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Abstract
Rapidly growing empirical evidence supports the hypothesis that the cortex operates near criticality. Although the confirmation of this hypothesis would mark a significant advance in fundamental understanding of cortical physiology, a natural question arises: What functional benefits are endowed to cortical circuits that operate at criticality? In this review, we first describe an introductory-level thought experiment to provide the reader with an intuitive understanding of criticality. Second, we discuss some practical approaches for investigating criticality. Finally, we review quantitative evidence that three functional properties of the cortex are optimized at criticality: 1) dynamic range, 2) information transmission, and 3) information capacity. We focus on recently reported experimental evidence and briefly discuss the theory and history of these ideas.
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Affiliation(s)
- Woodrow L. Shew
- University of Arkansas, Department of Physics, Fayetteville, AR, USA
| | - Dietmar Plenz
- National Institutes of Health, NIMH, Bethesda, MD, USA
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202
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203
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Gollo LL, Mirasso C, Eguíluz VM. Signal integration enhances the dynamic range in neuronal systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:040902. [PMID: 22680413 DOI: 10.1103/physreve.85.040902] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2011] [Revised: 12/09/2011] [Indexed: 06/01/2023]
Abstract
The dynamic range measures the capacity of a system to discriminate the intensity of an external stimulus. Such an ability is fundamental for living beings to survive: to leverage resources and to avoid danger. Consequently, the larger is the dynamic range, the greater is the probability of survival. We investigate how the integration of different input signals affects the dynamic range, and in general the collective behavior of a network of excitable units. By means of numerical simulations and a mean-field approach, we explore the nonequilibrium phase transition in the presence of integration. We show that the firing rate in random and scale-free networks undergoes a discontinuous phase transition depending on both the integration time and the density of integrator units. Moreover, in the presence of external stimuli, we find that a system of excitable integrator units operating in a bistable regime largely enhances its dynamic range.
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Affiliation(s)
- Leonardo L Gollo
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain.
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204
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Boedecker J, Obst O, Lizier JT, Mayer NM, Asada M. Information processing in echo state networks at the edge of chaos. Theory Biosci 2011; 131:205-13. [DOI: 10.1007/s12064-011-0146-8] [Citation(s) in RCA: 86] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2010] [Accepted: 11/28/2010] [Indexed: 10/14/2022]
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205
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Leyva I, Navas A, Sendiña-Nadal I, Buldú JM, Almendral JA, Boccaletti S. Synchronization waves in geometric networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:065101. [PMID: 22304141 DOI: 10.1103/physreve.84.065101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2011] [Indexed: 05/31/2023]
Abstract
We report synchronization of networked excitable nodes embedded in a metric space, where the connectivity properties are mostly determined by the distance between units. Such a high clustered structure, combined with the lack of long-range connections, prevents full synchronization and yields instead the emergence of synchronization waves. We show that this regime is optimal for information transmission through the system, as it enhances the options of reconstructing the topology from the dynamics. Measurements of topological and functional centralities reveal that the wave-synchronization state allows detection of the most structurally relevant nodes from a single observation of the dynamics, without any a priori information on the model equations ruling the evolution of the ensemble.
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Affiliation(s)
- I Leyva
- Complex Systems Group, Rey Juan Carlos University, Móstoles E-28999, Madrid, Spain
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206
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Exploring the spectrum of dynamical regimes and timescales in spontaneous cortical activity. Cogn Neurodyn 2011; 6:239-50. [PMID: 23730355 DOI: 10.1007/s11571-011-9179-4] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2011] [Revised: 10/11/2011] [Accepted: 10/17/2011] [Indexed: 10/16/2022] Open
Abstract
Rhythms at slow (<1 Hz) frequency of alternating Up and Down states occur during slow-wave sleep states, under deep anaesthesia and in cortical slices of mammals maintained in vitro. Such spontaneous oscillations result from the interplay between network reverberations nonlinearly sustained by a strong synaptic coupling and a fatigue mechanism inhibiting the neurons firing in an activity-dependent manner. Varying pharmacologically the excitability level of brain slices we exploit the network dynamics underlying slow rhythms, uncovering an intrinsic anticorrelation between Up and Down state durations. Besides, a non-monotonic change of Down state duration is also observed, which shrinks the distribution of the accessible frequencies of the slow rhythms. Attractor dynamics with activity-dependent self-inhibition predicts a similar trend even when the system excitability is reduced, because of a stability loss of Up and Down states. Hence, such cortical rhythms tend to display a maximal size of the distribution of Up/Down frequencies, envisaging the location of the system dynamics on a critical boundary of the parameter space. This would be an optimal solution for the system in order to display a wide spectrum of dynamical regimes and timescales.
