Self-organized criticality: An explanation of the 1/<i>f</i>noise

Bak, Per; Tang, Chao; Wiesenfeld, Kurt

doi:10.1103/physrevlett.59.381

Cited by 7,212 publications

(5,990 citation statements)

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“…The most well known type of system displaying SOC, the paradigmatic example of which is the Bak-Tang-Wiesenfeld sandpile model (Bak, Tang et al, 1987), consists of a 2-dimensional grid of cells, each of which can contain up to four grains, after which a cell will 'topple' and distribute its contents to its neighbors. When grains are added randomly to the grid ('driving'), this inevitably leads to some cells to topple, resulting them to distribute their contents to their neighbors (which may render them unstable), and the cascade of toppling continues until the entire system reaches a state of stability, i.e.…”

Section: Self-organized Criticality As a Homeostatic Principle Duringmentioning

confidence: 99%

“…The critical state fits our hypothesis; the high variability of neuronal synchronization encountered is an intrinsic system feature. Critical states have been reported in a wide range of physical systems with non-linear propagation characteristics (Bak, Tang et al, 1987;Drossel and Schwabl, 1992;Christensen, Flyvbjerg et al, 1993;Paczuski, Maslov et al, 1996;Bak, Chen et al, 2001) and have been demonstrated in neuronal network simulations (for review see Plenz and Thiagarajan, 2007).…”

Section: Introductionmentioning

confidence: 99%

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Homeostasis of neuronal avalanches during postnatal cortex development in vitro

Stewart

Plenz

2008

Journal of Neuroscience Methods

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Cortical networks in vivo and in vitro are spontaneously active in the absence of inputs, generating highly variable bursts of neuronal activity separated by up to seconds of quiescence. Previous measurements in adult rat cortex revealed an intriguing underlying organization of these dynamics, termed neuronal avalanches, which is indicative of a critical network state. Here we demonstrate that neuronal avalanches persist throughout development in cortical slice cultures from newborn rats. More specifically, we find that in spite of large variations of average rate in activity, spontaneous bursts occur with power-law distributed sizes (exponent -1.5) and a critical branching parameter close to 1. Our findings suggest that cortical networks homeostatically regulate a critical state during postnatal maturation.

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Section: Self-organized Criticality As a Homeostatic Principle Duringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Homeostasis of neuronal avalanches during postnatal cortex development in vitro

Stewart

Plenz

2008

Journal of Neuroscience Methods

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“…One such is provided by the theory of self-organized criticality ("SOC", Bak, Tang and Wiesenfeld, 1987, Bak, 1996, Jensen, 1998Watters, 2000) backed by modeling cortical dynamics with nonlinear ordinary differential equations (Freeman, 1975 and Appendix 2.4). The classic SOC object of study was a sand pile as at the bottom of an hourglass.…”

Section: Eeg Phase Data and The Concept Of Self-organized Criticalitymentioning

confidence: 99%

Origin, structure, and role of background EEG activity. Part 2. Analytic phase

Freeman

2004

Clinical Neurophysiology

172

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Objective: To explain spontaneous EEG through measurements of spatiotemporal patterns of phase among beta-gamma oscillations.Methods: High-density 8x8 intracranial arrays were fixed over sensory cortices of rabbits. EEGs were spatially low pass filtered, temporally band pass filtered and segmented in overlapping windows stepped at 2 ms. Phase was measured with the cosine as the temporal basis function, using both Fourier and Hilbert transforms to compensate for their respective limitations. Spatial patterns in 2-D phase surfaces were measured with the geometric form of the cone as the spatial basis function.Results: Two fundamental state variables were measured at each digitizing step in the 64 EEGs: the rate of change in phase with time (frequency) and the rate of change in phase with distance (gradient). The parameters of location, diameter, duration, and phase velocity of the cone of phase were derived from these two state variables. Parameter distributions including recurrence intervals extending into the low theta range were fractal; the mean values varied with window duration and interelectrode distance. Conclusions:The formation of spatial amplitude patterns began with phase transitions that were documented by phase discontinuities and phase cones. The multiplicity of overlapping cones indicated that sensory neocortices maintained a scale-free state of self-organized criticality (SOC) in each hemisphere as the basis for its rapid integration of sensory input with prior learning stored in cortical synaptic webs. Further evidence came from the fractal properties of the phase parameters and the self-similarity of phase patterns in the ms/mm to m/s ranges.Significance: These EEG data suggest that neocortical dynamics is analogous to the dynamics of self-stabilizing systems, such as a sand pile that maintains its critical angle by avalanches, and a pan of boiling water that maintains its critical temperature by bubbles that release heat. Betagamma oscillations stem from the ability of neocortex to maintain its stability under continuous sensory bombardment. Modeling implies that the critical parameter of neocortex (analogous to angle of repose or temperature) is the mean firing rates of neurons that are homeostatically regulated by refractory periods everywhere at all times in cortex. The advantage of SOC in perception may be the ability it gives neocortex to generate instantaneous global phase transitions (avalanches, bubbles) large enough to include the multiple sensory areas that are necessary to form Gestalts (multisensory percepts).Background EEG analytic phase 3Walter J Freeman

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“…The second source of the scale‐free noise is a possible misparcellation into arbitrary brain areas during the preprocessing pipeline. From the perspective of network analysis, mixing signals of various frequencies is equivalent to inducing a pink noise in the underlying neuronal dynamics (Bak, Tang, & Wiesenfeld, 1987). Therefore, one should pursue efforts aiming at functional (as opposed to anatomical) segregation into ROIs.…”

Section: Discussionmentioning

confidence: 99%

The impact of hemodynamic variability and signal mixing on the identifiability of effective connectivity structures in BOLD fMRI

et al. 2017

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PurposeMultiple computational studies have demonstrated that essentially all current analytical approaches to determine effective connectivity perform poorly when applied to synthetic functional Magnetic Resonance Imaging (fMRI) datasets. In this study, we take a theoretical approach to investigate the potential factors facilitating and hindering effective connectivity research in fMRI.Materials and MethodsIn this work, we perform a simulation study with use of Dynamic Causal Modeling generative model in order to gain new insights on the influence of factors such as the slow hemodynamic response, mixed signals in the network and short time series, on the effective connectivity estimation in fMRI studies.ResultsFirst, we perform a Linear Discriminant Analysis study and find that not the hemodynamics itself but mixed signals in the neuronal networks are detrimental to the signatures of distinct connectivity patterns. This result suggests that for statistical methods (which do not involve lagged signals), deconvolving the BOLD responses is not necessary, but at the same time, functional parcellation into Regions of Interest (ROIs) is essential. Second, we study the impact of hemodynamic variability on the inference with use of lagged methods. We find that the local hemodynamic variability provide with an upper bound on the success rate of the lagged methods. Furthermore, we demonstrate that upsampling the data to TRs lower than the TRs in state‐of‐the‐art datasets does not influence the performance of the lagged methods.ConclusionsFactors such as background scale‐free noise and hemodynamic variability have a major impact on the performance of methods for effective connectivity research in functional Magnetic Resonance Imaging.

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Self-organized criticality: An explanation of the 1/fnoise

Cited by 7,212 publications

References 2 publications

Homeostasis of neuronal avalanches during postnatal cortex development in vitro

Homeostasis of neuronal avalanches during postnatal cortex development in vitro

Origin, structure, and role of background EEG activity. Part 2. Analytic phase

The impact of hemodynamic variability and signal mixing on the identifiability of effective connectivity structures in BOLD fMRI

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