Critical Neuronal Models with Relaxed Timescale Separation

Das, Anirban; Levina, Anna

doi:10.1103/physrevx.9.021062

Cited by 34 publications

(20 citation statements)

References 71 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For more detailed explanations of all this phenomenology we refer to [33,132] and, for applications in neuroscience, to [151][152][153][154][155][156][157][158][159][160][161].…”

Section: Theory Of Self-organized Quasi Criticality (Soqc)mentioning

confidence: 99%

Feedback Mechanisms for Self-Organization to the Edge of a Phase Transition

et al. 2020

View full text Add to dashboard Cite

Scale-free outbursts of activity are commonly observed in physical, geological, and biological systems. The idea of self-organized criticality (SOC), introduced back in 1987 by Bak, Tang, and Wiesenfeld suggests that, under certain circumstances, natural systems can seemingly self-tune to a critical state with its concomitant power-laws and scaling. Theoretical progress allowed for a rationalization of how SOC works by relating its critical properties to those of a standard non-equilibrium second-order phase transition that separates an active state in which dynamical activity reverberates indefinitely, from an absorbing or quiescent state where activity eventually ceases. The basic mechanism underlying SOC is the alternation of a slow driving process and fast dynamics with dissipation, which generates a feedback loop that tunes the system to the critical point of an absorbing-active continuous phase transition. Here, we briefly review these ideas as well as a recent closely-related concept: self-organized bistability (SOB). In SOB, the very same type of feedback operates in a system characterized by a discontinuous phase transition, which has no critical point but instead presents bistability between active and quiescent states. SOB also leads to scale-invariant avalanches of activity but, in this case, with a different type of scaling and coexisting with anomalously large outbursts. Moreover, SOB explains experiments with real sandpiles more closely than SOC. We review similarities and differences between SOC and SOB by presenting and analyzing them under a common theoretical framework, covering recent results as well as possible future developments. We also discuss other related concepts for "imperfect" self-organization such as "self-organized quasi-criticality" and "self-organized collective oscillations," of relevance in e.g., neuroscience, with the aim of providing an overview of feedback mechanisms for self-organization to the edge of a phase transition.

show abstract

“…For more detailed explanations of all this phenomenology we refer to [33,132] and, for applications in neuroscience, to [151][152][153][154][155][156][157][158][159][160][161].…”

Section: Theory Of Self-organized Quasi Criticality (Soqc)mentioning

confidence: 99%

Feedback Mechanisms for Self-Organization to the Edge of a Phase Transition

et al. 2020

View full text Add to dashboard Cite

show abstract

“…We thus expect that the fractional diffusion theory applies whenever the inputs have Lévy fluctuations, regardless of specific network structures. In addition, it should be noted that scale-free, Lévy-like fluctuations can emerge from neural networks with criticality [3,18,60,61]. In the future it would be interesting to apply our fractional framework for the formulation of critical neural dynamics, going beyond the demonstration of the presence of power-law distributions in some neural observables.…”

Section: Discussionmentioning

confidence: 99%

Fractional diffusion theory of balanced heterogeneous neural networks

Wardak

Gong

2020

Preprint

View full text Add to dashboard Cite

Interactions of large numbers of spiking neurons give rise to complex neural dynamics with fluctuations occurring at multiple scales. Understanding the dynamical mechanisms underlying such complex neural dynamics is a long-standing topic of interest in neuroscience, statistical physics and nonlinear dynamics. Conventionally, fluctuating neural dynamics are formulated as balanced, uncorrelated excitatory and inhibitory inputs with Gaussian properties. However, heterogeneous, non-Gaussian properties have been widely observed in both neural connections and neural dynamics. Here, based on balanced neural networks with heterogeneous, non-Gaussian features, our analysis reveals that in the limit of large network size, synaptic inputs possess power-law fluctuations, leading to a remarkable relation of complex neural dynamics to the fractional diffusion formalisms of non-equilibrium physical systems. By uniquely accounting for the leapovers caused by the fluctuations of spiking activity, we further develop a fractional Fokker-Planck equation with absorbing boundary conditions. This body of formalisms represents a novel fractional diffusion theory of heterogeneous neural networks and results in an exact description of the network activity states. This theory is further implemented in a biologically plausible, balanced neural network and identifies a novel type of network state with rich, nonlinear response properties, providing a unified account of a variety of experimental findings on neural dynamics at the individual neuron and the network levels, including fluctuations of membrane potentials and population firing rates. We illustrate that this novel state endows neural networks with a fundamental computational advantage; that is, the neural response is maximised as a function of structural connectivity. Our theory and its network implementations provide a framework for investigating complex neural dynamics emerging from large networks of spiking neurons and their functional roles in neural processing.

show abstract

“…3,[17][18][19]41,46,52 This network cooperates directly and uninterruptedly with the nervous system and exhibits similar cascade-like dynamics as in "neuronal avalanches." 7,39 It is no small coincidence that tensegrity and avalanche models all converge on multiplicativity 11,54 that inspired multiscale quantification of non-Gaussianity. 23,24,53 Hence, MFT approaches suggest multiple points of entry through which stimulation elicits cascades to spread across scales-from the surface underfoot 36 to the loads at hand 38 and now from the incoming visual information.…”

Section: Discussionmentioning

confidence: 99%

Visual effort moderates postural cascade dynamics

Mangalam¹,

Lee

Newell

et al. 2020

Preprint

View full text Add to dashboard Cite

Standing still and focusing on a visible target in front of us is a preamble to many coordinated behaviors (e.g., reaching an object). Hiding behind its apparent simplicity is a deep layering of texture at many scales. The task of standing still laces together activities at multiple scales: from ensuring that a few photoreceptors on the retina cover the target in the visual field on an extremely fine-scale to synergies spanning the limbs and joints at smaller scales to the mechanical layout of the ground underfoot and optic flow in the visual field on the coarser scales. Here, we used multiscale probability distribution function (PDF) analysis to show that postural fluctuations exhibit similar statistical signatures of cascade dynamics as found in fluid flow. Critically, the oculomotor strain of visually fixating different distances moderates postural cascade dynamics. Visually fixating at a comfortable viewing distance elicited posture with a similar cascade dynamics as posture with eyes closed. Greater viewing distances known to stabilize posture showed more diminished cascade dynamics. In contrast, nearest and farthest viewing distances requiring greater oculomotor strain to focus on targets elicited a dramatic strengthening postural cascade dynamics, reflecting active postural adjustments. Critically, these findings suggest that vision stabilizes posture by reconfiguring the prestressed poise that prepares the body to interact with different spatial layouts.

show abstract

Critical Neuronal Models with Relaxed Timescale Separation

Cited by 34 publications

References 71 publications

Feedback Mechanisms for Self-Organization to the Edge of a Phase Transition

Feedback Mechanisms for Self-Organization to the Edge of a Phase Transition

Fractional diffusion theory of balanced heterogeneous neural networks

Visual effort moderates postural cascade dynamics

Contact Info

Product

Resources

About