scholarly journals The interaction between the stratosphere and the troposphere as revealed by singular vectors

2007 ◽  
Vol 16 (6) ◽  
pp. 723-739 ◽  
Author(s):  
Jan-Otto Hooghoudt ◽  
Jan Barkmeijer
Keyword(s):  
Singular Vectors

Using NOGAPS Singular Vectors to Diagnose Large-scale Influences on Tropical Cyclogenesis

2011 ◽  
Author(s):  
Sharanya J. Majumdar ◽  
Melinda S. Peng ◽  
Carolyn A. Reynolds ◽  
James D. Doyle ◽  
Chun-Chieh Wu ◽  
...  
Keyword(s):  
Large Scale ◽  
Tropical Cyclogenesis ◽  
Singular Vectors

scholarly journals Classification of Degenerate Verma Modules for E(5, 10)

2021 ◽  
Author(s):  
Nicoletta Cantarini ◽  
Fabrizio Caselli ◽  
Victor Kac
Keyword(s):  
Infinite Number ◽  
Verma Module ◽  
Lie Superalgebra ◽  
Verma Modules ◽  
Singular Vectors ◽  
Finite Dimensional ◽  
De Rham ◽  
Via Classification

AbstractGiven a Lie superalgebra $${\mathfrak {g}}$$ g with a subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 , and a finite-dimensional irreducible $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 -module F, the induced $${\mathfrak {g}}$$ g -module $$M(F)={\mathcal {U}}({\mathfrak {g}})\otimes _{{\mathcal {U}}({\mathfrak {g}}_{\ge 0})}F$$ M ( F ) = U ( g ) ⊗ U ( g ≥ 0 ) F is called a finite Verma module. In the present paper we classify the non-irreducible finite Verma modules over the largest exceptional linearly compact Lie superalgebra $${\mathfrak {g}}=E(5,10)$$ g = E ( 5 , 10 ) with the subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 of minimal codimension. This is done via classification of all singular vectors in the modules M(F). Besides known singular vectors of degree 1,2,3,4 and 5, we discover two new singular vectors, of degrees 7 and 11. We show that the corresponding morphisms of finite Verma modules of degree 1,4,7, and 11 can be arranged in an infinite number of bilateral infinite complexes, which may be viewed as “exceptional” de Rham complexes for E(5, 10).

scholarly journals A Machine Learning-Based Seismic Data Compression and Interpretation Using a Novel Shifted-Matrix Decomposition Algorithm

2021 ◽  
Vol 11 (11) ◽  
pp. 4874
Author(s):  
Milan Brankovic ◽  
Eduardo Gildin ◽  
Richard L. Gibson ◽  
Mark E. Everett
Keyword(s):  
Real Time ◽  
Seismic Data ◽  
Matrix Decomposition ◽  
Original Data ◽  
Velocity Estimation ◽  
Singular Vectors ◽  
Well Stimulation ◽  
Marine Seismic ◽  
Value Decomposition ◽  
Seismic Data Compression

Seismic data provides integral information in geophysical exploration, for locating hydrocarbon rich areas as well as for fracture monitoring during well stimulation. Because of its high frequency acquisition rate and dense spatial sampling, distributed acoustic sensing (DAS) has seen increasing application in microseimic monitoring. Given large volumes of data to be analyzed in real-time and impractical memory and storage requirements, fast compression and accurate interpretation methods are necessary for real-time monitoring campaigns using DAS. In response to the developments in data acquisition, we have created shifted-matrix decomposition (SMD) to compress seismic data by storing it into pairs of singular vectors coupled with shift vectors. This is achieved by shifting the columns of a matrix of seismic data before applying singular value decomposition (SVD) to it to extract a pair of singular vectors. The purpose of SMD is data denoising as well as compression, as reconstructing seismic data from its compressed form creates a denoised version of the original data. By analyzing the data in its compressed form, we can also run signal detection and velocity estimation analysis. Therefore, the developed algorithm can simultaneously compress and denoise seismic data while also analyzing compressed data to estimate signal presence and wave velocities. To show its efficiency, we compare SMD to local SVD and structure-oriented SVD, which are similar SVD-based methods used only for denoising seismic data. While the development of SMD is motivated by the increasing use of DAS, SMD can be applied to any seismic data obtained from a large number of receivers. For example, here we present initial applications of SMD to readily available marine seismic data.

