, Montreal Neurological Institute and Hospital, McGill University, Montreal, QC, Canada
| | - Hyo Min Lee
- Neuroimaging of Epilepsy Laboratory, McConnell Brain Imaging Center, Montreal Neurological Institute and Hospital, McGill University, Montreal, QC, Canada
| | - Benoit Caldairou
- Neuroimaging of Epilepsy Laboratory, McConnell Brain Imaging Center, Montreal Neurological Institute and Hospital, McGill University, Montreal, QC, Canada
| | - Viviane Sziklas
- Department of Neurology and Neurosurgery, Montreal Neurological Institute and Hospital, McGill University, Montreal, QC, Canada
| | - Joelle Crane
- Department of Neurology and Neurosurgery, Montreal Neurological Institute and Hospital, McGill University, Montreal, QC, Canada
| | - Boris C Bernhardt
- Multimodal Imaging and Connectome Analysis Lab, McConnell Brain Imaging Center, Montreal Neurological Institute and Hospital, McGill University, Montreal, QC, Canada
| | - Andrea Bernasconi
- Neuroimaging of Epilepsy Laboratory, McConnell Brain Imaging Center, Montreal Neurological Institute and Hospital, McGill University, Montreal, QC, Canada
| | - Neda Bernasconi
- Neuroimaging of Epilepsy Laboratory, McConnell Brain Imaging Center, Montreal Neurological Institute and Hospital, McGill University, Montreal, QC, Canada
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7
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Kirch C, Gollo LL. Spatially resolved dendritic integration: towards a functional classification of neurons. PeerJ 2020; 8:e10250. [PMID: 33282551 PMCID: PMC7694565 DOI: 10.7717/peerj.10250] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Accepted: 10/06/2020] [Indexed: 01/19/2023] Open
Abstract
The vast tree-like dendritic structure of neurons allows them to receive and integrate input from many neurons. A wide variety of neuronal morphologies exist, however, their role in dendritic integration, and how it shapes the response of the neuron, is not yet fully understood. Here, we study the evolution and interactions of dendritic spikes in excitable neurons with complex real branch structures. We focus on dozens of digitally reconstructed illustrative neurons from the online repository NeuroMorpho.org, which contains over 130,000 neurons. Yet, our methods can be promptly extended to any other neuron. This approach allows us to estimate and map specific and heterogeneous patterns of activity observed across extensive dendritic trees with thousands of compartments. We propose a classification of neurons based on the location of the soma (centrality) and the number of branches connected to the soma. These are key topological factors in determining the neuron's energy consumption, firing rate, and the dynamic range, which quantifies the range in synaptic input rate that can be reliably encoded by the neuron's firing rate. Moreover, we find that bifurcations, the structural building blocks of complex dendrites, play a major role in increasing the dynamic range of neurons. Our results provide a better understanding of the effects of neuronal morphology in the diversity of neuronal dynamics and function.
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Affiliation(s)
- Christoph Kirch
- QIMR Berghofer Medical Research Institute, Brisbane, QLD, Australia
- Queensland University of Technology, Brisbane, QLD, Australia
| | - Leonardo L. Gollo
- QIMR Berghofer Medical Research Institute, Brisbane, QLD, Australia
- Queensland University of Technology, Brisbane, QLD, Australia
- Turner Institute for Brain and Mental Health, School of Psychological Sciences, Monash University, Melbourne, VIC, Australia
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8
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Kades L, Pawlowski JM. Discrete Langevin machine: Bridging the gap between thermodynamic and neuromorphic systems. Phys Rev E 2020; 101:063304. [PMID: 32688507 DOI: 10.1103/physreve.101.063304] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2020] [Accepted: 04/08/2020] [Indexed: 01/09/2023]
Abstract
A formulation of Langevin dynamics for discrete systems is derived as a class of generic stochastic processes. The dynamics simplify for a two-state system and suggest a network architecture which is implemented by the Langevin machine. The Langevin machine represents a promising approach to compute successfully quantitative exact results of Boltzmann distributed systems by LIF neurons. Besides a detailed introduction of the dynamics, different simplified models of a neuromorphic hardware system are studied with respect to a control of emerging sources of errors.
