51
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Carvalho TTA, Fontenele AJ, Girardi-Schappo M, Feliciano T, Aguiar LAA, Silva TPL, de Vasconcelos NAP, Carelli PV, Copelli M. Subsampled Directed-Percolation Models Explain Scaling Relations Experimentally Observed in the Brain. Front Neural Circuits 2021; 14:576727. [PMID: 33519388 PMCID: PMC7843423 DOI: 10.3389/fncir.2020.576727] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Accepted: 11/30/2002] [Indexed: 12/14/2022] Open
Abstract
Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations point to critical exponents whose values differ from those of a branching process, which has been the canonical model employed to understand brain criticality. This suggested that a different model, with a different phase transition, might be required to explain the data. Here we show that this is not necessarily the case. By employing two different models belonging to the same universality class as the branching process (mean-field directed percolation) and treating the simulation data exactly like experimental data, we reproduce most of the experimental results. We find that subsampling the model and adjusting the time bin used to define avalanches (as done with experimental data) are sufficient ingredients to change the apparent exponents of the critical point. Moreover, experimental data is only reproduced within a very narrow range in parameter space around the phase transition.
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Affiliation(s)
- Tawan T A Carvalho
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | | | - Mauricio Girardi-Schappo
- Department of Physics, University of Ottawa, Ottawa, ON, Canada.,Departamento de Física, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto, Brazil
| | - Thaís Feliciano
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | - Leandro A A Aguiar
- Departamento de Ciências Fundamentais e Sociais, Universidade Federal da Paraíba, Areia, Brazil
| | - Thais P L Silva
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | - Nivaldo A P de Vasconcelos
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga, Portugal.,Life and Health Sciences Research Institute/Biomaterials, Biodegradables and Biomimetics, Braga, Portugal
| | - Pedro V Carelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | - Mauro Copelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
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52
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Chen T, Bobbert PA, Wiel WG. 1/
f
Noise and Machine Intelligence in a Nonlinear Dopant Atom Network. SMALL SCIENCE 2021. [DOI: 10.1002/smsc.202000014] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Affiliation(s)
- Tao Chen
- NanoElectronics Group MESA+ Institute for Nanotechnology and BRAINS Center for Brain-Inspired Nano Systems University of Twente PO Box 217 Enschede AE 7500 The Netherlands
| | - Peter A. Bobbert
- NanoElectronics Group MESA+ Institute for Nanotechnology and BRAINS Center for Brain-Inspired Nano Systems University of Twente PO Box 217 Enschede AE 7500 The Netherlands
- Molecular Materials and Nanosystems & Center for Computational Energy Research Department of Applied Physics Eindhoven University of Technology PO Box 513 Eindhoven MB 5600 The Netherlands
| | - Wilfred G. Wiel
- NanoElectronics Group MESA+ Institute for Nanotechnology and BRAINS Center for Brain-Inspired Nano Systems University of Twente PO Box 217 Enschede AE 7500 The Netherlands
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53
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André M, Planche L. The effect of graph connectivity on metastability in a stochastic system of spiking neurons. Stoch Process Their Appl 2021. [DOI: 10.1016/j.spa.2020.09.013] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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54
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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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55
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Weistuch C, Agozzino L, Mujica-Parodi LR, Dill KA. Inferring a network from dynamical signals at its nodes. PLoS Comput Biol 2020; 16:e1008435. [PMID: 33253160 PMCID: PMC7728228 DOI: 10.1371/journal.pcbi.1008435] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Revised: 12/10/2020] [Accepted: 10/12/2020] [Indexed: 12/26/2022] Open
Abstract
We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they are inter-connected. We use Maximum Caliber as an inference principle. The combinatorial challenge of high-dimensional data is handled using two different approximations to the pairwise couplings. We show two proofs of principle: in a nonlinear genetic toggle switch circuit, and in a toy neural network.
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Affiliation(s)
- Corey Weistuch
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York, USA
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, USA
| | - Luca Agozzino
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York, USA
| | - Lilianne R. Mujica-Parodi
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York, USA
- Department of Biomedical Engineering, Stony Brook University, Stony Brook, New York, USA
- Program in Neuroscience, Stony Brook University, Stony Brook, New York, USA
- Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts, USA
| | - Ken A. Dill
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York, USA
- Department of Chemistry, Stony Brook University, Stony Brook, New York, USA
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56
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Manjunath G. Stability and memory-loss go hand-in-hand: three results in dynamics and computation. Proc Math Phys Eng Sci 2020. [DOI: 10.1098/rspa.2020.0563] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The search for universal laws that help establish a relationship between dynamics and computation is driven by recent expansionist initiatives in biologically inspired computing. A general setting to understand both such dynamics and computation is a driven dynamical system that responds to a temporal input. Surprisingly, we find memory-loss a feature of driven systems to forget their internal states helps provide unambiguous answers to the following fundamental stability questions that have been unanswered for decades: what is necessary and sufficient so that slightly different inputs still lead to mostly similar responses? How does changing the driven system’s parameters affect stability? What is the mathematical definition of the edge-of-criticality? We anticipate our results to be timely in understanding and designing biologically inspired computers that are entering an era of dedicated hardware implementations for neuromorphic computing and state-of-the-art reservoir computing applications.
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Affiliation(s)
- G. Manjunath
- Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0028, South Africa
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57
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Ma Z, Liu H, Komiyama T, Wessel R. Stability of motor cortex network states during learning-associated neural reorganizations. J Neurophysiol 2020; 124:1327-1342. [PMID: 32937084 DOI: 10.1152/jn.00061.2020] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
A substantial reorganization of neural activity and neuron-to-movement relationship in motor cortical circuits accompanies the emergence of reproducible movement patterns during motor learning. Little is known about how this tempest of neural activity restructuring impacts the stability of network states in recurrent cortical circuits. To investigate this issue, we reanalyzed data in which we recorded for 14 days via population calcium imaging the activity of the same neural populations of pyramidal neurons in layer 2/3 and layer 5 of forelimb motor and premotor cortex in mice during the daily learning of a lever-press task. We found that motor cortex network states remained stable with respect to the critical network state during the extensive reorganization of both neural population activity and its relation to lever movement throughout learning. Specifically, layer 2/3 cortical circuits unceasingly displayed robust evidence for operating at the critical network state, a regime that maximizes information capacity and transmission and provides a balance between network robustness and flexibility. In contrast, layer 5 circuits operated away from the critical network state for all 14 days of recording and learning. In conclusion, this result indicates that the wide-ranging malleability of synapses, neurons, and neural connectivity during learning operates within the constraint of a stable and layer-specific network state regarding dynamic criticality, and suggests that different cortical layers operate under distinct constraints because of their specialized goals.NEW & NOTEWORTHY The neural activity reorganizes throughout motor learning, but how this reorganization impacts the stability of network states is unclear. We used two-photon calcium imaging to investigate how the network states in layer 2/3 and layer 5 of forelimb motor and premotor cortex are modulated by motor learning. We show that motor cortex network states are layer-specific and constant regarding criticality during neural activity reorganization, and suggests that layer-specific constraints could be motivated by different functions.
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Affiliation(s)
- Zhengyu Ma
- Department of Physics, Washington University in St. Louis, Saint Louis, Missouri
| | - Haixin Liu
- Neurobiology Section and Department of Neuroscience, University of California San Diego, La Jolla, California
| | - Takaki Komiyama
- Neurobiology Section and Department of Neuroscience, University of California San Diego, La Jolla, California
| | - Ralf Wessel
- Department of Physics, Washington University in St. Louis, Saint Louis, Missouri
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58
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Deutsch A, Friedl P, Preziosi L, Theraulaz G. Multi-scale analysis and modelling of collective migration in biological systems. Philos Trans R Soc Lond B Biol Sci 2020; 375:20190377. [PMID: 32713301 PMCID: PMC7423374 DOI: 10.1098/rstb.2019.0377] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 06/11/2020] [Indexed: 02/06/2023] Open
Abstract
Collective migration has become a paradigm for emergent behaviour in systems of moving and interacting individual units resulting in coherent motion. In biology, these units are cells or organisms. Collective cell migration is important in embryonic development, where it underlies tissue and organ formation, as well as pathological processes, such as cancer invasion and metastasis. In animal groups, collective movements may enhance individuals' decisions and facilitate navigation through complex environments and access to food resources. Mathematical models can extract unifying principles behind the diverse manifestations of collective migration. In biology, with a few exceptions, collective migration typically occurs at a 'mesoscopic scale' where the number of units ranges from only a few dozen to a few thousands, in contrast to the large systems treated by statistical mechanics. Recent developments in multi-scale analysis have allowed linkage of mesoscopic to micro- and macroscopic scales, and for different biological systems. The articles in this theme issue on 'Multi-scale analysis and modelling of collective migration' compile a range of mathematical modelling ideas and multi-scale methods for the analysis of collective migration. These approaches (i) uncover new unifying organization principles of collective behaviour, (ii) shed light on the transition from single to collective migration, and (iii) allow us to define similarities and differences of collective behaviour in groups of cells and organisms. As a common theme, self-organized collective migration is the result of ecological and evolutionary constraints both at the cell and organismic levels. Thereby, the rules governing physiological collective behaviours also underlie pathological processes, albeit with different upstream inputs and consequences for the group. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.
