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Probe Matrix Problems: Totally Balanced Matrices [chapter]

David B. Chandler, Jiong Guo, Ton Kloks, Rolf Niedermeier
Algorithmic Aspects in Information and Management  
We show that for M being the class of totally balanced matrices, it can be decided in polynomial time whether A is a probe totally balanced matrix.  ...  Let M be a class of 0/1-matrices. A 0/1/ -matrix A where the s induce a submatrix is a probe matrix of M if the s in A can be replaced by 0s and 1s such that A becomes a member of M.  ...  Probe totally balanced matrices can be recognized in polynomial time. Future Work With this paper we try to initiate research on special matrix sandwich problems, that is, probe matrix problems.  ... 
doi:10.1007/978-3-540-72870-2_35 dblp:conf/aaim/ChandlerGKN07 fatcat:3rui6jwfnvdmvec67w74jicxwe

Contiguous Graph Partitioning For Optimal Total Or Bottleneck Communication [article]

Peter Ahrens
2021 arXiv   pre-print
Traditional objectives such as the simple edge cut, hyperedge cut, or hypergraph connectivity minimize the total cost of all parts under a balance constraint.  ...  We propose the first near-linear time algorithms for several graph partitioning problems in the contiguous regime.  ...  Several approaches seek to use a two-phase approach to nonsymmetric partitioning where the matrix is first partitioned to minimize total communication volume, then the partition is refined to balance the  ... 
arXiv:2007.16192v4 fatcat:lrjtllq7e5emfclfu3wfcejhne

Matrix probing: a randomized preconditioner for the wave-equation Hessian [article]

Laurent Demanet, Pierre-David Létourneau, Nicolas Boumal, Henri Calandra, Jiawei Chiu, Stanley Snelson
2011 arXiv   pre-print
Numerical experiments show that randomized operator fitting offers a compelling preconditioner for the linearized seismic inversion problem.  ...  This paper considers the problem of approximating the inverse of the wave-equation Hessian, also called normal operator, in seismology and other types of wave-based imaging.  ...  LD, PDL, and NB are supported by a grant from Total SA.  ... 
arXiv:1101.3615v1 fatcat:gtcqxhp4x5htnec2b6gmozitge

Matrix probing: A randomized preconditioner for the wave-equation Hessian

Laurent Demanet, Pierre-David Létourneau, Nicolas Boumal, Henri Calandra, Jiawei Chiu, Stanley Snelson
2012 Applied and Computational Harmonic Analysis  
Numerical experiments show that randomized operator fitting offers a compelling preconditioner for the linearized seismic inversion problem.  ...  This paper considers the problem of approximating the inverse of the wave-equation Hessian, also called normal operator, in seismology and other types of wave-based imaging.  ...  The right balance of parameters in each dimension was obtained manually for best accuracy; only their total number (their product) is reported.  ... 
doi:10.1016/j.acha.2011.03.006 fatcat:v67igefw7ngmzc2jlretu4hi3q

A Mueller-Matrix Formalism for Modeling Polarization Azimuth and Ellipticity Angle in Semiconductor Optical Amplifiers in a Pump–Probe Scheme

L. Q. Guo, Michael J. Connelly
2007 Journal of Lightwave Technology  
This paper presents a Mueller-matrix approach to simulate the azimuth and ellipticity trajectory of a probe light in a tensile-strained bulk semiconductor optical amplifier (SOA) in a conventional pump-probe  ...  The Mueller-matrix formalism is utilized to predict the variations of azimuth and ellipticity angle, which greatly reduces the complexity of the simulations in comparison with Jones-matrix formalism.  ...  While the problems could be treated using the amplitude formulation, the use of the Mueller-matrix formalism greatly simplifies the simulation herein.  ... 
doi:10.1109/jlt.2006.886674 fatcat:pfpytonmzradznjwuqlcb6yeoy

Solving the Inverse Problem of Electrocardiography Using a Duncan and Horn Formulation of the Kalman Filter

K.L. Berrier, D.C. Sorensen, D.S. Khoury
2004 IEEE Transactions on Biomedical Engineering  
Numeric regularization methods most often used to solve the ill-posed inverse problem of electrocardiography are spatial and ignore the temporal nature of the problem.  ...  In this study, a reformulation of Index Terms -Inverse problem, noncontact mapping, regularization, Kalman filter.  ...  The underlying ill-posedness is manifested in the ill-conditioning of the transfer matrix . Calculating the endocardial potentials given the probe potentials is the inverse problem.  ... 
doi:10.1109/tbme.2003.821027 pmid:15000381 fatcat:o7j4j5iz3rbyjkokaxh7jj3ose

Relaxation Methods for Constrained Matrix Factorization Problems: Solving the Phase Mapping Problem in Materials Discovery [chapter]

Junwen Bai, Johan Bjorck, Yexiang Xue, Santosh K. Suram, John Gregoire, Carla Gomes
2017 Lecture Notes in Computer Science  
Matrix factorization is a robust and widely adopted technique in data science, in which a given matrix is decomposed as the product of low rank matrices.  ...  We study a challenging constrained matrix factorization problem in materials discovery, the so-called phase mapping problem.  ...  In non-negative matrix-factorization, the goal is to explain a non-negative signal as the product of (typically) two nonnegative low rank matrices.  ... 
doi:10.1007/978-3-319-59776-8_9 fatcat:ubyjrjwjefgapavo2ojl4wjrle

