Biomedical subjects
Publications and source records attributed to H U Voss.
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.
The evidence for the aperiodic self-excited oscillations of flow-conveying collapsible tubes being mathematically chaotic is re-examined. Many cases which powerfully suggest nonlinear deterministic behaviour have not been recorded over time-spans which allow their exhaustive examination. The present investigation centred on a previously recorded robust and generic oscillation, but more recent and more discerning tests were applied. Despite hints that a low embedding dimension might suffice, the data appeared on most indices high-dimensional. A U-shaped return map was found and modelled using both radial basis functions and polynomials, but lack of detailed structure in the map prevented effective parameter estimation. On the basis of power-law rather than exponential divergence of nearby trajectories, and of inability to discriminate against behaviour which would also be manifested by a surrogate consisting of a noise-perturbed nonlinear periodic oscillator, it is concluded that the data do not support the idea that the aperiodicity in the particular oscillation examined is caused by deterministic chaos. There was evidence that the distributed nature of the physical system might underlie aspects of the high dimensionality. We advocate equally searching testing of any future candidate chaotic oscillations in the investigation of collapsed-tube flows.
The unpredictability of the occurrence of epileptic seizures contributes to the burden of the disease to a major degree. Thus, various methods have been proposed to predict the onset of seizures based on EEG recordings. A nonlinear feature motivated by the correlation dimension is a seemingly promising approach. In a previous study this method was reported to identify 'preictal dimension drops' up to 19 min before seizure onset, exceeding the variability of interictal data sets of 30-50 min duration. Here we have investigated the sensitivity and specificity of this method based on invasive long-term recordings from 21 patients with medically intractable partial epilepsies, who underwent invasive pre-surgical monitoring. The evaluation of interictal 24-h recordings comprising the sleep-wake cycle showed that only one out of 88 seizures was preceded by a significant preictal dimension drop. In a second analysis, the relation between dimension drops within time windows of up to 50 min before seizure onset and interictal periods was investigated. For false-prediction rates below 0.1/h, the sensitivity ranged from 8.3 to 38.3% depending on the prediction window length. Overall, the mean length and amplitude of dimension drops showed no significant differences between interictal and preictal data sets.
The problem of identifying continuous spatiotemporal nonlinear systems from noisy and indirect observations is determined by its computational complexity. We propose a solution by means of nonlinear state space filtering along with a state partition technique. The method is demonstrated to be computationally feasible for spatiotemporal data with properties that occur typically in experimental recordings. It is applied to one component of the simulated chaotic data of a two-component reaction diffusion system, yielding estimates of both the unobserved state component and the diffusion constant.
The unpredictability of seizures is a central problem for all patients suffering from uncontrolled epilepsy. Recently, numerous methods have been suggested that claim to predict from the EEG the onset of epileptic seizures. In parallel, new therapeutic devices are in development that could control upcoming seizures provided that their onset is known in advance. A reliable clinical application controlling seizures, consisting of a seizure prediction method and an intervention system, would improve patient quality of life. The question therefore arises as to whether the performance of the seizure prediction methods is already sufficient for clinical applications. The answer requires assessment criteria to judge and compare these methods, but recognized criteria still do not exist. Based on clinical, behavioral, and statistical considerations, we suggest the "seizure prediction characteristic" to evaluate seizure prediction methods. Results of this approach are exemplified by its application to the "dynamical similarity index" seizure prediction method using 582 hours of intracranial EEG data, including 88 seizures.
The problem of constructing synchronizing systems to observed signals is approached from a data driven perspective, in which it is assumed that neither the drive nor the response systems are known explicitly but have to be derived from the observations. The response systems are modeled by utilizing standard methods of nonlinear time series analysis applied to sections of the driving signals. As a result, synchronization is more robust than what might be expected, given that the reconstructed systems are only approximations of the unknown true systems. Successful synchronization also may be accomplished in cases where the driving signals result from nonlinearly transformed chaotic states. The method is readily extended and applied to limited real-time predictions of chaotic signals.
Signal data from DNA-microarray ("chip") technology can be noisy; i.e., the signal variation of one gene on a series of repetitive chips can be substantial. It is becoming more and more recognized that a sufficient number of chip replicates has to be made in order to separate correct from incorrect signals. To reduce the systematic fraction of the noise deriving from pipetting errors, from different treatment of chips during hybridization, and from chip-to-chip manufacturing variability, normalization schemes are employed. We present here an iterative nonparametric nonlinear normalization scheme called simultaneous alternating conditional expectation (sACE), which is designed to maximize correlation between chip repeats in all-chip-against-all space. We tested sACE on 28 experiments with 158 Affymetrix one-color chips. The procedure should be equally applicable to other DNA-microarray technologies, e.g., two-color chips. We show that the reduction of noise compared to a simple normalization scheme like the widely used linear global normalization leads to fewer false-positive calls, i.e., to fewer genes which have to be laboriously confirmed by independent methods such as TaqMan or quantitative PCR.
We study the problem of simultaneous estimation of parameters and unobserved states from noisy data of nonlinear time-continuous systems, including the case of additive stochastic forcing. We propose a solution by adapting the recently developed statistical method of unscented Kalman filtering to this problem. Due to its recursive and derivative-free structure, this method minimizes the cost function in a computationally efficient and robust way. It is found that parameters as well as unobserved components can be estimated with high accuracy, including confidence bands, from heavily noise-corrupted data.
Introducing a short time delay into the coupling of two synchronizing chaotic systems, it was shown recently that the driven system may anticipate the driving system in real time. Augmenting the phase space of the driven system, we accomplish anticipation times that are multiples of the coupling delay time and exceed characteristic time scales of the chaotic dynamics. The stability properties of the associated anticipatory synchronization manifold in certain cases turn out to be the same as for identically synchronizing oscillators.