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Affiliation(s)
- Andreas Deutsch
- Department of Innovative Methods of Computing, Center for Information Services and High Performance Computing, Technische Universität Dresden, Dresden, Germany
| | - Peter Friedl
- Department of Cell Biology, Radboud Institute for Molecular Life Sciences, Radboud University Medical Centre, Nijmegen, The Netherlands
- Cancer Genomics Center, Utrecht, The Netherlands
- Department of Genitourinary Medicine, University of Texas MD Anderson Cancer Center, Houston, TX, USA
| | - Luigi Preziosi
- Department of Mathematical Sciences, Politecnico di Torino, Torino, Italy
| | - Guy Theraulaz
- Centre de Recherches sur la Cognition Animale, Centre de Biologie Intégrative, Université de Toulouse, CNRS, UPS, Toulouse, France
- Centre for Ecological Sciences, Indian Institute of Science, Bengaluru, India
- Institute for Advanced Study in Toulouse, Toulouse, France
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59
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C. elegans episodic swimming is driven by multifractal kinetics. Sci Rep 2020; 10:14775. [PMID: 32901071 PMCID: PMC7478975 DOI: 10.1038/s41598-020-70319-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2020] [Accepted: 07/27/2020] [Indexed: 12/21/2022] Open
Abstract
Fractal scaling is a common property of temporal change in various modes of animal behavior. The molecular mechanisms of fractal scaling in animal behaviors remain largely unexplored. The nematode C. elegans alternates between swimming and resting states in a liquid solution. Here, we report that C. elegans episodic swimming is characterized by scale-free kinetics with long-range temporal correlation and local temporal clusterization, namely consistent with multifractal kinetics. Residence times in actively-moving and inactive states were distributed in a power law-based scale-free manner. Multifractal analysis showed that temporal correlation and temporal clusterization were distinct between the actively-moving state and the inactive state. These results indicate that C. elegans episodic swimming is driven by transition between two behavioral states, in which each of two transition kinetics follows distinct multifractal kinetics. We found that a conserved behavioral modulator, cyclic GMP dependent kinase (PKG) may regulate the multifractal kinetics underlying an animal behavior. Our combinatorial analysis approach involving molecular genetics and kinetics provides a platform for the molecular dissection of the fractal nature of physiological and behavioral phenomena.
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60
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Zimmern V. Why Brain Criticality Is Clinically Relevant: A Scoping Review. Front Neural Circuits 2020; 14:54. [PMID: 32982698 PMCID: PMC7479292 DOI: 10.3389/fncir.2020.00054] [Citation(s) in RCA: 56] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2020] [Accepted: 07/23/2020] [Indexed: 12/13/2022] Open
Abstract
The past 25 years have seen a strong increase in the number of publications related to criticality in different areas of neuroscience. The potential of criticality to explain various brain properties, including optimal information processing, has made it an increasingly exciting area of investigation for neuroscientists. Recent reviews on this topic, sometimes termed brain criticality, make brief mention of clinical applications of these findings to several neurological disorders such as epilepsy, neurodegenerative disease, and neonatal hypoxia. Other clinicallyrelevant domains - including anesthesia, sleep medicine, developmental-behavioral pediatrics, and psychiatry - are seldom discussed in review papers of brain criticality. Thorough assessments of these application areas and their relevance for clinicians have also yet to be published. In this scoping review, studies of brain criticality involving human data of all ages are evaluated for their current and future clinical relevance. To make the results of these studies understandable to a more clinical audience, a review of the key concepts behind criticality (e.g., phase transitions, long-range temporal correlation, self-organized criticality, power laws, branching processes) precedes the discussion of human clinical studies. Open questions and forthcoming areas of investigation are also considered.
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Affiliation(s)
- Vincent Zimmern
- Division of Child Neurology, The University of Texas Southwestern Medical Center, Dallas, TX, United States
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61
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Keshmiri S. Entropy and the Brain: An Overview. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E917. [PMID: 33286686 PMCID: PMC7597158 DOI: 10.3390/e22090917] [Citation(s) in RCA: 54] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Revised: 07/25/2020] [Accepted: 08/19/2020] [Indexed: 12/17/2022]
Abstract
Entropy is a powerful tool for quantification of the brain function and its information processing capacity. This is evident in its broad domain of applications that range from functional interactivity between the brain regions to quantification of the state of consciousness. A number of previous reviews summarized the use of entropic measures in neuroscience. However, these studies either focused on the overall use of nonlinear analytical methodologies for quantification of the brain activity or their contents pertained to a particular area of neuroscientific research. The present study aims at complementing these previous reviews in two ways. First, by covering the literature that specifically makes use of entropy for studying the brain function. Second, by highlighting the three fields of research in which the use of entropy has yielded highly promising results: the (altered) state of consciousness, the ageing brain, and the quantification of the brain networks' information processing. In so doing, the present overview identifies that the use of entropic measures for the study of consciousness and its (altered) states led the field to substantially advance the previous findings. Moreover, it realizes that the use of these measures for the study of the ageing brain resulted in significant insights on various ways that the process of ageing may affect the dynamics and information processing capacity of the brain. It further reveals that their utilization for analysis of the brain regional interactivity formed a bridge between the previous two research areas, thereby providing further evidence in support of their results. It concludes by highlighting some potential considerations that may help future research to refine the use of entropic measures for the study of brain complexity and its function. The present study helps realize that (despite their seemingly differing lines of inquiry) the study of consciousness, the ageing brain, and the brain networks' information processing are highly interrelated. Specifically, it identifies that the complexity, as quantified by entropy, is a fundamental property of conscious experience, which also plays a vital role in the brain's capacity for adaptation and therefore whose loss by ageing constitutes a basis for diseases and disorders. Interestingly, these two perspectives neatly come together through the association of entropy and the brain capacity for information processing.
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Affiliation(s)
- Soheil Keshmiri
- The Thomas N. Sato BioMEC-X Laboratories, Advanced Telecommunications Research Institute International (ATR), Kyoto 619-0237, Japan
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62
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Time-dependent branching processes: a model of oscillating neuronal avalanches. Sci Rep 2020; 10:13678. [PMID: 32792658 PMCID: PMC7426838 DOI: 10.1038/s41598-020-69705-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2020] [Accepted: 07/15/2020] [Indexed: 11/08/2022] Open
Abstract
Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary continuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronal activity, yet they lack any such time-dependence. In the present work, we extend a basic branching process by allowing the extinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, we derive relevant observables in closed form. We support our findings by quantitative comparison to numerics and qualitative comparison to available experimental results.
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63
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Kaakinen JK, Simola J. Fluctuation in Pupil Size and Spontaneous Blinks Reflect Story Transportation. J Eye Mov Res 2020; 13:10.16910/jemr.13.3.6. [PMID: 33828801 PMCID: PMC7993253 DOI: 10.16910/jemr.13.3.6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022] Open
Abstract
Thirty-nine participants listened to 28 neutral and horror excerpts of Stephen King short stories while constantly tracking their emotional arousal. Pupil size was measured with an Eyelink 1000+, and participants rated valence and transportation after each story. In addition to computing mean pupil size across 1-sec intervals, we extracted blink count and used detrended fluctuation analysis (DFA) to obtain the scaling exponents of long-range temporal correlations (LRTCs) in pupil size time-series. Pupil size was expected to be sensitive also to emotional arousal, whereas blink count and LRTC's were expected to reflect cognitive engagement. The results showed that self-reported arousal increased, pupil size was overall greater, and the decreasing slope of pupil size was flatter for horror than for neutral stories. Horror stories induced higher transportation than neutral stories. High transportation was associated with a steeper increase in self-reported arousal across time, stronger LRTCs in pupil size fluctuations, and lower blink count. These results indicate that pupil size reflects emotional arousal induced by the text content, while LRTCs and blink count are sensitive to cognitive engagement associated with transportation, irrespective of the text type. The study demonstrates the utility of pupillometric measures and blink count to study literature reception.
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64
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Shu S, Qin L, Yin Y, Han M, Cui W, Gao JH. Cortical electrophysiological evidence for individual-specific temporal organization of brain functional networks. Hum Brain Mapp 2020; 41:2160-2172. [PMID: 31961469 PMCID: PMC7267903 DOI: 10.1002/hbm.24937] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2019] [Revised: 01/02/2020] [Accepted: 01/13/2020] [Indexed: 12/21/2022] Open
Abstract
The human brain has been demonstrated to rapidly and continuously form and dissolve networks on a subsecond timescale, offering effective and essential substrates for cognitive processes. Understanding how the dynamic organization of brain functional networks on a subsecond level varies across individuals is, therefore, of great interest for personalized neuroscience. However, it remains unclear whether features of such rapid network organization are reliably unique and stable in single subjects and, therefore, can be used in characterizing individual networks. Here, we used two sets of 5‐min magnetoencephalography (MEG) resting data from 39 healthy subjects over two consecutive days and modeled the spontaneous brain activity as recurring networks fast shifting between each other in a coordinated manner. MEG cortical maps were obtained through source reconstruction using the beamformer method and subjects' temporal structure of recurring networks was obtained via the Hidden Markov Model. Individual organization of dynamic brain activity was quantified with the features of the network‐switching pattern (i.e., transition probability and mean interval time) and the time‐allocation mode (i.e., fractional occupancy and mean lifetime). Using these features, we were able to identify subjects from the group with significant accuracies (~40% on average in 0.5–48 Hz). Notably, the default mode network displayed a distinguishable pattern, being the least frequently visited network with the longest duration for each visit. Together, we provide initial evidence suggesting that the rapid dynamic temporal organization of brain networks achieved in electrophysiology is intrinsic and subject specific.
