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Eventually DSDD Matrices and Eigenvalue Localization

2018
*
Symmetry
*

Firstly, the relationships among strictly diagonally dominant ( S D D )

doi:10.3390/sym10100448
fatcat:rmvgo6b5wrhqjnwp3qhozaslxy
*matrices*, doubly strictly diagonally dominant ( D S D D )*matrices*,*eventually*S D D*matrices**and**eventually*D S D D*matrices*are ... Secondly, by excluding some proper subsets of an existing*eigenvalue*inclusion set for*matrices*, which do not contain any*eigenvalues*of*matrices*,*a*tighter*eigenvalue*inclusion set of*matrices*is derived ... In 2015, Cvetković [7] et al. extended the class of*SDD**matrices*to the class of*eventually**SDD*(*SDD*∃ )*matrices*,*and*proved that*SDD*∃*matrices*are nonsingular. ...##
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Heteroclinic Dynamics of Localized Frequency Synchrony: Stability of Heteroclinic Cycles and Networks

2019
*
Journal of nonlinear science
*

Hence, our results elucidate how oscillator coupling influences sequential transitions along

doi:10.1007/s00332-019-09562-3
fatcat:c5favvtunzcfvhaxhsdbkvjnb4
*a*heteroclinic network where individual oscillator populations switch sequentially between*a*high*and**a*low ... While such networks cannot be asymptotically stable, the*local*attraction properties of each cycle in the network can be quantified by stability indices. ... reproduction in any medium, provided you give appropriate credit to the original author(s)*and*the source, provide*a*link to the Creative Commons license,*and*indicate if changes were made. ...##
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Heteroclinic Dynamics of Localized Frequency Synchrony: Stability of Heteroclinic Cycles and Networks
[article]

2018
*
arXiv
*
pre-print

Hence, our results elucidate how oscillator coupling influences sequential transitions along

arXiv:1810.06716v1
fatcat:bmwjpwxlrzeolj7xfnl7isjkxu
*a*heteroclinic network where individual oscillator populations switch sequentially between*a*high*and**a*low ... While such networks cannot be asymptotically stable, the*local*attraction properties of each cycle in the network can be quantified by stability indices. ... Acknowledgements The authors are grateful to P Ashwin, S Castro,*and*L Garrido-da-Silva for helpful discussions, as well as for mutual hospitality at the Universities of Hamburg*and*Exeter during several ...##
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Algorithm 805: computation and uses of the semidiscrete matrix decomposition

2000
*
ACM Transactions on Mathematical Software
*

Applications of the algorithms are presented to data compression, filtering,

doi:10.1145/358407.358424
fatcat:xffevpdj4fdqnilnlq4enx6kyi
*and*information retrieval; software is provided in C*and*in Matlab. ... We present algorithms for computing*a*semidiscrete approximation to*a*matrix in*a*weighted norm, with the Frobenius norm as*a*special case. ... ACKNOWLEDGMENTS We are grateful to Professor Walter Gander*and*Professor Martin Gutknecht for their hospitality at ETH. ...##
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iSIRA: Integrated shift–invert residual Arnoldi method for graph Laplacian matrices from big data

2019
*
Journal of Computational and Applied Mathematics
*

The

doi:10.1016/j.cam.2018.07.031
fatcat:mpg2p2rmzrfhjnpqol3bhzxcb4
*eigenvalue*problem of*a*graph Laplacian matrix L arising from*a*simple, connected*and*undirected graph has been given more attention due to its extensive applications, such as spectral clustering, ... ,*and*sensor systems because there is in general not only*local*connections. ... The first three authors would like to thank the grant support from the Ministry of Science*and*Technology in Taiwan,*and*the ST Yau Center*and*Big Data Research at the National Chiao Tung University. ...##
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On Sketching Quadratic Forms

2016
*
Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16
*

*A*sequence of work culminating in that of Batson, Spielman,

*and*Srivastava (SIAM Review, 2014), shows that by choosing

*and*reweighting O(ε −2 n) edges in

*a*graph,

*one*achieves the "for all" guarantee. ... Our results provide the first separation between the sketch size needed for the "for all"

*and*"for each" guarantees for Laplacian

*matrices*. ... In our case, each server

*locally*computes the "for each" data structure of Sec. 2.3.1

*on*its subgraph (for accuracy ε),

*and*sends it to

*a*central server. ...

##
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Invariant Feature Matching for Image Registration Application Based on New Dissimilarity of Spatial Features

2016
*
PLoS ONE
*

Deformation effects, such as affine

doi:10.1371/journal.pone.0149710
pmid:26985996
pmcid:PMC4795769
fatcat:g76hwyc7ergajcrqg7pfhhid3u
*and*homography, change the*local*information within the image*and*can result in ambiguous*local*information pertaining to image points. ... Thus, new descriptor's similarity metrics based*on*normalized Eigenvector correlation*and*signal directional differences, which are robust under*local*variation of the image information, are proposed to ... Acknowledgments The authors would like to thank the Center for Artificial Intelligence Technology (CAIT), Faculty of Information Science*and*Technology, National University of Malaysia*and*the anonymous ...##
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Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials
[article]

