Matrices with prescribed entries and eigenvalues. I

Oliveira, G. N. de

doi:10.1090/s0002-9939-1973-0309961-6

Cited by 26 publications

(9 citation statements)

References 8 publications

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“…4 The challenge in Netflix recommendation system is a classic MC problem. 4–8 As the inspiration of Netflix Prize contest, many efficient low rank MC algorithms were developed, for instance, Opt-Space, 7 SVT, 5 CF, 9 BellKor, 10 PF, 11 and FWLS. 12 Eventually, the team BellKor’s Pragmatic Chaos won this contest.…”

Section: Methodsmentioning

confidence: 99%

A Computational Framework for Influenza Antigenic Cartography

2010

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Influenza viruses have been responsible for large losses of lives around the world and continue to present a great public health challenge. Antigenic characterization based on hemagglutination inhibition (HI) assay is one of the routine procedures for influenza vaccine strain selection. However, HI assay is only a crude experiment reflecting the antigenic correlations among testing antigens (viruses) and reference antisera (antibodies). Moreover, antigenic characterization is usually based on more than one HI dataset. The combination of multiple datasets results in an incomplete HI matrix with many unobserved entries. This paper proposes a new computational framework for constructing an influenza antigenic cartography from this incomplete matrix, which we refer to as Matrix Completion-Multidimensional Scaling (MC-MDS). In this approach, we first reconstruct the HI matrices with viruses and antibodies using low-rank matrix completion, and then generate the two-dimensional antigenic cartography using multidimensional scaling. Moreover, for influenza HI tables with herd immunity effect (such as those from Human influenza viruses), we propose a temporal model to reduce the inherent temporal bias of HI tables caused by herd immunity. By applying our method in HI datasets containing H3N2 influenza A viruses isolated from 1968 to 2003, we identified eleven clusters of antigenic variants, representing all major antigenic drift events in these 36 years. Our results showed that both the completed HI matrix and the antigenic cartography obtained via MC-MDS are useful in identifying influenza antigenic variants and thus can be used to facilitate influenza vaccine strain selection. The webserver is available at http://sysbio.cvm.msstate.edu/AntigenMap.

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Section: Methodsmentioning

confidence: 99%

A Computational Framework for Influenza Antigenic Cartography

2010

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“…In the cycle of three papers [29,30,31], de Oliveira proved that ~l~e completion problem with I,cl = n (n > 2) is solvable over any field K; in this case, in the two situations described above, the necessary conditions indicated there are assumed to be fulfilled. For n = 2, in the general case, the algebraic closedness of the field K is necessary for the solvability of the problem.…”

Section: Completion Problems Of the General Type With Prescribed Eigementioning

confidence: 99%

Inverse matrix eigenvalue problems

Икрамов¹,

Chugunov²

2000

J Math Sci

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“…Subcase 1.4.5 Suppose that we prescribe one entry in (6) and another in (9). This subcase is similar to Subcase 1.4.4.…”

Section: Prescribed Entries 363mentioning

confidence: 99%

“…According to the induction assumption, Co is similar to a matrix Do = [di,j] that satisfies (4). Then B is similar to a matrix of the form (5) and A = TI?-] T::~~',-~~~~-~~-~ TA-,,, (D) has the prescribed form.Subcase 1.3.3 Suppose that we prescribe either two distinct entries in(6) or two distinct entries in (7). W.l.o.g., suppose that (in-2, jn-2) = (n-1, s) and (in-1, j n V l ) = (n-I, t), where s, t E (1,. .…”

mentioning

confidence: 99%