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Epilepsy creates a persistent increase in the probability of spontaneous seizures. An ictal episode evolves due to acute disturbance of the fine-tuned balance between excitatory vs. inhibitory inputs within a neural network in favor of…

Network theory provides novel concepts that promise an improved characterization of interacting dynamical systems. Within this framework, evolving networks can be considered as being composed of nodes, representing systems, and of…

Drug-resistant epilepsy is traditionally characterized by pathologic cortical tissue comprised of seizure-initiating `foci'. These `foci' are thought to be embedded within an epileptic network whose functional architecture dynamically…

The co-occurrence of action potentials of pairs of neurons within short time intervals is known since long. Such synchronous events can appear time-locked to the behavior of an animal and also theoretical considerations argue for a…

Neural oscillations are considered to be brain-specific signatures of information processing and communication in the brain. They also reflect pathological brain activity in neurological disorders, thus offering a basis for diagnoses and…

The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including, an…

Epileptic seizures are characterized by abnormal and excessive neural activity, where cortical network dynamics seem to become unstable. However, most of the time, during seizure-free periods, cortex of epilepsy patients shows perfectly…

The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics, and has been widely undertaken. Typically, however, networks employed in theoretical…

There is increasing evidence for specific cortical and subcortical large-scale human epileptic networks to be involved in the generation, spread, and termination of not only primary generalized but also focal onset seizures. The complex…

Cortical activity in-vivo displays relaxational time scales much longer than the membrane time constant of the neurons or the deactivation time of ionotropic synaptic conductances. The mechanisms responsible for such slow dynamics are not…

Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…

Bursting neurons are considered to be a potential cause of over-excitability and seizure susceptibility. The functional influence of these neurons in extended epileptic networks is still poorly understood. There is mounting evidence that…

Network architecture forms a critical constraint on neuronal function. Here we examine the role of structural autapses, when a neuron synapses onto itself, in driving network-wide bursting behavior. Using a simple spiking model of neuronal…

Collective rhythmic dynamics from neurons is vital for cognitive functions such as memory formation but how neurons self-organize to produce such activity is not well understood. Attractor-based models have been successfully implemented as…

Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary…

Inferring strength and direction of interactions from electroencephalographic (EEG) recordings is of crucial importance to improve our understanding of dynamical interdependencies underlying various physiologic and pathophysiologic…

Intermittent transitions, associated with critical dynamics and characterized by power-law distributions, are commonly observed during sleep. These critical behaviors are evident at the microscopic level through neuronal avalanches and at…

Excessively high, neural synchronisation has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronisation mechanisms can thus help control or even treat epilepsy.…

In many realistic networks, the edges representing the interactions between the nodes are time-varying. There is growing evidence that the complex network that models the dynamics of the human brain has time-varying interconnections, i.e.,…

Patients with epilepsy can manifest short, sub-clinical epileptic "bursts" in addition to full-blown clinical seizures. We believe the relationship between these two classes of events---something not previously studied…