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Information structure and general characterization of Mueller matrices [article]

José J. Gil, Ignacio San José
2021 arXiv   pre-print
In this work, a general and simple characterization of Mueller matrices is presented based on their statistical structure.  ...  manner all measurable information on such transformations.  ...  and meaningful general characterization of Mueller matrices is stated in Section VI; the structure and significance of the polarimetric information supported by M are analyzed in Section VII; the characterization  ... 
arXiv:2109.06877v3 fatcat:y43vu2flrvhanfd7pg7irh6hmq

Tri-weight codes and generalized hadamard matrices

P. Delsarte, J.M. Goethals
1969 Information and Control  
The existence is shown of a set of (p~ --1) generalized Hadamard matrices H(p, p~'~) of order p2'~, each of which is symmetric and regular.  ...  the tri-weight extended-BCIt code of length p2~% dimension 3m ~ 1, and minimum weight (p -1)p 2'~-1 -pro-1.  ...  (i) The q --1 matrices H , are symmetric and regular 1 Hadamard matrices.  ... 
doi:10.1016/s0019-9958(69)90411-2 fatcat:3msf3cahxrfg3kxz4yyxcx37ty

Almost Hadamard Matrices: General Theory and Examples

Teodor Banica, Ion Nechita, Karol Życzkowski
2012 Open systems & information dynamics  
We develop a general theory of "almost Hadamard matrices".  ...  These are by definition the matrices H ∈ M N (R) having the property that U = H/ √ N is orthogonal, and is a local maximum of the 1-norm on O(N ).  ...  We denote by D the generic diagonal matrices, by U the generic orthogonal or unitary matrices, and by H the generic Hadamard matrices, and their generalizations.  ... 
doi:10.1142/s1230161212500242 fatcat:nrr6aohgyrejjbya32iqg2spte

Ranks and Kernels of Codes From Generalized Hadamard Matrices

Steven T. Dougherty, Josep Rifa, Merce Villanueva
2016 IEEE Transactions on Information Theory  
The ranks and kernels of generalized Hadamard matrices are studied. It is proven that any generalized Hadamard matrix H(q,λ) over F_q, q>3, or q=3 and (3,λ) =1, generates a self-orthogonal code.  ...  This result puts a natural upper bound on the rank of the generalized Hadamard matrices.  ...  Although ordinary Hadamard matrices are a specific case of GH matrices, in general, the results obtained in [16] and [17] on the bounds for the rank and dimension of kernel when q = 2 can not be straightforwardly  ... 
doi:10.1109/tit.2015.2509061 fatcat:uiv5dqtusjdlfmjfeccjw3bg4a

Generalized turbo signal recovery for nonlinear measurements and orthogonal sensing matrices

Ting Liu, Chao-Kai Wen, Shi Jin, Xiaohu You
2016 2016 IEEE International Symposium on Information Theory (ISIT)  
The state evolution of the proposed algorithm is derived and is shown to be consistent with that obtained with the replica method.  ...  In this study, we propose a generalized turbo signal recovery algorithm to estimate a signal from quantized measurements, in which the sensing matrix is a row-orthogonal matrix, such as the partial discrete  ...  In contrast to the case with matrices with independent entries, AMP does not perform well for sensing matrices with a row-orthogonal ensemble.  ... 
doi:10.1109/isit.2016.7541826 dblp:conf/isit/LiuWJY16 fatcat:s4jwixvcknb4vkfq72wsf6wvo4

Ill-conditioned Information Matrices and the Generalized Linear Model: an Asymptotically Biased Estimation Approach [chapter]

Brian D. Marx
1989 Statistical Modelling  
Acknowledgements First of all, I would like to extend my thanks to the members of my family who were consistently supportive and encouraged my graduate work, who stood by me in my efforts to reach a personal  ...  Near-singular information matrices can often make desirable properties of accurate parameter estimation, precise prediction and testing with high power unattainable.  ...  ILL-CONDITIONED INFORMATION MATRICES 89 By investigating the general variance proportion decompositions outlined in section 4.5, problems can be immediately identiiied. See Table 5 .  ... 
doi:10.1007/978-1-4612-3680-1_24 fatcat:ma4c3q4iqvdrbnoobiufcvutaa

Information loss in coarse graining of polymer configurations via contact matrices

Patrik L Ferrari, Joel L Lebowitz
2003 Journal of Physics A: Mathematical and General  
Contact matrices provide a coarse grained description of the configuration omega of a linear chain (polymer or random walk) on Z^n: C_ij(omega)=1 when the distance between the position of the i-th and  ...  We prove that to leading order in N, the number of matrices equals the number of walks for SRW, but not for SAW.  ...  This makes it important to have information about the relation between the spaces of contact matrices and that of the proteins they represent.  ... 
doi:10.1088/0305-4470/36/21/303 fatcat:rkfsrnbnuvgs7g3pgrc4kamzya

