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Cortical activity recorded through EEG and MEG reflects complex dynamics that span multiple temporal and spatial scales. Spectral analyses of these signals consistently reveal power-law behaviour, a hallmark of turbulent systems. In this…
This chapter revisits the concept of excitability, a basic system property of neurons. The focus is on excitable systems regarded as behaviors rather than dynamical systems. By this we mean open systems modulated by specific interconnection…
Starting from the concept of binary interactions between pairs of particles, a kinetic framework for the description of the action potential dynamics on a neural network is proposed. It consists of two coupled levels: the description of a…
Activity in neocortex exhibits a range of behaviors, from irregular to temporally precise, and from weakly to strongly correlated. So far there has been no single theoretical framework that could explain all these behaviors, leaving open…
Neural activity patterns related to behavior occur at many scales in time and space from the atomic and molecular to the whole brain. Here we explore the feasibility of interpreting neurophysiological data in the context of many-body…
This paper presents an overview of some techniques and concepts coming from dynamical system theory and used for the analysis of dynamical neural networks models. In a first section, we describe the dynamics of the neuron, starting from the…
Neural dynamics of energy-based models are governed by energy minimization and the patterns stored in the network are retrieved when the system reaches equilibrium. However, when the system is driven by time-varying external input, the…
Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and…
We present a microscopic approach for the coupling of cortical activity, as resulting from proper dipole currents of pyramidal neurons, to the electromagnetic field in extracellular fluid in presence of diffusion and Ohmic conduction. As a…
This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…
The driving of vibrational motion by external electric fields is a topic of continued interest, due to the possibility of assessing new or metastable material phases with desirable properties. Here, we combine ab initio molecular dynamics…
Neurons convert the external stimuli into action potentials, or spikes, and encode the contained information into the biological nerve system. Despite the complexity of neurons and the synaptic interactions in between, the rate models are…
In this paper, we propose a new scheme for modelling the diverse behavior of neurons. We introduce the conditional activation, in which a neurons activation function is dynamically modified by a control signal. We apply this method to…
All living cells transport molecules and ions across membranes, often against concentration gradients. This active transport requires continual energy expenditure and is clearly a nonequilibrium process for which standard equilibrium…
Recording simultaneous activity of hundreds of neurons is now possible. Existing methods can model such population activity, but do not directly reveal the computations used by the brain. We present a fully unsupervised method that models…
We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural…
Persistent activity is postulated to drive neural network plasticity and learning. To investigate its underlying cellular mechanisms, we developed a biophysically tractable model that explains the emergence, sustenance, and eventual…
In a succession of articles published over 65 years ago, Sir Alan Lloyd Hodgkin and Sir Andrew Fielding Huxley established what now forms our physical understanding of excitation in nerve, and how the axon conducts the action potential.…
In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular…
The brain may be thought of as a many-body architecture with a spatio-temporal dynamics described by neuronal structures. The oscillatory nature of brain activity allows these structures (nodes) to be described as a set of coupled…