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Affiliation(s)
- Lukas Kades
- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
| | - Jan M Pawlowski
- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
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9
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Marhl U, Gosak M. Proper spatial heterogeneities expand the regime of scale-free behavior in a lattice of excitable elements. Phys Rev E 2019; 100:062203. [PMID: 31962506 DOI: 10.1103/physreve.100.062203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2019] [Indexed: 06/10/2023]
Abstract
Signatures of criticality, such as power law scaling of observables, have been empirically found in a plethora of real-life settings, including biological systems. The presence of critical states is believed to have many functional advantages and is associated with optimal operational abilities. Typically, critical dynamics arises in the proximity of phase transition points between absorbing disordered states (subcriticality) and ordered active regimes (supercriticality) and requires a high degree of fine tuning to emerge, which is unlikely to occur in real biological systems. In the present study we propose a rather simple, and biologically relevant mechanism that profoundly expands the critical-like region. In particular, by means of numerical simulation we show that incorporating spatial heterogeneities into the square lattice of map-based excitable oscillators broadens the parameter space in which the distribution of excitation wave sizes follows closely a power law. Most importantly, this behavior is only observed if the spatial profile exhibits intermediate-sized patches with similar excitability levels, whereas for large and small spatial clusters only marginal widening of the critical state is detected. Furthermore, it turned out that the presence of spatial disorder in general amplifies the size of excitation waves, whereby the relatively highest contributions are observed in the proximity of the critical point. We argue that the reported mechanism is of particular importance for excitable systems with local interactions between individual elements.
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Affiliation(s)
- Urban Marhl
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
- Institute of Mathematics, Physics and Mechanics, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia
| | - Marko Gosak
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
- Institute of Physiology, Faculty of Medicine, University of Maribor, Taborska ulica 8, SI-2000 Maribor, Slovenia
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10
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Liu D, Zhao S, Luo X, Yuan Y. Unidirectional Synchronization of Hodgkin-Huxley Neurons With Prescribed Performance Under Transcranial Magneto-Acoustical Simulation. Front Neurosci 2019; 13:1061. [PMID: 31680807 PMCID: PMC6803475 DOI: 10.3389/fnins.2019.01061] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2019] [Accepted: 09/20/2019] [Indexed: 11/13/2022] Open
Abstract
This paper exploits the unidirectional synchronization dynamics of two Hodgkin-Huxley (HH) neurons under transcranial magneto-acoustical stimulation (TMAS). The major purpose is to explore a control scheme to make the spiking modes of the neural potentials stimulated by TMAS achieve synchronization states under the feedback input. For this purpose, an adaptive neural controller, which makes the neurons satisfy the prescribed master-slaver synchronization performance, is designed by introducing a tracking error into Lyapunov analysis. Under the proposed control scheme, the slaver neuron can not only overcome the model uncertainties and the difficulties brought by prescribed performance, but also track the spiking patterns of the master neuron. Finally, the simulations are implemented to demonstrate the effectiveness of the proposed controller, that is, the TMAS induced synchronization states of the HH neuron system can achieve the prescribed performance under the proposed controller.
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Affiliation(s)
- Dan Liu
- School of Electrical Engineering, Yanshan University, Qinhuangdao, China
- College of Integrative Medicine, Hebei University of Chinese Medicine, Shijiazhuang, China
| | - Song Zhao
- Department of Medical Imaging, The Second Hospital of Hebei Medical University, Shijiazhuang, China
| | - Xiaoyuan Luo
- School of Electrical Engineering, Yanshan University, Qinhuangdao, China
| | - Yi Yuan
- School of Electrical Engineering, Yanshan University, Qinhuangdao, China
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11
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Aguirre LA, Portes LL, Letellier C. Observability and synchronization of neuron models. CHAOS (WOODBURY, N.Y.) 2017; 27:103103. [PMID: 29092444 DOI: 10.1063/1.4985291] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Observability is the property that enables recovering the state of a dynamical system from a reduced number of measured variables. In high-dimensional systems, it is therefore important to make sure that the variable recorded to perform the analysis conveys good observability of the system dynamics. The observability of a network of neuron models depends nontrivially on the observability of the node dynamics and on the topology of the network. The aim of this paper is twofold. First, to perform a study of observability using four well-known neuron models by computing three different observability coefficients. This not only clarifies observability properties of the models but also shows the limitations of applicability of each type of coefficients in the context of such models. Second, to study the emergence of phase synchronization in networks composed of neuron models. This is done performing multivariate singular spectrum analysis which, to the best of the authors' knowledge, has not been used in the context of networks of neuron models. It is shown that it is possible to detect phase synchronization: (i) without having to measure all the state variables, but only one (that provides greatest observability) from each node and (ii) without having to estimate the phase.
