101
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Moosavi SA, Montakhab A, Valizadeh A. Coexistence of scale-invariant and rhythmic behavior in self-organized criticality. Phys Rev E 2018; 98:022304. [PMID: 30253485 DOI: 10.1103/physreve.98.022304] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2018] [Indexed: 11/07/2022]
Abstract
Scale-free behavior as well as oscillations are frequently observed in the activity of many natural systems. One important example is the cortical tissues of mammalian brain where both phenomena are simultaneously observed. Rhythmic oscillations as well as critical (scale-free) dynamics are thought to be important, but theoretically incompatible, features of a healthy brain. Motivated by the above, we study the possibility of the coexistence of scale-free avalanches along with rhythmic behavior within the framework of self-organized criticality. In particular, we add an oscillatory perturbation to local threshold condition of the continuous Zhang model and characterize the subsequent activity of the system. We observe regular oscillations embedded in well-defined avalanches which exhibit scale-free size and duration in line with observed neuronal avalanches. The average amplitude of such oscillations are shown to decrease with increasing frequency consistent with real brain oscillations. Furthermore, it is shown that optimal amplification of oscillations occur at the critical point, further providing evidence for functional advantages of criticality.
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Affiliation(s)
- S Amin Moosavi
- Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan 45137-66731, Iran.,Department of Physics, College of Sciences, Shiraz University, Shiraz 71946-84795, Iran
| | - Afshin Montakhab
- Department of Physics, College of Sciences, Shiraz University, Shiraz 71946-84795, Iran
| | - Alireza Valizadeh
- Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan 45137-66731, Iran
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102
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Kosmidis EK, Contoyiannis YF, Papatheodoropoulos C, Diakonos FK. Traits of criticality in membrane potential fluctuations of pyramidal neurons in the CA1 region of rat hippocampus. Eur J Neurosci 2018; 48:2343-2353. [PMID: 30117214 DOI: 10.1111/ejn.14117] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2018] [Revised: 07/05/2018] [Accepted: 08/07/2018] [Indexed: 01/19/2023]
Abstract
Evidence that neural circuits are operating near criticality has been provided at various levels of brain organisation with a presumed role in maximising information processing and multiscale activity association. Criticality has been linked to excitation at both the single-cell and network levels, as action potential generation marks an obvious phase transition from a resting to an excitable state. Using in vitro intracellular recordings, we examine irregular, small amplitude membrane potential fluctuations from CA1 pyramidal neurons of Wistar male rats. We show that these fluctuations, confounded with noise, carry information relevant to the neuronal state. The underlying dynamics exhibit intermittent characteristics shown to describe the temporal fluctuations of the order parameter of a macroscopic system at its critical point even in the absence of firing. An externally applied stimulus serves as the control parameter, driving the system in and out of its critical state. Based on our experimental observations we calculate the equivalent of the isothermal critical exponent δh finding a value which depends on the applied stimulus. For each neuron there is a stimulus amplitude for which the critical behaviour becomes most pronounced. The corresponding mean value of δh in the considered ensemble of neurons is δh ≈ 1.89, close to theoretical predictions for critical networks. Finally, we show that the firing rate of a neuron decreases exponentially with δh .
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Affiliation(s)
- Efstratios K Kosmidis
- Department of Medicine, Laboratory of Physiology, Aristotle University of Thessaloniki, Thessaloniki, Greece
| | - Yiannis F Contoyiannis
- Department of Electrical and Electronics Engineering, University of West Attica, Aigaleo, Athens, Greece
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103
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Takagi K. Information-Based Principle Induces Small-World Topology and Self-Organized Criticality in a Large Scale Brain Network. Front Comput Neurosci 2018; 12:65. [PMID: 30131688 PMCID: PMC6090464 DOI: 10.3389/fncom.2018.00065] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2018] [Accepted: 07/19/2018] [Indexed: 12/16/2022] Open
Abstract
The information processing in the large scale network of the human brain is related to its cognitive functions. Due to requirements for adaptation to changing environments under biological constraints, these processes in the brain can be hypothesized to be optimized. The principles based on the information optimization are expected to play a central role in affecting the dynamics and topological structure of the brain network. Recent studies on the functional connectivity between brain regions, referred to as the functional connectome, reveal characteristics of their networks, such as self-organized criticality of brain dynamics and small-world topology. However, these important attributes are established separately, and their relations to the principle of the information optimization are unclear. Here, we show that the maximization principle of the mutual information entropy induces the optimal state, at which the small-world network topology and the criticality in the activation dynamics emerge. Our findings, based on the functional connectome analyses, show that according to the increasing mutual information entropy, the coactivation pattern converges to the state of self-organized criticality, and a phase transition of the network topology, which is responsible for the small-world topology, arises simultaneously at the same point. The coincidence of these phase transitions at the same critical point indicates that the criticality of the dynamics and the phase transition of the network topology are essentially rooted in the same phenomenon driven by the mutual information maximization. As a consequence, the two different attributes of the brain, self-organized criticality and small-world topology, can be understood within a unified perspective under the information-based principle. Thus, our study provides an insight into the mechanism underlying the information processing in the brain.
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104
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Muthukumaraswamy SD, Liley DT. 1/f electrophysiological spectra in resting and drug-induced states can be explained by the dynamics of multiple oscillatory relaxation processes. Neuroimage 2018; 179:582-595. [PMID: 29959047 DOI: 10.1016/j.neuroimage.2018.06.068] [Citation(s) in RCA: 58] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2017] [Revised: 06/20/2018] [Accepted: 06/25/2018] [Indexed: 02/01/2023] Open
Abstract
Neurophysiological recordings are dominated by arhythmical activity whose spectra can be characterised by power-law functions, and on this basis are often referred to as reflecting scale-free brain dynamics (1/fβ). Relatively little is known regarding the neural generators and temporal dynamics of this arhythmical behaviour compared to rhythmical behaviour. Here we used Irregularly Resampled AutoSpectral Analysis (IRASA) to quantify β, in both the high (5-100 Hz, βhf) and low frequency bands (0.1-2.5 Hz, βlf) in MEG/EEG/ECoG recordings and to separate arhythmical from rhythmical modes of activity, such as, alpha rhythms. In MEG/EEG/ECoG data, we demonstrate that oscillatory alpha power dynamically correlates over time with βhf and similarly, participants with higher rhythmical alpha power have higher βhf. In a series of pharmaco-MEG investigations using the GABA reuptake inhibitor tiagabine, the glutamatergic AMPA receptor antagonist perampanel, the NMDA receptor antagonist ketamine and the mixed partial serotonergic agonist LSD, a variety of effects on both βhf and βlf were observed. Additionally, strong modulations of βhf were seen in monkey ECoG data during general anaesthesia using propofol and ketamine. We develop and test a unifying model which can explain, the 1/f nature of electrophysiological spectra, their dynamic interaction with oscillatory rhythms as well as the sensitivity of 1/f activity to drug interventions by considering electrophysiological spectra as being generated by a collection of stochastically perturbed damped oscillators having a distribution of relaxation rates.
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Affiliation(s)
- Suresh D Muthukumaraswamy
- School of Pharmacy and Centre for Brain Research, Faculty of Medical and Health Sciences, The University of Auckland, Auckland, New Zealand.
| | - David Tj Liley
- Centre for Human Psychopharmacology, School of Health Sciences, Swinburne University of Technology, Melbourne, Australia
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105
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Kang C, Aguilar B, Shmulevich I. Emergence of diversity in homogeneous coupled Boolean networks. Phys Rev E 2018; 97:052415. [PMID: 29906914 DOI: 10.1103/physreve.97.052415] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Indexed: 01/03/2023]
Abstract
The origin of multicellularity in metazoa is one of the fundamental questions of evolutionary biology. We have modeled the generic behaviors of gene regulatory networks in isogenic cells as stochastic nonlinear dynamical systems-coupled Boolean networks with perturbation. Model simulations under a variety of dynamical regimes suggest that the central characteristic of multicellularity, permanent spatial differentiation (diversification), indeed can arise. Additionally, we observe that diversification is more likely to occur near the critical regime of Lyapunov stability.
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Affiliation(s)
- Chris Kang
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA
| | - Boris Aguilar
- Institute for Systems Biology, Seattle, Washington 98109, USA
| | - Ilya Shmulevich
- Institute for Systems Biology, Seattle, Washington 98109, USA
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106
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Li W, Ovchinnikov IV, Chen H, Wang Z, Lee A, Lee H, Cepeda C, Schwartz RN, Meier K, Wang KL. A Basic Phase Diagram of Neuronal Dynamics. Neural Comput 2018; 30:2418-2438. [PMID: 29894659 DOI: 10.1162/neco_a_01103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
The extreme complexity of the brain has attracted the attention of neuroscientists and other researchers for a long time. More recently, the neuromorphic hardware has matured to provide a new powerful tool to study neuronal dynamics. Here, we study neuronal dynamics using different settings on a neuromorphic chip built with flexible parameters of neuron models. Our unique setting in the network of leaky integrate-and-fire (LIF) neurons is to introduce a weak noise environment. We observed three different types of collective neuronal activities, or phases, separated by sharp boundaries, or phase transitions. From this, we construct a rudimentary phase diagram of neuronal dynamics and demonstrate that a noise-induced chaotic phase (N-phase), which is dominated by neuronal avalanche activity (intermittent aperiodic neuron firing), emerges in the presence of noise and its width grows with the noise intensity. The dynamics can be manipulated in this N-phase. Our results and comparison with clinical data is consistent with the literature and our previous work showing that healthy brain must reside in the N-phase. We argue that the brain phase diagram with further refinement may be used for the diagnosis and treatment of mental disease and also suggest that the dynamics may be manipulated to serve as a means of new information processing (e.g., for optimization). Neuromorphic chips, similar to the one we used but with a variety of neuron models, may be used to further enhance the understanding of human brain function and accelerate the development of neuroscience research.