scholarly journals Singular vectors and conservation laws of quantum KdV type equations

1992 ◽  
Vol 278 (1-2) ◽  
pp. 79-84 ◽  
Author(s):  
P. Di Francesco ◽  
P. Mathieu
Keyword(s):  
Conservation Laws ◽  
Singular Vectors ◽  
Kdv Type Equations

ROBUST SVD FILTERING FOR LOW SIGNAL-TO-NOISE RATIO SEISMIC DATA

Geophysics ◽  
2021 ◽  
pp. 1-51
Author(s):  
Chao Wang ◽  
Yun Wang
Keyword(s):  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Singular Values ◽  
New Method ◽  
Signal To Noise ◽  
Coherent Noise ◽  
Edge Preserving ◽  
Singular Vectors ◽  
Reduced Rank ◽  
Noise Ratio

Reduced-rank filtering is a common method for attenuating noise in seismic data. As conventional reduced-rank filtering distinguishes signals from noises only according to singular values, it performs poorly when the signal-to-noise ratio is very low, or when data contain high levels of isolate or coherent noise. Therefore, we developed a novel and robust reduced-rank filtering based on the singular value decomposition in the time-space domain. In this method, noise is recognized and attenuated according to the characteristics of both singular values and singular vectors. The left and right singular vectors corresponding to large singular values are selected firstly. Then, the right singular vectors are classified into different categories according to their curve characteristics, such as jump, pulse, and smooth. Each kind of right singular vector is related to a type of noise or seismic event, and is corrected by using a different filtering technology, such as mean filtering, edge-preserving smoothing or edge-preserving median filtering. The left singular vectors are also corrected by using the filtering methods based on frequency attributes like main-frequency and frequency bandwidth. To process seismic data containing a variety of events, local data are extracted along the local dip of event. The optimal local dip is identified according to the singular values and singular vectors of the data matrices that are extracted along different trial directions. This new filtering method has been applied to synthetic and field seismic data, and its performance is compared with that of several conventional filtering methods. The results indicate that the new method is more robust for data with a low signal-to-noise ratio, strong isolate noise, or coherent noise. The new method also overcomes the difficulties associated with selecting an optimal rank.

Singular vector filtering method for mitigation of disturbance enhancement in multichannel active noise control systems

2021 ◽  
Vol 69 (5) ◽  
pp. 451-459
Author(s):  
Yongjie Zhuang ◽  
Xuchen Wang ◽  
Yangfan Liu
Keyword(s):  
Noise Control ◽  
Active Noise Control ◽  
Singular Values ◽  
Control Performance ◽  
Frequency Bands ◽  
Singular Vectors ◽  
Singular Value Decomposition Method ◽  
Autocorrelation Matrix ◽  
Frequency Responses ◽  
Active Noise

In the design of multichannel active noise control filters, the disturbance enhancement phenomenon will sometimes occur, i.e., the resulting sound is enhanced instead of being reduced in some frequency bands, if the control filter is designed to minimize the power of error signals in other frequency bands or across all frequencies. In previous work, a truncated singular value decomposition method was applied to the system autocorrelation matrix to mitigate the disturbance enhancement. Some small singular values and the associated singular vectors are removed, if they are responsible for unwanted disturbance enhancement in some frequency bands. However, some of these removed singular vectors may still contribute to the noise control performance in other frequency bands; thus, a direct truncation will degrade the noise control performance. In the present work, through an additional filtering process, the set of singular vectors that causes the disturbance enhancement is replaced by a set of new singular vectors whose frequency responses are attenuated in the frequency band where disturbance enhancement occurs, while the frequency responses in other frequency bands are unchanged. Compared with truncation approach, the proposed method can maintain the performance in the noise reduction bands, while mitigating the influence in disturbance enhancement bands.

scholarly journals The super-Virasoro singular vectors and Jack superpolynomials relationship revisited

2016 ◽  
Vol 913 ◽  
pp. 34-63 ◽  
Author(s):  
O. Blondeau-Fournier ◽  
P. Mathieu ◽  
D. Ridout ◽  
S. Wood
Keyword(s):  
Singular Vectors
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