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Affiliation(s)
- Su Shu
- Beijing City Key Lab for Medical Physics and Engineering, Institution of Heavy Ion Physics, School of Physics, Peking University, Beijing, China.,Center for MRI Research, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China.,McGovern Institute for Brain Research, Peking University, Beijing, China
| | - Lang Qin
- Center for MRI Research, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China.,Department of Linguistics, The University of Hong Kong, Hong Kong, China
| | - Yayan Yin
- Department of Radiology, Xuanwu Hospital of Capital Medical University, Beijing, China
| | - Meizhen Han
- Beijing City Key Lab for Medical Physics and Engineering, Institution of Heavy Ion Physics, School of Physics, Peking University, Beijing, China.,Center for MRI Research, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China.,McGovern Institute for Brain Research, Peking University, Beijing, China
| | - Wei Cui
- Center for MRI Research, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China.,Center for Biomedical Engineering, University of Science and Technology of China, Hefei, Anhui, China
| | - Jia-Hong Gao
- Beijing City Key Lab for Medical Physics and Engineering, Institution of Heavy Ion Physics, School of Physics, Peking University, Beijing, China.,Center for MRI Research, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China.,McGovern Institute for Brain Research, Peking University, Beijing, China
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65
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The Emergence of Integrated Information, Complexity, and 'Consciousness' at Criticality. ENTROPY 2020; 22:e22030339. [PMID: 33286113 PMCID: PMC7516800 DOI: 10.3390/e22030339] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Revised: 03/06/2020] [Accepted: 03/12/2020] [Indexed: 11/16/2022]
Abstract
Integrated Information Theory (IIT) posits that integrated information ( Φ ) represents the quantity of a conscious experience. Here, the generalized Ising model was used to calculate Φ as a function of temperature in toy models of fully connected neural networks. A Monte-Carlo simulation was run on 159 normalized, random, positively weighted networks analogous to small five-node excitatory neural network motifs. Integrated information generated by this sample of small Ising models was measured across model parameter spaces. It was observed that integrated information, as an order parameter, underwent a phase transition at the critical point in the model. This critical point was demarcated by the peak of the generalized susceptibility (or variance in configuration due to temperature) of integrated information. At this critical point, integrated information was maximally receptive and responsive to perturbations of its own states. The results of this study provide evidence that Φ can capture integrated information in an empirical dataset, and display critical behavior acting as an order parameter from the generalized Ising model.
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66
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Ezaki T, Fonseca Dos Reis E, Watanabe T, Sakaki M, Masuda N. Closer to critical resting-state neural dynamics in individuals with higher fluid intelligence. Commun Biol 2020; 3:52. [PMID: 32015402 PMCID: PMC6997374 DOI: 10.1038/s42003-020-0774-y] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2019] [Accepted: 01/13/2020] [Indexed: 01/05/2023] Open
Abstract
According to the critical brain hypothesis, the brain is considered to operate near criticality and realize efficient neural computations. Despite the prior theoretical and empirical evidence in favor of the hypothesis, no direct link has been provided between human cognitive performance and the neural criticality. Here we provide such a key link by analyzing resting-state dynamics of functional magnetic resonance imaging (fMRI) networks at a whole-brain level. We develop a data-driven analysis method, inspired from statistical physics theory of spin systems, to map out the whole-brain neural dynamics onto a phase diagram. Using this tool, we show evidence that neural dynamics of human participants with higher fluid intelligence quotient scores are closer to a critical state, i.e., the boundary between the paramagnetic phase and the spin-glass (SG) phase. The present results are consistent with the notion of "edge-of-chaos" neural computation.
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Affiliation(s)
- Takahiro Ezaki
- PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama, Japan
- Research Center for Advanced Science and Technology, The University of Tokyo, Meguro-ku, Tokyo, Japan
| | | | - Takamitsu Watanabe
- Institute of Cognitive Neuroscience, University College London, 17 Queen Square, London, WC1N 3AZ, UK
- RIKEN Center for Brain Science, Wako, Saitama, Japan
| | - Michiko Sakaki
- School of Psychology and Clinical Language Sciences, University of Reading, Earley Gate, Whiteknights Road, Reading, UK
- Research Institute, Kochi University of Technology, Kami, Kochi, Japan
| | - Naoki Masuda
- Department of Engineering Mathematics, University of Bristol, Clifton, Bristol, UK.
- Department of Mathematics, University at Buffalo, State University of New York, Buffalo, New York, USA.
- Computational and Data-Enabled Science and Engineering Program, University at Buffalo, State University of New York, Buffalo, New York, USA.
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67
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Faqeeh A, Osat S, Radicchi F, Gleeson JP. Emergence of power laws in noncritical neuronal systems. Phys Rev E 2020; 100:010401. [PMID: 31499795 PMCID: PMC7217540 DOI: 10.1103/physreve.100.010401] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2019] [Indexed: 11/07/2022]
Abstract
Experimental and computational studies provide compelling evidence that neuronal systems are characterized by power-law distributions of neuronal avalanche sizes. This fact is interpreted as an indication that these systems are operating near criticality, and, in turn, typical properties of critical dynamical processes, such as optimal information transmission and stability, are attributed to neuronal systems. The purpose of this Rapid Communication is to show that the presence of power-law distributions for the size of neuronal avalanches is not a sufficient condition for the system to operate near criticality. Specifically, we consider a simplistic model of neuronal dynamics on networks and show that the degree distribution of the underlying neuronal network may trigger power-law distributions for neuronal avalanches even when the system is not in its critical regime. To certify and explain our findings we develop an analytical approach based on percolation theory and branching processes techniques.
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Affiliation(s)
- Ali Faqeeh
- Mathematics Consortium for Science and Industry, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland.,Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA
| | - Saeed Osat
- Deep Quantum Labs, Skolkovo Institute of Science and Technology, Moscow 143026, Russia
| | - Filippo Radicchi
- Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA
| | - James P Gleeson
- Mathematics Consortium for Science and Industry, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
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68
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Takagi K. Principles of Mutual Information Maximization and Energy Minimization Affect the Activation Patterns of Large Scale Networks in the Brain. Front Comput Neurosci 2020; 13:86. [PMID: 31998106 PMCID: PMC6962300 DOI: 10.3389/fncom.2019.00086] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2019] [Accepted: 12/12/2019] [Indexed: 12/12/2022] Open
Abstract
Successive patterns of activation and deactivation in local areas of the brain indicate the mechanisms of information processing in the brain. It is possible that this process can be optimized by principles, such as the maximization of mutual information and the minimization of energy consumption. In the present paper, I showed evidence for this argument by demonstrating the correlation among mutual information, the energy of the activation, and the activation patterns. Modeling the information processing based on the functional connectome datasets of the human brain, I simulated information transfer in this network structure. Evaluating the statistical quantities of the different network states, I clarified the correlation between them. First, I showed that mutual information and network energy have a close relationship, and that the values are maximized and minimized around a same network state. This implies that there is an optimal network state in the brain that is organized according to the principles regarding mutual information and energy. On the other hand, the evaluation of the network structure revealed that the characteristic network structure known as the criticality also emerges around this state. These results imply that the characteristic features of the functional network are also affected strongly by these principles. To assess the functional aspects of this state, I investigated the output activation patterns in response to random input stimuli. Measuring the redundancy of the responses in terms of the number of overlapping activation patterns, the results indicate that there is a negative correlation between mutual information and the redundancy in the patterns, suggesting that there is a trade-off between communication efficiency and robustness due to redundancy, and the principles of mutual information and network energy are important to network formation and its function in the human brain.
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69
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Burrows DRW, Samarut É, Liu J, Baraban SC, Richardson MP, Meyer MP, Rosch RE. Imaging epilepsy in larval zebrafish. Eur J Paediatr Neurol 2020; 24:70-80. [PMID: 31982307 PMCID: PMC7035958 DOI: 10.1016/j.ejpn.2020.01.006] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Revised: 01/03/2020] [Accepted: 01/04/2020] [Indexed: 12/19/2022]
Abstract
Our understanding of the genetic aetiology of paediatric epilepsies has grown substantially over the last decade. However, in order to translate improved diagnostics to personalised treatments, there is an urgent need to link molecular pathophysiology in epilepsy to whole-brain dynamics in seizures. Zebrafish have emerged as a promising new animal model for epileptic seizure disorders, with particular relevance for genetic and developmental epilepsies. As a novel model organism for epilepsy research they combine key advantages: the small size of larval zebrafish allows high throughput in vivo experiments; the availability of advanced genetic tools allows targeted modification to model specific human genetic disorders (including genetic epilepsies) in a vertebrate system; and optical access to the entire central nervous system has provided the basis for advanced microscopy technologies to image structure and function in the intact larval zebrafish brain. There is a growing body of literature describing and characterising features of epileptic seizures and epilepsy in larval zebrafish. Recently genetically encoded calcium indicators have been used to investigate the neurobiological basis of these seizures with light microscopy. This approach offers a unique window into the multiscale dynamics of epileptic seizures, capturing both whole-brain dynamics and single-cell behaviour concurrently. At the same time, linking observations made using calcium imaging in the larval zebrafish brain back to an understanding of epileptic seizures largely derived from cortical electrophysiological recordings in human patients and mammalian animal models is non-trivial. In this review we briefly illustrate the state of the art of epilepsy research in zebrafish with particular focus on calcium imaging of epileptic seizures in the larval zebrafish. We illustrate the utility of a dynamic systems perspective on the epileptic brain for providing a principled approach to linking observations across species and identifying those features of brain dynamics that are most relevant to epilepsy. In the following section we survey the literature for imaging features associated with epilepsy and epileptic seizures and link these to observations made from humans and other more traditional animal models. We conclude by identifying the key challenges still facing epilepsy research in the larval zebrafish and indicate strategies for future research to address these and integrate more directly with the themes and questions that emerge from investigating epilepsy in other model systems and human patients.
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Affiliation(s)
- D R W Burrows
- MRC Centre for Neurodevelopmental Disorders, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | - É Samarut
- Department of Neurosciences, Research Center of the University of Montreal Hospital Center, Montreal, Quebec, Canada
| | - J Liu
- Department of Neurological Surgery and Weill Institute for Neuroscience, University of California, San Francisco, San Francisco, CA, USA
| | - S C Baraban
- Department of Neurological Surgery and Weill Institute for Neuroscience, University of California, San Francisco, San Francisco, CA, USA
| | - M P Richardson
- Department of Basic and Clinical Neuroscience, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | - M P Meyer
- MRC Centre for Neurodevelopmental Disorders, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK; Centre for Developmental Neurobiology, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | - R E Rosch
- MRC Centre for Neurodevelopmental Disorders, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK; Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, USA; Department of Paediatric Neurology, Great Ormond Street Hospital for Children NHS Foundation Trust, London, UK.
