The Experts below are selected from a list of 17595 Experts worldwide ranked by ideXlab platform
Cristina Masoller - One of the best experts on this subject based on the ideXlab platform.
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state space reconstruction of spatially extended systems and of time delayed systems from the time series of a Scalar Variable
Chaos, 2018Co-Authors: C Quinteroquiroz, M. C. Torrent, Cristina MasollerAbstract:The space-time representation of high-dimensional dynamical systems that have a well defined characteristic time scale has proven to be very useful to deepen the understanding of such systems and to uncover hidden features in their output signals. By using the space-time representation many analogies between one-dimensional spatially extended systems (1D SESs) and time delayed systems (TDSs) have been found, including similar pattern formation and propagation of localized structures. An open question is whether such analogies are limited to the space-time representation, or it is also possible to recover similar evolutions in a low-dimensional pseudo-space. To address this issue, we analyze a 1D SES (a bistable reaction-diffusion system), a Scalar TDS (a bistable system with delayed feedback), and a non-Scalar TDS (a model of two delay-coupled lasers). In these three examples, we show that we can reconstruct the dynamics in a three-dimensional phase space, where the evolution is governed by the same polynomial potential. We also discuss the limitations of the analogy between 1D SESs and TDSs.The space-time representation of high-dimensional dynamical systems that have a well defined characteristic time scale has proven to be very useful to deepen the understanding of such systems and to uncover hidden features in their output signals. By using the space-time representation many analogies between one-dimensional spatially extended systems (1D SESs) and time delayed systems (TDSs) have been found, including similar pattern formation and propagation of localized structures. An open question is whether such analogies are limited to the space-time representation, or it is also possible to recover similar evolutions in a low-dimensional pseudo-space. To address this issue, we analyze a 1D SES (a bistable reaction-diffusion system), a Scalar TDS (a bistable system with delayed feedback), and a non-Scalar TDS (a model of two delay-coupled lasers). In these three examples, we show that we can reconstruct the dynamics in a three-dimensional phase space, where the evolution is governed by the same polyn...
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Reconstructing the attractor of spatial and time-delayed systems from the time series of a Scalar Variable
arXiv: Data Analysis Statistics and Probability, 2018Co-Authors: C. Quintero-quiroz, M. C. Torrent, Cristina MasollerAbstract:The space-time representation of high-dimensional dynamical systems that have a well defined characteristic time scale has proven to be very useful to deepen the understanding of such systems and to uncover hidden features in their output signals. Genuine analogies between one-dimensional (1D) spatially extended systems (1D SESs) and time delayed systems (TDSs) have been observed, including similar pattern formation and propagation of localized structures. An open question is if such analogies are limited to the space-time representation, or, if it is possible to reconstruct similar attractors, from the time series of an observed Variable. In this work we address this issue by considering a bistable 1D SES and two TDSs (a bistable system and a model of two lasers with time delayed coupling). In these three examples we find that we can reconstruct the underlying attractor in a three-dimensional pseudo-space, where the evolution is governed by a polynomial potential. We also discuss the limitations of the analogy between 1D SESs and TDSs.
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state space reconstruction of spatially extended systems and of time delayed systems from the time series of a Scalar Variable
arXiv: Data Analysis Statistics and Probability, 2018Co-Authors: C Quinteroquiroz, M. C. Torrent, Cristina MasollerAbstract:The space-time representation of high-dimensional dynamical systems that have a well defined characteristic time scale has proven to be very useful to deepen the understanding of such systems and to uncover hidden features in their output signals. Genuine analogies between one-dimensional (1D) spatially extended systems (1D SESs) and time delayed systems (TDSs) have been observed, including similar pattern formation and propagation of localized structures. An open question is if such analogies are limited to the space-time representation, or, if it is possible to reconstruct similar attractors, from the time series of an observed Variable. In this work we address this issue by considering a bistable 1D SES and two TDSs (a bistable system and a model of two lasers with time delayed coupling). In these three examples we find that we can reconstruct the underlying attractor in a three-dimensional pseudo-space, where the evolution is governed by a polynomial potential. We also discuss the limitations of the analogy between 1D SESs and TDSs.
Linrang Zhang - One of the best experts on this subject based on the ideXlab platform.