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Affiliation(s)
- Luis A Aguirre
- Departamento de Engenharia Eletrônica, Universidade Federal de Minas Gerais, Belo Horizonte 31.270-901, Minas Gerais, Brazil
| | - Leonardo L Portes
- Programa de Pós-Graduação em Engenharia Elétrica da Universidade Federal de Minas Gerais-Av. Antônio Carlos 6627, 31.270-901 Belo Horizonte, Minas Gerais, Brazil
| | - Christophe Letellier
- CORIA-UMR 6614, Normandie Université, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France
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12
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A Mathematical Model for Storage and Recall of Images using Targeted Synchronization of Coupled Maps. Sci Rep 2017; 7:8921. [PMID: 28827555 PMCID: PMC5566478 DOI: 10.1038/s41598-017-09440-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2017] [Accepted: 07/25/2017] [Indexed: 11/22/2022] Open
Abstract
We propose a mathematical model for storage and recall of images using coupled maps. We start by theoretically investigating targeted synchronization in coupled map systems wherein only a desired (partial) subset of the maps is made to synchronize. A simple method is introduced to specify coupling coefficients such that targeted synchronization is ensured. The principle of this method is extended to storage/recall of images using coupled Rulkov maps. The process of adjusting coupling coefficients between Rulkov maps (often used to model neurons) for the purpose of storing a desired image mimics the process of adjusting synaptic strengths between neurons to store memories. Our method uses both synchronisation and synaptic weight modification, as the human brain is thought to do. The stored image can be recalled by providing an initial random pattern to the dynamical system. The storage and recall of the standard image of Lena is explicitly demonstrated.
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13
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Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons. ENTROPY 2017. [DOI: 10.3390/e19080399] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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14
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Maslennikov OV, Shchapin DS, Nekorkin VI. Transient sequences in a hypernetwork generated by an adaptive network of spiking neurons. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:20160288. [PMID: 28507233 PMCID: PMC5434079 DOI: 10.1098/rsta.2016.0288] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 11/24/2016] [Indexed: 05/24/2023]
Abstract
We propose a model of an adaptive network of spiking neurons that gives rise to a hypernetwork of its dynamic states at the upper level of description. Left to itself, the network exhibits a sequence of transient clustering which relates to a traffic in the hypernetwork in the form of a random walk. Receiving inputs the system is able to generate reproducible sequences corresponding to stimulus-specific paths in the hypernetwork. We illustrate these basic notions by a simple network of discrete-time spiking neurons together with its FPGA realization and analyse their properties.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.
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Affiliation(s)
- Oleg V Maslennikov
- Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
| | - Dmitry S Shchapin
- Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
| | - Vladimir I Nekorkin
- Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
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15
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Girardi-Schappo M, Bortolotto GS, Stenzinger RV, Gonsalves JJ, Tragtenberg MHR. Phase diagrams and dynamics of a computationally efficient map-based neuron model. PLoS One 2017; 12:e0174621. [PMID: 28358843 PMCID: PMC5373601 DOI: 10.1371/journal.pone.0174621] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2016] [Accepted: 03/12/2017] [Indexed: 11/18/2022] Open
Abstract
We introduce a new map-based neuron model derived from the dynamical perceptron family that has the best compromise between computational efficiency, analytical tractability, reduced parameter space and many dynamical behaviors. We calculate bifurcation and phase diagrams analytically and computationally that underpins a rich repertoire of autonomous and excitable dynamical behaviors. We report the existence of a new regime of cardiac spikes corresponding to nonchaotic aperiodic behavior. We compare the features of our model to standard neuron models currently available in the literature.