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70
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Decomposing alpha and 1/f brain activities reveals their differential associations with cognitive processing speed. Neuroimage 2020; 205:116304. [DOI: 10.1016/j.neuroimage.2019.116304] [Citation(s) in RCA: 72] [Impact Index Per Article: 18.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2019] [Revised: 10/12/2019] [Accepted: 10/19/2019] [Indexed: 11/22/2022] Open
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71
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Entropy of the Multi-Channel EEG Recordings Identifies the Distributed Signatures of Negative, Neutral and Positive Affect in Whole-Brain Variability. ENTROPY 2019. [PMCID: PMC7514573 DOI: 10.3390/e21121228] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Individuals’ ability to express their subjective experiences in terms of such attributes as pleasant/unpleasant or positive/negative feelings forms a fundamental property of their affect and emotion. However, neuroscientific findings on the underlying neural substrates of the affect appear to be inconclusive with some reporting the presence of distinct and independent brain systems and others identifying flexible and distributed brain regions. A common theme among these studies is the focus on the change in brain activation. As a result, they do not take into account the findings that indicate the brain activation and its information content does not necessarily modulate and that the stimuli with equivalent sensory and behavioural processing demands may not necessarily result in differential brain activation. In this article, we take a different stance on the analysis of the differential effect of the negative, neutral and positive affect on the brain functioning in which we look into the whole-brain variability: that is the change in the brain information processing measured in multiple distributed regions. For this purpose, we compute the entropy of individuals’ muti-channel EEG recordings who watched movie clips with differing affect. Our results suggest that the whole-brain variability significantly differentiates between the negative, neutral and positive affect. They also indicate that although some brain regions contribute more to such differences, it is the whole-brain variational pattern that results in their significantly above chance level prediction. These results imply that although the underlying brain substrates for negative, neutral and positive affect exhibit quantitatively differing degrees of variability, their differences are rather subtly encoded in the whole-brain variational patterns that are distributed across its entire activity.
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72
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Aguilera M. Scaling Behaviour and Critical Phase Transitions in Integrated Information Theory. ENTROPY 2019. [PMCID: PMC7514544 DOI: 10.3390/e21121198] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Integrated Information Theory proposes a measure of conscious activity (Φ), characterised as the irreducibility of a dynamical system to the sum of its components. Due to its computational cost, current versions of the theory (IIT 3.0) are difficult to apply to systems larger than a dozen units, and, in general, it is not well known how integrated information scales as systems grow larger in size. In this article, we propose to study the scaling behaviour of integrated information in a simple model of a critical phase transition: an infinite-range kinetic Ising model. In this model, we assume a homogeneous distribution of couplings to simplify the computation of integrated information. This simplified model allows us to critically review some of the design assumptions behind the measure and connect its properties with well-known phenomena in phase transitions in statistical mechanics. As a result, we point to some aspects of the mathematical definitions of IIT that 3.0 fail to capture critical phase transitions and propose a reformulation of the assumptions made by integrated information measures.
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Affiliation(s)
- Miguel Aguilera
- IAS-Research Center for Life, Mind and Society, University of the Basque Country, 20018 Donostia, Spain;
- ISAAC Lab, Aragón Institute of Engineering Research, University of Zaragoza, 50018 Zaragoza, Spain
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73
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Trujillo LT. Mental Effort and Information-Processing Costs Are Inversely Related to Global Brain Free Energy During Visual Categorization. Front Neurosci 2019; 13:1292. [PMID: 31866809 PMCID: PMC6906157 DOI: 10.3389/fnins.2019.01292] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2019] [Accepted: 11/14/2019] [Indexed: 12/19/2022] Open
Abstract
Mental effort is a neurocognitive process that reflects the controlled expenditure of psychological information-processing resources during perception, cognition, and action. There is a practical need to operationalize and measure mental effort in order to minimize detrimental effects of mental fatigue on real-world human performance. Previous research has identified several neurocognitive indices of mental effort, but these indices are indirect measures that are also sensitive to experimental demands or general factors such as sympathetic arousal. The present study investigated a potential direct neurocognitive index of mental effort based in theories where bounded rational decision makers (realized as embodied brains) are modeled as generalized thermodynamic systems. This index is called free energy, an information-theoretic system property of the brain that reflects the difference between the brain's current and predicted states. Theory predicts that task-related differences in a decision makers' free energy are inversely related to information-processing costs related to task decisions. The present study tested this prediction by quantifying global brain free energy from electroencephalographic (EEG) measures of human brain function. EEG signals were recorded while participants engaged in two visual categorization tasks in which categorization decisions resulted from the allocation of different levels of mental information processing resources. A novel method was developed to quantify brain free energy from machine learning classification of EEG trials. Participant information-processing resource costs were estimated via computational analysis of behavior, whereas the subjective expression of mental effort was estimated via participant ratings of mental workload. Following theoretical predictions, task-related differences in brain free energy negatively correlated with increased allocation of information-processing resource costs. These brain free energy differences were smaller for the visual categorization task that required a greater versus lesser allocation of information-processing resources. Ratings of mental workload were positively correlated with information-processing resource costs, and negatively correlated with global brain free energy differences, only for the categorization task requiring the larger amount of information-processing resource costs. These findings support theoretical thermodynamic approaches to decision making and provide the first empirical evidence of a relationship between mental effort, brain free energy, and neurocognitive information-processing.
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Affiliation(s)
- Logan T Trujillo
- Department of Psychology, Texas State University, San Marcos, TX, United States
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74
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Putting the variability–stability–flexibility pattern to use: Adapting instruction to how children develop. NEW IDEAS IN PSYCHOLOGY 2019. [DOI: 10.1016/j.newideapsych.2019.04.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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75
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Lima Dias Pinto I, Copelli M. Oscillations and collective excitability in a model of stochastic neurons under excitatory and inhibitory coupling. Phys Rev E 2019; 100:062416. [PMID: 31962449 DOI: 10.1103/physreve.100.062416] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2019] [Indexed: 06/10/2023]
Abstract
We study a model with excitable neurons modeled as stochastic units with three states, representing quiescence, firing, and refractoriness. The transition rates between quiescence and firing depend exponentially on the number of firing neighbors, whereas all other rates are kept constant. This model class was shown to exhibit collective oscillations (synchronization) if neurons are spiking autonomously, but not if neurons are in the excitable regime. In both cases, neurons were restricted to interact through excitatory coupling. Here we show that a plethora of collective phenomena appear if inhibitory coupling is added. Besides the usual transition between an absorbing and an active phase, the model with excitatory and inhibitory neurons can also undergo reentrant transitions to an oscillatory phase. In the mean-field description, oscillations can emerge through supercritical or subcritical Hopf bifurcations, as well as through infinite period bifurcations. The model has bistability between active and oscillating behavior, as well as collective excitability, a regime where the system can display a peak of global activity when subject to a sufficiently strong perturbation. We employ a variant of the Shinomoto-Kuramoto order parameter to characterize the phase transitions and their system-size dependence.
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Affiliation(s)
| | - Mauro Copelli
- Physics Department, Federal University of Pernambuco (UFPE), Recife, PE 50670-901, Brazil
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76
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Abstract
Integrated information theory (IIT) describes consciousness as information integrated across highly differentiated but irreducible constituent parts in a system. However, in a complex dynamic system such as the brain, the optimal conditions for large integrated information systems have not been elucidated. In this study, we hypothesized that network criticality, a balanced state between a large variation in functional network configuration and a large constraint on structural network configuration, may be the basis of the emergence of a large Φ¯, a surrogate of integrated information. We also hypothesized that as consciousness diminishes, the brain loses network criticality and Φ¯ decreases. We tested these hypotheses with a large-scale brain network model and high-density electroencephalography (EEG) acquired during various levels of human consciousness under general anesthesia. In the modeling study, maximal criticality coincided with maximal Φ¯. The EEG study demonstrated an explicit relationship between Φ¯, criticality, and level of consciousness. The conscious resting state showed the largest Φ¯ and criticality, whereas the balance between variation and constraint in the brain network broke down as the response rate dwindled. The results suggest network criticality as a necessary condition of a large Φ¯ in the human brain.
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77
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Ma Z, Turrigiano GG, Wessel R, Hengen KB. Cortical Circuit Dynamics Are Homeostatically Tuned to Criticality In Vivo. Neuron 2019; 104:655-664.e4. [PMID: 31601510 DOI: 10.1016/j.neuron.2019.08.031] [Citation(s) in RCA: 105] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2019] [Revised: 06/26/2019] [Accepted: 08/19/2019] [Indexed: 11/26/2022]
Abstract
Homeostatic mechanisms stabilize neuronal activity in vivo, but whether this process gives rise to balanced network dynamics is unknown. Here, we continuously monitored the statistics of network spiking in visual cortical circuits in freely behaving rats for 9 days. Under control conditions in light and dark, networks were robustly organized around criticality, a regime that maximizes information capacity and transmission. When input was perturbed by visual deprivation, network criticality was severely disrupted and subsequently restored to criticality over 48 h. Unexpectedly, the recovery of excitatory dynamics preceded homeostatic plasticity of firing rates by >30 h. We utilized model investigations to manipulate firing rate homeostasis in a cell-type-specific manner at the onset of visual deprivation. Our results suggest that criticality in excitatory networks is established by inhibitory plasticity and architecture. These data establish that criticality is consistent with a homeostatic set point for visual cortical dynamics and suggest a key role for homeostatic regulation of inhibition.
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Affiliation(s)
- Zhengyu Ma
- Department of Physics, Washington University in St. Louis, St. Louis, MO 63130, USA
| | | | - Ralf Wessel
- Department of Physics, Washington University in St. Louis, St. Louis, MO 63130, USA
| | - Keith B Hengen
- Department of Biology, Washington University in St. Louis, St. Louis, MO 63130, USA.