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Affiliation(s)
- Wenyuan Li
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Igor V Ovchinnikov
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Honglin Chen
- Department of Mathematics, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Zhe Wang
- Department of Mechanical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Albert Lee
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Houchul Lee
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Carlos Cepeda
- David Geffen School of Medicine, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Robert N Schwartz
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
| | - Karlheinz Meier
- Kirchhoff Institute for Physics, Heidelberg University, 69120 Heidelberg, Germany
| | - Kang L Wang
- Department of Electrical Engineering, UCLA, Los Angeles, CA 90095, U.S.A.
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107
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Wang DJJ, Jann K, Fan C, Qiao Y, Zang YF, Lu H, Yang Y. Neurophysiological Basis of Multi-Scale Entropy of Brain Complexity and Its Relationship With Functional Connectivity. Front Neurosci 2018; 12:352. [PMID: 29896081 PMCID: PMC5986880 DOI: 10.3389/fnins.2018.00352] [Citation(s) in RCA: 69] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2018] [Accepted: 05/07/2018] [Indexed: 01/06/2023] Open
Abstract
Recently, non-linear statistical measures such as multi-scale entropy (MSE) have been introduced as indices of the complexity of electrophysiology and fMRI time-series across multiple time scales. In this work, we investigated the neurophysiological underpinnings of complexity (MSE) of electrophysiology and fMRI signals and their relations to functional connectivity (FC). MSE and FC analyses were performed on simulated data using neural mass model based brain network model with the Brain Dynamics Toolbox, on animal models with concurrent recording of fMRI and electrophysiology in conjunction with pharmacological manipulations, and on resting-state fMRI data from the Human Connectome Project. Our results show that the complexity of regional electrophysiology and fMRI signals is positively correlated with network FC. The associations between MSE and FC are dependent on the temporal scales or frequencies, with higher associations between MSE and FC at lower temporal frequencies. Our results from theoretical modeling, animal experiment and human fMRI indicate that (1) Regional neural complexity and network FC may be two related aspects of brain's information processing: the more complex regional neural activity, the higher FC this region has with other brain regions; (2) MSE at high and low frequencies may represent local and distributed information processing across brain regions. Based on literature and our data, we propose that the complexity of regional neural signals may serve as an index of the brain's capacity of information processing—increased complexity may indicate greater transition or exploration between different states of brain networks, thereby a greater propensity for information processing.
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Affiliation(s)
- Danny J J Wang
- Laboratory of FMRI Technology, Stevens Neuroimaging and Informatics Institute, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States
| | - Kay Jann
- Laboratory of FMRI Technology, Stevens Neuroimaging and Informatics Institute, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States
| | - Chang Fan
- Laboratory of FMRI Technology, Stevens Neuroimaging and Informatics Institute, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States
| | - Yang Qiao
- Department of Psychology, Center for Cognition and Brain Disorders, Hangzhou Normal University, Hangzhou, China.,Neuroimaging Research Branch, National Institute on Drug Abuse, National Institutes of Health, Baltimore, MD, United States
| | - Yu-Feng Zang
- Department of Psychology, Center for Cognition and Brain Disorders, Hangzhou Normal University, Hangzhou, China
| | - Hanbing Lu
- Neuroimaging Research Branch, National Institute on Drug Abuse, National Institutes of Health, Baltimore, MD, United States
| | - Yihong Yang
- Neuroimaging Research Branch, National Institute on Drug Abuse, National Institutes of Health, Baltimore, MD, United States
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108
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Weber R, Alicea B, Huskey R, Mathiak K. Network Dynamics of Attention During a Naturalistic Behavioral Paradigm. Front Hum Neurosci 2018; 12:182. [PMID: 29780313 PMCID: PMC5946671 DOI: 10.3389/fnhum.2018.00182] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2017] [Accepted: 04/17/2018] [Indexed: 11/13/2022] Open
Abstract
This study investigates the dynamics of attention during continuous, naturalistic interactions in a video game. Specifically, the effect of repeated distraction on a continuous primary task is related to a functional model of network connectivity. We introduce the Non-linear Attentional Saturation Hypothesis (NASH), which predicts that effective connectivity within attentional networks increases non-linearly with decreasing distraction over time, and exhibits dampening at critical parameter values. Functional magnetic resonance imaging (fMRI) data collected using a naturalistic behavioral paradigm coupled with an interactive video game is used to test the hypothesis. As predicted, connectivity in pre-defined regions corresponding to attentional networks increases as distraction decreases. Moreover, the functional relationship between connectivity and distraction is convex, that is, network connectivity somewhat increases as distraction decreases during the continuous primary task, however, connectivity increases considerably as distraction falls below critical levels. This result characterizes the non-linear pattern of connectivity within attentional networks, particularly with respect to their dynamics during behavior. These results are also summarized in the form of a network structure analysis, which underscores the role of various nodes in regulating the global network state. In conclusion, we situate the implications of this research in the context of cognitive complexity and an emerging theory of flow during media exposure.
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Affiliation(s)
- René Weber
- Media Neuroscience Lab, Department of Communication, University of California, Santa Barbara, Santa Barbara, CA, United States
| | - Bradly Alicea
- Orthogonal Research and Teaching Laboratory, Champaign, IL, United States
| | - Richard Huskey
- Cognitive Communication Science Lab, School of Communication, The Ohio State University, Columbus, OH, United States
| | - Klaus Mathiak
- Department of Psychiatry, Psychotherapy and Psychosomatics, RWTH Aachen University, Aachen, Germany
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109
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Garcia JO, Ashourvan A, Muldoon SF, Vettel JM, Bassett DS. Applications of community detection techniques to brain graphs: Algorithmic considerations and implications for neural function. PROCEEDINGS OF THE IEEE. INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS 2018; 106:846-867. [PMID: 30559531 PMCID: PMC6294140 DOI: 10.1109/jproc.2017.2786710] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
The human brain can be represented as a graph in which neural units such as cells or small volumes of tissue are heterogeneously connected to one another through structural or functional links. Brain graphs are parsimonious representations of neural systems that have begun to offer fundamental insights into healthy human cognition, as well as its alteration in disease. A critical open question in network neuroscience lies in how neural units cluster into densely interconnected groups that can provide the coordinated activity that is characteristic of perception, action, and adaptive behaviors. Tools that have proven particularly useful for addressing this question are community detection approaches, which can identify communities or modules: groups of neural units that are densely interconnected with other units in their own group but sparsely interconnected with units in other groups. In this paper, we describe a common community detection algorithm known as modularity maximization, and we detail its applications to brain graphs constructed from neuroimaging data. We pay particular attention to important algorithmic considerations, especially in recent extensions of these techniques to graphs that evolve in time. After recounting a few fundamental insights that these techniques have provided into brain function, we highlight potential avenues of methodological advancements for future studies seeking to better characterize the patterns of coordinated activity in the brain that accompany human behavior. This tutorial provides a naive reader with an introduction to theoretical considerations pertinent to the generation of brain graphs, an understanding of modularity maximization for community detection, a resource of statistical measures that can be used to characterize community structure, and an appreciation of the usefulness of these approaches in uncovering behaviorally-relevant network dynamics in neuroimaging data.
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Affiliation(s)
- Javier O Garcia
- U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 USA
- Department of Bioengineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 USA
- Penn Center for Neuroengineering and Therapeutics, University of Pennsylvania, Philadelphia, PA 19104 USA
- Department of Mathematics and CDSE Program, University at Buffalo, Buffalo, NY 14260 USA
- Department of Psychological & Brain Sciences, University of California, Santa Barbara, CA, 93106 USA
- Department of Electrical & Systems Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 USA
| | - Arian Ashourvan
- U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 USA
- Department of Bioengineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 USA
- Penn Center for Neuroengineering and Therapeutics, University of Pennsylvania, Philadelphia, PA 19104 USA
- Department of Mathematics and CDSE Program, University at Buffalo, Buffalo, NY 14260 USA
- Department of Psychological & Brain Sciences, University of California, Santa Barbara, CA, 93106 USA
- Department of Electrical & Systems Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 USA
| | - Sarah F Muldoon
- U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 USA
- Department of Bioengineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 USA
- Penn Center for Neuroengineering and Therapeutics, University of Pennsylvania, Philadelphia, PA 19104 USA
- Department of Mathematics and CDSE Program, University at Buffalo, Buffalo, NY 14260 USA
- Department of Psychological & Brain Sciences, University of California, Santa Barbara, CA, 93106 USA
- Department of Electrical & Systems Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 USA
| | - Jean M Vettel
- U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 USA
- Department of Bioengineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 USA
- Penn Center for Neuroengineering and Therapeutics, University of Pennsylvania, Philadelphia, PA 19104 USA
- Department of Mathematics and CDSE Program, University at Buffalo, Buffalo, NY 14260 USA
- Department of Psychological & Brain Sciences, University of California, Santa Barbara, CA, 93106 USA
- Department of Electrical & Systems Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 USA
| | - Danielle S Bassett
- U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 USA
- Department of Bioengineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 USA
- Penn Center for Neuroengineering and Therapeutics, University of Pennsylvania, Philadelphia, PA 19104 USA
- Department of Mathematics and CDSE Program, University at Buffalo, Buffalo, NY 14260 USA
- Department of Psychological & Brain Sciences, University of California, Santa Barbara, CA, 93106 USA
- Department of Electrical & Systems Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 USA
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110
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Daffertshofer A, Ton R, Pietras B, Kringelbach ML, Deco G. Scale-freeness or partial synchronization in neural mass phase oscillator networks: Pick one of two? Neuroimage 2018; 180:428-441. [PMID: 29625237 DOI: 10.1016/j.neuroimage.2018.03.070] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2017] [Revised: 03/22/2018] [Accepted: 03/28/2018] [Indexed: 11/18/2022] Open
Abstract
Modeling and interpreting (partial) synchronous neural activity can be a challenge. We illustrate this by deriving the phase dynamics of two seminal neural mass models: the Wilson-Cowan firing rate model and the voltage-based Freeman model. We established that the phase dynamics of these models differed qualitatively due to an attractive coupling in the first and a repulsive coupling in the latter. Using empirical structural connectivity matrices, we determined that the two dynamics cover the functional connectivity observed in resting state activity. We further searched for two pivotal dynamical features that have been reported in many experimental studies: (1) a partial phase synchrony with a possibility of a transition towards either a desynchronized or a (fully) synchronized state; (2) long-term autocorrelations indicative of a scale-free temporal dynamics of phase synchronization. Only the Freeman phase model exhibited scale-free behavior. Its repulsive coupling, however, let the individual phases disperse and did not allow for a transition into a synchronized state. The Wilson-Cowan phase model, by contrast, could switch into a (partially) synchronized state, but it did not generate long-term correlations although being located close to the onset of synchronization, i.e. in its critical regime. That is, the phase-reduced models can display one of the two dynamical features, but not both.