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207
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Poil SS, Jansen R, van Aerde K, Timmerman J, Brussaard AB, Mansvelder HD, Linkenkaer-Hansen K. Fast network oscillations in vitro exhibit a slow decay of temporal auto-correlations. Eur J Neurosci 2011; 34:394-403. [PMID: 21692883 DOI: 10.1111/j.1460-9568.2011.07748.x] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Ongoing neuronal oscillations in vivo exhibit non-random amplitude fluctuations as reflected in a slow decay of temporal auto-correlations that persist for tens of seconds. Interestingly, the decay of auto-correlations is altered in several brain-related disorders, including epilepsy, depression and Alzheimer's disease, suggesting that the temporal structure of oscillations depends on intact neuronal networks in the brain. Whether structured amplitude modulation occurs only in the intact brain or whether isolated neuronal networks can also give rise to amplitude modulation with a slow decay is not known. Here, we examined the temporal structure of cholinergic fast network oscillations in acute hippocampal slices. For the first time, we show that a slow decay of temporal correlations can emerge from synchronized activity in isolated hippocampal networks from mice, and is maximal at intermediate concentrations of the cholinergic agonist carbachol. Using zolpidem, a positive allosteric modulator of GABA(A) receptor function, we found that increased inhibition leads to longer oscillation bursts and more persistent temporal correlations. In addition, we asked if these findings were unique for mouse hippocampus, and we therefore analysed cholinergic fast network oscillations in rat prefrontal cortex slices. We observed significant temporal correlations, which were similar in strength to those found in mouse hippocampus and human cortex. Taken together, our data indicate that fast network oscillations with temporal correlations can be induced in isolated networks in vitro in different species and brain areas, and therefore may serve as model systems to investigate how altered temporal correlations in disease may be rescued with pharmacology.
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Affiliation(s)
- Simon-Shlomo Poil
- Department of Integrative Neurophysiology, Center for Neurogenomics and Cognitive Research, Neuroscience Campus Amsterdam, VU University Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands
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208
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Neurobiologically realistic determinants of self-organized criticality in networks of spiking neurons. PLoS Comput Biol 2011; 7:e1002038. [PMID: 21673863 PMCID: PMC3107249 DOI: 10.1371/journal.pcbi.1002038] [Citation(s) in RCA: 140] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2010] [Accepted: 03/10/2011] [Indexed: 11/19/2022] Open
Abstract
Self-organized criticality refers to the spontaneous emergence of self-similar dynamics in complex systems poised between order and randomness. The presence of self-organized critical dynamics in the brain is theoretically appealing and is supported by recent neurophysiological studies. Despite this, the neurobiological determinants of these dynamics have not been previously sought. Here, we systematically examined the influence of such determinants in hierarchically modular networks of leaky integrate-and-fire neurons with spike-timing-dependent synaptic plasticity and axonal conduction delays. We characterized emergent dynamics in our networks by distributions of active neuronal ensemble modules (neuronal avalanches) and rigorously assessed these distributions for power-law scaling. We found that spike-timing-dependent synaptic plasticity enabled a rapid phase transition from random subcritical dynamics to ordered supercritical dynamics. Importantly, modular connectivity and low wiring cost broadened this transition, and enabled a regime indicative of self-organized criticality. The regime only occurred when modular connectivity, low wiring cost and synaptic plasticity were simultaneously present, and the regime was most evident when between-module connection density scaled as a power-law. The regime was robust to variations in other neurobiologically relevant parameters and favored systems with low external drive and strong internal interactions. Increases in system size and connectivity facilitated internal interactions, permitting reductions in external drive and facilitating convergence of postsynaptic-response magnitude and synaptic-plasticity learning rate parameter values towards neurobiologically realistic levels. We hence infer a novel association between self-organized critical neuronal dynamics and several neurobiologically realistic features of structural connectivity. The central role of these features in our model may reflect their importance for neuronal information processing.
