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Mangalam M, Kelty-Stephen DG, Sommerfeld JH, Stergiou N, Likens AD. Temporal organization of stride-to-stride variations contradicts predictive models for sensorimotor control of footfalls during walking. PLoS One 2023; 18:e0290324. [PMID: 37616227 PMCID: PMC10449478 DOI: 10.1371/journal.pone.0290324] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 08/04/2023] [Indexed: 08/26/2023] Open
Abstract
Walking exhibits stride-to-stride variations. Given ongoing perturbations, these variations critically support continuous adaptations between the goal-directed organism and its surroundings. Here, we report that stride-to-stride variations during self-paced overground walking show cascade-like intermittency-stride intervals become uneven because stride intervals of different sizes interact and do not simply balance each other. Moreover, even when synchronizing footfalls with visual cues with variable timing of presentation, asynchrony in the timings of the cue and footfall shows cascade-like intermittency. This evidence conflicts with theories about the sensorimotor control of walking, according to which internal predictive models correct asynchrony in the timings of the cue and footfall from one stride to the next on crossing thresholds leading to the risk of falling. Hence, models of the sensorimotor control of walking must account for stride-to-stride variations beyond the constraints of threshold-dependent predictive internal models.
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Affiliation(s)
- Madhur Mangalam
- Division of Biomechanics and Research Development, Department of Biomechanics, and Center for Research in Human Movement Variability, University of Nebraska at Omaha, Omaha, NE, United States of America
| | - Damian G. Kelty-Stephen
- Department of Psychology, State University of New York at New Paltz, New Paltz, NY, United States of America
| | - Joel H. Sommerfeld
- Division of Biomechanics and Research Development, Department of Biomechanics, and Center for Research in Human Movement Variability, University of Nebraska at Omaha, Omaha, NE, United States of America
| | - Nick Stergiou
- Division of Biomechanics and Research Development, Department of Biomechanics, and Center for Research in Human Movement Variability, University of Nebraska at Omaha, Omaha, NE, United States of America
- Department of Department of Physical Education, & Sport Science, Aristotle University, Thessaloniki, Greece
| | - Aaron D. Likens
- Division of Biomechanics and Research Development, Department of Biomechanics, and Center for Research in Human Movement Variability, University of Nebraska at Omaha, Omaha, NE, United States of America
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2
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Safari N, Shahbazi F, Dehghani-Habibabadi M, Esghaei M, Zare M. Spike-phase coupling as an order parameter in a leaky integrate-and-fire model. Phys Rev E 2020; 102:052202. [PMID: 33327067 DOI: 10.1103/physreve.102.052202] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Accepted: 09/22/2020] [Indexed: 06/12/2023]
Abstract
It is known that the leaky integrate-and-fire neural model shows a transition from irregular to synchronous firing by increasing the coupling between the neurons. However, a quantitative characterization of this order-disorder transition, that is, the determination of the order of transition and also the critical exponents in the case of continuous transition, is not entirely known. In this work, we consider a network of N excitatory neurons with local connections, residing on a square lattice with periodic boundary conditions. The cooperation between neurons K plays the role of the control parameter that generates criticality when the critical cooperation strength K_{c} is adopted. We introduce the population-averaged voltage (PAV) as a representative value of the network's cooperative activity. Then, we show that the coupling between the timing of spikes and the phase of temporal fluctuations of PAV defined as m resorts to identify a Kuramoto order parameter. By increasing K, we find a continuous transition from irregular spiking to a phase-locked state at the critical point K_{c}. We deploy the finite-size scaling analysis to calculate the critical exponents of this transition. To explore the formal indicator of criticality, we study the neuronal avalanches profile at this critical point and find a scaling behavior with the exponents in a fair agreement with the experimental values both in vivo and in vitro.
