Criticality in Spreading Processes without Timescale Separation and the Critical Brain Hypothesis

Korchinski, Daniel; Orlandi, Javier G.; Son, Seung‐Woo; Davidsen, Jörn

doi:10.1103/physrevx.11.021059

Cited by 27 publications

(18 citation statements)

References 86 publications

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“…Clearly, magnets, swarms and brains are quite different systems, and in particular the special network structure of neuronal assemblies poses specific problems (Korchinski et al, 2021). Certainly it is not the case to take tools developed in the statistical mechanics of condensed matter and blindly apply them to study the brain.…”

Section: Space-time Correlations In Neuronal Networkmentioning

confidence: 99%

“…Actually, the relaxation time is the time scale for the system to return to stationarity after an external static perturbation is applied or removed. These two scales are equal for systems in thermodynamic equilibrium, as a consequence of the fluctuation-dissipation theorem(Kubo et al, 1998), so the exchange of terms is admissible in that case. However, this is not to be taken for granted in the general out-of-equilibrium case.…”

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confidence: 99%

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Correlation functions as a tool to study collective behaviour phenomena in biological systems

Grigera

2021

Preprint

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Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation functions are a fundamental tool to study these fluctuations. We give a self-contained presentation of definitions and techniques for computation of correlation functions aimed at providing students and researchers outside the field of statistical physics a practical guide to calculating correlation functions from experimental and simulation data. We discuss some properties of correlations in critical systems, and the effect of finite system size, which is particularly relevant for most biological experimental systems. Finally we apply these to the case of the dynamical transition in a simple neuronal model,

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Section: Space-time Correlations In Neuronal Networkmentioning

confidence: 99%

mentioning

confidence: 99%

Correlation functions as a tool to study collective behaviour phenomena in biological systems

Grigera

2021

Preprint

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“…A hypothesis that is increasingly being considered in light of growing experimental [9, 10] and theoretical [11, 12] results is that collective emergent patterns are signatures of brain self-organization to a critical point [13, 14], i.e., the brain dynamics may be poised at the edge of a phase transition. Over the years, evidence to support this hypothesis emerged in the presence of scale-free neural avalanches [15] and cluster size distributions [16, 17], long-range temporal and spatial [18, 19] correlations during spontaneous brain activity - exemplary properties of a system near its critical point. Furthermore, it was recently shown that the collective dynamics of neurons may be associated with a non-trivial fixed point of phenomenological renormalization groups [20, 21].…”

Section: Introductionmentioning

confidence: 99%

Criticality and network structure drive emergent oscillations in a stochastic whole-brain model

Barzon

Nicoletti

Mariani

et al. 2022

Preprint

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Understanding the relation between the structure of brain networks and its functions is a fundamental open question. Simple models of neural activity based on real anatomical networks have proven effective in describing features of whole-brain spontaneous activity when tuned at their critical point. In this work, we show that indeed structural networks are a crucial ingredient in the emergence of synchronized oscillations in a whole-brain stochastic model at criticality. We study such model in the mean-field limit, providing an analytical understanding of the associated first-order phase transition, arising from the presence of a bistable region in the parameters space. Then, we derive the power spectrum in the linear noise approximation and we show that, in the mean-field limit, no global oscillations emerge. Finally, by adding back an underlying brain network structure with homeostatic normalization, we numerically show how the bi-stability region is disrupted and concomitantly a synchronized phase with maximal dynamic range is observed. Hence, both the structure of brain networks and criticality are fundamental in driving the collective coordinated responses and maximal sensitivity of whole-brain stochastic models.

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“…[5,6]), and in a diversity of numerical simulations. Several caveats, such as subsampling [7], thresholding [8], or the artifacts introduced by the coexistence of overlapping avalanches [9], as well as alternative interpretations of the results [10] prompted the exploration of complementary approaches.…”

mentioning

confidence: 99%

“…To estimate how close the system is to criticality by using this approach, several parameters need to be defined and adjusted, such as the time binning, minimum and values of considered avalanches, and a non-zero threshold for defining avalanches in the cases the activity never ceases (i.e., as in very large number of neurons). Furthermore, additional experimental caveats need to be considered, such as subsampling [7], windowing (i.e., avalanches involving neurons outside of the observation window), or the existence of several simultaneous unrelated avalanches [9].…”

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confidence: 99%

Finite-size correlation behavior near a critical point: a simple metric for monitoring the state of a neural network

Trejo¹,

Martı́n²,

Grigera³

et al. 2022

Preprint

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In this note, a correlation metric κc is proposed which is based on the universal behavior of the linear/logarithmic growth of the correlation length near/far the critical point of a continuous phase transition. The problem is studied on a previously described neuronal network model for which is known the scaling of the correlation length with the size of the observation region. It is verified that the κc metric is maximized for the conditions at which a power law distribution of neuronal avalanches sizes is observed, thus characterizing well the critical state of the network. Potential applications and limitations for its use with currently available optical imaging techniques are discussed.

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Criticality in Spreading Processes without Timescale Separation and the Critical Brain Hypothesis

Cited by 27 publications

References 86 publications

Correlation functions as a tool to study collective behaviour phenomena in biological systems

Correlation functions as a tool to study collective behaviour phenomena in biological systems

Criticality and network structure drive emergent oscillations in a stochastic whole-brain model

Finite-size correlation behavior near a critical point: a simple metric for monitoring the state of a neural network

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