Power-law statistics and universal scaling in the absence of criticality

Can power-law scaling and neuronal avalanches arise from stochastic dynamics?

The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not necessarily mean that the system exhibits self-organized criticality. We first provide an analysis of multisite local field potential (LFP) recordings of brain activity and show that event size distributions defined as negative LFP peaks can be close to power-law distributions. However, this result is not robust to change in detection threshold, or when tested usin…

Self-organized criticality in a network of interacting neurons

This paper contains an analysis of a simple neural network that exhibits self-organized criticality. Such criticality follows from the combination of a simple neural network with an excitatory feedback loop that generates bistability, in combination with an anti-Hebbian synapse in its input pathway. Using the methods of statistical field theory, we show how one can formulate the stochastic dynamics of such a network as the action of a path integral, which we then investigate using renormalization group methods. The results indicate that the network exhibits hysteresis in switching back and for…

Identification of criticality in neuronal avalanches: II. A theoretical and empirical investigation of the driven case

The observation of apparent power-laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a separation of timescales is thought to be crucial for the observation of power-law dynamics and computational models are often constructed with this property. However, this is not necessarily a characteristic of physiological neural networks - external input does not only occur when the network is at rest/a steady state. In this paper we study a simple neuronal n…

Robustness of functional networks at criticality against structural defects

The robustness of dynamical properties of neuronal networks against structural damages is a central problem in computational and experimental neuroscience. Research has shown that the cortical network of a healthy brain works near a critical state, and moreover, that functional neuronal networks often have scale-free and small-world properties. In this work, we study how the robustness of simple functional networks at criticality is affected by structural defects. In particular, we consider a 2D Ising model at the critical temperature and investigate how its functional network changes with the…

Self-organized criticality in neural networks from activity-based rewiring

Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis which suggests that neural systems reach such a state by self-organizing towards the critical point of a dynamical phase transition. Here, we study a minimal neural network model that exhibits self-organized criticality in the presence of stochastic noise using a rewiring rule which only utilizes local information. For network evolution, incoming links are added to a node or deleted, depending on the node's average activity. Based on this rewiring-rule only…

临界边缘的神经元模型：一种受 Ising 启发的脑动力学方法

A Neuronal Model at the Edge of Criticality: An Ising-Inspired Approach to Brain Dynamics

本文构建受 Ising 模型启发、含不应期约束的二维神经元网络，揭示其在临界温度附近呈现同步转变及长程关联等临界特征。

Spectral peculiarity and criticality of the human connectome

We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our analysis indicates several new peculiar features of the human connectome. We found that the spectral density of human connectome has the maximal deviation from the spectral density of the randomized network compared to all other organisms. For many animals except human structural peculiarities of connectomes are well reproduced in the network evolution induced by the preference of 3-cycles formation. To get the reliable fit , we discovered the crucial role of the cons…

Self-organized criticality in neural network models

It has long been argued that neural networks have to establish and maintain a certain intermediate level of activity in order to keep away from the regimes of chaos and silence. Strong evidence for criticality has been observed in terms of spatio-temporal activity avalanches first in cultures of rat cortex by Beggs and Plenz (2003) and subsequently in many more experimental setups. These findings sparked intense research on theoretical models for criticality and avalanche dynamics in neural networks, where usually some dynamical order parameter is fed back onto the network topology by adapting…