Data-driven optimal filtering for phase and frequency of noisy oscillations: Application to vortex flow metering

Algorithmic design of a noise-resistant and efficient closed-loop deep brain stimulation system: A computational approach

Advances in the field of closed-loop neuromodulation call for analysis and modeling approaches capable of confronting challenges related to the complex neuronal response to stimulation and the presence of strong internal and measurement noise in neural recordings. Here we elaborate on the algorithmic aspects of a noise-resistant closed-loop subthalamic nucleus deep brain stimulation system for advanced Parkinson’s disease and treatment-refractory obsessive-compulsive disorder, ensuring remarkable performance in terms of both efficiency and selectivity of stimulation, as well as in terms of computational speed. First, we propose an efficient method drawn from dynamical systems theory, for the reliable assessment of significant nonlinear coupling between beta and high-frequency subthalamic neuronal activity, as a biomarker for feedback control. Further, we present a model-based strategy through which optimal parameters of stimulation for minimum energy desynchronizing control of neuronal activity are being identified. The strategy integrates stochastic modeling and derivative-free optimization of neural dynamics based on quadratic modeling. On the basis of numerical simulations, we demonstrate the potential of the presented modeling approach to identify, at a relatively low computational cost, stimulation settings potentially associated with a significantly higher degree of efficiency and selectivity compared with stimulation settings determined post-operatively. Our data reinforce the hypothesis that model-based control strategies are crucial for the design of novel stimulation protocols at the backstage of clinical applications.

Unified framework for detecting phase synchronization in coupled time series

Phase synchronization (PS) has drawn increasing attention in recent years for its extensive applications in analyzing time series observed from coupled systems. In this paper, we examine the detection of PS in bivariate time series from the viewpoints of signal processing and circular statistics. Several definitions of instantaneous phase (IP) are first revisited and further unified into a framework, which defines IP as the argument of the signal with a specific bandpass filter applied. With this framework, the constraints for IP definition are discussed and the effect of noise in IP estimation is studied. The estimate error of IP, which is due to noise, is shown to obey a scale mixture of normal (SMN) distributions. Further, under the assumption that the SMN of IP error can be approximated by a particular normal distribution, the estimate of mean phase coherence of bivariate time series is shown to be degraded by a factor, which is determined by only the level of in-band noise. Finally, simulations are provided to support the theoretical results.

Detecting phase synchronization in noisy data from coupled chaotic oscillators

Two schemes are proposed to detect phase synchronization from chaotic data contaminated by noise. The first is a neighborhood-based method which links time delay embedding with instantaneous phase estimation. The second adopts the local projection method as a preprocessing filter to noisy data. Both schemes utilize the state recurrence, an important feature of chaotic data. The proposed schemes are applied to data measured from two typical chaotic systems, i.e., the coupled Rössler systems and the coupled Lorenz systems, respectively. The results show that phase synchronization, which may be buried by noise, is detected even when the noise level is high. Moreover, the overestimation of the degree of phase synchronization, which may be introduced by the Hilbert transform combined with a traditional linear bandpass filter, can be avoided when the data are contaminated by only measurement noise.

Experimental evidence for mixed reality states in an interreality system

We present experimental data on the limiting behavior of an interreality system comprising a virtual horizontally driven pendulum coupled to its real-world counterpart, where the interaction time scale is much shorter than the time scale of the dynamical system. We present experimental evidence that, if the physical parameters of the simplified virtual system match those of the real system within a certain tolerance, there is a transition from an uncorrelated dual reality state to a mixed reality state of the system in which the motion of the two pendula is highly correlated. The region in parameter space for stable solutions has an Arnold tongue structure for both the experimental data and a numerical simulation. As virtual systems better approximate real ones, even weak coupling in other interreality systems may produce sudden changes to mixed reality states.

Towards a proper estimation of phase synchronization from time series

In experimental synchronization studies a continuous phase variable is commonly estimated from a scalar time series by means of its representation on the complex plane. The aim is to obtain a pair of functions [A(t), phi(t)] defining its instantaneous amplitude and phase, respectively. However, any arbitrary pair of functions cannot be considered as the amplitude and the phase of the real observable. Here, we point out some criteria that the pair [A(t), phi(t)] must observe to unambiguously define the instantaneous amplitude and phase of the observed signal. In this work, we illustrate how the complex representation may fail if the signal possesses a multi-component or a broadband spectra. We also point out a practical procedure to test whether a signal, not displaying a single oscillation at a unique frequency, has a narrow-band behavior. Implications for the study of phase interdependencies are illustrated and discussed. Phase dynamics estimated from electric brain activities recorded from an epileptic patient are also discussed.

Testing statistical significance of multivariate time series analysis techniques for epileptic seizure prediction

Nonlinear time series analysis techniques have been proposed to detect changes in the electroencephalography dynamics prior to epileptic seizures. Their applicability in practice to predict seizure onsets is hampered by the present lack of generally accepted standards to assess their performance. We propose an analytic approach to judge the prediction performance of multivariate seizure prediction methods. Statistical tests are introduced to assess patient individual results, taking into account that prediction methods are applied to multiple time series and several seizures. Their performance is illustrated utilizing a bivariate seizure prediction method based on synchronization theory.

Phase synchronization from noisy univariate signals

We present methods for detecting phase synchronization of two unidirectionally coupled, self-sustained noisy oscillators from a signal of the driven oscillator alone. One method detects soft phase locking; another hard phase locking. Both are applied to the problem of detecting phase synchronization in von Kármán vortex flow meters.