: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

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Nonlinear Time Series Analysis.

Methods from nonlinear dynamics (NLD) have shown new insights into heart rate (HR) variability changes under various physiological and pathological conditions, providing additional prognostic information and complementing traditional time- and frequency-domain analyses. In this review, some of the most prominent indices of nonlinear and fractal dynamics are summarized and their algorithmic implementations and applications in clinical trials are discussed. Several of those indices have been proven to be of diagnostic relevance or have contributed to risk stratification. In particular, techniques based on mono- and multifractal analyses and symbolic dynamics have been successfully applied to clinical studies. Further advances in HR variability analysis are expected through multidimensional and multivariate assessments. Today, the question is no longer about whether or not methods from NLD should be applied; however, it is relevant to ask which of the methods should be selected and under which basic and standardized conditions should they be applied.

Methods derived from nonlinear dynamics for analysing heart rate variability

Alpha Power Increase After Transcranial Alternating Current Stimulation at Alpha Frequency (α-tACS) Reflects Plastic Changes Rather Than Entrainment.

Automated sleep stage identification system based on time-frequency analysis of a single EEG channel and random forest classifier

EEG oscillations: From correlation to causality.

http://www.fdm.uni-freiburg.de/publications-preprints/publications/papers/ComparisonMethodsDetectDirectInterrelations_printed

Comparison of linear signal processing techniques to infer directed interactions in multivariate neural systems

Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect.

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Modeling brain resonance phenomena using a neural mass model.

Visual stimulation by repetitive flashes of light can lead to an entrainment of the alpha rhythm in electroencephalogram recordings (also called photic driving) We report a comparison of simultaneously recorded electric and magnetic data in a photic driving experiment, adapted to the individual alpha rhythm of 10 healthy volunteers We show that there is a stronger frequency entrainment in magnetoencephalogram than in electroencephalogram recordings in all volunteers, which indicates a possible tangential brain activity underlying the dominant entrainment effect The entrainment in the magnetoencephalogram lasts over significantly more frequencies and is most effective in the region around the individual alpha and a half alpha For different channels, we found different degrees of entrainment showing topological and time-varying properties

Alpha entrainment in human electroencephalogram and magnetoencephalogram recordings.

ObjectiveA coupled system of nonlinear neural oscillators with an individual resonance frequency is assumed to form the neuronal substrate for the photic driving phenomenon. The aim was to investigate the spatiotemporal stability of these oscillators and quantify the spatiotemporal process of engage

Topographic analysis of engagement and disengagement of neural oscillators in photic driving: a combined electroencephalogram/magnetoencephalogram study.

Time-variant partial directed coherence (tvPDC) is used for the first time in a multivariate analysis of heart rate variability (HRV), respiratory movements (RMs) and (systolic) arterial blood pressure. It is shown that respirationrelated HRV components which also occur at other frequencies besides the RM frequency (= respiratory sinus arrhythmia, RSA) can be identified. These additional components are known to be an effect of the ‘half-the-mean-heartrate-dilemma’ (‘cardiac aliasing’ CA). These CA components may contaminate the entire frequency range of HRV and can lead to misinterpretation of the RSA analysis. TvPDC analysis of simulated and clinical data (full-term neonates and sedated patients) reveals these contamination effects and, in addition, the respiration-related CA components can be separated from the RSA component and the Traube–Hering–Mayer wave. It can be concluded that tvPDC can be beneficially applied to avoid misinterpretations in HRV analyses as well as to quantify partial correlative interaction properties between RM and RSA.

Karin Schwab

Papers

Comparison of linear signal processing techniques to infer directed interactions in multivariate neural systems

Modeling brain resonance phenomena using a neural mass model.

Alpha entrainment in human electroencephalogram and magnetoencephalogram recordings.

Topographic analysis of engagement and disengagement of neural oscillators in photic driving: a combined electroencephalogram/magnetoencephalogram study.

Time-variant partial directed coherence in analysis of the cardiovascular system. A methodological study.