Event--related desynchronization in diffusively coupled oscillator models

We seek explanation for the neurophysiological phenomenon of event related desynchronization (ERD) by using models of diffusively coupled nonlinear oscillators. We demonstrate that when the strength of the event is sufficient, ERD is found to emerge and the accomplishment of a behavioral/functional task is determined by the nature of the desynchronized state. We illustrate the phenomenon for the case of limit cycle and chaotic systems. We numerically demonstrate the occurrence of ERD and provide analytical explanation. We also discuss possible applications of the observed phenomenon in real physical systems other than the brain.Comment: Accepted in Physical Review Letter

Non-resonant dot-cavity coupling and its applications in resonant quantum dot spectroscopy

We present experimental investigations on the non-resonant dot-cavity coupling of a single quantum dot inside a micro-pillar where the dot has been resonantly excited in the s-shell, thereby avoiding the generation of additional charges in the QD and its surrounding. As a direct proof of the pure single dot-cavity system, strong photon anti-bunching is consistently observed in the autocorrelation functions of the QD and the mode emission, as well as in the cross-correlation function between the dot and mode signals. Strong Stokes and anti-Stokes-like emission is observed for energetic QD-mode detunings of up to ~100 times the QD linewidth. Furthermore, we demonstrate that non-resonant dot-cavity coupling can be utilized to directly monitor and study relevant QD s-shell properties like fine-structure splittings, emission saturation and power broadening, as well as photon statistics with negligible background contributions. Our results open a new perspective on the understanding and implementation of dot-cavity systems for single-photon sources, single and multiple quantum dot lasers, semiconductor cavity quantum electrodynamics, and their implementation, e.g. in quantum information technology.Comment: 17 pages, 4 figure

Properties of a single photon generated by a solid-state emitter: effects of pure dephasing

We investigate the properties of a single photon generated by a solid-state emitter subject to strong pure dephasing. We employ a model in which all the elements of the system, including the propagating fields, are treated quantum mechanically. We analytically derive the density matrix of the emitted photon, which contains full information about the photon, such as its pulse profile, power spectrum, and purity. We visualize these analytical results using realistic parameters and reveal the conditions for maximizing the purity of generated photons.Comment: 25pages(one column), 10 figure

A simple spontaneously active Hebbian learning model: homeostasis of activity and connectivity, and consequences for learning and epileptogenesis

A spontaneously active neural system that is capable of continual learning should also be capable of homeostasis of both firing rate and connectivity. Experimental evidence suggests that both types of homeostasis exist, and that connectivity is maintained at a state that is optimal for information transmission and storage. This state is referred to as the critical state. We present a simple stochastic computational Hebbian learning model that incorporates both firing rate and critical homeostasis, and we explore its stability and connectivity properties. We also examine the behavior of our model with a simulated seizure and with simulated acute deafferentation. We argue that a neural system that is more highly connected than the critical state (i.e., one that is "supercritical") is epileptogenic. Based on our simulations, we predict that the post-seizural and post-deafferentation states should be supercritical and epileptogenic. Furthermore, interventions that boost spontaneous activity should be protective against epileptogenesis.Comment: 37 pages, 1 table, 7 figure

Scaling Effects and Spatio-Temporal Multilevel Dynamics in Epileptic Seizures

Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of body control. In this paper, we aim to contribute towards a better understanding of the dynamical systems phenomena that cause seizures. Based on data analysis and modelling, seizure dynamics can be identified to possess multiple spatial scales and on each spatial scale also multiple time scales. At each scale, we reach several novel insights. On the smallest spatial scale we consider single model neurons and investigate early-warning signs of spiking. This introduces the theory of critical transitions to excitable systems. For clusters of neurons (or neuronal regions) we use patient data and find oscillatory behavior and new scaling laws near the seizure onset. These scalings lead to substantiate the conjecture obtained from mean-field models that a Hopf bifurcation could be involved near seizure onset. On the largest spatial scale we introduce a measure based on phase-locking intervals and wavelets into seizure modelling. It is used to resolve synchronization between different regions in the brain and identifies time-shifted scaling laws at different wavelet scales. We also compare our wavelet-based multiscale approach with maximum linear cross-correlation and mean-phase coherence measures

Loss of neuronal network resilience precedes seizures and determines the ictogenic nature of interictal synaptic perturbations

The mechanisms of seizure emergence, and the role of brief interictal epileptiform discharges (IEDs) in seizure generation are two of the most important unresolved issues in modern epilepsy research. Our study shows that the transition to seizure is not a sudden phenomenon,but a slow process characterized by the progressive loss of neuronal network resilience. From a dynamical perspective, the slow transition is governed by the principles of critical slowing, a robust natural phenomenon observable in systems characterized by transitions between dynamical regimes. In epilepsy, this process is modulated by the synchronous synaptic input from IEDs. IEDs are external perturbations that produce phasic changes in the slow transition process and exert opposing effects on the dynamics of a seizure-generating network, causing either anti-seizure or pro-seizure effects. We show that the multifaceted nature of IEDs is defined by the dynamical state of the network at the moment of the discharge occurrence

An investigation of the phase locking index for measuring of interdependency of cortical source signals recorded in the EEG

The phase locking index (PLI) was introduced to quantify in a statistical sense the phase synchronization of two signals. It has been commonly used to process biosignals. In this article, we investigate the PLI for measuring the interdependency of cortical source signals (CSSs) recorded in the Electroencephalogram (EEG). To this end, we consider simple analytical models for the mapping of simulated CSSs into the EEG. For these models, the PLI is investigated analytically and through numerical simulations. An evaluation is made of the sensitivity of the PLI to the amount of crosstalk between the sources through biological tissues of the head. It is found that the PLI is a useful interdependency measure for CSSs, especially when the amount of crosstalk is small. Another common interdependency measure is the coherence. A direct comparison of both measures has not been made in the literature so far. We assess the performance of the PLI and coherence for estimation and detection purposes based on, respectively, a normalized variance and a novel statistical measure termed contrast. Based on these performance measures, it is found that the PLI is similar or better than the CM in most cases. This result is also confirmed through analysis of EEGs recorded from epileptic patients