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Affiliation(s)
- Andreas Daffertshofer
- Institute for Brain and Behavior Amsterdam & Amsterdam Movement Sciences, Faculty of Behavioural and Movement Sciences, Vrije Universiteit Amsterdam, van der Boechorststraat 9, 1081BT, Amsterdam, The Netherlands.
| | - Robert Ton
- Institute for Brain and Behavior Amsterdam & Amsterdam Movement Sciences, Faculty of Behavioural and Movement Sciences, Vrije Universiteit Amsterdam, van der Boechorststraat 9, 1081BT, Amsterdam, The Netherlands; Center for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Carrer Tanger 122-140, 08018, Barcelona, Spain
| | - Bastian Pietras
- Institute for Brain and Behavior Amsterdam & Amsterdam Movement Sciences, Faculty of Behavioural and Movement Sciences, Vrije Universiteit Amsterdam, van der Boechorststraat 9, 1081BT, Amsterdam, The Netherlands; Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - Morten L Kringelbach
- University Department of Psychiatry, University of Oxford, Oxford, OX3 7JX, UK; Center for Music in the Brain, Department of Clinical Medicine, Aarhus University, Denmark
| | - Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Carrer Tanger 122-140, 08018, Barcelona, Spain; Institució Catalana de la Recerca i Estudis Avanats (ICREA), Universitat Pompeu Fabra, Carrer Tanger 122-140, 08018, Barcelona, Spain
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111
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Greenwood PM, Blumberg EJ, Scheldrup MR. Hypothesis for cognitive effects of transcranial direct current stimulation: Externally- and internally-directed cognition. Neurosci Biobehav Rev 2018; 86:226-238. [DOI: 10.1016/j.neubiorev.2017.11.006] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2017] [Revised: 11/13/2017] [Accepted: 11/14/2017] [Indexed: 11/24/2022]
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112
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Zhou S, Yu Y. Synaptic E-I Balance Underlies Efficient Neural Coding. Front Neurosci 2018; 12:46. [PMID: 29456491 PMCID: PMC5801300 DOI: 10.3389/fnins.2018.00046] [Citation(s) in RCA: 90] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2017] [Accepted: 01/19/2018] [Indexed: 12/19/2022] Open
Abstract
Both theoretical and experimental evidence indicate that synaptic excitation and inhibition in the cerebral cortex are well-balanced during the resting state and sensory processing. Here, we briefly summarize the evidence for how neural circuits are adjusted to achieve this balance. Then, we discuss how such excitatory and inhibitory balance shapes stimulus representation and information propagation, two basic functions of neural coding. We also point out the benefit of adopting such a balance during neural coding. We conclude that excitatory and inhibitory balance may be a fundamental mechanism underlying efficient coding.
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Affiliation(s)
- Shanglin Zhou
- State Key Laboratory of Medical Neurobiology, School of Life Science and the Collaborative Innovation Center for Brain Science, Institutes of Brain Science, Center for Computational Systems Biology, Fudan University, Shanghai, China
| | - Yuguo Yu
- State Key Laboratory of Medical Neurobiology, School of Life Science and the Collaborative Innovation Center for Brain Science, Institutes of Brain Science, Center for Computational Systems Biology, Fudan University, Shanghai, China
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113
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Pfeffer T, Avramiea AE, Nolte G, Engel AK, Linkenkaer-Hansen K, Donner TH. Catecholamines alter the intrinsic variability of cortical population activity and perception. PLoS Biol 2018; 16:e2003453. [PMID: 29420565 PMCID: PMC5821404 DOI: 10.1371/journal.pbio.2003453] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2017] [Revised: 02/21/2018] [Accepted: 01/23/2018] [Indexed: 11/18/2022] Open
Abstract
The ascending modulatory systems of the brain stem are powerful regulators of global brain state. Disturbances of these systems are implicated in several major neuropsychiatric disorders. Yet, how these systems interact with specific neural computations in the cerebral cortex to shape perception, cognition, and behavior remains poorly understood. Here, we probed into the effect of two such systems, the catecholaminergic (dopaminergic and noradrenergic) and cholinergic systems, on an important aspect of cortical computation: its intrinsic variability. To this end, we combined placebo-controlled pharmacological intervention in humans, recordings of cortical population activity using magnetoencephalography (MEG), and psychophysical measurements of the perception of ambiguous visual input. A low-dose catecholaminergic, but not cholinergic, manipulation altered the rate of spontaneous perceptual fluctuations as well as the temporal structure of "scale-free" population activity of large swaths of the visual and parietal cortices. Computational analyses indicate that both effects were consistent with an increase in excitatory relative to inhibitory activity in the cortical areas underlying visual perceptual inference. We propose that catecholamines regulate the variability of perception and cognition through dynamically changing the cortical excitation-inhibition ratio. The combined readout of fluctuations in perception and cortical activity we established here may prove useful as an efficient and easily accessible marker of altered cortical computation in neuropsychiatric disorders.
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Affiliation(s)
- Thomas Pfeffer
- Department of Neurophysiology and Pathophysiology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
| | - Arthur-Ervin Avramiea
- Center for Neurogenomics and Cognitive Research, Neuroscience Campus Amsterdam, VU University Amsterdam, Amsterdam, the Netherlands
| | - Guido Nolte
- Department of Neurophysiology and Pathophysiology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
| | - Andreas K. Engel
- Department of Neurophysiology and Pathophysiology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
| | - Klaus Linkenkaer-Hansen
- Center for Neurogenomics and Cognitive Research, Neuroscience Campus Amsterdam, VU University Amsterdam, Amsterdam, the Netherlands
| | - Tobias H. Donner
- Department of Neurophysiology and Pathophysiology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
- Department of Psychology, University of Amsterdam, Amsterdam, the Netherlands
- Amsterdam Brain and Cognition, University of Amsterdam, Amsterdam, the Netherlands
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114
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Fractal Analyses of Networks of Integrate-and-Fire Stochastic Spiking Neurons. COMPLEX NETWORKS IX 2018. [DOI: 10.1007/978-3-319-73198-8_14] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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115
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Atasoy S, Roseman L, Kaelen M, Kringelbach ML, Deco G, Carhart-Harris RL. Connectome-harmonic decomposition of human brain activity reveals dynamical repertoire re-organization under LSD. Sci Rep 2017; 7:17661. [PMID: 29247209 PMCID: PMC5732294 DOI: 10.1038/s41598-017-17546-0] [Citation(s) in RCA: 98] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2017] [Accepted: 11/24/2017] [Indexed: 12/31/2022] Open
Abstract
Recent studies have started to elucidate the effects of lysergic acid diethylamide (LSD) on the human brain but the underlying dynamics are not yet fully understood. Here we used 'connectome-harmonic decomposition', a novel method to investigate the dynamical changes in brain states. We found that LSD alters the energy and the power of individual harmonic brain states in a frequency-selective manner. Remarkably, this leads to an expansion of the repertoire of active brain states, suggestive of a general re-organization of brain dynamics given the non-random increase in co-activation across frequencies. Interestingly, the frequency distribution of the active repertoire of brain states under LSD closely follows power-laws indicating a re-organization of the dynamics at the edge of criticality. Beyond the present findings, these methods open up for a better understanding of the complex brain dynamics in health and disease.
