scispace - formally typeset
Search or ask a question
Topic

Biorthogonal system

About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: In this article, the identification of zonal flows in fusion plasmas is addressed by using a novel quadrature technique based on the Hilbert transform, which can distinguish propagating global modes (such as MHD modes) from the non-propagating, synchronous (zonal flow-like) global component.
Abstract: This work addresses the identification of zonal flows in fusion plasmas. Zonal flows are large scale phenomena, hence multipoint measurements taken at remote locations are required for their identification. Given such data, the Biorthogonal Decomposition (or Singular Value Decomposition) is capable of extracting the globally correlated component of the multipoint fluctuations. By using a novel quadrature technique based on the Hilbert transform, propagating global modes (such as MHD modes) can be distinguished from the non-propagating, synchronous (zonal flow-like) global component. The combination of these techniques with further information such as the spectrogram and the spatial structure then allows an unambiguous identification of the zonal flow component of the fluctuations. The technique is tested using gyro-kinetic simulations. The first unambiguous identification of a zonal flow at the TJ-II stellarator is presented, based on multipoint Langmuir probe measurements.

9 citations

Journal ArticleDOI
TL;DR: It is demonstrated how TDMVCC in the limit of a complete cluster expansion becomes equivalent to multiconfiguration time-dependent Hartree for the same active-space size, while equivalent results are obtained for complete expansions and full one-mode basis sets.
Abstract: We develop time-dependent vibrational coupled cluster with time-dependent modals (TDMVCC), where an active set of one-mode basis functions (modals) is evolved in time alongside coupled-cluster wave-function parameters. A biorthogonal second quantization formulation of many-mode dynamics is introduced, allowing separate biorthogonal bases for the bra and ket states, thus ensuring complex analyticity. We employ the time-dependent bivariational principle to derive equations of motion for both the one-mode basis functions and the parameters describing the cluster (T) and linear de-excitation (L) operators. The choice of constraint (or gauge) operators for the modal time evolution is discussed. In the case of untruncated cluster expansion, the result is independent of this choice, but restricting the excitation space removes this invariance; equations for the variational determination of the constraint operators are derived for the latter case. We show that all single-excitation parts of T and L are redundant and can be left out in the case of variationally determined constraint-operator evolution. Based on a pilot implementation, test computations on Henon–Heiles model systems, the water molecule, and a reduced-dimensionality bi-thiophene model are presented, showing highly encouraging results for TDMVCC. It is demonstrated how TDMVCC in the limit of a complete cluster expansion becomes equivalent to multiconfiguration time-dependent Hartree for the same active-space size. Similarly, it is discussed how TDMVCC generally gives better and more stable results than its time-independent-modals counterpart, while equivalent results are obtained for complete expansions and full one-mode basis sets.

9 citations

Patent
05 May 2003
TL;DR: In this article, a probability density model of coefficients in the form of a generalized Gaussian is associated with each subband, the parameters α and β of this density model are estimated, while minimizing the relative entropy, or Kullback-Leibler distance, between this model and the empirical distribution of coefficients of each sub-band, and from this model, an optimum quantization step is determined such that the rate allocated is distributed in the various subbands and the total distortion is minimal.
Abstract: The invention concerns a method for compressing data, in particular images, by transform, in which method this data is projected onto a base of localized orthogonal or biorthogonal functions, such as wavelets To quantize each of the localized functions with a quantization step that enables an overall set rate Rc to be satisfied, the method includes the following steps: a probability density model of coefficients in the form of a generalized Gaussian is associated with each subband, the parameters α and β of this density model are estimated, while minimizing the relative entropy, or Kullback-Leibler distance, between this model and the empirical distribution of coefficients of each subband, and from this model, for each subband, an optimum quantization step is determined such that the rate allocated is distributed in the various subbands and such that the total distortion is minimal As a preference, for each subband, the graphs of rate R and distortion D are deduced, from the parameters α and β, as a function of the quantization step and these graphs are tabulated to determine said optimum quantization step

9 citations

Patent
22 May 2013
TL;DR: In this article, a second generation small-wave support vector machine assessment method for damage and remaining life of a metal structure is presented, where an intrinsic mode function is obtained through decomposition of an experience mode, a time-frequency domain statistic characteristic of the intrinsic mode is extracted, a most sensitive characteristic is chosen according to a distance accessment principle to construct a best characteristic set, a minimum quantization error indicator which has an obvious performance degradation trend along with time changes is constructed by means of self-organization neural network characteristic fusion techniques, a biorthogonal small
Abstract: The invention discloses a second generation small-wave support vector machine assessment method for damage and remaining life of a metal structure. According to the method, an intrinsic mode function is obtained through decomposition of an experience mode, a time-frequency domain statistic characteristic of the intrinsic mode function is extracted, a most sensitive characteristic is chosen according to a distance accessment principle to construct a best characteristic set, a minimum quantization error indicator which has an obvious performance degradation trend along with time changes is constructed by means of self-organization neural network characteristic fusion techniques, a biorthogonal small-wave support vector machine kernel function of second generation small-wave transform is provided, a service life prediction model of the second generation small-wave support vector machine is constructed, the minimum quantization error indicator serves as a prediction characteristic, and quantitative assessment for the damage and the remainig service life of a metal structural component of mechanical equipment under a small subsample is achieved.

9 citations

Proceedings ArticleDOI
01 Oct 2006
TL;DR: This work presents the design, implementation and application of two families of biorthogonal dual-tree complex wavelet transform (CWT) filters using lifting scheme and introduces a new theorem that suggests that lifting implementation of filters that are time-reversals of each other is closely related.
Abstract: In this work, we present the design, implementation and application of two families of biorthogonal dual-tree complex wavelet transform (CWT) filters using lifting scheme The first design is achieved using exhaustive search with coding gain, DC leakage and directional selectivity as the fundamental criteria The second set of filters are derived from the biorthogonal design procedure that was recently suggested by Selesnick Furthermore, this paper also introduces a new theorem that suggests that lifting implementation of filters that are time-reversals of each other is closely related Various applications are presented to validate the proposed design scheme, including performance in denoising as well as in the JPEG-2000 image coding standard

9 citations


Network Information
Related Topics (5)
Wavelet
78K papers, 1.3M citations
84% related
Bounded function
77.2K papers, 1.3M citations
80% related
Nonlinear system
208.1K papers, 4M citations
80% related
Matrix (mathematics)
105.5K papers, 1.9M citations
79% related
Partial differential equation
70.8K papers, 1.6M citations
79% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
202329
2022105
202155
202058
201960