Related papers: Multifractality in critical neural field dynamics
Synchronization of brain activity fluctuations is believed to represent communication between spatially distant neural processes. These inter-areal functional interactions develop in the background of a complex network of axonal connections…
Critical dynamics are assumed to be an attractive mode for normal brain functioning as information processing and computational capabilities are found to be optimized there. Recent experimental observations of neuronal activity patterns…
Over the past two decades, an increasing array of control-theoretic methods have been used to study the brain as a complex dynamical system and better understand its structure-function relationship. This article provides an overview on one…
Recent experimental results based on multi-electrode and imaging techniques have reinvigorated the idea that large neural networks operate near a critical point, between order and disorder. However, evidence for criticality has relied on…
Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity dependent…
Abrupt shifts in ecosystems, brains, markets, and climate are often diagnosed as signs of approaching a tipping point, i.e. a critical bifurcation where stability is lost. Here we reveal a broader and more deceptive mechanism:…
The cooperative behavior of neurons and neuronal areas associated with the synchronization behavior proves to be a fundamental neural mechanism. In addition, abnormal levels of synchronization have been related to unhealthy neural…
Metastable brain dynamics are characterized by abrupt, jump-like modulations so that the neural activity in single trials appears to unfold as a sequence of discrete, quasi-stationary states. Evidence that cortical neural activity unfolds…
Multifractals arise in various systems across nature whose scaling behavior is characterized by a continuous spectrum of multifractal exponents $\Delta_q$. In the context of Anderson transitions, the multifractality of critical wave…
Criticality in the cortex emerges from the seemingly random interaction of microscopic components and produces higher cognitive functions at mesoscopic and macroscopic scales. Random graphs and percolation theory provide natural means to…
Oscillatory activities are widely observed in specific frequency bands of recorded field potentials in different brain regions, and play critical roles in processing neural information. Understanding the structure of these oscillatory…
A multifractal phase transition is associated to a nonanalyticity in the generalised dimensions. We show that its occurrence is an artifact of the asymptotic scaling behaviour of integral moments and that it is not observed in an analysis…
The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated…
Functional oscillator networks, such as neuronal networks in the brain, exhibit switching between metastable states involving many oscillators. We give exact results how such global dynamics can arise in paradigmatic phase oscillator…
We study domain formation in the two-dimensional O(3) model near criticality. The fractal dimension of these domains is determined with good statistical accuracy.
Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons…
Critical phenomena arise ubiquitously in various context of physics, from condensed matter, high energy physics, cosmology, to biological systems, and consist of slow and long-distance fluctuations near a phase transition or critical point.…
Many studies have found evidence that the brain operates at a critical point, a processus known as self-organized criticality. A recent paper found remarkable scalings suggestive of criticality in systems as different as neural cultures,…
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…
In artificial neural networks, the activation dynamics of non-trainable variables is strongly coupled to the learning dynamics of trainable variables. During the activation pass, the boundary neurons (e.g., input neurons) are mapped to the…