Nonlinear optical microscopy with vibrational contrast.

Nonlinear optical techniques which provide vibrational contrast have gained increasing attention in microscopy during the last two decades. After outlining the potential of these techniques, we give a brief introduction to coherent anti-Stokes Raman scattering, stimulated Raman scattering and sum frequency generation and discuss their suitability for contrast generation in optical microscopy. The rapid developments in these fields during the last decade have resulted in many different applications. Three exemplary application areas will therefore be presented in the last part of this manuscript.

Toward far-field vibrational spectroscopy of single molecules at room temperature.

We propose a new scheme for the extraction of chemically sensitive vibrational information from a single fluorescent molecule at room temperature. Our approach is based on a three-photon fluorescence excitation scheme, with selectivity in the production of a vibrational population of the ground state. We estimate the expected signal in perturbation theory for a standard dye molecule, compare its magnitude qualitatively to noise and various background sources, and discuss the experimental realization of this scheme.

Mixing properties of the Rössler system and consequences for coherence and synchronization analysis.

Cross-spectral and synchronization analysis of two independent, identical chaotic Rössler systems suggest a coupling although there is no interaction. This spuriously detected interaction can either be explained by the absence of mixing or by finite size effects. To decide which alternative holds the phase dynamics is studied by a model of the fluctuations derived from the system's equations. The basic assumption of the model is a diffusive character for the system which corresponds to mixing. Comparison of theoretical properties of the model with empirical properties of the Rössler system suggests that the system is mixing but the rate of mixing appears to be rather low.

Aperiodic flow-induced oscillations of collapsible tubes: a critical reappraisal.

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.

How well can epileptic seizures be predicted? An evaluation of a nonlinear method.

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 seizure prediction characteristic: a general framework to assess and compare seizure prediction methods.

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.