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78
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Bocaccio H, Pallavicini C, Castro MN, Sánchez SM, De Pino G, Laufs H, Villarreal MF, Tagliazucchi E. The avalanche-like behaviour of large-scale haemodynamic activity from wakefulness to deep sleep. J R Soc Interface 2019; 16:20190262. [PMID: 31506046 PMCID: PMC6769314 DOI: 10.1098/rsif.2019.0262] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Accepted: 08/08/2019] [Indexed: 02/02/2023] Open
Abstract
Increasing evidence suggests that responsiveness is associated with critical or near-critical cortical dynamics, which exhibit scale-free cascades of spatio-temporal activity. These cascades, or 'avalanches', have been detected at multiple scales, from in vitro and in vivo microcircuits to voltage imaging and brain-wide functional magnetic resonance imaging (fMRI) recordings. Criticality endows the cortex with certain information-processing capacities postulated as necessary for conscious wakefulness, yet it remains unknown how unresponsiveness impacts on the avalanche-like behaviour of large-scale human haemodynamic activity. We observed a scale-free hierarchy of co-activated connected clusters by applying a point-process transformation to fMRI data recorded during wakefulness and non-rapid eye movement (NREM) sleep. Maximum-likelihood estimates revealed a significant effect of sleep stage on the scaling parameters of the cluster size power-law distributions. Post hoc statistical tests showed that differences were maximal between wakefulness and N2 sleep. These results were robust against spatial coarse graining, fitting alternative statistical models and different point-process thresholds, and disappeared upon phase shuffling the fMRI time series. Evoked neural bistabilities preventing arousals during N2 sleep do not suffice to explain these differences, which point towards changes in the intrinsic dynamics of the brain that could be necessary to consolidate a state of deep unresponsiveness.
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Affiliation(s)
- H. Bocaccio
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - C. Pallavicini
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - M. N. Castro
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Fisiología, Facultad de Medicina, UBA, Buenos Aires, Argentina
- Departamento Salud Mental, Unidad Docente FLENI, Facultad de Medicina, UBA, Buenos Aires, Argentina
| | - S. M. Sánchez
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - G. De Pino
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- Laboratorio de Neuroimágenes, Departamento de Imágenes, FLENI, Buenos Aires, Argentina
- Escuela de Ciencia y Tecnología (ECyT), Universidad Nacional de San Martín, Argentina
| | - H. Laufs
- Department of Neurology, Christian-Albrechts-University, Kiel, Germany
| | - M. F. Villarreal
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - E. Tagliazucchi
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
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79
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Wilting J, Priesemann V. 25 years of criticality in neuroscience - established results, open controversies, novel concepts. Curr Opin Neurobiol 2019; 58:105-111. [PMID: 31546053 DOI: 10.1016/j.conb.2019.08.002] [Citation(s) in RCA: 66] [Impact Index Per Article: 13.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Accepted: 08/25/2019] [Indexed: 12/19/2022]
Abstract
Twenty-five years ago, Dunkelmann and Radons (1994) showed that neural networks can self-organize to a critical state. In models, the critical state offers a number of computational advantages. Thus this hypothesis, and in particular the experimental work by Beggs and Plenz (2003), has triggered an avalanche of research, with thousands of studies referring to it. Nonetheless, experimental results are still contradictory. How is it possible, that a hypothesis has attracted active research for decades, but nonetheless remains controversial? We discuss the experimental and conceptual controversy, and then present a parsimonious solution that (i) unifies the contradictory experimental results, (ii) avoids disadvantages of a critical state, and (iii) enables rapid, adaptive tuning of network properties to task requirements.
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Affiliation(s)
- J Wilting
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - V Priesemann
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany; Bernstein-Center for Computational Neuroscience, Göttingen, Germany
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80
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Villegas P, di Santo S, Burioni R, Muñoz MA. Time-series thresholding and the definition of avalanche size. Phys Rev E 2019; 100:012133. [PMID: 31499802 DOI: 10.1103/physreve.100.012133] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2019] [Indexed: 11/07/2022]
Abstract
Avalanches whose sizes and durations are distributed as power laws appear in many contexts, from physics to geophysics and biology. Here we show that there is a hidden peril in thresholding continuous times series-from either empirical or synthetic data-for the identification of avalanches. In particular, we consider two possible alternative definitions of avalanche size used, e.g., in the empirical determination of avalanche exponents in the analysis of neural-activity data. By performing analytical and computational studies of an Ornstein-Uhlenbeck process (taken as a guiding example) we show that (1) if relatively large threshold values are employed to determine the beginning and ending of avalanches and (2) if-as sometimes done in the literature-avalanche sizes are defined as the total area (above zero) of the avalanche, then true asymptotic scaling behavior is not seen, instead the observations are dominated by transient effects. This problem-that we have detected in some recent works-leads to misinterpretations of the resulting scaling regimes.
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Affiliation(s)
- Pablo Villegas
- Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain
| | - Serena di Santo
- Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain.,Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, via G.P. Usberti, 7/A-43124, Parma, Italy.,INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A-43124, Parma, Italy
| | - Raffaella Burioni
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, via G.P. Usberti, 7/A-43124, Parma, Italy.,INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A-43124, Parma, Italy
| | - Miguel A Muñoz
- Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain.,Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, via G.P. Usberti, 7/A-43124, Parma, Italy
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81
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Santos FAN, Raposo EP, Coutinho-Filho MD, Copelli M, Stam CJ, Douw L. Topological phase transitions in functional brain networks. Phys Rev E 2019; 100:032414. [PMID: 31640025 DOI: 10.1103/physreve.100.032414] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2018] [Indexed: 06/10/2023]
Abstract
Functional brain networks are often constructed by quantifying correlations between time series of activity of brain regions. Their topological structure includes nodes, edges, triangles, and even higher-dimensional objects. Topological data analysis (TDA) is the emerging framework to process data sets under this perspective. In parallel, topology has proven essential for understanding fundamental questions in physics. Here we report the discovery of topological phase transitions in functional brain networks by merging concepts from TDA, topology, geometry, physics, and network theory. We show that topological phase transitions occur when the Euler entropy has a singularity, which remarkably coincides with the emergence of multidimensional topological holes in the brain network. The geometric nature of the transitions can be interpreted, under certain hypotheses, as an extension of percolation to high-dimensional objects. Due to the universal character of phase transitions and noise robustness of TDA, our findings open perspectives toward establishing reliable topological and geometrical markers for group and possibly individual differences in functional brain network organization.
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Affiliation(s)
- Fernando A N Santos
- Departamento de Matemática, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil and Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil
| | - Ernesto P Raposo
- Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil
| | - Maurício D Coutinho-Filho
- Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil
| | - Mauro Copelli
- Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil
| | - Cornelis J Stam
- Department of Clinical Neurophysiology and MEG Center, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam Neuroscience, 1081 HV, Amsterdam, The Netherlands
| | - Linda Douw
- Department of Anatomy & Neurosciences, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam Neuroscience, 1081 HZ, Amsterdam, The Netherlands
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82
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Pospelov N, Nechaev S, Anokhin K, Valba O, Avetisov V, Gorsky A. Spectral peculiarity and criticality of a human connectome. Phys Life Rev 2019; 31:240-256. [PMID: 31353222 DOI: 10.1016/j.plrev.2019.07.003] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2019] [Accepted: 07/06/2019] [Indexed: 12/12/2022]
Abstract
We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our results indicate new peculiar features of connectomes of higher organisms. We found that the spectral density of adjacency matrices of human connectome has maximal deviation from the one of randomized network, compared to other organisms. Considering the network evolution induced by the preference of 3-cycles formation, we discovered that for macaque and human connectomes the evolution with the conservation of local clusterization is crucial, while for primitive organisms the conservation of averaged clusterization is sufficient. Investigating for the first time the level spacing distribution of the spectrum of human connectome Laplacian matrix, we explicitly demonstrate that the spectral statistics corresponds to the critical regime, which is hybrid of Wigner-Dyson and Poisson distributions. This observation provides strong support for debated statement of the brain criticality.
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Affiliation(s)
- N Pospelov
- Lomonosov Moscow State University, 119991, Moscow, Russia
| | - S Nechaev
- Interdisciplinary Scientific Center Poncelet (CNRS UMI 2615), 119002 Moscow, Russia; P.N. Lebedev Physical Institute RAS, Moscow, Russia.
| | - K Anokhin
- Lomonosov Moscow State University, 119991, Moscow, Russia; National Research Center "Kurchatov Institute", 123098, Moscow, Russia
| | - O Valba
- N.N. Semenov Institute of Chemical Physics RAS, 119991 Moscow, Russia; Department of Applied Mathematics, National Research University Higher School of Economics, 101000 Moscow, Russia
| | - V Avetisov
- N.N. Semenov Institute of Chemical Physics RAS, 119991 Moscow, Russia
| | - A Gorsky
- Institute for Information Transmission Problems RAS, 127051 Moscow, Russia; Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Russia
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83
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Tyukin IY, Iudin D, Iudin F, Tyukina T, Kazantsev V, Mukhina I, Gorban AN. Simple model of complex dynamics of activity patterns in developing networks of neuronal cultures. PLoS One 2019; 14:e0218304. [PMID: 31246978 PMCID: PMC6597067 DOI: 10.1371/journal.pone.0218304] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2018] [Accepted: 05/30/2019] [Indexed: 12/16/2022] Open
Abstract
Living neuronal networks in dissociated neuronal cultures are widely known for their ability to generate highly robust spatiotemporal activity patterns in various experimental conditions. Such patterns are often treated as neuronal avalanches that satisfy the power scaling law and thereby exemplify self-organized criticality in living systems. A crucial question is how these patterns can be explained and modeled in a way that is biologically meaningful, mathematically tractable and yet broad enough to account for neuronal heterogeneity and complexity. Here we derive and analyse a simple network model that may constitute a response to this question. Our derivations are based on few basic phenomenological observations concerning the input-output behavior of an isolated neuron. A distinctive feature of the model is that at the simplest level of description it comprises of only two variables, the network activity variable and an exogenous variable corresponding to energy needed to sustain the activity, and few parameters such as network connectivity and efficacy of signal transmission. The efficacy of signal transmission is modulated by the phenomenological energy variable. Strikingly, this simple model is already capable of explaining emergence of network spikes and bursts in developing neuronal cultures. The model behavior and predictions are consistent with published experimental evidence on cultured neurons. At the larger, cellular automata scale, introduction of the energy-dependent regulatory mechanism results in the overall model behavior that can be characterized as balancing on the edge of the network percolation transition. Network activity in this state shows population bursts satisfying the scaling avalanche conditions. This network state is self-sustainable and represents energetic balance between global network-wide processes and spontaneous activity of individual elements.