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Affiliation(s)
- Selen Atasoy
- Center of Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Barcelona, Spain.
| | - Leor Roseman
- Psychedelic Research Group, Psychopharmacology Unit, Centre for Psychiatry, Department of Medicine, Imperial College London, London, UK
| | - Mendel Kaelen
- Psychedelic Research Group, Psychopharmacology Unit, Centre for Psychiatry, Department of Medicine, Imperial College London, London, UK
| | - Morten L Kringelbach
- Department of Psychiatry, University of Oxford, Oxford, UK
- Center for Music in the Brain, Clinical Medicine, Aarhus University, Aarhus, Denmark
| | - Gustavo Deco
- Center of Brain and Cognition, Computational Neuroscience Group, 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
| | - Robin L Carhart-Harris
- Psychedelic Research Group, Psychopharmacology Unit, Centre for Psychiatry, Department of Medicine, Imperial College London, London, UK
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116
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Kunze T, Peterson ADH, Haueisen J, Knösche TR. A model of individualized canonical microcircuits supporting cognitive operations. PLoS One 2017; 12:e0188003. [PMID: 29200435 PMCID: PMC5714354 DOI: 10.1371/journal.pone.0188003] [Citation(s) in RCA: 9] [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: 05/29/2017] [Accepted: 10/25/2017] [Indexed: 12/13/2022] Open
Abstract
Major cognitive functions such as language, memory, and decision-making are thought to rely on distributed networks of a large number of basic elements, called canonical microcircuits. In this theoretical study we propose a novel canonical microcircuit model and find that it supports two basic computational operations: a gating mechanism and working memory. By means of bifurcation analysis we systematically investigate the dynamical behavior of the canonical microcircuit with respect to parameters that govern the local network balance, that is, the relationship between excitation and inhibition, and key intrinsic feedback architectures of canonical microcircuits. We relate the local behavior of the canonical microcircuit to cognitive processing and demonstrate how a network of interacting canonical microcircuits enables the establishment of spatiotemporal sequences in the context of syntax parsing during sentence comprehension. This study provides a framework for using individualized canonical microcircuits for the construction of biologically realistic networks supporting cognitive operations.
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Affiliation(s)
- Tim Kunze
- Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
- Institute of Biomedical Engineering and Informatics, Ilmenau University of Technology, Ilmenau, Germany
- * E-mail:
| | | | - Jens Haueisen
- Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
- Institute of Biomedical Engineering and Informatics, Ilmenau University of Technology, Ilmenau, Germany
| | - Thomas R. Knösche
- Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
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117
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Bettinger JS. Comparative approximations of criticality in a neural and quantum regime. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2017; 131:445-462. [PMID: 29031703 DOI: 10.1016/j.pbiomolbio.2017.09.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2017] [Revised: 09/01/2017] [Accepted: 09/04/2017] [Indexed: 06/07/2023]
Abstract
Under a variety of conditions, stochastic and non-linear systems with many degrees of freedom tend to evolve towards complexity and criticality. Over the last decades, a steady proliferation of models re: far-from-equilibrium thermodynamics of metastable, many-valued systems arose, serving as attributes of a 'critical' attractor landscape. Building off recent data citing trademark aspects of criticality in the brain-including: power-laws, scale-free (1/f) behavior (scale invariance, or scale independence), critical slowing, and avalanches-it has been conjectured that operating at criticality entails functional advantages such as: optimized neural computation and information processing; boosted memory; large dynamical ranges; long-range communication; and an increased ability to react to highly diverse stimuli. In short, critical dynamics provide a necessary condition for neurobiologically significant elements of brain dynamics. Theoretical predictions have been verified in specific models such as Boolean networks, liquid state machines, and neural networks. These findings inspired the neural criticality hypothesis, proposing that the brain operates in a critical state because the associated optimal computational capabilities provide an evolutionarily advantage. This paper develops in three parts: after developing the critical landscape, we will then shift gears to rediscover another inroad to criticality via stochastic quantum field theory and dissipative dynamics. The existence of these two approaches deserves some consideration, given both neural and quantum criticality hypotheses propose specific mechanisms that leverage the same phenomena. This suggests that understanding the quantum approach could help to shed light on brain-based modeling. In the third part, we will turn to Whitehead's actual entities and modes of perception in order to demonstrate a concomitant logic underwriting both models. In the discussion, I briefly motivate a reading of criticality and its properties as responsive to the characterization of tenets from Eastern wisdom traditions.
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Affiliation(s)
- Jesse Sterling Bettinger
- Johns Hopkins University, Center for Talented Youth, Baltimore, MD, United States; Center for Process Studies, Claremont, CA, United States.
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118
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Barbey AK. Network Neuroscience Theory of Human Intelligence. Trends Cogn Sci 2017; 22:8-20. [PMID: 29167088 DOI: 10.1016/j.tics.2017.10.001] [Citation(s) in RCA: 133] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2017] [Revised: 10/05/2017] [Accepted: 10/06/2017] [Indexed: 10/18/2022]
Abstract
An enduring aim of research in the psychological and brain sciences is to understand the nature of individual differences in human intelligence, examining the stunning breadth and diversity of intellectual abilities and the remarkable neurobiological mechanisms from which they arise. This Opinion article surveys recent neuroscience evidence to elucidate how general intelligence, g, emerges from individual differences in the network architecture of the human brain. The reviewed findings motivate new insights about how network topology and dynamics account for individual differences in g, represented by the Network Neuroscience Theory. According to this framework, g emerges from the small-world topology of brain networks and the dynamic reorganization of its community structure in the service of system-wide flexibility and adaptation.
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Affiliation(s)
- Aron K Barbey
- Decision Neuroscience Laboratory, University of Illinois at Urbana-Champaign, IL, USA; Department of Psychology, University of Illinois at Urbana-Champaign, IL, USA; Department of Bioengineering, University of Illinois at Urbana-Champaign, IL, USA; Neuroscience Program, University of Illinois at Urbana-Champaign, IL, USA; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, IL, USA; https://www.DecisionNeuroscienceLab.org.
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119
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Functional connectivity dynamically evolves on multiple time-scales over a static structural connectome: Models and mechanisms. Neuroimage 2017; 160:84-96. [DOI: 10.1016/j.neuroimage.2017.03.045] [Citation(s) in RCA: 218] [Impact Index Per Article: 31.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2016] [Revised: 01/27/2017] [Accepted: 03/20/2017] [Indexed: 11/20/2022] Open
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120
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Gollo LL. Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding. J R Soc Interface 2017; 14:20170207. [PMID: 28954848 PMCID: PMC5636266 DOI: 10.1098/rsif.2017.0207] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2017] [Accepted: 08/17/2017] [Indexed: 11/12/2022] Open
Abstract
The vicinity of phase transitions selectively amplifies weak stimuli, yielding optimal sensitivity to distinguish external input. Along with this enhanced sensitivity, enhanced levels of fluctuations at criticality reduce the specificity of the response. Given that the specificity of the response is largely compromised when the sensitivity is maximal, the overall benefit of criticality for signal processing remains questionable. Here, it is shown that this impasse can be solved by heterogeneous systems incorporating functional diversity, in which critical and subcritical components coexist. The subnetwork of critical elements has optimal sensitivity, and the subnetwork of subcritical elements has enhanced specificity. Combining segregated features extracted from the different subgroups, the resulting collective response can maximize the trade-off between sensitivity and specificity measured by the dynamic-range-to-noise ratio. Although numerous benefits can be observed when the entire system is critical, our results highlight that optimal performance is obtained when only a small subset of the system is at criticality.
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Affiliation(s)
- Leonardo L Gollo
- Systems Neuroscience Group, QIMR Berghofer Medical Research Institute, Brisbane, Australia
- The University of Queensland, Centre for Clinical Research, Brisbane, Australia
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121
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Tan TL, Cheong SA. Statistical complexity is maximized in a small-world brain. PLoS One 2017; 12:e0183918. [PMID: 28850587 PMCID: PMC5574548 DOI: 10.1371/journal.pone.0183918] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2017] [Accepted: 08/14/2017] [Indexed: 01/03/2023] Open
Abstract
In this paper, we study a network of Izhikevich neurons to explore what it means for a brain to be at the edge of chaos. To do so, we first constructed the phase diagram of a single Izhikevich excitatory neuron, and identified a small region of the parameter space where we find a large number of phase boundaries to serve as our edge of chaos. We then couple the outputs of these neurons directly to the parameters of other neurons, so that the neuron dynamics can drive transitions from one phase to another on an artificial energy landscape. Finally, we measure the statistical complexity of the parameter time series, while the network is tuned from a regular network to a random network using the Watts-Strogatz rewiring algorithm. We find that the statistical complexity of the parameter dynamics is maximized when the neuron network is most small-world-like. Our results suggest that the small-world architecture of neuron connections in brains is not accidental, but may be related to the information processing that they do.
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Affiliation(s)
- Teck Liang Tan
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Republic of Singapore
- Complexity Institute, Nanyang Technological University, Block 2 Innovation Centre, Level 2 Unit 245, 18 Nanyang Drive, Singapore 637723, Republic of Singapore
- * E-mail:
| | - Siew Ann Cheong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Republic of Singapore
- Complexity Institute, Nanyang Technological University, Block 2 Innovation Centre, Level 2 Unit 245, 18 Nanyang Drive, Singapore 637723, Republic of Singapore
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122
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Yu L, Yu Y. Energy-efficient neural information processing in individual neurons and neuronal networks. J Neurosci Res 2017; 95:2253-2266. [PMID: 28833444 DOI: 10.1002/jnr.24131] [Citation(s) in RCA: 43] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2016] [Revised: 07/07/2017] [Accepted: 07/10/2017] [Indexed: 12/22/2022]
Abstract
Brains are composed of networks of an enormous number of neurons interconnected with synapses. Neural information is carried by the electrical signals within neurons and the chemical signals among neurons. Generating these electrical and chemical signals is metabolically expensive. The fundamental issue raised here is whether brains have evolved efficient ways of developing an energy-efficient neural code from the molecular level to the circuit level. Here, we summarize the factors and biophysical mechanisms that could contribute to the energy-efficient neural code for processing input signals. The factors range from ion channel kinetics, body temperature, axonal propagation of action potentials, low-probability release of synaptic neurotransmitters, optimal input and noise, the size of neurons and neuronal clusters, excitation/inhibition balance, coding strategy, cortical wiring, and the organization of functional connectivity. Both experimental and computational evidence suggests that neural systems may use these factors to maximize the efficiency of energy consumption in processing neural signals. Studies indicate that efficient energy utilization may be universal in neuronal systems as an evolutionary consequence of the pressure of limited energy. As a result, neuronal connections may be wired in a highly economical manner to lower energy costs and space. Individual neurons within a network may encode independent stimulus components to allow a minimal number of neurons to represent whole stimulus characteristics efficiently. This basic principle may fundamentally change our view of how billions of neurons organize themselves into complex circuits to operate and generate the most powerful intelligent cognition in nature. © 2017 Wiley Periodicals, Inc.