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Affiliation(s)
- Mauricio Girardi-Schappo
- Neuroimaging of Epilepsy Laboratory, McConnell Brain Imaging Center, McGill University, Montreal Neurological Institute and Hospital, H3A 2B4, Montreal, Quebec, Canada
| | - Germano S. Bortolotto
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
| | - Rafael V. Stenzinger
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
| | - Jheniffer J. Gonsalves
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
| | - Marcelo H. R. Tragtenberg
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
- * E-mail:
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16
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Carmantini GS, Beim Graben P, Desroches M, Rodrigues S. A modular architecture for transparent computation in recurrent neural networks. Neural Netw 2016; 85:85-105. [PMID: 27814468 DOI: 10.1016/j.neunet.2016.09.001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2015] [Revised: 08/30/2016] [Accepted: 09/05/2016] [Indexed: 10/20/2022]
Abstract
Computation is classically studied in terms of automata, formal languages and algorithms; yet, the relation between neural dynamics and symbolic representations and operations is still unclear in traditional eliminative connectionism. Therefore, we suggest a unique perspective on this central issue, to which we would like to refer as transparent connectionism, by proposing accounts of how symbolic computation can be implemented in neural substrates. In this study we first introduce a new model of dynamics on a symbolic space, the versatile shift, showing that it supports the real-time simulation of a range of automata. We then show that the Gödelization of versatile shifts defines nonlinear dynamical automata, dynamical systems evolving on a vectorial space. Finally, we present a mapping between nonlinear dynamical automata and recurrent artificial neural networks. The mapping defines an architecture characterized by its granular modularity, where data, symbolic operations and their control are not only distinguishable in activation space, but also spatially localizable in the network itself, while maintaining a distributed encoding of symbolic representations. The resulting networks simulate automata in real-time and are programmed directly, in the absence of network training. To discuss the unique characteristics of the architecture and their consequences, we present two examples: (i) the design of a Central Pattern Generator from a finite-state locomotive controller, and (ii) the creation of a network simulating a system of interactive automata that supports the parsing of garden-path sentences as investigated in psycholinguistics experiments.
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Affiliation(s)
| | - Peter Beim Graben
- Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu Berlin, Berlin, Germany.
| | | | - Serafim Rodrigues
- School of Computing and Mathematics, Plymouth University, Plymouth, United Kingdom.
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Han X, Chen Z, Bi Q. Inverse period-doubling bifurcations determine complex structure of bursting in a one-dimensional non-autonomous map. CHAOS (WOODBURY, N.Y.) 2016; 26:023117. [PMID: 26931598 DOI: 10.1063/1.4942503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We propose a simple one-dimensional non-autonomous map, in which some novel bursting patterns (e.g., "fold/double inverse flip" bursting, "fold/multiple inverse flip" bursting, and "fold/a cascade of inverse flip" bursting) can be observed. Typically, these bursting patterns exhibit complex structures containing a chain of inverse period-doubling bifurcations. The active states related to these bursting can be period-2(n) (n = 1, 2, 3,…) attractors or chaotic attractors, which may evolve to quiescence by a chain of inverse period-doubling bifurcations when the slow excitation decreases through period-doubling bifurcation points of the map. This accounts for the complex inverse period-doubling bifurcation structures observed in bursting patterns. Our findings enrich the possible routes to bursting as well as the underlying mechanisms of bursting.
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Affiliation(s)
- Xiujing Han
- Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, People's Republic of China
| | - Zhenyang Chen
- Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, People's Republic of China
| | - Qinsheng Bi
- Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, People's Republic of China
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Palmieri I, Monteiro LHA, Miranda MD. The transfer function of neuron spike. Neural Netw 2015; 68:89-95. [PMID: 26001638 DOI: 10.1016/j.neunet.2015.04.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2014] [Revised: 03/09/2015] [Accepted: 04/08/2015] [Indexed: 10/23/2022]
Abstract
The mathematical modeling of neuronal signals is a relevant problem in neuroscience. The complexity of the neuron behavior, however, makes this problem a particularly difficult task. Here, we propose a discrete-time linear time-invariant (LTI) model with a rational function in order to represent the neuronal spike detected by an electrode located in the surroundings of the nerve cell. The model is presented as a cascade association of two subsystems: one that generates an action potential from an input stimulus, and one that represents the medium between the cell and the electrode. The suggested approach employs system identification and signal processing concepts, and is dissociated from any considerations about the biophysical processes of the neuronal cell, providing a low-complexity alternative to model the neuronal spike. The model is validated by using in vivo experimental readings of intracellular and extracellular signals. A computational simulation of the model is presented in order to assess its proximity to the neuronal signal and to observe the variability of the estimated parameters. The implications of the results are discussed in the context of spike sorting.
