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Eventually DSDD Matrices and Eigenvalue Localization

Caili Sang, Jianxing Zhao
2018 Symmetry  
Firstly, the relationships among strictly diagonally dominant ( S D D ) 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 SDDmatrices are nonsingular.  ... 
doi:10.3390/sym10100448 fatcat:rmvgo6b5wrhqjnwp3qhozaslxy

Heteroclinic Dynamics of Localized Frequency Synchrony: Stability of Heteroclinic Cycles and Networks

Christian Bick, Alexander Lohse
2019 Journal of nonlinear science  
Hence, our results elucidate how oscillator coupling influences sequential transitions along 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.  ... 
doi:10.1007/s00332-019-09562-3 fatcat:c5favvtunzcfvhaxhsdbkvjnb4

Heteroclinic Dynamics of Localized Frequency Synchrony: Stability of Heteroclinic Cycles and Networks [article]

Christian Bick, Alexander Lohse
2018 arXiv   pre-print
Hence, our results elucidate how oscillator coupling influences sequential transitions along 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  ... 
arXiv:1810.06716v1 fatcat:bmwjpwxlrzeolj7xfnl7isjkxu

Algorithm 805: computation and uses of the semidiscrete matrix decomposition

Tamara G. Kolda, Dianne P. O'Leary
2000 ACM Transactions on Mathematical Software  
Applications of the algorithms are presented to data compression, filtering, 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.  ... 
doi:10.1145/358407.358424 fatcat:xffevpdj4fdqnilnlq4enx6kyi

iSIRA: Integrated shift–invert residual Arnoldi method for graph Laplacian matrices from big data

Wei-Qiang Huang, Wen-Wei Lin, Henry Horng-Shing Lu, Shing-Tung Yau
2019 Journal of Computational and Applied Mathematics  
The 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.  ... 
doi:10.1016/j.cam.2018.07.031 fatcat:mpg2p2rmzrfhjnpqol3bhzxcb4

On Sketching Quadratic Forms

Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, Qin Zhang
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.  ... 
doi:10.1145/2840728.2840753 dblp:conf/innovations/AndoniCKQWZ16 fatcat:i337kczyfzhbxnwjhokjfyohr4

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

Seyed Mostafa Mousavi Kahaki, Md Jan Nordin, Amir H. Ashtari, Sophia J. Zahra, Jesus Malo
2016 PLoS ONE  
Deformation effects, such as affine 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  ... 
doi:10.1371/journal.pone.0149710 pmid:26985996 pmcid:PMC4795769 fatcat:g76hwyc7ergajcrqg7pfhhid3u

Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials [article]

Yang Zheng and Giovanni Fantuzzi and Antonis Papachristodoulou
2018 arXiv   pre-print
Optimization over non-negative polynomials is fundamental for nonlinear systems analysis 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.  ... 
arXiv:1807.05463v1 fatcat:7jyiqbxl7bcepawmoulmo5hg7q

Recent advances in the solution of quadratic assignment problems

Kurt M. Anstreicher
2003 Mathematical programming  
In the past few years 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.  ... 
doi:10.1007/s10107-003-0437-z fatcat:jdllh6idbnfmzkelphkfepbi3a

Lecture Notes on Spectral Graph Methods [article]

Michael W. Mahoney
2016 arXiv   pre-print
These are lecture 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.  ... 
arXiv:1608.04845v1 fatcat:ppy6mlmfsvfcxedriwnndv6ztq

Optimization over Nonnegative and Convex Polynomials With and Without Semidefinite Programming [article]

Georgina Hall
2018 arXiv   pre-print
In the second part of this thesis, we focus 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).  ... 
arXiv:1806.06996v1 fatcat:ywvkxguvobh43jvdaedk2tf3ju

Schrödinger operator on the zigzag half-nanotube in magnetic field [article]

Alexei Iantchenko, Evgeny Korotyaev
2010 arXiv   pre-print
We describe all 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  ... 
arXiv:0906.1231v2 fatcat:x6gbydpjzreldicyco7okd7auq

Decentralized Approximate Newton Methods for Convex Optimization on Networked Systems [article]

Hejie Wei, Zhihai Qu, Xuyang Wu, Hao Wang, Jie Lu
2020 arXiv   pre-print
The proposed DEAN algorithms allow each node to repeatedly perform 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.  ... 
arXiv:1903.09481v3 fatcat:n23oyzclmfcujfghohxhgbmpj4

Randomized Dynamical Decoupling Strategies and Improved One-Way Key Rates for Quantum Cryptography [article]

Oliver Kern
2009 arXiv   pre-print
The focus is 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.  ... 
arXiv:0906.2927v2 fatcat:bbelbmayjzhopgh7gcf3cadz7m

Nonobservable nature of the nuclear shell structure: Meaning, illustrations, and consequences

T. Duguet, H. Hergert, J. D. Holt, V. Somà
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.  ... 
doi:10.1103/physrevc.92.034313 fatcat:timp5a7asnd7jnburw2grb5wia
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