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Affiliation(s)
- Lianchun Yu
- Institute of Theoretical Physics, Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou, China
| | - Yuguo Yu
- School of Life Science and the State Key Laboratory of Medical Neurobiology, Institutes of Brain Science and the Collaborative Innovation Center for Brain Science, Fudan University, Shanghai, China
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123
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Refractory period in network models of excitable nodes: self-sustaining stable dynamics, extended scaling region and oscillatory behavior. Sci Rep 2017; 7:7107. [PMID: 28769096 PMCID: PMC5541036 DOI: 10.1038/s41598-017-07135-6] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2016] [Accepted: 06/23/2017] [Indexed: 11/12/2022] Open
Abstract
Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons is thought to be an important dynamical property. We therefore consider a simple model of excitable nodes which is known to exhibit a transition to instability at a critical point (λ = 1), and introduce refractory period into its dynamics. We use mean-field analytical calculations as well as numerical simulations to calculate the activity dependent branching ratio that is useful to characterize the behavior of critical systems. We also define avalanches and calculate probability distribution of their size and duration. We find that in the presence of refractory period the dynamics stabilizes while various parameter regimes become accessible. A sub-critical regime with λ < 1.0, a standard critical behavior with exponents close to critical branching process for λ = 1, a regime with 1 < λ < 2 that exhibits an interesting scaling behavior, and an oscillating regime with λ > 2.0. We have therefore shown that refractory behavior leads to a wide range of scaling as well as periodic behavior which are relevant to real neuronal dynamics.
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124
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Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons. ENTROPY 2017. [DOI: 10.3390/e19080399] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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125
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Abstract
Recent advances in connectomics have led to a synthesis of perspectives regarding the brain's functional organization that reconciles classical concepts of localized specialization with an appreciation for properties that emerge from interactions across distributed functional networks. This provides a more comprehensive framework for understanding neural mechanisms of normal cognition and disease. Although fMRI has not become a routine clinical tool, research has already had important influences on clinical concepts guiding diagnosis and patient management. Here we review illustrative examples. Studies demonstrating the network plasticity possible in adults and the global consequences of even focal brain injuries or disease both have had substantial impact on modern concepts of disease evolution and expression. Applications of functional connectomics in studies of clinical populations are challenging traditional disease classifications and helping to clarify biological relationships between clinical syndromes (and thus also ways of extending indications for, or "re-purposing," current treatments). Large datasets from prospective, longitudinal studies promise to enable the discovery and validation of functional connectomic biomarkers with the potential to identify people at high risk of disease before clinical onset, at a time when treatments may be most effective. Studies of pain and consciousness have catalyzed reconsiderations of approaches to clinical management, but also have stimulated debate about the clinical meaningfulness of differences in internal perceptual or cognitive states inferred from functional connectomics or other physiological correlates. By way of a closing summary, we offer a personal view of immediate challenges and potential opportunities for clinically relevant applications of fMRI-based functional connectomics.
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Affiliation(s)
- Paul M Matthews
- Division of Brain Sciences, Department of Medicine and Centre for Neurotechnology, Imperial College London, London WC12 0NN, UK.
| | - Adam Hampshire
- Division of Brain Sciences, Department of Medicine and Centre for Neurotechnology, Imperial College London, London WC12 0NN, UK
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126
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Lord LD, Stevner AB, Deco G, Kringelbach ML. Understanding principles of integration and segregation using whole-brain computational connectomics: implications for neuropsychiatric disorders. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:rsta.2016.0283. [PMID: 28507228 PMCID: PMC5434074 DOI: 10.1098/rsta.2016.0283] [Citation(s) in RCA: 64] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 12/05/2016] [Indexed: 05/18/2023]
Abstract
To survive in an ever-changing environment, the brain must seamlessly integrate a rich stream of incoming information into coherent internal representations that can then be used to efficiently plan for action. The brain must, however, balance its ability to integrate information from various sources with a complementary capacity to segregate information into modules which perform specialized computations in local circuits. Importantly, evidence suggests that imbalances in the brain's ability to bind together and/or segregate information over both space and time is a common feature of several neuropsychiatric disorders. Most studies have, however, until recently strictly attempted to characterize the principles of integration and segregation in static (i.e. time-invariant) representations of human brain networks, hence disregarding the complex spatio-temporal nature of these processes. In the present Review, we describe how the emerging discipline of whole-brain computational connectomics may be used to study the causal mechanisms of the integration and segregation of information on behaviourally relevant timescales. We emphasize how novel methods from network science and whole-brain computational modelling can expand beyond traditional neuroimaging paradigms and help to uncover the neurobiological determinants of the abnormal integration and segregation of information in neuropsychiatric disorders.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.
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Affiliation(s)
| | - Angus B Stevner
- Department of Psychiatry, University of Oxford, Oxford, UK
- Center for Music in the Brain, Aarhus University, Aarhus, Denmark
| | - Gustavo Deco
- Center for Brain and Cognition, Universitat Pompeu Fabra, Barcelona, Spain
- Instituci Catalana de la Recerca i Estudis Avanats (ICREA), Universitat Pompeu Fabra, Barcelona, Spain
- Department of Neuropsychology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
- School of Psychological Sciences, Monash University, Melbourne, Australia, Clayton VIC 3800
| | - Morten L Kringelbach
- Department of Psychiatry, University of Oxford, Oxford, UK
- Center for Music in the Brain, Aarhus University, Aarhus, Denmark
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127
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Simola J, Zhigalov A, Morales-Muñoz I, Palva JM, Palva S. Critical dynamics of endogenous fluctuations predict cognitive flexibility in the Go/NoGo task. Sci Rep 2017; 7:2909. [PMID: 28588303 PMCID: PMC5460255 DOI: 10.1038/s41598-017-02750-9] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2016] [Accepted: 04/18/2017] [Indexed: 12/11/2022] Open
Abstract
Fluctuations with power-law scaling and long-range temporal correlations (LRTCs) are characteristic to human psychophysical performance. Systems operating in a critical state exhibit such LRTCs, but phenomenologically similar fluctuations and LRTCs may also be caused by slow decay of the system’s memory without the system being critical. Theoretically, criticality endows the system with the greatest representational capacity and flexibility in state transitions. Without criticality, however, slowly decaying system memory would predict inflexibility. We addressed these contrasting predictions of the ‘criticality’ and ‘long-memory’ candidate mechanisms of human behavioral LRTCs by using a Go/NoGo task wherein the commission errors constitute a measure of cognitive flexibility. Response time (RT) fluctuations in this task exhibited power-law frequency scaling, autocorrelations, and LRTCs. We show here that the LRTC scaling exponents, quantifying the strength of long-range correlations, were negatively correlated with the commission error rates. Strong LRTCs hence parallel optimal cognitive flexibility and, in line with the criticality hypothesis, indicate a functionally advantageous state. This conclusion was corroborated by a positive correlation between the LRTC scaling exponents and executive functions measured with the Rey-Osterrieth Complex Figure test. Our results hence support the notion that LRTCs arise from critical dynamics that is functionally significant for human cognitive performance.
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Affiliation(s)
- Jaana Simola
- Helsinki Institute for Lifesciences, Neuroscience Center, University of Helsinki, P.O. Box 56 (Viikinkaari 4), FI-00014, Helsinki, Finland.
| | - Alexander Zhigalov
- Helsinki Institute for Lifesciences, Neuroscience Center, University of Helsinki, P.O. Box 56 (Viikinkaari 4), FI-00014, Helsinki, Finland
| | - Isabel Morales-Muñoz
- Helsinki Institute for Lifesciences, Neuroscience Center, University of Helsinki, P.O. Box 56 (Viikinkaari 4), FI-00014, Helsinki, Finland
| | - J Matias Palva
- Helsinki Institute for Lifesciences, Neuroscience Center, University of Helsinki, P.O. Box 56 (Viikinkaari 4), FI-00014, Helsinki, Finland
| | - Satu Palva
- Helsinki Institute for Lifesciences, Neuroscience Center, University of Helsinki, P.O. Box 56 (Viikinkaari 4), FI-00014, Helsinki, Finland.