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Affiliation(s)
- Ivan Y. Tyukin
- Nizhny Novgorod State University, Nizhny Novgorod, Russia
- Saint-Petersburg State Electrotechnical University (LETI), Saint-Petersburg, Russia
- University of Leicester, Leicester, United Kingdom
- * E-mail:
| | - Dmitriy Iudin
- Nizhny Novgorod State University, Nizhny Novgorod, Russia
- Institute of Applied Physics of RAS, Nizhny Novgorod, Russia
| | - Feodor Iudin
- Nizhny Novgorod State University, Nizhny Novgorod, Russia
| | | | - Victor Kazantsev
- Nizhny Novgorod State University, Nizhny Novgorod, Russia
- Institute of Applied Physics of RAS, Nizhny Novgorod, Russia
| | - Irina Mukhina
- Nizhny Novgorod State University, Nizhny Novgorod, Russia
| | - Alexander N. Gorban
- Nizhny Novgorod State University, Nizhny Novgorod, Russia
- University of Leicester, Leicester, United Kingdom
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84
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Moyal R, Edelman S. Dynamic Computation in Visual Thalamocortical Networks. ENTROPY (BASEL, SWITZERLAND) 2019; 21:E500. [PMID: 33267214 PMCID: PMC7514988 DOI: 10.3390/e21050500] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 03/13/2019] [Revised: 05/10/2019] [Accepted: 05/14/2019] [Indexed: 02/06/2023]
Abstract
Contemporary neurodynamical frameworks, such as coordination dynamics and winnerless competition, posit that the brain approximates symbolic computation by transitioning between metastable attractive states. This article integrates these accounts with electrophysiological data suggesting that coherent, nested oscillations facilitate information representation and transmission in thalamocortical networks. We review the relationship between criticality, metastability, and representational capacity, outline existing methods for detecting metastable oscillatory patterns in neural time series data, and evaluate plausible spatiotemporal coding schemes based on phase alignment. We then survey the circuitry and the mechanisms underlying the generation of coordinated alpha and gamma rhythms in the primate visual system, with particular emphasis on the pulvinar and its role in biasing visual attention and awareness. To conclude the review, we begin to integrate this perspective with longstanding theories of consciousness and cognition.
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Affiliation(s)
- Roy Moyal
- Department of Psychology, Cornell University, Ithaca, NY 14853, USA
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85
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Ashourvan A, Telesford QK, Verstynen T, Vettel JM, Bassett DS. Multi-scale detection of hierarchical community architecture in structural and functional brain networks. PLoS One 2019; 14:e0215520. [PMID: 31071099 PMCID: PMC6508662 DOI: 10.1371/journal.pone.0215520] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2018] [Accepted: 04/03/2019] [Indexed: 12/31/2022] Open
Abstract
Community detection algorithms have been widely used to study the organization of complex networks like the brain. These techniques provide a partition of brain regions (or nodes) into clusters (or communities), where nodes within a community are densely interconnected with one another. In their simplest application, community detection algorithms are agnostic to the presence of community hierarchies: clusters embedded within clusters of other clusters. To address this limitation, we exercise a multi-scale extension of a common community detection technique, and we apply the tool to synthetic graphs and to graphs derived from human neuroimaging data, including structural and functional imaging data. Our multi-scale community detection algorithm links a graph to copies of itself across neighboring topological scales, thereby becoming sensitive to conserved community organization across levels of the hierarchy. We demonstrate that this method is sensitive to topological inhomogeneities of the graph's hierarchy by providing a local measure of community stability and inter-scale reliability across topological scales. We compare the brain's structural and functional network architectures, and we demonstrate that structural graphs display a more prominent hierarchical community organization than functional graphs. Finally, we build an explicitly multimodal multiplex graph that combines both structural and functional connectivity in a single model, and we identify the topological scales where resting state functional connectivity and underlying structural connectivity show similar versus unique hierarchical community architecture. Together, our results demonstrate the advantages of the multi-scale community detection algorithm in studying hierarchical community structure in brain graphs, and they illustrate its utility in modeling multimodal neuroimaging data.
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Affiliation(s)
- Arian Ashourvan
- Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA, 19104 United States of America
- U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 United States of America
| | - Qawi K. Telesford
- Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA, 19104 United States of America
- U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 United States of America
| | - Timothy Verstynen
- Department of Psychology, Center for the Neural Basis of Cognition, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 United States of America
| | - Jean M. Vettel
- Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA, 19104 United States of America
- U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 United States of America
- Department of Psychological & Brain Sciences, University of California, Santa Barbara, CA, 93106 United States of America
| | - Danielle S. Bassett
- Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA, 19104 United States of America
- Department of Electrical & Systems Engineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA 19104 United States of America
- Department of Physics & Astronomy, College of Arts & Sciences, University of Pennsylvania, Philadelphia, PA 19104 United States of America
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104 United States of America
- Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104 United States of America
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86
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Shine JM. Neuromodulatory Influences on Integration and Segregation in the Brain. Trends Cogn Sci 2019; 23:572-583. [PMID: 31076192 DOI: 10.1016/j.tics.2019.04.002] [Citation(s) in RCA: 123] [Impact Index Per Article: 24.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2018] [Revised: 04/01/2019] [Accepted: 04/04/2019] [Indexed: 12/20/2022]
Abstract
Cognitive function relies on the dynamic cooperation of specialized regions of the brain; however, the elements of the system responsible for coordinating this interaction remain poorly understood. In this Opinion article I argue that this capacity is mediated in part by competitive and cooperative dynamic interactions between two prominent metabotropic neuromodulatory systems - the cholinergic basal forebrain and the noradrenergic locus coeruleus (LC). I assert that activity in these projection nuclei regulates the amount of segregation and integration within the whole brain network by modulating the activity of a diverse set of specialized regions of the brain on a timescale relevant for cognition and attention.
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Affiliation(s)
- James M Shine
- Brain and Mind Centre, The University of Sydney, Sydney, NSW, Australia.
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87
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Single-Cell Membrane Potential Fluctuations Evince Network Scale-Freeness and Quasicriticality. J Neurosci 2019; 39:4738-4759. [PMID: 30952810 DOI: 10.1523/jneurosci.3163-18.2019] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Revised: 03/01/2019] [Accepted: 03/25/2019] [Indexed: 11/21/2022] Open
Abstract
What information single neurons receive about general neural circuit activity is a fundamental question for neuroscience. Somatic membrane potential (V m) fluctuations are driven by the convergence of synaptic inputs from a diverse cross-section of upstream neurons. Furthermore, neural activity is often scale-free, implying that some measurements should be the same, whether taken at large or small scales. Together, convergence and scale-freeness support the hypothesis that single V m recordings carry useful information about high-dimensional cortical activity. Conveniently, the theory of "critical branching networks" (one purported explanation for scale-freeness) provides testable predictions about scale-free measurements that are readily applied to V m fluctuations. To investigate, we obtained whole-cell current-clamp recordings of pyramidal neurons in visual cortex of turtles with unknown genders. We isolated fluctuations in V m below the firing threshold and analyzed them by adapting the definition of "neuronal avalanches" (i.e., spurts of population spiking). The V m fluctuations which we analyzed were scale-free and consistent with critical branching. These findings recapitulated results from large-scale cortical population data obtained separately in complementary experiments using microelectrode arrays described previously (Shew et al., 2015). Simultaneously recorded single-unit local field potential did not provide a good match, demonstrating the specific utility of V m Modeling shows that estimation of dynamical network properties from neuronal inputs is most accurate when networks are structured as critical branching networks. In conclusion, these findings extend evidence of critical phenomena while also establishing subthreshold pyramidal neuron V m fluctuations as an informative gauge of high-dimensional cortical population activity.SIGNIFICANCE STATEMENT The relationship between membrane potential (V m) dynamics of single neurons and population dynamics is indispensable to understanding cortical circuits. Just as important to the biophysics of computation are emergent properties such as scale-freeness, where critical branching networks offer insight. This report makes progress on both fronts by comparing statistics from single-neuron whole-cell recordings with population statistics obtained with microelectrode arrays. Not only are fluctuations of somatic V m scale-free, they match fluctuations of population activity. Thus, our results demonstrate appropriation of the brain's own subsampling method (convergence of synaptic inputs) while extending the range of fundamental evidence for critical phenomena in neural systems from the previously observed mesoscale (fMRI, LFP, population spiking) to the microscale, namely, V m fluctuations.
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88
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Georgiadis D, Sornette D. Pattern phase diagram of spiking neurons on spatial networks. Phys Rev E 2019; 99:042410. [PMID: 31108692 DOI: 10.1103/physreve.99.042410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2018] [Indexed: 06/09/2023]
Abstract
We study an abstracted model of neuronal activity via numerical simulation and report spatiotemporal pattern formation and criticallike dynamics. A population of pulse coupled, discretized, relaxation oscillators is simulated over networks with varying edge density and spatial embeddedness. For intermediate edge density and sufficiently strong spatial embeddedness, we observe a spatiotemporal pattern in the field of oscillator phases, visually resembling the surface of a frothing liquid. Increasing the edge density results in a distribution of neuronal avalanche sizes which follows a power law with exponent one (Zipf's law). Further increasing edge density yields metastability between pattern formation and synchronization, before transitioning entirely into synchrony.