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Affiliation(s)
- Igor Palmieri
- Departamento de Engenharia de Telecomunicações e Controle, Escola Politécnica da Universidade de São Paulo, Av. Prof. Luciano Gualberto, travessa 3, n. 158, 05508-900, São Paulo, SP, Brazil.
| | - Luiz H A Monteiro
- Escola de Engenharia da Universidade Presbiteriana Mackenzie, Pós-graduação em Engenharia Elétrica, Rua da Consolação, n. 896, 01302-907, São Paulo, SP, Brazil; Departamento de Engenharia de Telecomunicações e Controle, Escola Politécnica da Universidade de São Paulo, Av. Prof. Luciano Gualberto, travessa 3, n. 158, 05508-900, São Paulo, SP, Brazil.
| | - Maria D Miranda
- Departamento de Engenharia de Telecomunicações e Controle, Escola Politécnica da Universidade de São Paulo, Av. Prof. Luciano Gualberto, travessa 3, n. 158, 05508-900, São Paulo, SP, Brazil.
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19
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Inoue T, Fujiwara T, Rikitake Y, Maruo T, Mandai K, Kimura K, Kayahara T, Wang S, Itoh Y, Sai K, Mori M, Mori K, Mizoguchi A, Takai Y. Nectin-1 spots as a novel adhesion apparatus that tethers mitral cell lateral dendrites in a dendritic meshwork structure of the developing mouse olfactory bulb. J Comp Neurol 2015; 523:1824-39. [DOI: 10.1002/cne.23762] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Revised: 02/15/2015] [Accepted: 02/18/2015] [Indexed: 12/16/2022]
Affiliation(s)
- Takahito Inoue
- Division of Molecular and Cellular Biology; Department of Biochemistry and Molecular Biology; Kobe University Graduate School of Medicine; Kobe Hyogo 650-0017 Japan
- Division of Pathogenetic Signaling; Department of Biochemistry and Molecular Biology; Kobe University Graduate School of Medicine; Kobe Hyogo 650-0047 Japan
- CREST, Japan Science and Technology Agency; Kobe Japan
| | - Takeshi Fujiwara
- CREST, Japan Science and Technology Agency; Kobe Japan
- Department of Neural Regeneration and Cell Communication; Mie University Graduate School of Medicine; Tsu Mie 514-8507 Japan
| | - Yoshiyuki Rikitake
- Division of Molecular and Cellular Biology; Department of Biochemistry and Molecular Biology; Kobe University Graduate School of Medicine; Kobe Hyogo 650-0017 Japan
- CREST, Japan Science and Technology Agency; Kobe Japan
- Division of Signal Transduction; Department of Biochemistry and Molecular Biology; Kobe University Graduate School of Medicine; Kobe Hyogo 650-0017 Japan
| | - Tomohiko Maruo
- Division of Molecular and Cellular Biology; Department of Biochemistry and Molecular Biology; Kobe University Graduate School of Medicine; Kobe Hyogo 650-0017 Japan
- Division of Pathogenetic Signaling; Department of Biochemistry and Molecular Biology; Kobe University Graduate School of Medicine; Kobe Hyogo 650-0047 Japan
- CREST, Japan Science and Technology Agency; Kobe Japan
| | - Kenji Mandai
- Division of Molecular and Cellular Biology; Department of Biochemistry and Molecular Biology; Kobe University Graduate School of Medicine; Kobe Hyogo 650-0017 Japan
- Division of Pathogenetic Signaling; Department of Biochemistry and Molecular Biology; Kobe University Graduate School of Medicine; Kobe Hyogo 650-0047 Japan
- CREST, Japan Science and Technology Agency; Kobe Japan
| | - Kazushi Kimura
- Department of Physical Therapy; Faculty of Human Science; Hokkaido Bunkyo University; Eniwa Hokkaido 061-1449 Japan
| | - Tetsuro Kayahara
- Department of Medical Rehabilitation; Faculty of Rehabilitation; Kobe Gakuin University; Kobe Hyogo 651-2180 Japan
| | - Shujie Wang
- CREST, Japan Science and Technology Agency; Kobe Japan
- Department of Neural Regeneration and Cell Communication; Mie University Graduate School of Medicine; Tsu Mie 514-8507 Japan
| | - Yu Itoh
- CREST, Japan Science and Technology Agency; Kobe Japan
- Department of Neural Regeneration and Cell Communication; Mie University Graduate School of Medicine; Tsu Mie 514-8507 Japan
| | - Kousyoku Sai
- Department of Neural Regeneration and Cell Communication; Mie University Graduate School of Medicine; Tsu Mie 514-8507 Japan
| | - Masahiro Mori
- CREST, Japan Science and Technology Agency; Kobe Japan
- Faculty of Health Sciences; Kobe University Graduate School of Health Sciences; Kobe Hyogo 654-0142 Japan
