Self-organized criticality in a simple model of neurons based on small-world networks

Lin, Min; Tian-Lun, Chen

doi:10.1103/physreve.71.016133

Cited by 50 publications

(26 citation statements)

References 12 publications

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“…Unfortunately, existing studies on broadband field potentials focusing on arrhythmic, 1/ f -β activity remain scarce (Buiatti et al, 2007; Freeman and Zhai, 2009; Manning et al, 2009; Miller et al, 2009b; Onton and Makeig, 2009), and usually characterize only the gross properties of the power spectrum such as the power-law exponent or total variance. Many simulations of scale-free dynamics have been constructed by physicists (e.g., Bak, 1996; de Arcangelis et al, 2006; De Los Rios and Zhang, 1999; Lin and Chen, 2005; Mandelbrot, 1999; Ward and Greenwood, 2007), but it remains to be seen whether these general models also describe the neurophysiological processes giving rise to 1/ f -β signals in the brain. Notably, scale-free properties have recently been described in the amplitude and synchronization of oscillatory brain activity (Linkenkaer-Hansen et al, 2001; Stam and de Bruin, 2004), and in the temporal and spatial distributions of negative LFP peaks (Plenz and Thiagarajan, 2007).…”

Section: Introductionmentioning

confidence: 99%

The Temporal Structures and Functional Significance of Scale-free Brain Activity

Zempel

Snyder

et al. 2010

Neuron

931

908

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SUMMARY Scale-free dynamics, with a power spectrum following P ∝ f-β, are an intrinsic feature of many complex processes in nature. In neural systems, scale-free activity is often neglected in electrophysiological research. Here, we investigate scale-free dynamics in human brain and show that it contains extensive nested frequencies, with the phase of lower frequencies modulating the amplitude of higher frequencies in an upward progression across the frequency spectrum. The functional significance of scale-free brain activity is indicated by task performance modulation and regional variation, with β being larger in default network and visual cortex and smaller in hippocampus and cerebellum. The precise patterns of nested frequencies in the brain differ from other scale-free dynamics in nature, such as earth seismic waves and stock market fluctuations, suggesting system-specific generative mechanisms. Our findings reveal robust temporal structures and behavioral significance of scale-free brain activity and should motivate future study on its physiological mechanisms and cognitive implications.

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Section: Introductionmentioning

confidence: 99%

The Temporal Structures and Functional Significance of Scale-free Brain Activity

Zempel

Snyder

et al. 2010

Neuron

931

908

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“…Kauffman & Johnsen 1991;Kauffman 1993) modelled cellular protein interactions with random Boolean networks and showed that under selection pressure these networks would self-organize into a nearly critical state where perturbations propagated in the form of avalanches. Neural models have also picked up on this idea, and several authors have suggested that neural networks should operate close to the chaotic regime (Chialvo & Bak 1999;Bak & Chialvo 2001;Bertschinger & Natschlager 2004;Lin & Chen 2006;Legenstein & Maass 2007). Collectively, these simulations predict that living systems will self-organize to operate near a critical point.…”

Section: Introductionmentioning

confidence: 99%

The criticality hypothesis: how local cortical networks might optimize information processing

Beggs

2007

Phil. Trans. R. Soc. A.

434

408

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Early theoretical and simulation work independently undertaken by Packard, Langton and Kauffman suggested that adaptability and computational power would be optimized in systems at the 'edge of chaos', at a critical point in a phase transition between total randomness and boring order. This provocative hypothesis has received much attention, but biological experiments supporting it have been relatively few. Here, we review recent experiments on networks of cortical neurons, showing that they appear to be operating near the critical point. Simulation studies capture the main features of these data and suggest that criticality may allow cortical networks to optimize information processing. These simulations lead to predictions that could be tested in the near future, possibly providing further experimental evidence for the criticality hypothesis.

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“…For example, for complete connectivity, effects due to the internal neural adaptation are distinguishable from network effects. See, for example, the work by Lin and Chen [30] and Teramae and Fukai [31], where often small-world connectivity is found to contribute to criticality.…”

Section: Toward a Realistic Model: Network Structure Leakage And Inmentioning

confidence: 99%

Theoretical Neuroscience of Self‐Organized Criticality: From Formal Approaches to Realistic Models

Levina

Herrmann

Geisel

2014

Criticality in Neural Systems

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Self-organized criticality (SOC) is a common phenomenon in nature [1] and became a fascinating research subject for neuroscience when critical avalanches were predicted theoretically and observed experimentally to occur in networks of neurons [2][3][4]. Models of SOC in neural network evolve from early sandpile-like models [5, 6] on a lattice to large-scale realistically connected networks [7,8]. In this chapter we will present a model of criticality in the brain which identifies a number of contributing factors such as short-term synaptic dynamics and homeostatic plasticity in the synapses. This model is but one approach among an ever-increasing number of other studies on the subject. We were aiming for a family of models that are simple enough to permit an analytical solution but can still account for several biological principles that are known to be relevant here.As we try to identify the components of a neuronal network that can make it self-organized critical or, at least, bring it closer to a critical state, we have to be aware that criticality (in the sense of the existence of full-fledged power law event distributions) does not exist in finite systems. This emphasizes the importance of analytical treatments for infinite systems, while a theory of finite-size effects is also required to relate precisely to biological experiments. Such a theory exists only for the simplest abstract models (see Section 20.2), which forces us to apply a combination of analytical and numerical work on models including dynamic synapses (Section 20.3) and homeostatic adaptation (Section 20.4). The Eurich Model of Criticality in Neural NetworksIn 2002, Eurich et al. [2] presented a model of a globally coupled neural network that exhibits critical avalanches. In contrast to earlier work on criticality [5,6,[9][10][11], here an explicit analytical derivation of the distribution of sizes of neural avalanches was given not only for the idealization of very large networks but Criticality in Neural Systems, First Edition. Edited by Dietmar Plenz and Ernst Niebur.

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Self-organized criticality in a simple model of neurons based on small-world networks

Cited by 50 publications

References 12 publications

The Temporal Structures and Functional Significance of Scale-free Brain Activity

The Temporal Structures and Functional Significance of Scale-free Brain Activity

The criticality hypothesis: how local cortical networks might optimize information processing

Theoretical Neuroscience of Self‐Organized Criticality: From Formal Approaches to Realistic Models

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