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209
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Kitzbichler MG, Henson RNA, Smith ML, Nathan PJ, Bullmore ET. Cognitive effort drives workspace configuration of human brain functional networks. J Neurosci 2011; 31:8259-70. [PMID: 21632947 PMCID: PMC6622866 DOI: 10.1523/jneurosci.0440-11.2011] [Citation(s) in RCA: 270] [Impact Index Per Article: 20.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2011] [Revised: 03/29/2011] [Accepted: 04/19/2011] [Indexed: 12/23/2022] Open
Abstract
Effortful cognitive performance is theoretically expected to depend on the formation of a global neuronal workspace. We tested specific predictions of workspace theory, using graph theoretical measures of network topology and physical distance of synchronization, in magnetoencephalographic data recorded from healthy adult volunteers (N = 13) during performance of a working memory task at several levels of difficulty. We found that greater cognitive effort caused emergence of a more globally efficient, less clustered, and less modular network configuration, with more long-distance synchronization between brain regions. This pattern of task-related workspace configuration was more salient in the β-band (16-32 Hz) and γ-band (32-63 Hz) networks, compared with both lower (α-band; 8-16 Hz) and higher (high γ-band; 63-125 Hz) frequency intervals. Workspace configuration of β-band networks was also greater in faster performing participants (with correct response latency less than the sample median) compared with slower performing participants. Processes of workspace formation and relaxation in relation to time-varying demands for cognitive effort could be visualized occurring in the course of task trials lasting <2 s. These experimental results provide support for workspace theory in terms of complex network metrics and directly demonstrate how cognitive effort breaks modularity to make human brain functional networks transiently adopt a more efficient but less economical configuration.
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Affiliation(s)
- Manfred G. Kitzbichler
- Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ, United Kingdom
| | - Richard N. A. Henson
- Cognition and Brain Sciences Unit, Medical Research Council, Cambridge CB2 7EF, United Kingdom
| | - Marie L. Smith
- Cognition and Brain Sciences Unit, Medical Research Council, Cambridge CB2 7EF, United Kingdom
| | - Pradeep J. Nathan
- Clinical Unit Cambridge, GlaxoSmithKline, Addenbrooke's Centre for Clinical Investigations, Cambridge CB2 0QQ, United Kingdom
| | - Edward T. Bullmore
- Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ, United Kingdom
- Clinical Unit Cambridge, GlaxoSmithKline, Addenbrooke's Centre for Clinical Investigations, Cambridge CB2 0QQ, United Kingdom
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210
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Medina JM. Effects of multiplicative power law neural noise in visual information processing. Neural Comput 2011; 23:1015-46. [PMID: 21222525 DOI: 10.1162/neco_a_00102] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
The human visual system is intrinsically noisy. The benefits of internal noise as part of visual code are controversial. Here the information-theoretic properties of multiplicative (i.e. signal-dependent) neural noise are investigated. A quasi-linear communication channel model is presented. The model shows that multiplicative power law neural noise promotes the minimum information transfer after efficient coding. It is demonstrated that Weber's law and the human contrast sensitivity function arise on the basis of minimum transfer of information and power law neural noise. The implications of minimum information transfer in self-organized neural networks and weakly coupled neurons are discussed.
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Affiliation(s)
- Jos M Medina
- Center for Physics. University of Minho, Braga 4710-057, Portugal.
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211
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Werner G. Fractals in the nervous system: conceptual implications for theoretical neuroscience. Front Physiol 2010; 1:15. [PMID: 21423358 PMCID: PMC3059969 DOI: 10.3389/fphys.2010.00015] [Citation(s) in RCA: 91] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2010] [Accepted: 06/05/2010] [Indexed: 11/15/2022] Open
Abstract
This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power-law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review.
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Affiliation(s)
- Gerhard Werner
- Department of Biomedical Engineering, University of Texas at Austin TX, USA.
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212
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Kello CT, Brown GD, Ferrer-i-Cancho R, Holden JG, Linkenkaer-Hansen K, Rhodes T, Van Orden GC. Scaling laws in cognitive sciences. Trends Cogn Sci 2010; 14:223-32. [DOI: 10.1016/j.tics.2010.02.005] [Citation(s) in RCA: 163] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2009] [Revised: 02/21/2010] [Accepted: 02/22/2010] [Indexed: 10/19/2022]
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213
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Abstract
Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity. The shortcoming of these equations is that they take into account only the average firing rate, while leaving out higher-order statistics like correlations between firing. A stochastic theory of neural networks that includes statistics at all orders was recently formulated. We describe how this theory yields a systematic extension to population rate equations by introducing equations for correlations and appropriate coupling terms. Each level of the approximation yields closed equations; they depend only on the mean and specific correlations of interest, without an ad hoc criterion for doing so. We show in an example of an all-to-all connected network how our system of generalized activity equations captures phenomena missed by the mean field rate equations alone.
