Related papers: Quasi-Critical Brain Dynamics on a Non-Equilibrium…
Equilibrium quantum systems are often described by a gas of weakly-interacting normal modes. Bringing such systems far from equilibrium, however, can drastically enhance mode-to-mode interactions. Understanding the resulting liquid is a…
In this work we study numerically the out of equilibrium dynamics of the Hopfield model for associative memory inside its spin-glass phase. Besides its interest as a neural network model it can also be considered as a prototype of fully…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
Probabilistic cellular automata provide a simple framework for the exploration of classical nonequilibrium processes. Recently, quantum cellular automata have been proposed that rely on the propagation of a one-dimensional quantum state…
Focusing on a two-field Swift-Hohenberg model with linear nonreciprocal interactions, this study investigates how emerging higher-codimension points act as organizing centers for the nonequilibrium phase diagram that features various steady…
We investigate the localization properties of a quasi-one-dimensional two-channel system with symmetric and asymmetric onsite energies using the Aubry-Andr\'{e} model. By analyzing the Lyapunov exponent and localization length, we…
Advancing our knowledge of how the brain processes information remains a key challenge in neuroscience. This thesis combines three different approaches to the study of the dynamics of neural networks and their encoding representations: a…
We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model…
We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution and asymmetry. The network…
The concept of the brain as a critical system is very attractive because systems close to criticality are thought to maximise their dynamic range of information processing and communication. To date, there have been two key experimental…
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.…
Recent experimental advances in ultrafast phenomena have triggered renewed interest in the dynamics of correlated quantum systems away from equilibrium. We review nonequilibrium dynamical mean-field theory studies of both the transient and…
Nonequilibrium phenomena of the phase transitions are studied. It is shown that due to finite relaxation time of the particle distributions, the use of scalar background dependent distribution functions is inconsistent.This observation may…
Learning and decision making in the brain are key processes critical to survival, and yet are processes implemented by non-ideal biological building blocks which can impose significant error. We explore quantitatively how the brain might…
Modeling and optimization of metabolic networks has been one of the hottest topics in computational systems biology within recent years. However, the complexity and uncertainty of these networks in addition to the lack of necessary data has…
Cognitive function requires the coordination of neural activity across many scales, from neurons and circuits to large-scale networks. As such, it is unlikely that an explanatory framework focused upon any single scale will yield a…
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…
A network of propagating nonlinear oscillatory modes (waves) in the human brain is shown to generate collectively synchronized spiking activity (hypersynchronous spiking) when both amplitude and phase coupling between modes are taken into…
This paper addresses the problem of controlling the temporal dynamics of complex nonlinear network-coupled dynamical systems, specifically in terms of neurodynamics. Based on the Lyapunov direct method, we derive a control strategy with…
Neural collapse is a highly symmetric geometric pattern of neural networks that emerges during the terminal phase of training, with profound implications on the generalization performance and robustness of the trained networks. To…