Seminar - Biomedical Signal Processing - Geometry is Destiny: Causality, Prediction and Transition in Multivariate Time Series
Date: October 20, 2006
Time: 4:00 PM
Location: Matheson Hall, Room: 109
Paul E. Rapp, Ph.D.
Department of Pharmacology and Physiology, Drexel University, College of Medicine
Trauma and Resuscitative Medicine Department, Naval Medical Research Center
In biomedical signal processing, classical measures of correlation, coherence and mutual information can be used to establish a correlative relationship between two signals, but these measures do not identify causal relationships. Several methods have been developed with the objective of identifying these relationships. Notable examples include methods based on linear regression, procedures utilizing extensions of mutual information, and tests of the geometrical interdependence of embedded data. All of these measures are based on an operationalization of causality published by Norbert Wiener. If measuring variable X improves the prediction of variable Y, then Y is, in this limited operational sense, causally dependent on variable X, where it is stressed that this relationship is not necessarily unidirectional. The investigation of causality therefore requires time series prediction. Work in our research group has focused on prediction algorithms constructed with embedded data. Improvements over methods using naïve proximity sets can be obtained with the Delauney triangulation and the Dirichlet tessellation.
Causal relationships are not static in time. An analysis of causality must therefore be preceded by the identification of dynamically homogeneous epochs. This identification requires knowledge of the signal’s transition chronometry. Several methods for detecting dynamically significant transitions in noise-corrupted signals have been constructed with embedded data. Embedded data can play a central role in all three of the signal analysis objectives considered here (causality, prediction and transition). This presentation will therefore focus on embedding. An operational description of embedding will be followed by a statement of the Takens embedding theorem. The magnitude of the practical problems encountered when applying the Takens theorem to real world data should not be underestimated. Difficulties in discovering successful embedding criteria will be discussed and the results of a comparative study of embedding criteria will be presented.
A number of biological examples will be considered during the course of the presentation. Transition detection technologies will be used to examine the transition from tonic to clonic seizures, and prediction methods will be used to anticipate the onset of hyperbaric oxygen seizures
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Paul Rapp attended the University of Illinois as a James Scholar. He received a Bachelors degree in Physiology (minor in Chemistry) and a second Bachelors degree in Engineering Physics in 1972. He then attended Cambridge University as a Churchill Scholar and received his Ph.D. in 1975. His doctoral work, under the supervision of Professor Sir James Lighthill, was conducted in the Department of Applied Mathematics and Theoretical Physics. Following graduation he was elected to a Fellowship at Gonville and Caius College, Cambridge University. During this period he continued teaching in the Faculty of Mathematics and performed combined theoretical and experimental work in collaboration with Professor Sir Michael Berridge in the Invertebrate Chemistry and Physiology Unit at Cambridge. This work led to the publication of the calcium-cyclic nucleotide oscillator hypothesis. He joined the faculty of the Medical College of Pennsylvania in 1979.
At present, Rapp is Professor of Pharmacology and Physiology at Drexel University College of Medicine (the successor organization to the Medical College of Pennsylvania). He also holds an appointment to the Department of the Navy under the Interagency Personnel Act with assignment to the Naval Medical Research Center. Additional current appointments include appointment as a Professor of Military and Emergency Medicine at the Uniformed Services University of the Health Sciences and appointment as a Research Associate in the Physics Department at Bryn Mawr College. He is a past editor of Physica D, and is currently on the editorial boards of the International Journal of Bifurcation and Chaos, Chaos and Complexity Letters, and Cognitive Neurodynamics. Past honors include a Certificate of Commendation from the Central Intelligence Agency for “significant contributions to the mission of the Office of Research and Development.”
Matheson Hall is located at 32nd and Market Streets.