The Experts below are selected from a list of 35139 Experts worldwide ranked by ideXlab platform
Abel Klein - One of the best experts on this subject based on the ideXlab platform.
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Eigensystem Multiscale Analysis for Anderson localization in energy intervals
arXiv: Mathematical Physics, 2016Co-Authors: Alexander Elgart, Abel KleinAbstract:We present an eigensystem Multiscale Analysis for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model in an energy interval. In particular, it yields localization for the Anderson model in a nonempty interval at the bottom of the spectrum. This eigensystem Multiscale Analysis in an energy interval treats all energies of the finite volume operator at the same time, establishing level spacing and localization of eigenfunctions with eigenvalues in the energy interval in a fixed box with high probability. In contrast to the usual strategy, we do not study finite volume Green's functions. Instead, we perform a Multiscale Analysis based on finite volume eigensystems (eigenvalues and eigenfunctions). In any given scale we only have decay for eigenfunctions with eigenvalues in the energy interval, and no information about the other eigenfunctions. For this reason, going to a larger scale requires new arguments that were not necessary in our previous eigensystem Multiscale Analysis for the Anderson model at high disorder, where in a given scale we have decay for all eigenfunctions.
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Eigensystem Bootstrap Multiscale Analysis for the Anderson Model
arXiv: Mathematical Physics, 2016Co-Authors: Abel Klein, C. S. Sidney TsangAbstract:We use a bootstrap argument to enhance the eigensystem Multiscale Analysis, introduced by Elgart and Klein for proving localization for the Anderson model at high disorder. The eigensystem Multiscale Analysis studies finite volume eigensystems, not finite volume Green's functions. It yields pure point spectrum with exponentially decaying eigenfunctions and dynamical localization. The starting hypothesis for the eigensystem bootstrap Multiscale Analysis only requires the verification of polynomial decay of the finite volume eigenfunctions, at some sufficiently large scale, with some minimal probability independent of the scale. It yields exponential localization of finite volume eigenfunctions in boxes of side $L$, with the eigenvalues and eigenfunctions labeled by the sites of the box, with probability higher than $1-\mathrm{e}^{-L^\xi}$, for any desired $0
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Bootstrap Multiscale Analysis and localization for multi-particle continuous Anderson Hamiltonians
arXiv: Mathematical Physics, 2013Co-Authors: Abel Klein, Son T. NguyenAbstract:We extend the bootstrap Multiscale Analysis developed by Germinet and Klein to the multi-particle continuous Anderson Hamiltonian, obtaining Anderson localization with finite multiplicity of eigenvalues, decay of eigenfunction correlations, and a strong form of dynamical localization.
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Multiscale Analysis and Localization of Random Operators
arXiv: Mathematical Physics, 2007Co-Authors: Abel KleinAbstract:A discussion of the method of Multiscale Analysis in the study of localization of random operators based on lectures given at \emph{Random Schr\"odinger operators: methods, results, and perspectives}, \'Etats de la recherche, Universit\'e Paris 13, June 2002
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bootstrap Multiscale Analysis and localization in random media
Communications in Mathematical Physics, 2001Co-Authors: Francois Germinet, Abel KleinAbstract:We introduce an enhanced Multiscale Analysis that yields subexponentially decaying probabilities for bad events. For quantum and classical waves in random media, we obtain exponential decay for the resolvent of the corresponding random operators in boxes of side L with probability higher than 1 − e − L ζ, for any 0<ζ<1. The starting hypothesis for the enhanced Multiscale Analysis only requires the verification of polynomial decay of the finite volume resolvent, at some sufficiently large scale, with probability bigger than 1 − (d is the dimension). Note that from the same starting hypothesis we get conclusions that are valid for any 0 < ζ < 1. This is achieved by the repeated use of a bootstrap argument. As an application, we use a generalized eigenfunction expansion to obtain strong dynamical localization of any order in the Hilbert–Schmidt norm, and better estimates on the behavior of the eigenfunctions.
Riccardo Barbieri - One of the best experts on this subject based on the ideXlab platform.
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Point-Process High-Resolution Representations of Heartbeat Dynamics for Multiscale Analysis: a CHF Survivor Prediction Study
2015Co-Authors: Gaetano Valenza, Herwig Wendt, Ken Kiyono, Junihiro Hayano, Eiichi Watanabe, Yoshiharu Yamamoto, Patrice Abry, Riccardo BarbieriAbstract:Multiscale Analysis of human heartbeat dynamics has been proved effective in characterizeing cardiovascular control physiology in health and disease. However, estimation of Multiscale properties can be affected by the interpolation procedure used to preprocess the unevenly sampled R-R intervals derived from the ECG. To this extent, in this study we propose the estimation of wavelet coefficients and wavelet leaders on the output of inhomogeneous point process models of heartbeat dynamics. The RR interval series is modeled using probability density functions (pdfs) characterizing and predicting the time until the next heartbeat event occurs, as a linear function of the past history. Multiscale Analysis is then applied to the pdfs' instantaneous first order moment. The proposed approach is tested on experimental data gathered from 57 congestive heart failure (CHF) patients by evaluating the recognition accuracy in predicting survivor and non-survivor patients, and by comparing performances from the informative point-process based interpolation and non-informative spline-based interpolation. Results demonstrate that Multiscale Analysis of point-process high-resolution representations achieves the highest prediction accuracy of 65.45%, proving our method as a promising tool to assess risk prediction in CHF patients.
