983 research outputs found

    A quantitative version of Gordon's Theorem for Jacobi and Sturm-Liouville operators

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    We prove a quantitative version of Gordon's Theorem concerning absence of eigenvalues for Jacobi matrices and Sturm-Liouville operators with complex coefficients.Comment: 22 page

    Dynamical Component Analysis (DyCA) and its application on epileptic EEG

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    Dynamical Component Analysis (DyCA) is a recently-proposed method to detect projection vectors to reduce the dimensionality of multi-variate deterministic datasets. It is based on the solution of a generalized eigenvalue problem and therefore straight forward to implement. DyCA is introduced and applied to EEG data of epileptic seizures. The obtained eigenvectors are used to project the signal and the corresponding trajectories in phase space are compared with PCA and ICA-projections. The eigenvalues of DyCA are utilized for seizure detection and the obtained results in terms of specificity, false discovery rate and miss rate are compared to other seizure detection algorithms.Comment: 5 pages, 4 figures, accepted for IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 201