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bayesian rao and wald test for radar adaptive detection
International Conference on Acoustics Speech and Signal Processing, 2010Co-Authors: Yu Zhou, Linrang ZhangAbstract:This paper deals with the adaptive detection of a signal of interest in the presence of Gaussian noise with unknown covariance matrix (CM). To this end, we resort to a Bayesian approach based on a suitable model for the probability density function (PDF) of unknown CM. Under this assumption, the maximum a-posteriori (MAP) estimation of CM is derived. The MAP estimate is in turn used to yield Bayesian version of Rao and Wald test. And the importance of the a priori knowledge can be tuned through Scalar Variable. Remarkably the devised detectors outperform Kelly's GLRT and non Bayesian Rao and Wald test in the presence of strongly heterogeneous scenarios (where a very small number of training data is available). Meanwhile, the coincidence of Bayesian GLRT and Wald test is proved.
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ICASSP - Bayesian Rao and Wald test for radar adaptive detection
2010 IEEE International Conference on Acoustics Speech and Signal Processing, 2010Co-Authors: Yu Zhou, Linrang ZhangAbstract:This paper deals with the adaptive detection of a signal of interest in the presence of Gaussian noise with unknown covariance matrix (CM). To this end, we resort to a Bayesian approach based on a suitable model for the probability density function (PDF) of unknown CM. Under this assumption, the maximum a-posteriori (MAP) estimation of CM is derived. The MAP estimate is in turn used to yield Bayesian version of Rao and Wald test. And the importance of the a priori knowledge can be tuned through Scalar Variable. Remarkably the devised detectors outperform Kelly's GLRT and non Bayesian Rao and Wald test in the presence of strongly heterogeneous scenarios (where a very small number of training data is available). Meanwhile, the coincidence of Bayesian GLRT and Wald test is proved.
Bernardo Cockburn - One of the best experts on this subject based on the ideXlab platform.
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a priori error analysis for hdg methods using extensions from subdomains to achieve boundary conformity
Mathematics of Computation, 2013Co-Authors: Bernardo Cockburn, Manuel SolanoAbstract:We present the first a priori error analysis of a technique that allows us to numerically solve steady-state diffusion problems defined on curved domains Ω by using finite element methods defined in polyhedral subdomains Dh ⊂ Ω. For a wide variety of hybridizable discontinuous Galerkin and mixed methods, we prove that the order of convergence in the L2-norm of the approximate flux and Scalar unknowns is optimal as long as the distance between the boundary of the original domain Γ and that of the computational domain Γh is of order h. We also prove that the L 2-norm of a projection of the error of the Scalar Variable superconverges with a full additional order when the distance between Γ and Γh is of order h 5/4 but with only half an additional order when such a distance is of order h. Finally, we present numerical experiments confirming the theoretical results and showing that even when the distance between Γ and Γh is of order h, the above-mentioned projection of the error of the Scalar Variable can still superconverge with a full additional order.
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conditions for superconvergence of hdg methods for second order elliptic problems
Mathematics of Computation, 2012Co-Authors: Bernardo Cockburn, Weifeng Qiu, Ke ShiAbstract:We provide a projection-based analysis of a large class of finite element methods for second order elliptic problems. It includes the hybridized version of the main mixed and hybridizable discontinuous Galerkin methods. The main feature of this unifying approach is that it reduces the main difficulty of the analysis to the verification of some properties of an auxiliary, locally defined projection and of the local spaces defining the methods. Sufficient conditions for the optimal convergence of the approximate flux and the superconvergence of an element-by-element postprocessing of the Scalar Variable are obtained. New mixed and hybridizable discontinuous Galerkin methods with these properties are devised which are defined on squares, cubes and prisms.