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128
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Takagi K. A distribution model of functional connectome based on criticality and energy constraints. PLoS One 2017; 12:e0177446. [PMID: 28545048 PMCID: PMC5435242 DOI: 10.1371/journal.pone.0177446] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2017] [Accepted: 04/27/2017] [Indexed: 12/03/2022] Open
Abstract
The analysis of the network structure of the functional connectivity data constructed from fMRI images provides basic information about functions and features of the brain activity. We focus on the two features which are considered as relevant to the brain activity, the criticality and the constraint regarding energy consumptions. Within a wide variety of complex systems, the critical state occurs associated with a phase transition between distinct phases, random one and order one. Although the hypothesis that human brain activity is also in a state of criticality is supported by some experimental results, it still remains controversial. One issue is that experimental distributions exhibit deviations from the power law predicted by the criticality. Based on the assumption that constraints on brain from the biological costs cause these deviations, we derive a distribution model. The evaluation using the information criteria indicates an advantage of this model in fitting to experimental data compared to other representative distribution models, the truncated power law and the power law. Our findings also suggest that the mechanism underlying this model is closely related to the cost effective behavior in human brain with maximizing the network efficiency for the given network cost.
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Affiliation(s)
- Kosuke Takagi
- Uwado-shinmachi 5-4, Kawagoe-shi, Saitamaken, Japan
- * E-mail:
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129
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Blythe DAJ, Nikulin VV. Long-range temporal correlations in neural narrowband time-series arise due to critical dynamics. PLoS One 2017; 12:e0175628. [PMID: 28472078 PMCID: PMC5417502 DOI: 10.1371/journal.pone.0175628] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2016] [Accepted: 03/14/2017] [Indexed: 11/18/2022] Open
Abstract
We show theoretically that the hypothesis of criticality as a theory of long-range fluctuation in the human brain may be distinguished from the theory of passive filtering on the basis of macroscopic neuronal signals such as the electroencephalogram, using novel theory of narrowband amplitude time-series at criticality. Our theory predicts the division of critical activity into meta-universality classes. As a consequence our analysis shows that experimental electroencephalography data favours the hypothesis of criticality in the human brain.
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Affiliation(s)
| | - Vadim V. Nikulin
- Neurophysics group, Department of Neurology, Charité Medical University, Berlin, Germany
- Department of Neurology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
- Center for Cognition and Decision Making, National Research University Higher School of Economics, Moscow, Russian Federation
- * E-mail: (DAJB); (VVN)
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130
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Mohseni A, Gharibzadeh S, Bakouie F. The role of driver nodes in managing epileptic seizures: Application of Kuramoto model. J Theor Biol 2017; 419:108-115. [PMID: 28212785 DOI: 10.1016/j.jtbi.2017.02.013] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2016] [Revised: 02/04/2017] [Accepted: 02/11/2017] [Indexed: 11/29/2022]
Abstract
Synchronization is an important global phenomenon which could be found in a wide range of complex systems such as brain or electronic devices. However, in some circumstances the synchronized states are not desirable for the system and should be suppressed. For example, excessively synchronized activities in the brain network could be the root of neuronal disorders like epileptic seizures. According to the controllability theory of the complex networks, a minimum set of driver nodes has the ability to control the entire system. In this study, we examine the role of driver nodes in suppressing the excessive synchronization in a generalized Kuramoto model, which consists of two types of oscillators: contrarian and regular ones. We used two different structural topologies: Barabási-Albert scale-free (BASF) network and Caenorhabditis elegans (C.elegans) neuronal network. Our results show that contrarian driver nodes have the sufficient ability to break the synchronized level of the systems. In this case, the system coherency level is not fully suppressed that is avoiding dysfunctions of normal brain functions which require the neuronal synchronized activities. Moreover, in this case, the oscillators grouped in two distinct synchronized clusters that could be an indication of chaotic behavior of the system known as resting-state activity of the brain.
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Affiliation(s)
- Ali Mohseni
- Faculty of Biomedical Engineering, Amirkabir University of Technology, Iran
| | | | - Fatemeh Bakouie
- Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Iran.
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131
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Yadav CK, Doreswamy Y. Scale Invariance in Lateral Head Scans During Spatial Exploration. PHYSICAL REVIEW LETTERS 2017; 118:158104. [PMID: 28452503 DOI: 10.1103/physrevlett.118.158104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2016] [Indexed: 06/07/2023]
Abstract
Universality connects various natural phenomena through physical principles governing their dynamics, and has provided broadly accepted answers to many complex questions, including information processing in neuronal systems. However, its significance in behavioral systems is still elusive. Lateral head scanning (LHS) behavior in rodents might contribute to spatial navigation by actively managing (optimizing) the available sensory information. Our findings of scale invariant distributions in LHS lifetimes, interevent intervals and event magnitudes, provide evidence for the first time that the optimization takes place at a critical point in LHS dynamics. We propose that the LHS behavior is responsible for preprocessing of the spatial information content, critical for subsequent foolproof encoding by the respective downstream neural networks.
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Affiliation(s)
- Chetan K Yadav
- National Brain Research Centre, NH-8, Manesar, Haryana 122051, India
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132
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Kang J, Pae C, Park HJ. Energy landscape analysis of the subcortical brain network unravels system properties beneath resting state dynamics. Neuroimage 2017; 149:153-164. [DOI: 10.1016/j.neuroimage.2017.01.075] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Revised: 01/23/2017] [Accepted: 01/31/2017] [Indexed: 12/30/2022] Open
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133
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Kanders K, Lorimer T, Stoop R. Avalanche and edge-of-chaos criticality do not necessarily co-occur in neural networks. CHAOS (WOODBURY, N.Y.) 2017; 27:047408. [PMID: 28456175 DOI: 10.1063/1.4978998] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
There are indications that for optimizing neural computation, neural networks may operate at criticality. Previous approaches have used distinct fingerprints of criticality, leaving open the question whether the different notions would necessarily reflect different aspects of one and the same instance of criticality, or whether they could potentially refer to distinct instances of criticality. In this work, we choose avalanche criticality and edge-of-chaos criticality and demonstrate for a recurrent spiking neural network that avalanche criticality does not necessarily entrain dynamical edge-of-chaos criticality. This suggests that the different fingerprints may pertain to distinct phenomena.
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Affiliation(s)
- Karlis Kanders
- Institute of Neuroinformatics and Institute for Computational Science, University of Zurich and ETH Zurich, Winterthurerstr. 190, 8057 Zurich, Switzerland
| | - Tom Lorimer
- Institute of Neuroinformatics and Institute for Computational Science, University of Zurich and ETH Zurich, Winterthurerstr. 190, 8057 Zurich, Switzerland
| | - Ruedi Stoop
- Institute of Neuroinformatics and Institute for Computational Science, University of Zurich and ETH Zurich, Winterthurerstr. 190, 8057 Zurich, Switzerland
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134
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Kozma R, Freeman WJ. Cinematic Operation of the Cerebral Cortex Interpreted via Critical Transitions in Self-Organized Dynamic Systems. Front Syst Neurosci 2017; 11:10. [PMID: 28352218 PMCID: PMC5348494 DOI: 10.3389/fnsys.2017.00010] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2016] [Accepted: 02/16/2017] [Indexed: 11/10/2022] Open
Abstract
Measurements of local field potentials over the cortical surface and the scalp of animals and human subjects reveal intermittent bursts of beta and gamma oscillations. During the bursts, narrow-band metastable amplitude modulation (AM) patters emerge for a fraction of a second and ultimately dissolve to the broad-band random background activity. The burst process depends on previously learnt conditioned stimuli (CS), thus different AM patterns may emerge in response to different CS. This observation leads to our cinematic theory of cognition when perception happens in discrete steps manifested in the sequence of AM patterns. Our article summarizes findings in the past decades on experimental evidence of cinematic theory of cognition and relevant mathematical models. We treat cortices as dissipative systems that self-organize themselves near a critical level of activity that is a non-equilibrium metastable state. Criticality is arguably a key aspect of brains in their rapid adaptation, reconfiguration, high storage capacity, and sensitive response to external stimuli. Self-organized criticality (SOC) became an important concept to describe neural systems. We argue that transitions from one AM pattern to the other require the concept of phase transitions, extending beyond the dynamics described by SOC. We employ random graph theory (RGT) and percolation dynamics as fundamental mathematical approaches to model fluctuations in the cortical tissue. Our results indicate that perceptions are formed through a phase transition from a disorganized (high entropy) to a well-organized (low entropy) state, which explains the swiftness of the emergence of the perceptual experience in response to learned stimuli.
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Affiliation(s)
- Robert Kozma
- College of Information and Computer Sciences, University of MassachusettsAmherst, MA, USA; Department of Mathematical Sciences, University of MemphisMemphis, TN, USA
| | - Walter J Freeman
- Department of Molecular and Cell Biology, University of California at Berkeley Berkeley, CA, USA
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135
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Li S. Griffiths phase on hierarchical modular networks with small-world edges. Phys Rev E 2017; 95:032306. [PMID: 28415342 PMCID: PMC7217519 DOI: 10.1103/physreve.95.032306] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2016] [Revised: 12/30/2016] [Indexed: 12/21/2022]
Abstract
The Griffiths phase has been proposed to induce a stretched critical regime that facilitates self-organizing of brain networks for optimal function. This phase stems from the intrinsic structural heterogeneity of brain networks, i.e., the hierarchical modular structure. In this work, the Griffiths phase is studied in modified hierarchical networks with small-world connections based on the 3-regular Hanoi network. Through extensive simulations, the hierarchical level-dependent inter-module wiring probabilities are identified to determine the emergence of the Griffiths phase. Numerical results and the complementary spectral analysis of the relevant networks can be helpful for a deeper understanding of the essential structural characteristics of finite-dimensional networks to support the Griffiths phase.