2018
*
arXiv
*
pre-print

Optimization over non-negative polynomials is fundamental for nonlinear systems analysis

arXiv:1807.05463v1
fatcat:7jyiqbxl7bcepawmoulmo5hg7q
*and*control. ... the relation between three tractable relaxations for optimizing over sparse non-negative polynomials: sparse sum-of-squares (SSOS) optimization, diagonally dominant sum-of-squares (DSOS) optimization,*and*... To this end,*note*that any P ∈ SDSOS r n,2d (E) admits*a*Gram matrix representation (16) with an*SDD*matrix Q. ...##
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Recent advances in the solution of quadratic assignment problems

2003
*
Mathematical programming
*

In the past few years

doi:10.1007/s10107-003-0437-z
fatcat:jdllh6idbnfmzkelphkfepbi3a
*a*number of long-open QAPs, including those posed by Steinberg (1961) , Nugent et al. (1968)*and*Krarup (1972) were solved to optimality for the first time. ... The solution of these problems has utilized both new algorithms*and*novel computing structures. ... For symmetric*matrices**A**and*B,*A*B denotes that*A*− B is positive semidefinite,*and*λ(*A*) ∈ n denotes the vector of*eigenvalues*of*A*. ...##
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Lecture Notes on Spectral Graph Methods
[article]

2016
*
arXiv
*
pre-print

These are lecture

arXiv:1608.04845v1
fatcat:ppy6mlmfsvfcxedriwnndv6ztq
*notes*that are based*on*the lectures from*a*class I taught*on*the topic of Spectral Graph Methods at UC Berkeley during the Spring 2015 semester. ... .,*A*• B = Tr AB T = ij*A*ij B ij for*matrices**A**and*B.*Note*that, both here*and*below, I 0 is sometimes the Identity*on*the subspace perpendicular to the all-*ones*vector. ...*Note*that the first vertex is s*and*the last vertex is t. We'll use the α*and*S parameter to denote the*matrices*for the*localized*cut graph. ...##
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Optimization over Nonnegative and Convex Polynomials With and Without Semidefinite Programming
[article]

2018
*
arXiv
*
pre-print

In the second part of this thesis, we focus

arXiv:1806.06996v1
fatcat:ywvkxguvobh43jvdaedk2tf3ju
*on*the theory*and*applications of the problem of optimizing over convex polynomials,*a*subcase of the problem of optimizing over nonnegative polynomials. ... We then focus*on*the problem of finding tight lower bounds*on*polynomial optimization problems (POPs),*a*fundamental task in this area that is most commonly handled through the use of SDP-based sum of ... Here dd*and**sdd**matrices*refer to notions introduced in Definition 5. 3 .1.*Note*that any t which makes tI −*A*dd or*sdd*gives an upperbound*on*λ max (*A*). ...##
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Schrödinger operator on the zigzag half-nanotube in magnetic field
[article]

2010
*
arXiv
*
pre-print

We describe all

arXiv:0906.1231v2
fatcat:x6gbydpjzreldicyco7okd7auq
*eigenvalues**and*resonances of this operator,*and*theirs dependence*on*the magnetic field. ... We consider the zigzag half-nanotubes (tight-binding approximation) in*a*uniform magnetic field which is described by the magnetic Schr\"odinger operator with*a*periodic potential plus*a*finitely supported ... In particular, if b = 0, N 3 ∈ N, then J 0 N 3 is the Schrödinger operator. 4) Exner [Ex] obtained some duality between Schrödinger operators*on*graphs*and*certain Jacobi*matrices*, which depend*on*energy ...##
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Decentralized Approximate Newton Methods for Convex Optimization on Networked Systems
[article]

2020
*
arXiv
*
pre-print

The proposed DEAN algorithms allow each node to repeatedly perform

arXiv:1903.09481v3
fatcat:n23oyzclmfcujfghohxhgbmpj4
*a**local*approximate Newton update, which leverages tracking the global Newton direction*and*dissipating the discrepancies among the nodes ... In this paper,*a*class of Decentralized Approximate Newton (DEAN) methods for addressing convex optimization*on**a*networked system are developed, where nodes in the networked system seek for*a*consensus ... Also, since G is connected, L G has only*one**eigenvalue*at zero. ...##
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Randomized Dynamical Decoupling Strategies and Improved One-Way Key Rates for Quantum Cryptography
[article]

2009
*
arXiv
*
pre-print

The focus is

arXiv:0906.2927v2
fatcat:bbelbmayjzhopgh7gcf3cadz7m
*on*the BB84*and*the 6-state protocol making use of only*one*-way communication during the error correction*and*privacy amplification steps. ... Furthermore, it is investigated if*and*how the discussed decoupling strategies can be employed to protect*a*quantum computation running*on*the quantum memory. ... Thensrt =str = trs = tu =ūt for all t ∈*A**and*we havesr =ū. ...##
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Nonobservable nature of the nuclear shell structure: Meaning, illustrations, and consequences

2015
*
Physical Review C
*

*on*

*a*fixed resolution scale they have agreed

*on*prior to performing their analysis

*and*comparisons. ... C 85, 034330 (2012)], the dependence of ESPEs

*on*

*one*-nucleon transfer probability

*matrices*makes them purely theoretical quantities that "run" with the non-observable resolution scale λ employed in the ... Hagen for his early collaboration

*on*the topic of present interest. We thank C. Barbieri

*and*R. J. Furnstahl for useful discussions. We thank J. Menéndez,

*A*. Schwenk,

*and*J. ...

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