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A rigorous understanding of brain dynamics and function requires a conceptual bridge between multiple levels of organization, including neural spiking and network-level population activity. Mounting evidence suggests that neural networks of…
The brain is in a state of perpetual reverberant neural activity, even in the absence of specific tasks or stimuli. Shedding light on the origin and functional significance of such a dynamical state is essential to understanding how the…
Spreading processes on networks are ubiquitous in both human-made and natural systems. Understanding their behavior is of broad interest; from the control of epidemics to understanding brain dynamics. While in some cases there exists a…
Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A…
Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…
A classification of critical behavior is provided in systems for which the renormalization group equations are control-parameter dependent. It describes phase transitions in networks with a recursive, hierarchical structure but appears to…
Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural…
This paper addresses the question of the brain's critical dynamics after an injury such as a stroke. It is hypothesized that the healthy brain operates near a phase transition (critical point), which provides optimal conditions for…
Hallmarks of criticality, such as power-laws and scale invariance, have been empirically found in cortical networks and it has been conjectured that operating at criticality entails functional advantages, such as optimal computational…
The critical brain hypothesis states that there are information processing advantages for neuronal networks working close to the critical region of a phase transition. If this is true, we must ask how the networks achieve and maintain this…
Cortical neurons exhibit a hierarchy of timescales across brain regions in response to input stimuli, which is thought to be crucial for information processing of different temporal scales. Modeling studies suggest that both intra-regional…
Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…
The "critical brain hypothesis" posits that neural circuitry may be tuned close to a "critical point" or "phase transition" -- a boundary between different operating regimes of the circuit. The renormalization group and theory of critical…
The hierarchical organization of the brain is a fundamental structural principle, while brain criticality is a leading hypothesis for its collective dynamics. However, the connection between structure and signatures of criticality remains…
Criticality has been conjectured as an integral part of neuronal network dynamics. Operating at a critical threshold requires precise parameter tuning and a corresponding mechanism remains an open question. Recent studies have suggested…
Many-body systems when continuous phase transition occurs are mainly built in the interrelationship between particles, implemented through many-body correlations. Some of them may exhibit so-called topological order hardly measured by…
The brain criticality hypothesis has largely only characterized brain dynamics in terms of their self-similarity, although experimental evidence suggests that the brain exhibits significant multifractality. To understand how multifractality…
Neuronal networks alternate between high- and low-activity regimes, known as up and down states. They also display rhythmic patterns essential for perception, memory consolidation, and sensory processing. Despite their importance, the…
We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…
The criticality hypothesis posits that biological neural networks operate near a phase transition, yet within standard Gaussian mean-field theories this regime appears fragile and requires fine tuning. Here we show that heavy-tailed…