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an implicit high order hybridizable discontinuous galerkin method for nonlinear convection diffusion equations
Journal of Computational Physics, 2009Co-Authors: Ngoc Cuong Nguyen, Jaime Peraire, Bernardo CockburnAbstract:In this paper, we present hybridizable discontinuous Galerkin methods for the numerical solution of steady and time-dependent nonlinear convection-diffusion equations. The methods are devised by expressing the approximate Scalar Variable and corresponding flux in terms of an approximate trace of the Scalar Variable and then explicitly enforcing the jump condition of the numerical fluxes across the element boundary. Applying the Newton-Raphson procedure and the hybridization technique, we obtain a global equation system solely in terms of the approximate trace of the Scalar Variable at every Newton iteration. The high number of globally coupled degrees of freedom in the discontinuous Galerkin approximation is therefore significantly reduced. We then extend the method to time-dependent problems by approximating the time derivative by means of backward difference formulae. When the time-marching method is (p+1)th order accurate and when polynomials of degree p>=0 are used to represent the Scalar Variable, each component of the flux and the approximate trace, we observe that the approximations for the Scalar Variable and the flux converge with the optimal order of p+1 in the L^2-norm. Finally, we apply element-by-element postprocessing schemes to obtain new approximations of the flux and the Scalar Variable. The new approximate flux, which has a continuous interelement normal component, is shown to converge with order p+1 in the L^2-norm. The new approximate Scalar Variable is shown to converge with order p+2 in the L^2-norm. The postprocessing is performed at the element level and is thus much less expensive than the solution procedure. For the time-dependent case, the postprocessing does not need to be applied at each time step but only at the times for which an enhanced solution is required. Extensive numerical results are provided to demonstrate the performance of the present method.
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an implicit high order hybridizable discontinuous galerkin method for nonlinear convection diffusion equations
Journal of Computational Physics, 2009Co-Authors: Ngoc Cuong Nguyen, Jaime Peraire, Bernardo CockburnAbstract:In this paper, we present hybridizable discontinuous Galerkin methods for the numerical solution of steady and time-dependent nonlinear convection-diffusion equations. The methods are devised by expressing the approximate Scalar Variable and corresponding flux in terms of an approximate trace of the Scalar Variable and then explicitly enforcing the jump condition of the numerical fluxes across the element boundary. Applying the Newton-Raphson procedure and the hybridization technique, we obtain a global equation system solely in terms of the approximate trace of the Scalar Variable at every Newton iteration. The high number of globally coupled degrees of freedom in the discontinuous Galerkin approximation is therefore significantly reduced. We then extend the method to time-dependent problems by approximating the time derivative by means of backward difference formulae. When the time-marching method is (p+1)th order accurate and when polynomials of degree p>=0 are used to represent the Scalar Variable, each component of the flux and the approximate trace, we observe that the approximations for the Scalar Variable and the flux converge with the optimal order of p+1 in the L^2-norm. Finally, we apply element-by-element postprocessing schemes to obtain new approximations of the flux and the Scalar Variable. The new approximate flux, which has a continuous interelement normal component, is shown to converge with order p+1 in the L^2-norm. The new approximate Scalar Variable is shown to converge with order p+2 in the L^2-norm. The postprocessing is performed at the element level and is thus much less expensive than the solution procedure. For the time-dependent case, the postprocessing does not need to be applied at each time step but only at the times for which an enhanced solution is required. Extensive numerical results are provided to demonstrate the performance of the present method.
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A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems
SIAM Journal on Scientific Computing, 2009Co-Authors: Bernardo Cockburn, Bo Dong, Johnny Guzmán, Marco Restelli, Riccardo SaccoAbstract:In this article, we propose a novel discontinuous Galerkin method for convection-diffusion-reaction problems, characterized by three main properties. The first is that the method is hybridizable; this renders it efficiently implementable and competitive with the main existing methods for these problems. The second is that, when the method uses polynomial approximations of the same degree for both the total flux and the Scalar Variable, optimal convergence properties are obtained for both Variables; this is in sharp contrast with all other discontinuous methods for this problem. The third is that the method exhibits superconvergence properties of the approximation to the Scalar Variable; this allows us to postprocess the approximation in an element-by-element fashion to obtain another approximation to the Scalar Variable which converges faster than the original one. In this paper, we focus on the efficient implementation of the method and on the validation of its computational performance. With this aim, e...
C Quinteroquiroz - One of the best experts on this subject based on the ideXlab platform.