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Affiliation(s)
- Shanshan Li
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
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136
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Siekmeier PJ. An in Silico, Biomarker-Based Method for the Evaluation of Virtual Neuropsychiatric Drug Effects. Neural Comput 2017; 29:1021-1052. [PMID: 28181877 DOI: 10.1162/neco_a_00944] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
The recent explosion in neuroscience research has markedly increased our understanding of the neurobiological correlates of many psychiatric illnesses, but this has unfortunately not translated into more effective pharmacologic treatments for these conditions. At the same time, researchers have increasingly sought out biological markers, or biomarkers, as a way to categorize psychiatric illness, as these are felt to be closer to underlying genetic and neurobiological vulnerabilities. While biomarker-based drug discovery approaches have tended to employ in vivo (e.g., rodent) or in vitro test systems, relatively little attention has been paid to the potential of computational, or in silico, methodologies. Here we describe such a methodology, using as an example a biophysically detailed computational model of hippocampus that is made to generate putative schizophrenia biomarkers by the inclusion of a number of neuropathological changes that have been associated with the illness (NMDA system deficit, decreased neural connectivity, hyperdopaminergia). We use the specific inability to attune to gamma band (40 Hz) auditory stimulus as our illness biomarker. We expose this system to a large number of virtual medications, defined by systematic variation of model parameters corresponding to five cellular-level effects. The potential efficacy of virtual medications is determined by a wellness metric (WM) that we have developed. We identify a number of virtual agents that consist of combinations of mechanisms, which are not simply reversals of the causative lesions. The manner in which this methodology could be extended to other neuropsychiatric conditions, such as Alzheimer's disease, autism, and fragile X syndrome, is discussed.
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Affiliation(s)
- Peter J Siekmeier
- Harvard Medical School, Boston, MA 02115, and Laboratory for Computational Neuroscience, McLean Hospital, Belmont, MA 02478, U.S.A.
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137
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Touboul J, Destexhe A. Power-law statistics and universal scaling in the absence of criticality. Phys Rev E 2017; 95:012413. [PMID: 28208383 DOI: 10.1103/physreve.95.012413] [Citation(s) in RCA: 80] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2016] [Indexed: 11/07/2022]
Abstract
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.
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Affiliation(s)
- Jonathan Touboul
- The Mathematical Neuroscience Laboratory, CIRB/Collège de France (CNRS UMR 7241, INSERM U1050, UPMC ED 158, MEMOLIFE PSL), Paris, France.,MYCENAE Team, INRIA, Paris, France
| | - Alain Destexhe
- Unit for Neurosciences, Information and Complexity (UNIC), CNRS, Gif sur Yvette, France.,The European Institute for Theoretical Neuroscience (EITN), Paris, France
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138
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Haranas I, Gkigkitzis I, Kotsireas I, Austerlitz C. Neuronal Correlation Parameter and the Idea of Thermodynamic Entropy of an N-Body Gravitationally Bounded System. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2017; 987:35-44. [PMID: 28971445 DOI: 10.1007/978-3-319-57379-3_4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Understanding how the brain encodes information and performs computation requires statistical and functional analysis. Given the complexity of the human brain, simple methods that facilitate the interpretation of statistical correlations among different brain regions can be very useful. In this report we introduce a numerical correlation measure that may serve the interpretation of correlational neuronal data, and may assist in the evaluation of different brain states. The description of the dynamical brain system, through a global numerical measure may indicate the presence of an action principle which may facilitate a application of physics principles in the study of the human brain and cognition.
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Affiliation(s)
- Ioannis Haranas
- Department of Physics and Computer Science, Wilfrid Laurier University Science Building, 75 University Avenue West, Waterloo, ON, N2L 3C5, Canada
| | - Ioannis Gkigkitzis
- Department of Mathematics, East Carolina University, 124 Austin Building, East Fifth Street, Greenville, NC, 27858-4353, USA.
| | - Ilias Kotsireas
- Department of Physics and Computer Science, Wilfrid Laurier University Science Building, 75 University Avenue West, Waterloo, ON, N2L 3C5, Canada
| | - Carlos Austerlitz
- Department of Computer Science, Southern Illinois University, Carbondale, IL, 62901, USA
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139
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Reservoir Computing as a Model for In-Materio Computing. EMERGENCE, COMPLEXITY AND COMPUTATION 2017. [DOI: 10.1007/978-3-319-33924-5_22] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
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140
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Brochini L, de Andrade Costa A, Abadi M, Roque AC, Stolfi J, Kinouchi O. Phase transitions and self-organized criticality in networks of stochastic spiking neurons. Sci Rep 2016; 6:35831. [PMID: 27819336 PMCID: PMC5098137 DOI: 10.1038/srep35831] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2016] [Accepted: 10/05/2016] [Indexed: 12/03/2022] Open
Abstract
Phase transitions and critical behavior are crucial issues both in theoretical and experimental neuroscience. We report analytic and computational results about phase transitions and self-organized criticality (SOC) in networks with general stochastic neurons. The stochastic neuron has a firing probability given by a smooth monotonic function Φ(V) of the membrane potential V, rather than a sharp firing threshold. We find that such networks can operate in several dynamic regimes (phases) depending on the average synaptic weight and the shape of the firing function Φ. In particular, we encounter both continuous and discontinuous phase transitions to absorbing states. At the continuous transition critical boundary, neuronal avalanches occur whose distributions of size and duration are given by power laws, as observed in biological neural networks. We also propose and test a new mechanism to produce SOC: the use of dynamic neuronal gains - a form of short-term plasticity probably located at the axon initial segment (AIS) - instead of depressing synapses at the dendrites (as previously studied in the literature). The new self-organization mechanism produces a slightly supercritical state, that we called SOSC, in accord to some intuitions of Alan Turing.
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Affiliation(s)
- Ludmila Brochini
- Universidade de São Paulo, Departamento de Estatística-IME, São Paulo-SP, 05508-090, Brazil
| | | | - Miguel Abadi
- Universidade de São Paulo, Departamento de Estatística-IME, São Paulo-SP, 05508-090, Brazil
| | - Antônio C. Roque
- Universidade de São Paulo, Departamento de Física-FFCLRP, Ribeirão Preto-SP, 14040-901, Brazil
| | - Jorge Stolfi
- Universidade de Campinas, Instituto de Computação, Campinas-SP, 13083-852, Brazil
| | - Osame Kinouchi
- Universidade de São Paulo, Departamento de Física-FFCLRP, Ribeirão Preto-SP, 14040-901, Brazil
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141
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Llewellyn S. Crossing the invisible line: De-differentiation of wake, sleep and dreaming may engender both creative insight and psychopathology. Conscious Cogn 2016; 46:127-147. [DOI: 10.1016/j.concog.2016.09.018] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2016] [Accepted: 09/13/2016] [Indexed: 12/21/2022]
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142
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West T, Farmer S, Berthouze L, Jha A, Beudel M, Foltynie T, Limousin P, Zrinzo L, Brown P, Litvak V. The Parkinsonian Subthalamic Network: Measures of Power, Linear, and Non-linear Synchronization and their Relationship to L-DOPA Treatment and OFF State Motor Severity. Front Hum Neurosci 2016; 10:517. [PMID: 27826233 PMCID: PMC5078477 DOI: 10.3389/fnhum.2016.00517] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Accepted: 09/29/2016] [Indexed: 11/13/2022] Open
Abstract
In this paper we investigated the dopaminergic modulation of neuronal interactions occurring in the subthalamic nucleus (STN) during Parkinson's disease (PD). We utilized linear measures of local and long range synchrony such as power and coherence, as well as Detrended Fluctuation Analysis for Phase Synchrony (DFA-PS)- a recently developed non-linear method that computes the extent of long tailed autocorrelations present in the phase interactions between two coupled signals. Through analysis of local field potentials (LFPs) taken from the STN we seek to determine changes in the neurodynamics that may underpin the pathophysiology of PD in a group of 12 patients who had undergone surgery for deep brain stimulation. We demonstrate up modulation of alpha-theta (5-12 Hz) band power in response to L-DOPA treatment, whilst low beta band power (15-20 Hz) band-power is suppressed. We also find evidence for significant local connectivity within the region surrounding STN although there was evidence for its modulation via administration of L-DOPA. Further to this we present evidence for a positive correlation between the phase ordering of bilateral STN interactions and the severity of bradykinetic and rigidity symptoms in PD. Although, the ability of non-linear measures to predict clinical state did not exceed standard measures such as beta power, these measures may help identify the connections which play a role in pathological dynamics.
