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A method to characterize dynamical interdependence among nonlinear systems is derived based on mutual nonlinear prediction. Systems with nonlinear correlation will show mutual nonlinear prediction when standard analysis with linear cross correlation might fail. Mutual nonlinear prediction also provides information on the directionality of the coupling(More)
We developed a modern numerical approach to the multivariate linear discrimination of Fisher from 1936 based upon singular value decomposition that is sufficiently stable to permit widespread application to spatiotemporal neuronal patterns. We demonstrate this approach on an old problem in neuroscience--whether seizures have distinct dynamical states as(More)
Recent advances in Kalman filtering to estimate system state and parameters in nonlinear systems have offered the potential to apply such approaches to spatiotemporal nonlinear systems. We here adapt the nonlinear method of unscented Kalman filtering to observe the state and estimate parameters in a computational spatiotemporal excitable system that serves(More)
Paul So, 1,2 Edward Ott, 2,* Tim Sauer, 3 Bruce J. Gluckman, 4,1 Celso Grebogi, 2,† and Steven J. Schiff 1 Center for Neuroscience, Children’s Research Institute, Children’s National Medical Center and the George Washington University, NW, Washington, D.C. 20010 Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 Department(More)
OBJECTIVE To discriminate seizures from interictal dynamics based on multivariate synchrony measures, and to identify dynamics of a pre-seizure state. METHODS A linear discriminator was constructed from two different measures of synchronization: cross-correlation and phase synchronization. We applied this discriminator to a sequence of seizures recorded(More)
PURPOSE The majority of patients with acute myeloid leukemia (AML) who achieve complete remission (CR) relapse with conventional postremission chemotherapy. Allogeneic stem-cell transplantation (alloSCT) might improve survival at the expense of increased toxicity. It remains unknown for which patients alloSCT is preferable. PATIENTS AND METHODS We(More)
Paul So,1,2 Edward Ott,2,* Steven J. Schiff,1 Daniel T. Kaplan,3 Tim Sauer,4 and Celso Grebogi,2,† 1Department of Neurosurgery, Children’s National Medical Center and the George Washington University, NW, Washington, D.C. 20010 2Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 3Center for Nonlinear Dynamics, McGill(More)
The fact that the geometry of state space can be reconstructed from a time series of observations has led to innovative prediction and control algorithms for chaotic systems. In this article we show that state reconstruction of integrate-and-re dynamics is possible from a series of interspike intervals. In particular, a chaotic spike train generated in this(More)
Disturbances of circadian rhythms and mammalian clock genes have been implicated in the etiologies of many chronic illnesses, including cancer. We show that transcription factor CCAAT/enhancer-binding protein alpha (C/EBPalpha)-regulated PER2 activation is a potential tumor suppressor pathway in diffuse large B-cell lymphoma (DLBCL), one of the commonest(More)
This paper describes a homotopy method used to solve the kth-degree X-matrix problem (Akk q_ Akk__ + Al A0)x 0. A special homotopy equation is constructed for the case where all coefficients are general n n complex matrices. Smooth curves connecting trivial solutions to desired eigenpairs are shown to exist. The homotopy equations maintain the nonzero(More)