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EMBC - Point-process high-resolution representations of heartbeat dynamics for Multiscale Analysis: A CHF survivor prediction study
2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2015Co-Authors: Gaetano Valenza, Herwig Wendt, Ken Kiyono, Junihiro Hayano, Eiichi Watanabe, Yoshiharu Yamamoto, Patrice Abry, Riccardo BarbieriAbstract:Multiscale Analysis of human heartbeat dynamics has been proved effective in characterizeing cardiovascular control physiology in health and disease. However, estimation of Multiscale properties can be affected by the interpolation procedure used to preprocess the unevenly sampled R-R intervals derived from the ECG. To this extent, in this study we propose the estimation of wavelet coefficients and wavelet leaders on the output of inhomogeneous point process models of heartbeat dynamics. The RR interval series is modeled using probability density functions (pdfs) characterizing and predicting the time until the next heartbeat event occurs, as a linear function of the past history. Multiscale Analysis is then applied to the pdfs' instantaneous first order moment. The proposed approach is tested on experimental data gathered from 57 congestive heart failure (CHF) patients by evaluating the recognition accuracy in predicting survivor and non-survivor patients, and by comparing performances from the informative point-process based interpolation and non-informative spline-based interpolation. Results demonstrate that Multiscale Analysis of point-process high-resolution representations achieves the highest prediction accuracy of 65.45%, proving our method as a promising tool to assess risk prediction in CHF patients.
Francois Germinet - One of the best experts on this subject based on the ideXlab platform.
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bootstrap Multiscale Analysis and localization in random media
Communications in Mathematical Physics, 2001Co-Authors: Francois Germinet, Abel KleinAbstract:We introduce an enhanced Multiscale Analysis that yields subexponentially decaying probabilities for bad events. For quantum and classical waves in random media, we obtain exponential decay for the resolvent of the corresponding random operators in boxes of side L with probability higher than 1 − e − L ζ, for any 0<ζ<1. The starting hypothesis for the enhanced Multiscale Analysis only requires the verification of polynomial decay of the finite volume resolvent, at some sufficiently large scale, with probability bigger than 1 − (d is the dimension). Note that from the same starting hypothesis we get conclusions that are valid for any 0 < ζ < 1. This is achieved by the repeated use of a bootstrap argument. As an application, we use a generalized eigenfunction expansion to obtain strong dynamical localization of any order in the Hilbert–Schmidt norm, and better estimates on the behavior of the eigenfunctions.
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Bootstrap Multiscale Analysis and Localization¶in Random Media
Communications in Mathematical Physics, 2001Co-Authors: Francois Germinet, Abel KleinAbstract:We introduce an enhanced Multiscale Analysis that yields subexponentially decaying probabilities for bad events. For quantum and classical waves in random media, we obtain exponential decay for the resolvent of the corresponding random operators in boxes of side L with probability higher than 1 − e − L ζ, for any 0
J.-l. Starck - One of the best experts on this subject based on the ideXlab platform.
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Image processing through Multiscale Analysis and measurementnoise modeling
Statistics and Computing, 2000Co-Authors: F. Murtagh, J.-l. StarckAbstract:We describe a range of powerful Multiscale Analysis methods. We also focus on the pivotal issue of measurement noise in the physical sciences. From Multiscale Analysis and noise modeling, we develop a comprehensive methodology for data Analysis of 2D images, 1D signals (or spectra), and point pattern data. Noise modeling is based on the following: (i) Multiscale transforms, including wavelet transformss (ii) a data structure termed the multiresolution supports and (iii) multiple scale significance testing. The latter two aspects serve to characterize signal with respect to noise. The data Analysis objectives we deal with include noise filtering and scale decomposition for visualization or feature detection.