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214
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Chen W, Hobbs JP, Tang A, Beggs JM. A few strong connections: optimizing information retention in neuronal avalanches. BMC Neurosci 2010; 11:3. [PMID: 20053290 PMCID: PMC2824798 DOI: 10.1186/1471-2202-11-3] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2009] [Accepted: 01/06/2010] [Indexed: 02/02/2023] Open
Abstract
BACKGROUND How living neural networks retain information is still incompletely understood. Two prominent ideas on this topic have developed in parallel, but have remained somewhat unconnected. The first of these, the "synaptic hypothesis," holds that information can be retained in synaptic connection strengths, or weights, between neurons. Recent work inspired by statistical mechanics has suggested that networks will retain the most information when their weights are distributed in a skewed manner, with many weak weights and only a few strong ones. The second of these ideas is that information can be represented by stable activity patterns. Multineuron recordings have shown that sequences of neural activity distributed over many neurons are repeated above chance levels when animals perform well-learned tasks. Although these two ideas are compelling, no one to our knowledge has yet linked the predicted optimum distribution of weights to stable activity patterns actually observed in living neural networks. RESULTS Here, we explore this link by comparing stable activity patterns from cortical slice networks recorded with multielectrode arrays to stable patterns produced by a model with a tunable weight distribution. This model was previously shown to capture central features of the dynamics in these slice networks, including neuronal avalanche cascades. We find that when the model weight distribution is appropriately skewed, it correctly matches the distribution of repeating patterns observed in the data. In addition, this same distribution of weights maximizes the capacity of the network model to retain stable activity patterns. Thus, the distribution that best fits the data is also the distribution that maximizes the number of stable patterns. CONCLUSIONS We conclude that local cortical networks are very likely to use a highly skewed weight distribution to optimize information retention, as predicted by theory. Fixed distributions impose constraints on learning, however. The network must have mechanisms for preserving the overall weight distribution while allowing individual connection strengths to change with learning.
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Affiliation(s)
- Wei Chen
- Indiana University Department of Physics, 727 East 3rd Street, Bloomington, Indiana, USA
| | - Jon P Hobbs
- Indiana University Department of Physics, 727 East 3rd Street, Bloomington, Indiana, USA
| | - Aonan Tang
- Indiana University Department of Physics, 727 East 3rd Street, Bloomington, Indiana, USA
| | - John M Beggs
- Indiana University Department of Physics, 727 East 3rd Street, Bloomington, Indiana, USA
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215
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Schachter SC, Guttag J, Schiff SJ, Schomer DL. Advances in the application of technology to epilepsy: the CIMIT/NIO Epilepsy Innovation Summit. Epilepsy Behav 2009; 16:3-46. [PMID: 19780225 PMCID: PMC8118381 DOI: 10.1016/j.yebeh.2009.06.028] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
In 2008, a group of clinicians, scientists, engineers, and industry representatives met to discuss advances in the application of engineering technologies to the diagnosis and treatment of patients with epilepsy. The presentations also provided a guide for further technological development, specifically in the evaluation of patients for epilepsy surgery, seizure onset detection and seizure prediction, intracranial treatment systems, and extracranial treatment systems. This article summarizes the discussions and demonstrates that cross-disciplinary interactions can catalyze collaborations between physicians and engineers to address and solve many of the pressing unmet needs in epilepsy.
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Affiliation(s)
- Steven C Schachter
- Center for Integration of Medicine and Innovative Technology, Boston, MA, USA.
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216
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Hsu D, Hsu M. Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion. PMC BIOPHYSICS 2009; 2:6. [PMID: 19594920 PMCID: PMC2728514 DOI: 10.1186/1757-5036-2-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/22/2009] [Accepted: 07/13/2009] [Indexed: 11/24/2022]
Abstract
We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation of motion that has the form of a generalized Langevin equation (GLE), which requires knowledge only of macroscopic properties. The macroscopic properties can be extracted from experimental data by one of two possible variational principles. These variational principles are our principal contribution to the formalism. Potential applications are discussed, including applications to the theory of critical phenomena in the brain, Granger causality and Kalman filters. PACS code: 87.19.lj
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Affiliation(s)
- David Hsu
- Department of Neurology, University of Wisconsin, Madison WI, USA.