| | - Kensaku Mori
- Department of Physiology; Graduate School of Medicine, University of Tokyo; Tokyo Japan
- CREST, Japan Science and Technology Agency; Tokyo Japan
| | - Akira Mizoguchi
- CREST, Japan Science and Technology Agency; Kobe Japan
- Department of Neural Regeneration and Cell Communication; Mie University Graduate School of Medicine; Tsu Mie 514-8507 Japan
| | - Yoshimi Takai
- Division of Molecular and Cellular Biology; Department of Biochemistry and Molecular Biology; Kobe University Graduate School of Medicine; Kobe Hyogo 650-0017 Japan
- Division of Pathogenetic Signaling; Department of Biochemistry and Molecular Biology; Kobe University Graduate School of Medicine; Kobe Hyogo 650-0047 Japan
- CREST, Japan Science and Technology Agency; Kobe Japan
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Hadaeghi F, Hashemi Golpayegani MR, Murray G. Towards a complex system understanding of bipolar disorder: A map based model of a complex winnerless competition. J Theor Biol 2015; 376:74-81. [PMID: 25728789 DOI: 10.1016/j.jtbi.2015.02.020] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2014] [Revised: 02/06/2015] [Accepted: 02/17/2015] [Indexed: 12/20/2022]
Abstract
Bipolar disorder is characterized by repeated erratic episodes of mania and depression, which can be understood as pathological complex system behavior involving cognitive, affective and psychomotor disturbance. In order to illuminate dynamical aspects of the longitudinal course of the illness, we propose here a novel complex model based on the notion of competition between recurrent maps, which mathematically represent the dynamics of activation in excitatory (Glutamatergic) and inhibitory (GABAergic) pathways. We assume that manic and depressive states can be considered stable sub attractors of a dynamical system through which the mood trajectory moves. The model provides a theoretical framework which can account for a number of complex phenomena of bipolar disorder, including intermittent transition between the two poles of the disorder, rapid and ultra-rapid cycling of episodes and manicogenic effects of antidepressants.
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Affiliation(s)
- Fatemeh Hadaeghi
- Complex Systems and Cybernetics Control Laboratory, Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran
| | - Mohammad Reza Hashemi Golpayegani
- Complex Systems and Cybernetics Control Laboratory, Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran.
| | - Greg Murray
- Faculty of Health, Arts and Design, Swinburne University of Technology, Hawthorn, VIC, Australia
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21
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Stenzinger RV, Gonsalves JJ, Girardi-Schappo M, Tragtenberg MHR. A map-based logistic neuron model: an efficient way to obtain many different neural behaviors. BMC Neurosci 2014. [PMCID: PMC4126445 DOI: 10.1186/1471-2202-15-s1-p24] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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Girardi-Schappo M, Kinouchi O, Tragtenberg MHR. Critical avalanches and subsampling in map-based neural networks coupled with noisy synapses. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:024701. [PMID: 24032969 DOI: 10.1103/physreve.88.024701] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2012] [Revised: 05/29/2013] [Indexed: 06/02/2023]
Abstract
Many different kinds of noise are experimentally observed in the brain. Among them, we study a model of noisy chemical synapse and obtain critical avalanches for the spatiotemporal activity of the neural network. Neurons and synapses are modeled by dynamical maps. We discuss the relevant neuronal and synaptic properties to achieve the critical state. We verify that networks of functionally excitable neurons with fast synapses present power-law avalanches, due to rebound spiking dynamics. We also discuss the measuring of neuronal avalanches by subsampling our data, shedding light on the experimental search for self-organized criticality in neural networks.
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Affiliation(s)
- M Girardi-Schappo
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
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