[show abstract][hide abstract] ABSTRACT: We propose a simple dynamical system to interpret the gait time series from patients affected by three neurodegenerative diseases: Parkinson, Huntington and Amyotrophic Lateral Sclerosis. The model is shown to reproduce the main aspects of the experimental time series. Within this scenario, quantitative differences in specific indicators are detected thus opening up the perspective for innovative, non invasive, diagnosis procedures from direct measurements of gait dynamics.
[show abstract][hide abstract] ABSTRACT: A higher order recurrent neural network architecture learns to recognize and generate languages after being trained on categorized exemplars. Studying these networks from the perspective of dynamical systems yields two interesting discoveries: First, a longitudinal examination of the learning process illustrates a new form of mechanical inference: Induction by phase transition. A small weight adjustment causes a bifurcation in the limit behavior of the network. This phase transition corresponds to the onset of the network''s capacity for generalizing to arbitrary-length strings. Second, a study of the automata resulting from the acquisition of previously published training sets indicates that while the architecture is not guaranteed to find a minimal finite automaton consistent with the given exemplars, which is an NP-Hard problem, the architecture does appear capable of generating non-regular languages by exploiting fractal and chaotic dynamics. I end the paper with a hypothesis relating linguistic generative capacity to the behavioral regimes of non-linear dynamical systems.
[show abstract][hide abstract] ABSTRACT: Processing of functional magnetic resonance imaging (fMRI) data is a critical step in evaluating experimental results. We address the question of choosing between a Student t-test method, crosscorrelation method, or a weighted z-score method in analyzing functional MR images. We present an analytic analysis that makes it possible to make a statistical decision in setting the threshold for the crosscorrelation coefficient. Specifically, the theory for an receiver operating characteristic (ROC) analysis (description of type I and type II error) has been applied to the crosscorrelation method. Both theoretical predictions as well as model simulations are presented to prove that the crosscorrelation and weighted z-score method have the same statistical power. We introduce the concept of a variance image and use it to not only choose between the correlation image and a simple t-test image but also to obtain a final image that combines the efficient aspects of both the correlation and the simple t-test images. The variance image itself is shown to be an indicator of both patient motion and/or internal physiological motion in the brain. Furthermore, we delineate the importance of electrocardiogram (ECG) gating in reducing the variance in fMRI of human motor cortex.
Magnetic Resonance Imaging 02/1997; 15(2):169-81. · 2.06 Impact Factor
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