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217
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Generic aspects of complexity in brain imaging data and other biological systems. Neuroimage 2009; 47:1125-34. [PMID: 19460447 DOI: 10.1016/j.neuroimage.2009.05.032] [Citation(s) in RCA: 100] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2009] [Revised: 05/03/2009] [Accepted: 05/08/2009] [Indexed: 12/13/2022] Open
Abstract
A key challenge for systems neuroscience is the question of how to understand the complex network organization of the brain on the basis of neuroimaging data. Similar challenges exist in other specialist areas of systems biology because complex networks emerging from the interactions between multiple non-trivially interacting agents are found quite ubiquitously in nature, from protein interactomes to ecosystems. We suggest that one way forward for analysis of brain networks will be to quantify aspects of their organization which are likely to be generic properties of a broader class of biological systems. In this introductory review article we will highlight four important aspects of complex systems in general: fractality or scale-invariance; criticality; small-world and related topological attributes; and modularity. For each concept we will provide an accessible introduction, an illustrative data-based example of how it can be used to investigate aspects of brain organization in neuroimaging experiments, and a brief review of how this concept has been applied and developed in other fields of biomedical and physical science. The aim is to provide a didactic, focussed and user-friendly introduction to the concepts of complexity science for neuroscientists and neuroimagers.
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218
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Priesemann V, Munk MHJ, Wibral M. Subsampling effects in neuronal avalanche distributions recorded in vivo. BMC Neurosci 2009; 10:40. [PMID: 19400967 PMCID: PMC2697147 DOI: 10.1186/1471-2202-10-40] [Citation(s) in RCA: 82] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2008] [Accepted: 04/29/2009] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Many systems in nature are characterized by complex behaviour where large cascades of events, or avalanches, unpredictably alternate with periods of little activity. Snow avalanches are an example. Often the size distribution f(s) of a system's avalanches follows a power law, and the branching parameter sigma, the average number of events triggered by a single preceding event, is unity. A power law for f(s), and sigma = 1, are hallmark features of self-organized critical (SOC) systems, and both have been found for neuronal activity in vitro. Therefore, and since SOC systems and neuronal activity both show large variability, long-term stability and memory capabilities, SOC has been proposed to govern neuronal dynamics in vivo. Testing this hypothesis is difficult because neuronal activity is spatially or temporally subsampled, while theories of SOC systems assume full sampling. To close this gap, we investigated how subsampling affects f(s) and sigma by imposing subsampling on three different SOC models. We then compared f(s) and sigma of the subsampled models with those of multielectrode local field potential (LFP) activity recorded in three macaque monkeys performing a short term memory task. RESULTS Neither the LFP nor the subsampled SOC models showed a power law for f(s). Both, f(s) and sigma, depended sensitively on the subsampling geometry and the dynamics of the model. Only one of the SOC models, the Abelian Sandpile Model, exhibited f(s) and sigma similar to those calculated from LFP activity. CONCLUSION Since subsampling can prevent the observation of the characteristic power law and sigma in SOC systems, misclassifications of critical systems as sub- or supercritical are possible. Nevertheless, the system specific scaling of f(s) and sigma under subsampling conditions may prove useful to select physiologically motivated models of brain function. Models that better reproduce f(s) and sigma calculated from the physiological recordings may be selected over alternatives.
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Affiliation(s)
- Viola Priesemann
- Department of Neurophysiology, Max Planck Institute for Brain Research, Deutschordenstrasse 46, D-60528 Frankfurt am Main, Germany.