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Affiliation(s)
- Dionysios Georgiadis
- Future Resilient Systems, Singapore and Department of Management, Technology and Economics, ETH Zurich, Switzerland
| | - Didier Sornette
- Department of Management, Technology and Economics, ETH Zurich, Switzerland
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89
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Estevez-Rams E, Estevez-Moya D, Garcia-Medina K, Lora-Serrano R. Computational capabilities at the edge of chaos for one dimensional systems undergoing continuous transitions. CHAOS (WOODBURY, N.Y.) 2019; 29:043105. [PMID: 31042953 DOI: 10.1063/1.5062364] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2018] [Accepted: 03/11/2019] [Indexed: 06/09/2023]
Abstract
While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular automata, there is an enhancement of computation capabilities as the system moves towards cellular automata with chaotic spatiotemporal behavior. The computation capabilities are followed by looking into the Shannon entropy rate and the excess entropy, which allow identifying the balance between unpredictability and complexity. Enhanced computation power shows an increase of excess entropy, while the system entropy density has a sudden jump to values near one. The analysis is extended to a system of non-linear locally coupled oscillators that have been reported to exhibit spatiotemporal diagrams similar to cellular automata.
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Affiliation(s)
- E Estevez-Rams
- Facultad de Física, Instituto de Ciencias y Tecnología de Materiales (IMRE), University of Havana, San Lazaro y L, La Habana CP 10400, Cuba
| | - D Estevez-Moya
- Facultad de Física, University of Havana, San Lazaro y L, La Habana CP 10400, Cuba
| | - K Garcia-Medina
- Facultad de Física, University of Havana, San Lazaro y L, La Habana CP 10400, Cuba
| | - R Lora-Serrano
- Instituto de Física, Universidade Federal de Uberlandia, Av. Joao Naves de Avila, 2121-Campus Santa Monica, Uberlandia, Minas Gerais CEP 38408-144, Brazil
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90
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Hu G, Huang X, Jiang T, Yu S. Multi-Scale Expressions of One Optimal State Regulated by Dopamine in the Prefrontal Cortex. Front Physiol 2019; 10:113. [PMID: 30873039 PMCID: PMC6404637 DOI: 10.3389/fphys.2019.00113] [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: 09/28/2018] [Accepted: 01/30/2019] [Indexed: 11/13/2022] Open
Abstract
The prefrontal cortex (PFC), which plays key roles in many higher cognitive processes, is a hierarchical system consisting of multi-scale organizations. Optimizing the working state at each scale is essential for PFC's information processing. Typical optimal working states at different scales have been separately reported, including the dopamine-mediated inverted-U profile of the working memory (WM) at the system level, critical dynamics at the network level, and detailed balance of excitatory and inhibitory currents (E/I balance) at the cellular level. However, it remains unclear whether these states are scale-specific expressions of the same optimal state and, if so, what is the underlying mechanism for its regulation traversing across scales. Here, by studying a neural network model, we show that the optimal performance of WM co-occurs with the critical dynamics at the network level and the E/I balance at the level of individual neurons, suggesting the existence of a unified, multi-scale optimal state for the PFC. Importantly, such a state could be modulated by dopamine at the synaptic level through a series of U or inverted-U profiles. These results suggest that seemingly different optimal states for specific scales are multi-scale expressions of one condition regulated by dopamine. Our work suggests a cross-scale perspective to understand the PFC function and its modulation.
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Affiliation(s)
- Guyue Hu
- Brainnetome Center, Institute of Automation, Chinese Academy of Sciences, Beijing, China.,National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing, China.,University of Chinese Academy of Sciences, Beijing, China
| | - Xuhui Huang
- Brainnetome Center, Institute of Automation, Chinese Academy of Sciences, Beijing, China.,National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing, China.,Research Center for Brain-inspired Intelligence, Institute of Automation, Chinese Academy of Sciences, Beijing, China.,CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Beijing, China
| | - Tianzi Jiang
- Brainnetome Center, Institute of Automation, Chinese Academy of Sciences, Beijing, China.,National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing, China.,CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Beijing, China.,University of Chinese Academy of Sciences, Beijing, China
| | - Shan Yu
- Brainnetome Center, Institute of Automation, Chinese Academy of Sciences, Beijing, China.,National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing, China.,CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Beijing, China.,University of Chinese Academy of Sciences, Beijing, China
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91
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Kinouchi O, Brochini L, Costa AA, Campos JGF, Copelli M. Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems. Sci Rep 2019; 9:3874. [PMID: 30846773 PMCID: PMC6405991 DOI: 10.1038/s41598-019-40473-1] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2018] [Accepted: 01/28/2019] [Indexed: 12/04/2022] Open
Abstract
In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all these systems present stochastic oscillations hovering around the critical region that are incompatible with standard SOC. Here we make a linear stability analysis of the mean field fixed points of two self-organized quasi-critical systems: a fully connected network of discrete time stochastic spiking neurons with firing rate adaptation produced by dynamic neuronal gains and an excitable cellular automata with depressing synapses. We find that the fixed point corresponds to a stable focus that loses stability at criticality. We argue that when this focus is close to become indifferent, demographic noise can elicit stochastic oscillations that frequently fall into the absorbing state. This mechanism interrupts the oscillations, producing both power law avalanches and dragon king events, which appear as bands of synchronized firings in raster plots. Our approach differs from standard SOC models in that it predicts the coexistence of these different types of neuronal activity.
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Affiliation(s)
- Osame Kinouchi
- Universidade de São Paulo, Departamento de Física-FFCLRP, Ribeirão Preto, SP, Brazil.
| | - Ludmila Brochini
- Universidade de São Paulo, Instituto de Matemática e Estatística, São Paulo, SP, Brazil
| | - Ariadne A Costa
- Universidade Federal de Goiás, Unidade Acadêmica Especial de Ciências Exatas, Jataí, GO, Brazil
| | | | - Mauro Copelli
- Universidade de São Paulo, Departamento de Física-FFCLRP, Ribeirão Preto, SP, Brazil.,Universidade Federal de Pernambuco, Departamento de Física, Recife, PE, Brazil
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92
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Turkheimer FE, Hellyer P, Kehagia AA, Expert P, Lord LD, Vohryzek J, De Faria Dafflon J, Brammer M, Leech R. Conflicting emergences. Weak vs. strong emergence for the modelling of brain function. Neurosci Biobehav Rev 2019; 99:3-10. [PMID: 30684520 DOI: 10.1016/j.neubiorev.2019.01.023] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2018] [Revised: 01/11/2019] [Accepted: 01/19/2019] [Indexed: 02/03/2023]
Abstract
The concept of "emergence" has become commonplace in the modelling of complex systems, both natural and man-made; a functional property" emerges" from a system when it cannot be readily explained by the properties of the system's sub-units. A bewildering array of adaptive and sophisticated behaviours can be observed from large ensembles of elementary agents such as ant colonies, bird flocks or by the interactions of elementary material units such as molecules or weather elements. Ultimately, emergence has been adopted as the ontological support of a number of attempts to model brain function. This manuscript aims to clarify the ontology of emergence and delve into its many facets, particularly into its "strong" and "weak" versions that underpin two different approaches to the modelling of behaviour. The first group of models is here represented by the "free energy" principle of brain function and the "integrated information theory" of consciousness. The second group is instead represented by computational models such as oscillatory networks that use mathematical scalable representations to generate emergent behaviours and are then able to bridge neurobiology with higher mental functions. Drawing on the epistemological literature, we observe that due to their loose mechanistic links with the underlying biology, models based on strong forms of emergence are at risk of metaphysical implausibility. This, in practical terms, translates into the over determination that occurs when the proposed model becomes only one of a large set of possible explanations for the observable phenomena. On the other hand, computational models that start from biologically plausible elementary units, hence are weakly emergent, are not limited by ontological faults and, if scalable and able to realistically simulate the hierarchies of brain output, represent a powerful vehicle for future neuroscientific research programmes.
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Affiliation(s)
| | | | | | - Paul Expert
- EPSRC Centre for Mathematics of Precision Healthcare, Imperial College London, UK
| | | | | | | | - Mick Brammer
- Institute of Psychiatry, King's College London, UK
| | - Robert Leech
- Institute of Psychiatry, King's College London, UK
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93
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Trujillo LT. K-th Nearest Neighbor (KNN) Entropy Estimates of Complexity and Integration from Ongoing and Stimulus-Evoked Electroencephalographic (EEG) Recordings of the Human Brain. ENTROPY 2019; 21:e21010061. [PMID: 33266777 PMCID: PMC7514170 DOI: 10.3390/e21010061] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/08/2018] [Revised: 01/10/2019] [Accepted: 01/11/2019] [Indexed: 12/02/2022]
Abstract
Information-theoretic measures for quantifying multivariate statistical dependence have proven useful for the study of the unity and diversity of the human brain. Two such measures–integration, I(X), and interaction complexity, CI(X)–have been previously applied to electroencephalographic (EEG) signals recorded during ongoing wakeful brain states. Here, I(X) and CI(X) were computed for empirical and simulated visually-elicited alpha-range (8–13 Hz) EEG signals. Integration and complexity of evoked (stimulus-locked) and induced (non-stimulus-locked) EEG responses were assessed using nonparametric k-th nearest neighbor (KNN) entropy estimation, which is robust to the nonstationarity of stimulus-elicited EEG signals. KNN-based I(X) and CI(X) were also computed for the alpha-range EEG of ongoing wakeful brain states. I(X) and CI(X) patterns differentiated between induced and evoked EEG signals and replicated previous wakeful EEG findings obtained using Gaussian-based entropy estimators. Absolute levels of I(X) and CI(X) were related to absolute levels of alpha-range EEG power and phase synchronization, but stimulus-related changes in the information-theoretic and other EEG properties were independent. These findings support the hypothesis that visual perception and ongoing wakeful mental states emerge from complex, dynamical interaction among segregated and integrated brain networks operating near an optimal balance between order and disorder.
