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An Analysis of the Vector Decomposition Problem
[chapter]

*
Public Key Cryptography – PKC 2008
*

*The*

*vector*

*decomposition*

*problem*(VDP) has been proposed as a computational

*problem*on which to base

*the*security

*of*public key cryptosystems. ... We give a generalisation and simplification

*of*

*the*results

*of*Yoshida on

*the*VDP. ... Acknowledgements We thank Iwan Duursma, Seung-Kook Park, Maura Paterson and a number

*of*anonymous referees for helpful comments on a much earlier draft

*of*

*the*paper. ...

##
###
Analysis-Based Nonlocal-Approximate Sparsity Representation in Image Processing

2016
*
International Journal of Signal Processing, Image Processing and Pattern Recognition
*

we proposed a nonlocal-approximate sparsity regularizer in

doi:10.14257/ijsip.2016.9.9.08
fatcat:kt5to4g2rnaihnyfwxn2puv3si
*analysis*domains by minimizing*the*sum*of**the*2 l norms*of*those*vectors*with*the*same nonzero pattern like signal*vectors*. ... In this paper, based on a simple observation that*the*non-zero entries*of**the*sparsity*vector*in various image*analysis*domains should be also approximate when*the*relevant signal values are proximate, ...*The*authors would like to thank three anonymous reviewers for their valuable comments and constructive suggestions. ...##
###
Tensorial resolution: A direct trilinear decomposition

1990
*
Journal of Chemometrics
*

APPENDIX III: DIRECT TRILINEAR

doi:10.1002/cem.1180040105
fatcat:x6h32x6jfvezfazgpbjfdvvgaq
*DECOMPOSITION*ALGORITHM*The*direct solution*of**the*trilinear*decomposition**problem*by reduction to*an*eigenvalue—eigenvector*problem*can be outlined in three steps: (1) Tucker ... Unfortunately, there are*an*infinite number*of*possible*decompositions**of*R, and no unambiguous solution*of**the**problem*is possible without further information. ...##
###
Original Derivation of the Modal Decomposition Analysis for Solving Mixed Boundary-Initial Value Problems

2004
*
International Journal of Acoustics and Vibration
*

This paper using

doi:10.20855/ijav.2004.9.3164
fatcat:qfjpqmbvvbdvtouc7daetnklnm
*an*original approach introduces*the*well-known modal*decomposition**analysis*for solving mixed boundary-initial value*problems*. ... These particular*problems*have been studied by means*of**the*so-called modal*decomposition**analysis*1 by mechanical engineers since*the*fifties 2 . ...##
###
Large-scale smooth plastic topology optimization using domain decomposition

2021
*
Comptes Rendus Mecanique
*

It takes advantage

doi:10.5802/crmeca.88
fatcat:ufm4zpiqpjhs7oeqcibn5z6ema
*of**the*favorable features*of**the*integrated limit*analysis*and design formulation*of**the*smooth topology design*problem*. ...*The*integrated approach preserves*the*mathematical structure and properties*of**the*underlying static, lower bound*problem**of*limit*analysis*. ...*The*displacements or velocities can be interpreted as dual variables in*the*dual*problem*, which is*an*expression*of**the*kinematic (upper bound)*problem**of*limit*analysis*. ...##
###
Frame-based Approach for Sparse Representation of Signal Decomposition and Reconstruction
[article]

2017
*
arXiv
*
pre-print

A celebrated result indicates that if a synthesis frame is chosen for reconstruction, then its canonical dual frame is

arXiv:1603.09492v2
fatcat:pg4qc6nxkngm3kbwvt7g6k5yma
*the**analysis*frame that performs*decomposition*, yielding coefficients that minimizes ... However, we present some conditions on a dual frame so that*the*minimizer*of**the*l1-norm can be derived from*the*coefficients*of**the*dual frame. ...*The*composition*of**the*reconstruction operation after*the**decomposition*operation must be*an*identity operation. ...##
###
Fast computation of minimal elementary decompositions of metabolic flux vectors

2011
*
Automatica
*

Fast computation

doi:10.1016/j.automatica.2011.01.011
fatcat:qp22v3cyfngslfh4pedcvqftr4
*of*minimal elementary*decompositions**of*metabolic flux*vectors*. a b s t r a c t*The*concept*of*elementary flux*vector*is valuable in a number*of*applications*of*metabolic engineering. ... For instance, in metabolic flux*analysis*, each admissible flux*vector*can be expressed as a non-negative linear combination*of*a small number*of*elementary flux*vectors*. ... A matlab implementation*of*our algorithms is available on http://www.inma.ucl.ac.be/~jungers/contents/efm.zip. ...##
###
Rapid singular value decomposition for time-domain analysis of magnetic resonance signals by use of the lanczos algorithm