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219
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Broadband criticality of human brain network synchronization. PLoS Comput Biol 2009; 5:e1000314. [PMID: 19300473 PMCID: PMC2647739 DOI: 10.1371/journal.pcbi.1000314] [Citation(s) in RCA: 301] [Impact Index Per Article: 20.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2008] [Accepted: 02/02/2009] [Indexed: 11/19/2022] Open
Abstract
Self-organized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in large-scale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, long-range correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phase-lock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phase-locking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal “avalanches” previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05–0.11 to 62.5–125 Hz, confirming that criticality is a property of human brain functional network organization at all frequency intervals in the brain's physiological bandwidth. Systems in a critical state are poised on the cusp of a transition between ordered and random behavior. At this point, they demonstrate complex patterning of fluctuations at all scales of space and time. Criticality is an attractive model for brain dynamics because it optimizes information transfer, storage capacity, and sensitivity to external stimuli in computational models. However, to date there has been little direct experimental evidence for critical dynamics of human brain networks. Here, we considered two measures of functional coupling or phase synchronization between components of a dynamic system: the phase lock interval or duration of synchronization between a specific pair of time series or processes in the system and the lability of global synchronization among all pairs of processes. We confirmed that both synchronization metrics demonstrated scale invariant behaviors in two computational models of critical dynamics as well as in human brain functional systems oscillating at low frequencies (<0.5 Hz, measured using functional MRI) and at higher frequencies (1–125 Hz, measured using magnetoencephalography). We conclude that human brain functional networks demonstrate critical dynamics in all frequency intervals, a phenomenon we have described as broadband criticality.
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220
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Hsu D, Chen W, Hsu M, Beggs JM. An open hypothesis: is epilepsy learned, and can it be unlearned? Epilepsy Behav 2008; 13:511-22. [PMID: 18573694 PMCID: PMC2611958 DOI: 10.1016/j.yebeh.2008.05.007] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/22/2008] [Revised: 05/13/2008] [Accepted: 05/14/2008] [Indexed: 10/21/2022]
Abstract
Plasticity is central to the ability of a neural system to learn and also to its ability to develop spontaneous seizures. What is the connection between the two? Learning itself is known to be a destabilizing process at the algorithmic level. We have investigated necessary constraints on a spontaneously active Hebbian learning system and find that the ability to learn appears to confer an intrinsic vulnerability to epileptogenesis on that system. We hypothesize that epilepsy arises as an abnormal learned response of such a system to certain repeated provocations. This response is a network-level effect. If epilepsy really is a learned response, then it should be possible to reverse it, that is, to unlearn epilepsy. Unlearning epilepsy may then provide a new approach to its treatment.
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Affiliation(s)
- David Hsu
- Department of Neurology, University of Wisconsin, Madison, WI 53792, USA.
| | - Wei Chen
- Department of Physics, Indiana University, Bloomington IN
| | - Murielle Hsu
- Department of Neurology, University of Wisconsin, Madison WI
| | - John M. Beggs
- Department of Physics, Indiana University, Bloomington IN
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221
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Poil SS, van Ooyen A, Linkenkaer-Hansen K. Avalanche dynamics of human brain oscillations: relation to critical branching processes and temporal correlations. Hum Brain Mapp 2008; 29:770-7. [PMID: 18454457 DOI: 10.1002/hbm.20590] [Citation(s) in RCA: 73] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Human brain oscillations fluctuate erratically in amplitude during rest and exhibit power-law decay of temporal correlations. It has been suggested that this dynamics reflects self-organized activity near a critical state. In this framework, oscillation bursts may be interpreted as neuronal avalanches propagating in a network with a critical branching ratio. However, a direct comparison of the temporal structure of ongoing oscillations with that of activity propagation in a model network with critical connectivity has never been made. Here, we simulate branching processes and characterize the activity propagation in terms of avalanche life-time distributions and temporal correlations. An equivalent analysis is introduced for characterizing ongoing oscillations in the alpha-frequency band recorded with magnetoencephalography (MEG) during rest. We found that models with a branching ratio near the critical value of one exhibited power-law scaling in life-time distributions with similar scaling exponents as observed in the MEG data. The models reproduced qualitatively the power-law decay of temporal correlations in the human data; however, the correlations in the model appeared on time scales only up to the longest avalanche, whereas human data indicate persistence of correlations on time scales corresponding to several burst events. Our results support the idea that neuronal networks generating ongoing alpha oscillations during rest operate near a critical state, but also suggest that factors not included in the simple classical branching process are needed to account for the complex temporal structure of ongoing oscillations during rest on time scales longer than the duration of individual oscillation bursts.
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Affiliation(s)
- Simon-Shlomo Poil
- Department of Experimental Neurophysiology, Center for Neurogenomics and Cognitive Research (CNCR), VU University Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands
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Beggs JM, Klukas J, Chen W. Connectivity and Dynamics in Local Cortical Networks. UNDERSTANDING COMPLEX SYSTEMS 2007. [DOI: 10.1007/978-3-540-71512-2_3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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