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state space reconstruction of spatially extended systems and of time delayed systems from the time series of a Scalar Variable
Chaos, 2018Co-Authors: C Quinteroquiroz, M. C. Torrent, Cristina MasollerAbstract:The space-time representation of high-dimensional dynamical systems that have a well defined characteristic time scale has proven to be very useful to deepen the understanding of such systems and to uncover hidden features in their output signals. By using the space-time representation many analogies between one-dimensional spatially extended systems (1D SESs) and time delayed systems (TDSs) have been found, including similar pattern formation and propagation of localized structures. An open question is whether such analogies are limited to the space-time representation, or it is also possible to recover similar evolutions in a low-dimensional pseudo-space. To address this issue, we analyze a 1D SES (a bistable reaction-diffusion system), a Scalar TDS (a bistable system with delayed feedback), and a non-Scalar TDS (a model of two delay-coupled lasers). In these three examples, we show that we can reconstruct the dynamics in a three-dimensional phase space, where the evolution is governed by the same polynomial potential. We also discuss the limitations of the analogy between 1D SESs and TDSs.The space-time representation of high-dimensional dynamical systems that have a well defined characteristic time scale has proven to be very useful to deepen the understanding of such systems and to uncover hidden features in their output signals. By using the space-time representation many analogies between one-dimensional spatially extended systems (1D SESs) and time delayed systems (TDSs) have been found, including similar pattern formation and propagation of localized structures. An open question is whether such analogies are limited to the space-time representation, or it is also possible to recover similar evolutions in a low-dimensional pseudo-space. To address this issue, we analyze a 1D SES (a bistable reaction-diffusion system), a Scalar TDS (a bistable system with delayed feedback), and a non-Scalar TDS (a model of two delay-coupled lasers). In these three examples, we show that we can reconstruct the dynamics in a three-dimensional phase space, where the evolution is governed by the same polyn...
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state space reconstruction of spatially extended systems and of time delayed systems from the time series of a Scalar Variable
arXiv: Data Analysis Statistics and Probability, 2018Co-Authors: C Quinteroquiroz, M. C. Torrent, Cristina MasollerAbstract:The space-time representation of high-dimensional dynamical systems that have a well defined characteristic time scale has proven to be very useful to deepen the understanding of such systems and to uncover hidden features in their output signals. Genuine analogies between one-dimensional (1D) spatially extended systems (1D SESs) and time delayed systems (TDSs) have been observed, including similar pattern formation and propagation of localized structures. An open question is if such analogies are limited to the space-time representation, or, if it is possible to reconstruct similar attractors, from the time series of an observed Variable. In this work we address this issue by considering a bistable 1D SES and two TDSs (a bistable system and a model of two lasers with time delayed coupling). In these three examples we find that we can reconstruct the underlying attractor in a three-dimensional pseudo-space, where the evolution is governed by a polynomial potential. We also discuss the limitations of the analogy between 1D SESs and TDSs.
Yu Zhou - One of the best experts on this subject based on the ideXlab platform.
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bayesian rao and wald test for radar adaptive detection
International Conference on Acoustics Speech and Signal Processing, 2010Co-Authors: Yu Zhou, Linrang ZhangAbstract:This paper deals with the adaptive detection of a signal of interest in the presence of Gaussian noise with unknown covariance matrix (CM). To this end, we resort to a Bayesian approach based on a suitable model for the probability density function (PDF) of unknown CM. Under this assumption, the maximum a-posteriori (MAP) estimation of CM is derived. The MAP estimate is in turn used to yield Bayesian version of Rao and Wald test. And the importance of the a priori knowledge can be tuned through Scalar Variable. Remarkably the devised detectors outperform Kelly's GLRT and non Bayesian Rao and Wald test in the presence of strongly heterogeneous scenarios (where a very small number of training data is available). Meanwhile, the coincidence of Bayesian GLRT and Wald test is proved.
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ICASSP - Bayesian Rao and Wald test for radar adaptive detection
2010 IEEE International Conference on Acoustics Speech and Signal Processing, 2010Co-Authors: Yu Zhou, Linrang ZhangAbstract:This paper deals with the adaptive detection of a signal of interest in the presence of Gaussian noise with unknown covariance matrix (CM). To this end, we resort to a Bayesian approach based on a suitable model for the probability density function (PDF) of unknown CM. Under this assumption, the maximum a-posteriori (MAP) estimation of CM is derived. The MAP estimate is in turn used to yield Bayesian version of Rao and Wald test. And the importance of the a priori knowledge can be tuned through Scalar Variable. Remarkably the devised detectors outperform Kelly's GLRT and non Bayesian Rao and Wald test in the presence of strongly heterogeneous scenarios (where a very small number of training data is available). Meanwhile, the coincidence of Bayesian GLRT and Wald test is proved.