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Affiliation(s)
- Nahid Safari
- Department of Physics, Isfahan University of Technology, 84156-83111 Isfahan, Iran
| | - Farhad Shahbazi
- Department of Physics, Isfahan University of Technology, 84156-83111 Isfahan, Iran
| | | | - Moein Esghaei
- Cognitive Neuroscience Laboratory, German Primate Center-Leibniz Institute for Primate Research, 37077 Göttingen, Germany
- School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), 19395 Tehran, Iran
- Royan Institute for Stem Cell Biology and Technology, ACECR, 16635, Tehran, Iran
| | - Marzieh Zare
- Département de psychologie, Université de Montréal, H3C 3J7 Montréal, Canada
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Jannesari M, Saeedi A, Zare M, Ortiz-Mantilla S, Plenz D, Benasich AA. Stability of neuronal avalanches and long-range temporal correlations during the first year of life in human infants. Brain Struct Funct 2020; 225:1169-1183. [PMID: 32095901 PMCID: PMC7166209 DOI: 10.1007/s00429-019-02014-4] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2018] [Accepted: 06/26/2019] [Indexed: 11/27/2022]
Abstract
During infancy, the human brain rapidly expands in size and complexity as neural networks mature and new information is incorporated at an accelerating pace. Recently, it was shown that single-electrode EEG in preterms at birth exhibits scale-invariant intermittent bursts. Yet, it is currently not known whether the normal infant brain, in particular, the cortex, maintains a distinct dynamical state during development that is characterized by scale-invariant spatial as well as temporal aspects. Here we employ dense-array EEG recordings acquired from the same infants at 6 and 12 months of age to characterize brain activity during an auditory odd-ball task. We show that suprathreshold events organize as spatiotemporal clusters whose size and duration are power-law distributed, the hallmark of neuronal avalanches. Time series of local suprathreshold EEG events display significant long-range temporal correlations (LRTCs). No differences were found between 6 and 12 months, demonstrating stability of avalanche dynamics and LRTCs during the first year after birth. These findings demonstrate that the infant brain is characterized by distinct spatiotemporal dynamical aspects that are in line with expectations of a critical cortical state. We suggest that critical state dynamics, which theory and experiments have shown to be beneficial for numerous aspects of information processing, are maintained by the infant brain to process an increasingly complex environment during development.
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Affiliation(s)
- Mostafa Jannesari
- School of Computer Science, Institute for Research in Fundamental Sciences (IPM), 70 Lavasani Avenue, Tehran, 19395, Iran
| | - Alireza Saeedi
- Department of Physiology of Cognitive Processes, Max-Planck-Institute for Biological Cybernetics, 72076, Tübingen, Germany
| | - Marzieh Zare
- School of Computer Science, Institute for Research in Fundamental Sciences (IPM), 70 Lavasani Avenue, Tehran, 19395, Iran.
| | - Silvia Ortiz-Mantilla
- Center for Molecular and Behavioral Neuroscience, Rutgers University-Newark, 197 University Avenue, Newark, NJ, 07102, USA
| | - Dietmar Plenz
- Section on Critical Brain Dynamics, Laboratory of Systems Neuroscience, National Institute of Mental Health, Porter Neuroscience Research Center, MSC 3735, Bethesda, MD, 20892, USA
| | - April A Benasich
- Center for Molecular and Behavioral Neuroscience, Rutgers University-Newark, 197 University Avenue, Newark, NJ, 07102, USA
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4
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Jannesari M, Saeedi A, Zare M, Ortiz-Mantilla S, Plenz D, Benasich AA. Stability of neuronal avalanches and long-range temporal correlations during the first year of life in human infant. Brain Struct Funct 2019; 224:2453-2465. [PMID: 31267171 PMCID: PMC6698269 DOI: 10.1007/s00429-019-01918-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2018] [Accepted: 06/26/2019] [Indexed: 11/29/2022]
Abstract
During infancy, the human brain rapidly expands in size and complexity as neural networks mature and new information is incorporated at an accelerating pace. Recently, it was shown that single electrode EEG in preterms at birth exhibits scale-invariant intermittent bursts. Yet, it is currently not known whether the normal infant brain, in particular, the cortex maintains a distinct dynamical state during development that is characterized by scale-invariant spatial as well as temporal aspects. Here we employ dense-array EEG recordings acquired from the same infants at 6 and 12 months of age to characterize brain activity during an auditory oddball task. We show that suprathreshold events organize as spatiotemporal clusters whose size and duration are power-law distributed, the hallmark of neuronal avalanches. Time series of local suprathreshold EEG events display significant long-range temporal correlations (LRTCs). No differences were found between 6 and 12 months, demonstrating stability of avalanche dynamics and LRTCs during the first year after birth. These findings demonstrate that the infant brain is characterized by distinct spatiotemporal dynamical aspects that are in line with expectations of a critical cortical state. We suggest that critical state dynamics, which theory and experiments have shown to be beneficial for numerous aspects of information processing, are maintained by the infant brain to process an increasingly complex environment during development.
