Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise

We discuss control techniques for noisy self-sustained oscillators with a focus on reliability, stability of the response to noisy driving, and oscillation coherence understood in the sense of constancy of oscillation frequency. For any kind of linear feedback control--single and multiple delay feedback, linear frequency filter, etc.--the phase diffusion constant, quantifying coherence, and the Lyapunov exponent, quantifying reliability, can be efficiently controlled but their ratio remains constant. Thus, an "uncertainty principle" can be formulated: the loss of reliability occurs when coherence is enhanced and, vice versa, coherence is weakened when reliability is enhanced. Treatment of this principle for ensembles of oscillators synchronized by common noise or global coupling reveals a substantial difference between the cases of slightly non-identical oscillators and identical ones with intrinsic noise.Comment: 10 pages, 5 figure

Microwave generation in synchronized semiconductor superlattices

We study high-frequency generation in a system of electromagnetically coupled semiconductor superlattices fabricated on the same doped substrate. Applying a bias voltage to a single superlattice generates high-frequency current oscillations. We demonstrate that within a certain range of the applied voltage, the current oscillations within the superlattices can be self-synchronized, which leads to a dramatic rise in the generated microwave power. These results, which are in good agreement with our numerical model, open a promising practical route towards the design of high-power miniature microwave generators

Spike-wave discharges in WAG/Rij rats are preceded by delta and theta precursor activity in cortex and thalamus

Objective: In order to unravel the mechanisms underlying the "sudden" onset of spontaneous absences in genetically prone subjects, we investigated the immediate precursors of spike-wave discharges (SWDs) produced in cortico-thalamo-cortical neuronal networks. Methods: A time-frequency analysis of the cortical and thalamic ECoG of WAG/Rij rats was accomplished with a continuous wavelet decomposition of SWDs, 3 s prior to the onset of SWDs (pre-SWD), and in control periods devoid of SWDs. Results: The pre-SWD ECoG consisted of delta and theta components in 80-90% of all SWDs simultaneously in cortex and thalamus, the co-occurrence of delta and theta was rare (7%) during control periods. The occurrence of delta and theta events in pre-SWDs in the cortex preceded that in the thalamus. The frequency of theta component in cortex correlated positively with that in thalamus, this correlation was less strong for delta. Conclusion: Precursors of SWDs comprise of delta and theta, their co-occurrence is typical for non-epileptic periods. Thalamic and cortical theta are strongly related. Rhythmic precursors appear earlier in cortex than in thalamus, and this is in line with the cortical origin of SWD. Significance: Simultaneous presence of delta and theta events in EEG is a condition for the occurrence of SWDs

An algorithm for real-time detection of spike-wave discharges in rodents

The automatic real-time detection of spike-wave discharges (SWDs), the electroencephalographic hallmark of absence seizures, would provide a complementary tool for rapid interference with electrical deep brain stimulation in both patients and animal models. This paper describes a real-time detection algorithm for SWDs based on continuous wavelet analyses in rodents. It has been implemented in a commercially available data acquisition system and its performance experimentally verified. ECoG recordings lasting 5–8 h from rats (n = 8) of the WAG/Rij strain were analyzed using the real-time SWD detection system. The results indicate that the algorithm is able to detect SWDs within 1 s with 100% sensitivity and with a precision of 96.6% for the number of SWDs. Similar results are achieved for 24-h ECoG recordings of two rats. The dependence of accuracy and speed of detection on program settings and attributes of ECoG are discussed. It is concluded that the wavelet based real-time detecting algorithm is well suited for automatic, real-time detection of SWDs in rodents

Sleep spindles and spike-wave discharges in EEG: Their generic features, similarities and distinctions disclosed with Fourier transform and continuous wavelet analysis

Contains fulltext : 77354.pdf (publisher's version ) (Closed access)Epileptic activity in the form of spike-wave discharges (SWD) appears in the electroencephalogram (EEG) during absence seizures. A relationship between SWD and normal sleep spindles is often assumed. This study compares time-frequency parameters of SW and sleep spindles as recorded in the EEG in the WAG/Rij rat model of absence epilepsy. Fast Fourier transformation and continuous wavelet transformation were used for EEG analysis. Wavelet analysis was performed in non-segmented full-length EEG. A specific wavelet-based algorithm was developed for the automatic identification of sleep spindles and SWD. None of standard wavelet templates provided precise identification of all sleep spindles and SWD in the EEG and different wavelet templates were imperative in order to accomplish this task. SWD were identified with high probability using standard Morlet wavelet, but sleep spindles were identified using two types of customized adoptive 'spindle wavelets'. It was found that (1) almost 100% of SWD (but only 50-60% of spindles) were identified using the Morlet-based wavelet transform. (2) 82-91% of sleep spindles were selected using adoptive 'spindle wavelet 1'(template's peak frequency similar to 12.2 Hz), the remaining sleep spindles with 'spindle wavelet 2' (peak frequency similar to 20-25 Hz). (3) Sleep spindles and SWD were detected by the elevation of wavelet energy in different frequencies: SWD, in 30-50 Hz band, sleep spindles, in 7-14Hz. It is concluded that the EEG patterns of sleep spindles and SWD belong to different families of phasic EEG events with different time frequency characteristics