Methods to detect, characterize, and remove motion artifact in resting state fMRI

: 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.

Autism spectrum disorder (ASD) is a neurodevelopmental disorder characterized by social deficits and repetitive behaviors that typically emerge by 24 months of age. To develop effective early interventions that can potentially ameliorate the defining deficits of ASD and improve long-term outcomes, early detection is essential. Using prospective neuroimaging of 59 6-month-old infants with a high familial risk for ASD, we show that functional connectivity magnetic resonance imaging correctly identified which individual children would receive a research clinical best-estimate diagnosis of ASD at 24 months of age. Functional brain connections were defined in 6-month-old infants that correlated with 24-month scores on measures of social behavior, language, motor development, and repetitive behavior, which are all features common to the diagnosis of ASD. A fully cross-validated machine learning algorithm applied at age 6 months had a positive predictive value of 100% [95% confidence interval (CI), 62.9 to 100], correctly predicting 9 of 11 infants who received a diagnosis of ASD at 24 months (sensitivity, 81.8%; 95% CI, 47.8 to 96.8). All 48 6-month-old infants who were not diagnosed with ASD were correctly classified [specificity, 100% (95% CI, 90.8 to 100); negative predictive value, 96.0% (95% CI, 85.1 to 99.3)]. These findings have clinical implications for early risk assessment and the feasibility of developing early preventative interventions for ASD.

Functional neuroimaging of high-risk 6-month-old infants predicts a diagnosis of autism at 24 months of age

In this study, a sliding mode control system with a proportional+integral+derivative (PID) sliding surface is adopted to control the speed of an electromechanical plant. A robust sliding mode controller is derived so that the actual trajectory tracks the desired trajectory despite uncertainty, nonlinear dynamics, and external disturbances. The proposed sliding mode controller is chosen to ensure the stability of overall dynamics during the reaching phase and sliding phase. The stability of the system is guaranteed in the sense of the Lyapunov stability theorem. The chattering problem is overcome using a hyperbolic function for the sliding surface. Experimental results that are compared with the results of conventional PID verify that the proposed sliding mode controller can achieve favorable tracking performance, and it is robust with regard to uncertainties and disturbances.

Sliding mode control with PID sliding surface and experimental application to an electromechanical plant.

Spectral analysis of nonuniformly sampled data -- a review

In this paper, we present a spectral analysis method based upon least square approximation. Our method deals with nonuniform sampling. It provides meaningful phase information that varies in a predictable way as the samples are shifted in time. We compare least square approximations of real and complex series, analyze their properties for sample count towards infinity as well as estimator behaviour, and show the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case. We propose a way to deal with the undesirable side effects of nonuniform sampling in the presence of constant offsets. By using weighted least square approximation, we introduce an analogue to the Morlet wavelet transform for nonuniformly sampled data. Asymptotically fast divide-and-conquer schemes for the computation of the variants of the proposed method are presented. The usefulness is demonstrated in some relevant applications.

Algorithms for Spectral Analysis of Irregularly Sampled Time Series

An enhanced version of the well known Wolf algorithm for the estimation of the Lyapunov characteristic exponents (LCEs) is proposed. It permits interpretation of the local behavior of non-linear flows. The new variant allows for reliable calculation of the non-uniformity-factors (NUFs). The NUFs can be interpreted as standard deviations of the LCEs. Since the latter can also be estimated by the Wolf algorithm, however, without local information on the flow, the new version ensures local interpretability and therefore allows the calculation of the NUFs. The local contributions to the LCEs which we call “local LCEs” can at least be calculated up to three dimensions. Application of the modified method to a hyperchaotic flow in four dimensions shows that an extension to many dimensions is possible and promises new insight into so far not fully understood high-dimensional non-linear systems.

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A robust, locally interpretable algorithm for Lyapunov exponents

We introduce an adaptive system for dynamics recognition. Thereby, an externally presented dynamics (stimulus) is mapped onto a mirror dynamics which is capable to simulate (simulus). A sudden change of the external dynamics leads to an surprisingly quick re-adaptation of the simulus, even if the presented dynamics is chaotic. The system consists of an internal pool of dynamical modules. The modules are forced to the latter dynamics in the sense of Pyragas' control mechanism by the stimulus. The control term, i.e. the strength of forcing, is used as a measure for which modules fit best to the external dynamics. In a sense, this defines a “dynamics-gradient” within the pool. The mirror dynamics now can be constructed by a linear combination of the best fitting modules with weights given by the control term amplitudes. If one adds the so-constructed mirror dynamics to the pool, one has a representation of the corresponding external dynamics within the pool. Later if the same external dynamics is presented again an even quicker adaptation is possible since a well-fitting module is already present. In order not to blow up the dimensionality of the pool, one can eliminate modules that have not been used for a long time. In principle, the modules can undergo an internal control. In addition, one principally can introduce evolution within the pool. Therefore, the system is able to show what sometimes is called a “second cybernetics”, i.e. a hyper-dynamics of the dynamics modules.

Towards a second cybernetics model for cognitive systems

Hans H. Diebnera, Axel A. Hoffb, Adolf Mathiasa, Horst Prehnc, Marco Rohrbacha;c, and Sven Sahlea a Institute for Basic Research, Center for Art and Media, Lorenzstr. 19, D-76135 Karlsruhe b Steinbeis-Transferzentrum for Innovative Systems and Services, Am Seemooser Horn 20, D-88045 Friedrichshafen c Institute of Biomedical Engineering, University of Applied Sciences, Wiesenstr. 14, D-35390 Giesen

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Adolf Mathias

Papers

Algorithms for Spectral Analysis of Irregularly Sampled Time Series

A robust, locally interpretable algorithm for Lyapunov exponents

Towards a second cybernetics model for cognitive systems

Control and Adaptation of Spatio-temporal Patterns

c-Variations 2002