1989
*
Journal of Magnetic Resonance (1969)
*

Time-series

doi:10.1016/0022-2364(89)90175-3
fatcat:llgkylymeba6rialhdjtt67tka
*analysis*has become*an*integral part*of*signal interpretation in magnetic resonance and other experiments. ...*The*minimal goal*of*time-series*analysis*is to separate signal from noise. ...*The*SVD*problem*can be reduced to*an*eigenelement*problem*by construction*of**the*real symmetric matrix 0- 0 T, = 0 P3 0 a** 0 [51 . . . 0 0 0 *** ij -0 0 0 *'* @j O- and{ul,u2,... ...##
###
Book announcements

1991
*
Discrete Applied Mathematics
*

*The*MSCCC queueing discipline). Reversible queueing networks. Applications

*of*queueing network models (Queueing network models

*of*computer systems. ... Queueing network model

*of*a distributed computer system. Queueing network models

*of*communication networks. Queueing model

*of*a network

*of*workstations. Queueing model

*of*a circuit-switched network. ... Properties

*of*

*the*A matrix. Representation

*of*a nonbasic

*vector*in terms

*of*

*the*basic

*vectors*.

*The*simplex method for network flow

*problems*.

*An*example

*of*

*the*network simplex method. ...

##
###
Page 7034 of Mathematical Reviews Vol. , Issue 99j
[page]

1999
*
Mathematical Reviews
*

These techniques are justified by

*an**analysis**of**the*regularized solutions based on*the*singular value*decomposition*and*the*generalized singular value*decomposition*. ...*The*ULV*decomposition*(ULVD) is*an*important member*of*a class*of*rank-revealing two-sided orthogonal*decompositions*used to approximate*the*singular value*decomposition*(SVD). ...##
###
Smooth orthogonal decomposition for modal analysis of randomly excited systems

2008
*
Journal of Sound and Vibration
*

Using output response ensembles only,

doi:10.1016/j.jsv.2008.02.052
fatcat:hs3fiv7bera4zimsajeayd2voe
*the*generalized eigenvalue*problem*is formed to estimate eigen frequencies and modal*vectors*for*an*eight-degree-*of*-freedom lightly damped vibratory system. ... This work shows that under certain conditions,*the*smooth orthogonal*decomposition*eigenvalue*problem*formulated from white noise induced response data can be tied to*the*unforced structural eigenvalue ... For visualization,*the*modal*vectors*from smooth orthogonal*decomposition*and*the*structural eigenvalue*problem*are compared in Fig. 2 . ...##
###
Page 966 of Mathematical Reviews Vol. , Issue 2003B
[page]

2003
*
Mathematical Reviews
*

*The*idea

*of*considering ab- stract

*vector*variables came from

*an*attempt to formulate Clifford algebra and

*analysis*independent

*of*

*the*choice

*of*

*the*dimension m, independent

*of*coordinates and bases and ... [Sommen, Franciscus] (B-GHNT-

*AN*; Ghent) Clifford

*analysis*on

*the*level

*of*abstract

*vector*variables. (English summary) Clifford

*analysis*and its applications (Prague, 2000), 303-322, NATO Sci. Ser. ...

##
###
Two alternative ways for solving the coordination problem in multilevel optimization

1993
*
Structural Optimization
*

NE(13)
System

doi:10.1007/bf01743377
fatcat:mj6l6jdv5rfb5p6nn6vvl4uqmq
*Analysis*, designated SA, is regarded as a black box that converts*an*input*vector*{,5'I}*of*length NS[ into*an*output*vector*{SO}*of*length NSO. ...*The*above approach suggests*decomposition**of**the*framework*analysis*into*the*assembled framework*analysis*(system level*analysis*) and*the*beam analyses (subsystem level analyses). ...*The*old and*the*new formulations are presentedin detail,illustrated by*an*exampleof a structuraloptimization. ...##
###
Stochastic and Deterministic Tensorization for Blind Signal Separation
[chapter]

2015
*
Lecture Notes in Computer Science
*

*The*source signals, mixing

*vectors*and sensor signals are contained in S, M and X, respectively. One can see that

*the*

*problem*consists

*of*a matrix factorization

*of*X. ... Introduction Given a mixture

*of*some source signals,

*the*Blind Signal Separation (BSS)

*problem*consists

*of*

*the*identification

*of*both

*the*mixing matrix and

*the*original sources. ...

*The*source signals, mixing

*vectors*and sensor signals are contained in S, M and X, respectively. One can see that

*the*

*problem*consists

*of*a matrix factorization

*of*X. ...

##
###
ECG Energy Change Study Based on Variational Mode Decomposition

2020
*
American Journal of Biochemistry and Biotechnology
*

Then,

doi:10.3844/ajbbsp.2020.103.111
fatcat:6xd45wgjebfmhmxhks2bbyc2ru
*the*energy*vectors**of*ECG signals are obtained by calculating*the*energy*of*each IMTF and a comparative*analysis**of*energy*vectors*is conducted between healthy people and three kinds*of*heart disease ... thus very suitable for*the**analysis**of*nonlinear and non-stationary Electrocardiogram (ECG) signal. ... VMD Energy*Vector**Analysis**of*ECG VMD*Decomposition**of*ECG We selected*the*healthy people normal sinus rhythm database (nsrdb)*of*MIT-BIH as experimental data for VMD*decomposition*. ...
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