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The elapsed time model has been widely studied in the context of mathematical neuroscience with many open questions left. The model consists of an age-structured equation that describes the dynamics of interacting neurons structured by the…
The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior…
Dynamical systems are often time-varying, whose modeling requires a function that evolves with respect to time. Recent studies such as the neural ordinary differential equation proposed a time-dependent neural network, which provides a…
A seizure tracking system is crucial for monitoring and evaluating epilepsy treatments. Caretaker seizure diaries are used in epilepsy care today, but clinical seizure monitoring may miss seizures. Monitoring devices that can be worn may be…
Spiking neural network is a type of artificial neural network in which neurons communicate between each other with spikes. Spikes are identical Boolean events characterized by the time of their arrival. A spiking neuron has internal…
In the last decades, many authors have used the susceptible-infected-recovered model to study the impact of the disease spreading on the evolution of the infected individuals. However, few authors focused on the temporal unfolding of the…
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…
A perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network. A series expansion is constructed that converges for networks with noisy membrane potential and weak…
Epilepsy is one of the most common neurological disorders, typically observed via seizure episodes. Epileptic seizures are commonly monitored through electroencephalogram (EEG) recordings due to their routine and low expense collection. The…
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…
Epileptic seizure forecasting, combined with the delivery of preventative therapies, holds the potential to greatly improve the quality of life for epilepsy patients and their caregivers. Forecasting seizures could prevent some potentially…
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…
The collection of data on populations of networks is becoming increasingly common, where each data point can be seen as a realisation of a network-valued random variable. A canonical example is that of brain networks: a typical neuroimaging…
Neural networks are composed of neurons and synapses, which are responsible for learning in a slow adaptive dynamical process. Here we experimentally show that neurons act like independent anisotropic multiplex hubs, which relay and mute…
Networks are well-established representations of social systems, and temporal networks are widely used to study their dynamics. Temporal network data often consist in a succession of static networks over consecutive time windows whose…
Neural systems are comprised of interacting units, and relevant information regarding their function or malfunction can be inferred by analyzing the statistical dependencies between the activity of each unit. Whilst correlations and mutual…
We investigate dynamical systems characterized by a time series of distinct semi-stable activity patterns, as they are observed in cortical neural activity patterns. We propose and discuss a general mechanism allowing for an adiabatic…
Epileptic seizures are generated in cerebral networks that propagate ictal and interictal activity. The structure of cerebral networks underpinning epileptic activity can be inferred from diffusion-weighted MRI (DWI). However, publicly…
Objective: The aim of this study is to develop an efficient and reliable epileptic seizure prediction system using intracranial EEG (iEEG) data, especially for people with drug-resistant epilepsy. The prediction procedure should yield…
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…