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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…
We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some…
Neuronal avalanche is a spontaneous neuronal activity which obeys a power-law distribution of population event sizes with an exponent of -3/2. It has been observed in the superficial layers of cortex both \emph{in vivo} and \emph{in vitro}.…
In this paper we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate how they should perform in a…
Avalanches, or Avalanche-like, events are often observed in the dynamical behaviour of many complex systems which span from solar flaring to the Earth's crust dynamics and from traffic flows to financial markets. Self-organized criticality…
Cortical network functioning critically depends on finely tuned interactions to afford neuronal activity propagation over long distances while avoiding runaway excitation. This importance is highlighted by the pathological consequences and…
A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable…
Record-breaking avalanches generated by the dynamics of several driven nonlinear threshold models are studied. Such systems are characterized by intermittent behavior, where slow buildup of energy is punctuated by an abrupt release of…
We introduce a toy model displaying the avalanche dynamics of failure in scale-free networks. In the model, the network growth is based on the Barab\'asi and Albert model and each node is assigned a capacity or tolerance, which is constant…
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…
Converging research suggests that the resting brain operates at the cusp of dynamic instability signified by scale-free temporal correlations. We asked if the scaling properties of these correlations differ between amplitude and phase…
The $1/f$-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitute evidences of criticality in neuronal systems. Recent in vitro studies…
Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…
The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting…
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…
The critical brain hypothesis has emerged as an attractive framework to understand neuronal activity, but it is still widely debated. In this work, we analyze data from a multi-electrodes array in the rat's cortex and we find that power-law…
In the context of neuroscience the elapsed-time model is an age-structured equation that describes the behavior of interconnected spiking neurons through the time since the last discharge, with many interesting dynamics depending on the…
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…
When a spatial process is recorded over time and the observation at a given time instant is viewed as a point in a function space, the result is a time series taking values in a Banach space. To study the spatio-temporal extremal dynamics…
Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling $p$) and deterministic critical…