Efficient matrix decomposition for implicit algorithms

2007 ◽  
pp. 237-242
Author(s):  
Robert W. MacCormack
Keyword(s):  
Matrix Decomposition

A Survey of Network Embedding for Drug Analysis and Prediction

2020 ◽  
Vol 21 ◽  
Author(s):  
Zhixian Liu ◽  
Qingfeng Chen ◽  
Wei Lan ◽  
Jiahai Liang ◽  
Yiping Pheobe Chen ◽  
...  
Keyword(s):  
Deep Learning ◽  
Protein Function ◽  
Dimensional Space ◽  
Auxiliary Information ◽  
Matrix Decomposition ◽  
Drug Analysis ◽  
Machine Learning Algorithms ◽  
Superior Performance ◽  
Network Embedding ◽  
Similarity Estimation

: Traditional network-based computational methods have shown good results in drug analysis and prediction. However, these methods are time consuming and lack universality, and it is difficult to exploit the auxiliary information of nodes and edges. Network embedding provides a promising way for alleviating the above problems by transforming network into a low-dimensional space while preserving network structure and auxiliary information. This thus facilitates the application of machine learning algorithms for subsequent processing. Network embedding has been introduced into drug analysis and prediction in the last few years, and has shown superior performance over traditional methods. However, there is no systematic review of this issue. This article offers a comprehensive survey of the primary network embedding methods and their applications in drug analysis and prediction. The network embedding technologies applied in homogeneous network and heterogeneous network are investigated and compared, including matrix decomposition, random walk, and deep learning. Especially, the Graph neural network (GNN) methods in deep learning are highlighted. Further, the applications of network embedding in drug similarity estimation, drug-target interaction prediction, adverse drug reactions prediction, protein function and therapeutic peptides prediction are discussed. Several future potential research directions are also discussed.

scholarly journals Customized depolarization spatial patterns with dynamic retardance functions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
David Marco ◽  
Guadalupe López-Morales ◽  
María del Mar Sánchez-López ◽  
Ángel Lizana ◽  
Ignacio Moreno ◽  
...  
Keyword(s):  
Spatial Patterns ◽  
Detection System ◽  
Temporal Integration ◽  
Matrix Decomposition ◽  
Decomposition Methods ◽  
Time Dependent ◽  
Light Modulator ◽  
Dynamical Time ◽  
Depolarization Effect ◽  
Spatially Variant

AbstractIn this work we demonstrate customized depolarization spatial patterns by imaging a dynamical time-dependent pixelated retarder. A proof-of-concept of the proposed method is presented, where a liquid–crystal spatial light modulator is used as a spatial retarder that emulates a controlled spatially variant depolarizing sample by addressing a time-dependent phase pattern. We apply an imaging Mueller polarimetric system based on a polarization camera to verify the effective depolarization effect. Experimental validation is provided by temporal integration on the detection system. The effective depolarizance results are fully described within a simple graphical approach which agrees with standard Mueller matrix decomposition methods. The potential of the method is discussed by means of three practical cases, which include non-reported depolarization spatial patterns, including exotic structures as a spirally shaped depolarization pattern.

Small matrix modular path integral: iterative quantum dynamics in space and time

2021 ◽  
Author(s):  
Nancy Makri
Keyword(s):  
Path Integral ◽  
Quantum Dynamics ◽  
Matrix Decomposition ◽  
Propagation Time ◽  
Molecular Aggregates ◽  
Space And Time ◽  
Small Matrix

This work presents a small matrix decomposition of the modular path integral for spin arrays or molecular aggregates, which leads to an iterative treatment with respect to the units that comprise the system and the propagation time.

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.

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