Multi-frequency identification of defects in conducting media

A Pirani, M Ricci, R Specogna, A Tamburrino, F Trevisan
2008 Inverse Problems  
the total variation regularization.  ...  In particular, we exploit the collection of data at different probe positions as well as at different excitation frequencies in order to improve the amount of information content, the accuracy of the inverse  ...  The adoption of a multi-frequency excitation allows us to balance these opposite aspects.  ... 
doi:10.1088/0266-5611/24/3/035011 fatcat:xitg3xq5xrbz7n5xoi4f2npklm

Critical Evaluation of Different Techniques for Determining Soil Water Content [chapter]

Alejandro Zermeo-Gonzlez, Juan Munguia-Lpez, Martn Cadena-Zapata, Santos Gabriel, Luis Ibarra-Jimnez, Ral Rodrguez-Garc
2012 Problems, Perspectives and Challenges of Agricultural Water Management  
The energy status of water in soil can be expressed as follows (Hanks and Ashcroft, 1980) : total = matric + solute + grav. (2) Where total is the total soil water potential (MPa), matric soil matric  ...  Watermark blocks or granular matrix sensor, is a new style of electrical resistance block. The electrodes are embedded in a granular matrix material, similar to compressed fine sand.  ... 
doi:10.5772/30633 fatcat:pmxzpvmckzhfroc66zhcj4imuu

Multi-step quantum algorithm for solving the 3-bit exact cover problem [article]

Hefeng Wang
2018 arXiv   pre-print
We present a multi-step quantum algorithm for solving the 3-bit exact cover problem, which is one of the NP-complete problems.  ...  Our results indicate that quantum computers may be able to outperform classical computers in solving NP-complete problems.  ...  operators, respectively, σ x and σ z are the Pauli matrices.  ... 
arXiv:1603.05826v4 fatcat:pnl3vvilrfasph5kvsldvmgacq

Inverse Problems [chapter]

Thorsten Hohage, Benjamin Sprung, Frederic Weidling
2020 Topics in applied physics  
The minimization problems can be solved efficiently by Algorithm 5.1 without the need to set up the full Jacobi matrices F (f k ) in each step.  ...  The corresponding forward problems then consists in predicting experimental data given perfect knowledge of the probe.  ... 
doi:10.1007/978-3-030-34413-9_5 fatcat:53gnsq2u5rgotm5rlkcyhbue2m

Inverse Problems in Geophysics [chapter]

R. Snieder, J. Trampert
1999 CISM International Centre for Mechanical Sciences  
Just as in the previous section, the model parameters affect the way in which the probe (in this case the rays) samples the model.  ...  For many problems, this entails inverting the matrix A T A or an equivalent matrix that contains regularization terms as well.  ... 
doi:10.1007/978-3-7091-2486-4_3 fatcat:igmezotlijdohgkqxujotvd7ui

Efficient quantum algorithm for solving structured problems via multi-step quantum computation [article]

Hefeng Wang, Sixia Yu, Hua Xiang
2022 arXiv   pre-print
This algorithm can achieve an exponential speedup over classical algorithms in solving a type of structured search problems.  ...  In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly.  ...  In the case where f is balanced, the total number of N = 2 n states can be divided into two sets by using an oracle f . The set with eigenvalue −1 has N 1 = 2 n−1 items, thus the ratio N 1 /N = 1/2.  ... 
arXiv:1912.06959v3 fatcat:5lyx5zv76bh6lekl6vavreba7a

Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods [article]

Quirin Aumann, Steffen W. R. Werner
2022 arXiv   pre-print
This work compares structure-preserving model reduction methods based on rational interpolation and balanced truncation with a specific focus on their applicability to vibro-acoustic systems.  ...  compare the effectiveness of all considered methods by applying them to numerical models of vibro-acoustic systems depicting structural vibration, sound transmission, acoustic scattering, and poroelastic problems  ...  (a) Geometry sketch and probe location P 5 (orange ball)Sound pressure level at P 5 . Figure 12 :Figure 13 : 1213 Figure 12: Sketch and transfer function of the radiation problem.  ... 
arXiv:2201.06518v1 fatcat:jli2fdgmjvg6raol7bshk2pabm

Parallel solutions of inverse multiple scattering problems with born-type fast solvers

Mert Hidayetoglu, Chunxia Yang, Lang Wang, Anthony Podkowa, Michael Oelze, Wen-Mei Hwu, Weng Cho Chew
2016 2016 Progress in Electromagnetic Research Symposium (PIERS)  
We report parallel solutions of inverse multiple scattering problems with the Born iterative method (BIM) and the distorted Born iterative method (DBIM).  ...  This yields O(N 2 + N R + N T ) cost in total. We use MLFMA for reducing this cost down to O(N + R + T ), without storing any dense matrix.  ...  The receiver and transmitter locations are placed in accordance with an ultrasonic array probe (L9-4).  ... 
doi:10.1109/piers.2016.7734520 fatcat:kh3zc3czujb3dbrewbxylllj3m
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