Related papers: Observing scale-invariance in non-critical dynamic…
Scale-invariant avalanches -- with events of all sizes following power-law distributions -- are considered critical. Above the upper critical dimension of four, the mean-field solution with a robust $3/2$ size exponent describes the…
In this work, we report the preliminary analysis of the electrophysiological behavior of in vitro neuronal networks to identify when the networks are in a critical state based on the size distribution of network-wide avalanches of activity.…
The dynamics based on information transfer is proposed as an underlying mechanism for the scale-invariant dynamic critical behavior observed in a variety of systems. We apply the dynamics to the globally-coupled Ising model, which is…
Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state.…
The human brain exhibits a complex structure made of scale-free highly connected modules loosely interconnected by weaker links to form a small-world network. These features appear in healthy patients whereas neurological diseases often…
Recent experiments on cortical neural networks have revealed the existence of well-defined avalanches of electrical activity. Such avalanches have been claimed to be generically scale-invariant -- i.e. power-law distributed -- with many…
Scale invariance has received very little attention in physics. Nevertheless, it provides a natural conceptual foundation for a relational understanding of the universe, where absolute size loses meaning and only dimensionless ratios retain…
The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as their…
We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…
A salient feature of cyclically driven first-order phase transformations in crystals is their scale-free avalanche dynamics. This behavior has been linked to the presence of a classical critical point but the mechanism leading to…
Multiple studies of neural avalanches across different data modalities led to the prominent hypothesis that the brain operates near a critical point. The observed exponents often indicate the mean-field directed-percolation universality…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
The framework of Modern Theory of Critical State Transitions considers the relation between different levels of organization in complex systems in terms of Critical State Transitions. A State Transition between levels entails changes of…
Criticality, observed during second-order phase transitions, is an emergent phenomenon. The brain operates near criticality, where complex systems exhibit high correlations. The critical brain hypothesis suggests that the brain becomes an…
Analytical expressions for scaling of brain wave spectra derived from the general nonlinear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent nonlinear brain wave…
This paper applies the theory of continuous phase transitions of statistical mechanics to a slider-block model. The slider-block model is chosen as a representative of systems with avalanches. Similar behavior can be observed in a…
In recent years self organised critical neuronal models have provided insights regarding the origin of the experimentally observed avalanching behaviour of neuronal systems. It has been shown that dynamical synapses, as a form of short-term…
Scale invariance is a hallmark of criticality in complex dynamical systems. While random external inputs or tunable stochastic interactions are typically required to produce critical behavior, it remains unclear whether scale-invariant…
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…
We find that some equilibrium systems and their non-equilibrium counterparts actually show the same jerky response or avalanche behavior on many scales in response to slowly changing external conditions. In other words, their static and…