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Affiliation(s)
- Mostafa Jannesari
- School of Computer Science, Institute for Research in Fundamental Sciences (IPM), 70 Lavasani Avenue, Tehran, 19395, Iran
| | - Alireza Saeedi
- Department of Physiology of Cognitive Processes, Max-Planck-Institute for Biological Cybernetics, Tübingen, 72076, Germany
| | - Marzieh Zare
- School of Computer Science, Institute for Research in Fundamental Sciences (IPM), 70 Lavasani Avenue, Tehran, 19395, Iran.
| | - Silvia Ortiz-Mantilla
- Center for Molecular and Behavioral Neuroscience, Rutgers University-Newark, 197 University Avenue, Newark, NJ, 07102, USA
| | - Dietmar Plenz
- Section on Critical Brain Dynamics, Laboratory of Systems Neuroscience, National Institute of Mental Health, Porter Neuroscience Research Center, MSC 3735, Bethesda, MD, 20892, USA
| | - April A Benasich
- Center for Molecular and Behavioral Neuroscience, Rutgers University-Newark, 197 University Avenue, Newark, NJ, 07102, USA
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Dehghani-Habibabadi M, Zare M, Shahbazi F, Usefie-Mafahim J, Grigolini P. Neuronal avalanches: Where temporal complexity and criticality meet. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:101. [PMID: 29188466 DOI: 10.1140/epje/i2017-11590-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2017] [Accepted: 10/30/2017] [Indexed: 06/07/2023]
Abstract
The model of the current paper is an extension of a previous publication, wherein we have used the leaky integrate-and-fire model on a regular lattice with periodic boundary conditions, and introduced the temporal complexity as a genuine signature of criticality. In that work, the power-law distribution of neural avalanches was a manifestation of supercriticality rather than criticality. Here, however, we show that the continuous solution of the model and replacing the stochastic noise with a Gaussian zero-mean noise leads to the coincidence of power-law display of temporal complexity, and spatiotemporal patterns of neural avalanches at the critical point. We conclude that the source of inconsistency may be a numerical artifact originated by the discrete description of the model which may imply a slow numerical convergence of the avalanche distribution compared to temporal complexity.
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Affiliation(s)
| | - Marzieh Zare
- School of Computer Science, Institute for Research in Fundamental Sciences (IPM), 19395-5746, Tehran, Iran.
| | - Farhad Shahbazi
- Department of Physics, Isfahan University of Technology, 84156-83111, Isfahan, Iran
- School of Physics, Institute for Research in Fundamental Sciences (IPM), 19395-5531, Tehran, Iran
| | | | - Paolo Grigolini
- Center for Nonlinear Science, University of North Texas, 76203, Denton, TX, USA
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Pramukkul P, Svenkeson A, Grigolini P. Effect of noise and detector sensitivity on a dynamical process: inverse power law and Mittag-Leffler interevent time survival probabilities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022107. [PMID: 25353422 DOI: 10.1103/physreve.89.022107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2013] [Indexed: 06/04/2023]
Abstract
We study the combined effects of noise and detector sensitivity on a dynamical process that generates intermittent events mimicking the behavior of complex systems. By varying the sensitivity level of the detector we move between two forms of complexity, from inverse power law to Mittag-Leffler interevent time survival probabilities. Here fluctuations fight against complexity, causing an exponential truncation to the survival probability. We show that fluctuations of relatively weak intensity have a strong effect on the generation of Mittag-Leffler complexity, providing a reason why stretched exponentials are frequently found in nature. Our results afford a more unified picture of complexity resting on the Mittag-Leffler function and encompassing the standard inverse power law definition.
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Affiliation(s)
- Pensri Pramukkul
- Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427, USA and Faculty of Science and Technology, Chiang Mai Rajabhat University, 202 Chang Phuak Road, Muang, Chiang Mai 50300, Thailand
| | - Adam Svenkeson
- Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427, USA
| | - Paolo Grigolini
- Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427, USA
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Bologna M, West BJ, Grigolini P. Renewal and memory origin of anomalous diffusion: a discussion of their joint action. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062106. [PMID: 24483385 DOI: 10.1103/physreve.88.062106] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2013] [Indexed: 06/03/2023]
Abstract
The adoption of the formalism of fractional calculus is an elegant way to simulate either subdiffusion or superdiffusion from within a renewal perspective where the occurrence of an event at a given time t does not have any memory of the events occurring at earlier times. We illustrate a physical model to assign infinite memory to renewal anomalous diffusion and we find (i) a condition where the simultaneous action of a renewal and a memory source of subdiffusion generates localization and (ii) a condition where they make subdiffusion weaker and superdiffusion emerge. We argue that our approach may provide important contributions to the current search to distinguish the renewal from the memory source of subdiffusion.
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Affiliation(s)
- Mauro Bologna
- Instituto de Alta Investigación, Universidad de Tarapacá-Casilla 6-D Arica, Chile
| | - Bruce J West
- Information Science Directorate, Army Research Office, Research Triangle Park, North Carolina 27709, USA
| | - Paolo Grigolini
- Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427, USA
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Grigolini P. Comments on “Physiological time: A hypothesis”. Phys Life Rev 2013; 10:225-6. [DOI: 10.1016/j.plrev.2013.03.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2013] [Accepted: 03/07/2013] [Indexed: 10/26/2022]
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