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Affiliation(s)
- Timothy West
- Centre for Mathematics and Physics in the Life Sciences and Experimental Biology, UCLLondon, UK; Wellcome Trust Centre for Neuroimaging, UCL Institute of NeurologyLondon, UK
| | - Simon Farmer
- Department of Neurology, National Hospital for Neurology and NeurosurgeryLondon, UK; Sobell Department of Motor Neuroscience and Movement Disorders, Institute of Neurology, UCLLondon, UK
| | - Luc Berthouze
- Centre for Computational Neuroscience and Robotics, University of SussexFalmer, UK; UCL Great Ormond Street Institute of Child Health, UCLLondon, UK
| | - Ashwani Jha
- Sobell Department of Motor Neuroscience and Movement Disorders, Institute of Neurology, UCL London, UK
| | - Martijn Beudel
- Department of Neurology, University Medical Center Groningen, University of Groningen Groningen, Netherlands
| | - Thomas Foltynie
- Sobell Department of Motor Neuroscience and Movement Disorders, Institute of Neurology, UCL London, UK
| | - Patricia Limousin
- Sobell Department of Motor Neuroscience and Movement Disorders, Institute of Neurology, UCL London, UK
| | - Ludvic Zrinzo
- Sobell Department of Motor Neuroscience and Movement Disorders, Institute of Neurology, UCL London, UK
| | - Peter Brown
- Nuffield Department of Clinical Neurosciences, John Radcliffe HospitalOxford, UK; Medical Research Council Brain Network Dynamics Unit, University of OxfordOxford, UK
| | - Vladimir Litvak
- Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology London, UK
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143
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Timme NM, Marshall NJ, Bennett N, Ripp M, Lautzenhiser E, Beggs JM. Criticality Maximizes Complexity in Neural Tissue. Front Physiol 2016; 7:425. [PMID: 27729870 PMCID: PMC5037237 DOI: 10.3389/fphys.2016.00425] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2016] [Accepted: 09/08/2016] [Indexed: 11/25/2022] Open
Abstract
The analysis of neural systems leverages tools from many different fields. Drawing on techniques from the study of critical phenomena in statistical mechanics, several studies have reported signatures of criticality in neural systems, including power-law distributions, shape collapses, and optimized quantities under tuning. Independently, neural complexity-an information theoretic measure-has been introduced in an effort to quantify the strength of correlations across multiple scales in a neural system. This measure represents an important tool in complex systems research because it allows for the quantification of the complexity of a neural system. In this analysis, we studied the relationships between neural complexity and criticality in neural culture data. We analyzed neural avalanches in 435 recordings from dissociated hippocampal cultures produced from rats, as well as neural avalanches from a cortical branching model. We utilized recently developed maximum likelihood estimation power-law fitting methods that account for doubly truncated power-laws, an automated shape collapse algorithm, and neural complexity and branching ratio calculation methods that account for sub-sampling, all of which are implemented in the freely available Neural Complexity and Criticality MATLAB toolbox. We found evidence that neural systems operate at or near a critical point and that neural complexity is optimized in these neural systems at or near the critical point. Surprisingly, we found evidence that complexity in neural systems is dependent upon avalanche profiles and neuron firing rate, but not precise spiking relationships between neurons. In order to facilitate future research, we made all of the culture data utilized in this analysis freely available online.
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Affiliation(s)
- Nicholas M. Timme
- Department of Psychology, Indiana University - Purdue University IndianapolisIndianapolis, IN, USA
| | | | | | - Monica Ripp
- Department of Physics, Syracuse UniversitySyracuse, NY, USA
| | | | - John M. Beggs
- Department of Physics, Indiana UniversityBloomington, IN, USA
- Biocomplexity Institute, Indiana UniversityBloomington, IN, USA
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144
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Miskovic V, Owens M, Kuntzelman K, Gibb BE. Charting moment-to-moment brain signal variability from early to late childhood. Cortex 2016; 83:51-61. [PMID: 27479615 DOI: 10.1016/j.cortex.2016.07.006] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2016] [Revised: 05/20/2016] [Accepted: 07/06/2016] [Indexed: 01/08/2023]
Abstract
Large-scale brain signals exhibit rich intermittent patterning, reflecting the fact that the cortex actively eschews fixed points in favor of itinerant wandering with frequent state transitions. Fluctuations in endogenous cortical activity occur at multiple time scales and index a dynamic repertoire of network states that are continuously explored, even in the absence of external sensory inputs. Here, we quantified such moment-to-moment brain signal variability at rest in a large, cross-sectional sample of children ranging in age from seven to eleven years. Our findings revealed a monotonic rise in the complexity of electroencephalogram (EEG) signals as measured by sample entropy, from the youngest to the oldest age cohort, across a range of time scales and spatial regions. From year to year, the greatest changes in intraindividual brain signal variability were recorded at electrodes covering the anterior cortical zones. These results provide converging evidence concerning the age-dependent expansion of functional cortical network states during a critical developmental period ranging from early to late childhood.
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Affiliation(s)
- Vladimir Miskovic
- Center for Affective Science, State University of New York at Binghamton, USA.
| | - Max Owens
- Center for Affective Science, State University of New York at Binghamton, USA
| | - Karl Kuntzelman
- Center for Affective Science, State University of New York at Binghamton, USA
| | - Brandon E Gibb
- Center for Affective Science, State University of New York at Binghamton, USA
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145
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Trevelyan AJ. Do Cortical Circuits Need Protecting from Themselves? Trends Neurosci 2016; 39:502-511. [PMID: 27378547 DOI: 10.1016/j.tins.2016.06.002] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2016] [Revised: 05/09/2016] [Accepted: 06/09/2016] [Indexed: 01/27/2023]
Abstract
All hippocampal and neocortical networks can be driven to seize quite easily. This can be done using drugs, by altering the ionic constituency of the bathing medium [cerebrospinal fluid (CSF)], or by electrical stimulation (both experimentally and clinically, as in electroconvulsive therapy). It is worth asking why this is so, because this will both tell us more about potentially devastating neurological disorders and extend our understanding of cortical function and architecture. Here I review work examining the features of cortical networks that bias activity towards and away from hyperexcitability. I suggest that several cellular- and circuit-level features of rapidly responsive interneuron networks tip the balance away from seizure in the healthy brain.
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Affiliation(s)
- Andrew J Trevelyan
- Institute of Neuroscience, Medical School, Framlington Place, Newcastle upon Tyne NE2 4HH, UK.
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146
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Marshall N, Timme NM, Bennett N, Ripp M, Lautzenhiser E, Beggs JM. Analysis of Power Laws, Shape Collapses, and Neural Complexity: New Techniques and MATLAB Support via the NCC Toolbox. Front Physiol 2016; 7:250. [PMID: 27445842 PMCID: PMC4921690 DOI: 10.3389/fphys.2016.00250] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2016] [Accepted: 06/08/2016] [Indexed: 11/13/2022] Open
Abstract
Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of "neural avalanches" (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods-power-law fitting, avalanche shape collapse, and neural complexity-have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox.
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Affiliation(s)
- Najja Marshall
- Department of Neuroscience, Columbia University New York, NY, USA
| | - Nicholas M Timme
- Department of Psychology, Indiana University - Purdue University Indianapolis Indianapolis, IN, USA
| | | | - Monica Ripp
- Department of Physics, Syracuse University Syracuse, NY, USA
| | | | - John M Beggs
- Department of Physics, Indiana UniversityBloomington, IN, USA; Biocomplexity Institute, Indiana UniversityBloomington, IN, USA
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147
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Abstract
A simple theory of health has recently been proposed: while poor quality regulation corresponds to poor quality health so that improving regulation should improve health, optimal regulation optimizes function and optimizes health. Examining the term 'optimal regulation' in biological systems leads to a straightforward definition in terms of 'criticality' in complexity biology, a concept that seems to apply universally throughout biology. Criticality maximizes information processing and sensitivity of response to external stimuli, and for these reasons may be held to optimize regulation. In this way a definition of health has been given in terms of regulation, a scientific concept, which ties into detailed properties of complex systems, including brain cortices, and mental health. Models of experience and meditation built on complexity also point to criticality: it represents the condition making self-awareness possible, and is strengthened by meditation practices leading to the state of pure consciousness-the content-free state of mind in deep meditation. From this it follows that healthy function of the brain cortex, its sensitivity,y and consistency of response to external challenges should improve by practicing techniques leading to content-free awareness-transcending the original focus introduced during practice. Evidence for this is reviewed.
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Affiliation(s)
- Alex Hankey
- a Vivekananda Yoga Anusandhana Samsthana , Department of Yoga and Physical Science , Karnataka , India
| | - Rashmi Shetkar
- a Vivekananda Yoga Anusandhana Samsthana , Department of Yoga and Physical Science , Karnataka , India
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148
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Abstract
Biology is the study of dynamical systems. Yet most of us working in biology have limited pedagogical training in the theory of dynamical systems, an unfortunate historical fact that can be remedied for future generations of life scientists. In my particular field of systems neuroscience, neural circuits are rife with nonlinearities at all levels of description, rendering simple methodologies and our own intuition unreliable. Therefore, our ideas are likely to be wrong unless informed by good models. These models should be based on the mathematical theories of dynamical systems since functioning neurons are dynamic—they change their membrane potential and firing rates with time. Thus, selecting the appropriate type of dynamical system upon which to base a model is an important first step in the modeling process. This step all too easily goes awry, in part because there are many frameworks to choose from, in part because the sparsely sampled data can be consistent with a variety of dynamical processes, and in part because each modeler has a preferred modeling approach that is difficult to move away from. This brief review summarizes some of the main dynamical paradigms that can arise in neural circuits, with comments on what they can achieve computationally and what signatures might reveal their presence within empirical data. I provide examples of different dynamical systems using simple circuits of two or three cells, emphasizing that any one connectivity pattern is compatible with multiple, diverse functions.
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Affiliation(s)
- Paul Miller
- Volen National Center for Complex Systems, Brandeis University, Waltham, Massachusetts, 02454-9110, USA
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149
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Euler MJ, Wiltshire TJ, Niermeyer MA, Butner JE. Working memory performance inversely predicts spontaneous delta and theta-band scaling relations. Brain Res 2016; 1637:22-33. [DOI: 10.1016/j.brainres.2016.02.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2015] [Revised: 01/05/2016] [Accepted: 02/02/2016] [Indexed: 10/22/2022]
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150
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Affiliation(s)
- Victor Hernandez-Urbina
- School of Informatics, Institute of Perception, Action and Behaviour, The University of Edinburgh 10 Crichton St Edinburgh EH8 9AB UK
| | - J. Michael Herrmann
- School of Informatics, Institute of Perception, Action and Behaviour, The University of Edinburgh 10 Crichton St Edinburgh EH8 9AB UK
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