Minimal and canonical rational generator matrices for convolutional codes

G.D. Forney, R. Johannesson, Zhe-Xian Wan
1996 IEEE Transactions on Information Theory  
Index Terms-Algebraic structure of convolutional codes, minimal generator matrices, canonical generator matrices, behavioral system theory, valuation theory.  ...  A full-rank IC x n matrix G ( D ) over the rational functions F ( D ) generates a rate R = k / n convolutional code C.  ...  Valcher. and the reviewers on earlier versions of the manuscript.  ... 
doi:10.1109/18.556681 fatcat:gjpi6vsp6ndc7i7f3ulfhfafgy

On Fisher information matrices and profile log-likelihood functions in generalized skew-elliptical models

Christophe Ley, Davy Paindaveine
2010 Metron  
Fisher information matrices in the vicinity of symmetry.  ...  In the present paper, we provide a simple proof that, in generalized skew-elliptical models involving the same skewing scheme as in the skew-normal distributions, Fisher information matrices, in the vicinity  ...  associated with singular Fisher information matrices.  ... 
doi:10.1007/bf03263537 fatcat:qpfkg6k62jaf3pmsbm5thjxyfa

Tighter Generalization Bounds for Matrix Completion Via Factorization Into Constrained Matrices

Ken-ichiro MORIDOMI, Kohei HATANO, Eiji TAKIMOTO
2018 IEICE transactions on information and systems  
We prove generalization error bounds of classes of lowrank matrices with some norm constraints for collaborative filtering tasks.  ...  In particular, a major approach is to impose the constraints Manuscript Generalization: The second one is a slightly generalized class, consisting of all matricesX = UV T ∈ R N×M with U ∈ R N×K and V ∈  ...  Acknowledgments This work is supported in part by JSPS KAKENHI Grant † https://pypi.python.org/pypi/fancyimpute Number 16K00305 and JSPS KAKENHI Grant Number 15H02667, respectively.  ... 
doi:10.1587/transinf.2017edp7339 fatcat:g4usqhsvzncorcx523fo3745rq

The generalized inverse inequalities for the sum of symmetric nonnegative definite matrices

Ying Ma, Shiqing Wang
2010 2010 3rd International Conference on Computer Science and Information Technology  
Trace inequalities naturally arise in control theory and in communication systems with multiple input and multiple output.  ...  Keywords-trace inequality, column space, symmetric positive definite matrix, symmetric nonnegative definite matrix, Penrose-Moore inverse matrix, generalized inverse matrix. I.  ...  ACKNOWLEDGMENT Support by the Natural Science Foundation of Henan, No.0611052600 and the Natural Science Foundation of Education Department of Henan, No.2010A110011.  ... 
doi:10.1109/iccsit.2010.5564738 fatcat:v4x3gsiqbjhopnr3bikbel75hm

Kalman-filtering methods for computing information matrices for time-invariant, periodic, and generally time-varying VARMA models and samples

P.A. Zadrozny, S. Mittnik
1994 Computers and Mathematics with Applications  
First, it derives a recursive Kalman-filtering method for computing exact sample and asymptotic information matrices for timeinvariant, periodic, or generally time-varying Gaussian vector autoregressive  ...  Second, it specializes the recursive method to a nonrecursive method for computing exact asymptotic information matrices for time-invariant or periodic VARMA models and samples  ...  matrices, applicable to generally time-varying models and samples.  ... 
doi:10.1016/0898-1221(94)00132-4 fatcat:r6hsojzllrgdpgdzfrhlufjtqm

Comments on "Kalman-filtering methods for computing information matrices for time-invariant, periodic, and generally time-varying VARMA models and samples"

J. Terceiro
2000 Computers and Mathematics with Applications  
This paper discusses some results contained in a paper by Zadrozny and Mittnik [1] in relation to the work developed by Terceiro [2].  ...  It also considers several issues concerning the efficiency of the algorithm and the state-space formulation of VARMA models. (~)  ...  information matrices for general VARMA models."  ... 
doi:10.1016/s0898-1221(00)00168-1 fatcat:5pwii3eh7rd57beubyu3ixqxue

Standard J-Spectral Factorization of Rational Matrices via Generalized Algebraic Riccati Equation

Atsushi KAWAMOTO, Kiyotsugu TAKABA, Tohru KATAYAMA
1999 Transactions of the Institute of Systems Control and Information Engineers  
Let a Weierstrass canonical form10) of -SE+A+BF be (35) where M and N are real nonsingular matrices and Af is stable.  ...  However, in the case where J or J' is not positive definite, even if (S1) holds, (S4) does not hold in general.  ... 
doi:10.5687/iscie.12.471 fatcat:pf6bwnollnam3hgcrw4fpo6arq

Automatic Generation of Review Matrices as Multi-document Summarization of Scientific Papers

Hayato Hashimoto, Kazutoshi Shinoda, Hikaru Yokono, Akiko Aizawa
2017 Annual International ACM SIGIR Conference on Research and Development in Information Retrieval  
In our work, we specifically examine a problem of automatically generating a synthesis matrix for scientific literature review.  ...  We use LexRank and also incorporate query expansion and word embedding to compensate for tersely expressed queries.  ...  Conclusion We analyzed synthesis matrices in NLP-related papers and formulated the task of synthesis matrix generation, and proposed a system for the task using queryfocused and comparative summarization  ... 
dblp:conf/sigir/HashimotoSYA17 fatcat:sqiybvvjojbxjcmu72vwululcm
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