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Image processing through Multiscale Analysis and measurement noise modeling
Statistics and Computing, 2000Co-Authors: F. Murtagh, J.-l. StarckAbstract:We describe a range of powerful Multiscale Analysis methods. We also focus on the pivotal issue of measurement noise in the physical sciences. From Multiscale Analysis and noise modeling, we develop a comprehensive methodology for data Analysis of 2D images, 1D signals (or spectra), and point pattern data. Noise modeling is based on the following: (i) Multiscale transforms, including wavelet transforms; (ii) a data structure termed the multiresolution support; and (iii) multiple scale significance testing. The latter two aspects serve to characterize signal with respect to noise. The data Analysis objectives we deal with include noise filtering and scale decomposition for visualization or feature detection.
Yoshiharu Yamamoto - One of the best experts on this subject based on the ideXlab platform.
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Multiscale Analysis of Intensive Longitudinal Biomedical Signals and Its Clinical Applications
Proceedings of the IEEE, 2016Co-Authors: Toru Nakamura, Herwig Wendt, Ken Kiyono, Patrice Abry, Yoshiharu YamamotoAbstract:Recent advances in wearable and/or biomedical sensing technologies have made it possible to record very long-term, continuous biomedical signals, referred to as biomedical intensive longitudinal data (ILD). To link ILD to clinical applications, such as personalized healthcare and disease prevention, the development of robust and reliable data Analysis techniques is considered important. In this review, we introduce Multiscale Analysis methods for and the applications to two types of intensive longitudinal biomedical signals, heart rate variability (HRV) and spontaneous physical activity (SPA) time series. It has been shown that these ILD have robust characteristics unique to various Multiscale complex systems, and some parameters characterizing the Multiscale complexity are in fact altered in pathological states, showing potential usability as a new type of ambient diagnostic and/or prognostic tools. For example, parameters characterizing increased intermittency of HRV are found to be potentially useful in detecting abnormality in the state of the autonomic nervous system, in particular the sympathetic hyperactivity, and intermittency parameters of SPA might also be useful in evaluating symptoms of psychiatric patients with depressive as well as manic episodes, all in the daily settings. Therefore, Multiscale Analysis might be a useful tool to extract information on clinical events occurring at multiple time scales during daily life and the underlying physiological control mechanisms from biomedical ILD.
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Point-Process High-Resolution Representations of Heartbeat Dynamics for Multiscale Analysis: a CHF Survivor Prediction Study
2015Co-Authors: Gaetano Valenza, Herwig Wendt, Ken Kiyono, Junihiro Hayano, Eiichi Watanabe, Yoshiharu Yamamoto, Patrice Abry, Riccardo BarbieriAbstract:Multiscale Analysis of human heartbeat dynamics has been proved effective in characterizeing cardiovascular control physiology in health and disease. However, estimation of Multiscale properties can be affected by the interpolation procedure used to preprocess the unevenly sampled R-R intervals derived from the ECG. To this extent, in this study we propose the estimation of wavelet coefficients and wavelet leaders on the output of inhomogeneous point process models of heartbeat dynamics. The RR interval series is modeled using probability density functions (pdfs) characterizing and predicting the time until the next heartbeat event occurs, as a linear function of the past history. Multiscale Analysis is then applied to the pdfs' instantaneous first order moment. The proposed approach is tested on experimental data gathered from 57 congestive heart failure (CHF) patients by evaluating the recognition accuracy in predicting survivor and non-survivor patients, and by comparing performances from the informative point-process based interpolation and non-informative spline-based interpolation. Results demonstrate that Multiscale Analysis of point-process high-resolution representations achieves the highest prediction accuracy of 65.45%, proving our method as a promising tool to assess risk prediction in CHF patients.
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EMBC - Point-process high-resolution representations of heartbeat dynamics for Multiscale Analysis: A CHF survivor prediction study
2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2015Co-Authors: Gaetano Valenza, Herwig Wendt, Ken Kiyono, Junihiro Hayano, Eiichi Watanabe, Yoshiharu Yamamoto, Patrice Abry, Riccardo BarbieriAbstract:Multiscale Analysis of human heartbeat dynamics has been proved effective in characterizeing cardiovascular control physiology in health and disease. However, estimation of Multiscale properties can be affected by the interpolation procedure used to preprocess the unevenly sampled R-R intervals derived from the ECG. To this extent, in this study we propose the estimation of wavelet coefficients and wavelet leaders on the output of inhomogeneous point process models of heartbeat dynamics. The RR interval series is modeled using probability density functions (pdfs) characterizing and predicting the time until the next heartbeat event occurs, as a linear function of the past history. Multiscale Analysis is then applied to the pdfs' instantaneous first order moment. The proposed approach is tested on experimental data gathered from 57 congestive heart failure (CHF) patients by evaluating the recognition accuracy in predicting survivor and non-survivor patients, and by comparing performances from the informative point-process based interpolation and non-informative spline-based interpolation. Results demonstrate that Multiscale Analysis of point-process high-resolution representations achieves the highest prediction accuracy of 65.45%, proving our method as a promising tool to assess risk prediction in CHF patients.