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Affiliation(s)
- Logan T Trujillo
- Department of Psychology, Texas State University; San Marcos, TX 78666, USA
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94
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Abstract
The heterogeneity of molecular mechanisms, target neural circuits, and neurophysiologic effects of general anesthetics makes it difficult to develop a reliable and drug-invariant index of general anesthesia. No single brain region or mechanism has been identified as the neural correlate of consciousness, suggesting that consciousness might emerge through complex interactions of spatially and temporally distributed brain functions. The goal of this review article is to introduce the basic concepts of networks and explain why the application of network science to general anesthesia could be a pathway to discover a fundamental mechanism of anesthetic-induced unconsciousness. This article reviews data suggesting that reduced network efficiency, constrained network repertoires, and changes in cortical dynamics create inhospitable conditions for information processing and transfer, which lead to unconsciousness. This review proposes that network science is not just a useful tool but a necessary theoretical framework and method to uncover common principles of anesthetic-induced unconsciousness.
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Affiliation(s)
- UnCheol Lee
- From the Center for Consciousness Science, Department of Anesthesiology, University of Michigan Medical School, Ann Arbor, Michigan
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95
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Atasoy S, Vohryzek J, Deco G, Carhart-Harris RL, Kringelbach ML. Common neural signatures of psychedelics: Frequency-specific energy changes and repertoire expansion revealed using connectome-harmonic decomposition. PROGRESS IN BRAIN RESEARCH 2018; 242:97-120. [PMID: 30471684 DOI: 10.1016/bs.pbr.2018.08.009] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
The search for the universal laws of human brain function is still on-going but progress is being made. Here we describe the novel concepts of connectome harmonics and connectome-harmonic decomposition, which can be used to characterize the brain activity associated with any mental state. We use this new frequency-specific language to describe the brain activity elicited by psilocybin and LSD and find remarkably similar effects in terms of increases in total energy and power, as well as frequency-specific energy changes and repertoire expansion. In addition, we find enhanced signatures of criticality suggesting that the brain dynamics tune toward criticality in both psychedelic elicited states. Overall, our findings provide new evidence for the remarkable ability of psychedelics to change the spatiotemporal dynamics of the human brain.
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Affiliation(s)
- Selen Atasoy
- Department of Psychiatry, University of Oxford, Oxford, United Kingdom; Center for Music in the Brain, Aarhus University, Aarhus, Denmark
| | - Jakub Vohryzek
- Department of Psychiatry, University of Oxford, Oxford, United Kingdom; Center for Music in the Brain, Aarhus University, Aarhus, Denmark
| | - Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain; Institució Catalana de la Recerca i Estudis Avançats (ICREA), Barcelona, Spain; Department of Neuropsychology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany; School of Psychological Sciences, Monash University, Melbourne, Australia
| | | | - Morten L Kringelbach
- Department of Psychiatry, University of Oxford, Oxford, United Kingdom; Center for Music in the Brain, Aarhus University, Aarhus, Denmark.
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96
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Aguilera M, Bedia MG. Exploring Criticality as a Generic Adaptive Mechanism. Front Neurorobot 2018; 12:55. [PMID: 30333741 PMCID: PMC6176217 DOI: 10.3389/fnbot.2018.00055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2018] [Accepted: 08/20/2018] [Indexed: 11/19/2022] Open
Abstract
The activity of many biological and cognitive systems is not poised deep within a specific regime of activity. Instead, they operate near points of critical behavior located at the boundary between different phases. Certain authors link some of the properties of criticality with the ability of living systems to generate autonomous or intrinsically generated behavior. However, these claims remain highly speculative. In this paper, we intend to explore the connection between criticality and autonomous behavior through conceptual models that show how embodied agents may adapt themselves toward critical points. We propose to exploit maximum entropy models and their formal descriptions of indicators of criticality to present a learning model that drives generic agents toward critical points. Specifically, we derive such a learning model in an embodied Boltzmann machine by implementing a gradient ascent rule that maximizes the heat capacity of the controller in order to make the network maximally sensitive to external perturbations. We test and corroborate the model by implementing an embodied agent in the Mountain Car benchmark test, which is controlled by a Boltzmann machine that adjusts its weights according to the model. We find that the neural controller reaches an apparent point of criticality, which coincides with a transition point of the behavior of the agent between two regimes of behavior, maximizing the synergistic information between its sensors and the combination of hidden and motor neurons. Finally, we discuss the potential of our learning model to answer questions about the connection between criticality and the capabilities of living systems to autonomously generate intrinsic constraints on their behavior. We suggest that these “critical agents” are able to acquire flexible behavioral patterns that are useful for the development of successful strategies in different contexts.
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Affiliation(s)
- Miguel Aguilera
- Information and Autonomous Systems-Research Center for Life, Mind, and Society, University of the Basque Country, Donostia, Spain.,Department of Computer Science and Systems Engineering, University of Zaragoza, Zaragoza, Spain
| | - Manuel G Bedia
- Department of Computer Science and Systems Engineering, University of Zaragoza, Zaragoza, Spain.,Interactive Systems, Adaptivity, Autonomy and Cognition Lab, Aragón Institute of Engineering Research, University of Zaragoza, Zaragoza, Spain
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97
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Realpe-Gómez J, Andrighetto G, Nardin LG, Montoya JA. Balancing selfishness and norm conformity can explain human behavior in large-scale prisoner's dilemma games and can poise human groups near criticality. Phys Rev E 2018; 97:042321. [PMID: 29758626 DOI: 10.1103/physreve.97.042321] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2017] [Indexed: 01/16/2023]
Abstract
Cooperation is central to the success of human societies as it is crucial for overcoming some of the most pressing social challenges of our time; still, how human cooperation is achieved and may persist is a main puzzle in the social and biological sciences. Recently, scholars have recognized the importance of social norms as solutions to major local and large-scale collective action problems, from the management of water resources to the reduction of smoking in public places to the change in fertility practices. Yet a well-founded model of the effect of social norms on human cooperation is still lacking. Using statistical-physics techniques and integrating findings from cognitive and behavioral sciences, we present an analytically tractable model in which individuals base their decisions to cooperate both on the economic rewards they obtain and on the degree to which their action complies with social norms. Results from this parsimonious model are in agreement with observations in recent large-scale experiments with humans. We also find the phase diagram of the model and show that the experimental human group is poised near a critical point, a regime where recent work suggests living systems respond to changing external conditions in an efficient and coordinated manner.
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Affiliation(s)
- John Realpe-Gómez
- Quantum Artificial Intelligence Laboratory, NASA Ames Research Center, Moffett Field, California 94035, USA; Instituto de Matemáticas Aplicadas, Universidad de Cartagena, Cartagena de Indias, Bolívar 13001, Colombia; and SGT Inc., 7701 Greenbelt Road, Greenbelt, Maryland 20770, USA
| | - Giulia Andrighetto
- Institute of Cognitive Sciences and Technologies, National Research Council, Rome 00185, Italy; Mälardalen University, Högskoleplan 1, 721 23 Västerås, Sweden; and Institute for Futures Studies, Holländargatan 13, 101 31 Stockholm, Sweden
| | - Luis Gustavo Nardin
- Institute of Cognitive Sciences and Technologies, National Research Council, Rome 00185, Italy and Brandenburg University of Technology, 03046 Cottbus, Brandenburg, Germany
| | - Javier Antonio Montoya
- Grupo de Modelado Computacional, Universidad de Cartagena, Cartagena de Indias, Bolívar 13001, Colombia and The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
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98
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Daffertshofer A, Ton R, Kringelbach ML, Woolrich M, Deco G. Distinct criticality of phase and amplitude dynamics in the resting brain. Neuroimage 2018. [DOI: 10.1016/j.neuroimage.2018.03.002] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022] Open
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99
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Evaluation of the computational capabilities of a memristive random network (MN3) under the context of reservoir computing. Neural Netw 2018; 106:223-236. [DOI: 10.1016/j.neunet.2018.07.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2018] [Revised: 05/17/2018] [Accepted: 07/10/2018] [Indexed: 11/22/2022]
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100
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Daniels BC, Kim H, Moore D, Zhou S, Smith HB, Karas B, Kauffman SA, Walker SI. Criticality Distinguishes the Ensemble of Biological Regulatory Networks. PHYSICAL REVIEW LETTERS 2018; 121:138102. [PMID: 30312104 DOI: 10.1103/physrevlett.121.138102] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2018] [Revised: 07/21/2018] [Indexed: 06/08/2023]
Abstract
The hypothesis that many living systems should exhibit near-critical behavior is well motivated theoretically, and an increasing number of cases have been demonstrated empirically. However, a systematic analysis across biological networks, which would enable identification of the network properties that drive criticality, has not yet been realized. Here, we provide a first comprehensive survey of criticality across a diverse sample of biological networks, leveraging a publicly available database of 67 Boolean models of regulatory circuits. We find all 67 networks to be near critical. By comparing to ensembles of random networks with similar topological and logical properties, we show that criticality in biological networks is not predictable solely from macroscale properties such as mean degree ⟨K⟩ and mean bias in the logic functions ⟨p⟩, as previously emphasized in theories of random Boolean networks. Instead, the ensemble of real biological circuits is jointly constrained by the local causal structure and logic of each node. In this way, biological regulatory networks are more distinguished from random networks by their criticality than by other macroscale network properties such as degree distribution, edge density, or fraction of activating conditions.
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Affiliation(s)
- Bryan C Daniels
- ASU-SFI Center for Biosocial Complex Systems, Arizona State University, Tempe, Arizona 85287, USA
| | - Hyunju Kim
- School of Earth and Space Exploration, Arizona State University, Tempe, Arizona 85287, USA
- Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, Arizona 85287, USA
| | - Douglas Moore
- Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, Arizona 85287, USA
| | - Siyu Zhou
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
| | - Harrison B Smith
- School of Earth and Space Exploration, Arizona State University, Tempe, Arizona 85287, USA
| | - Bradley Karas
- Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, Arizona 85287, USA
| | | | - Sara I Walker
- ASU-SFI Center for Biosocial Complex Systems, Arizona State University, Tempe, Arizona 85287, USA
- School of Earth and Space Exploration, Arizona State University, Tempe, Arizona 85287, USA
- Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, Arizona 85287, USA
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