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Original Articles

Tensor ranks on tangent developable of Segre varieties

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Pages 881-894 | Received 21 Jul 2011, Accepted 20 Jul 2012, Published online: 28 Aug 2012

References

  • Allman , ES , Matias , C and Rhodes , JA . 2009 . Identifiability of parameters in latent structure models with many observed variables . Ann. Statist. , 37 : 3099 – 3132 .
  • Ballico , E and Bernardi , A . 2012 . Decomposition of homogeneous polynomials with low rank . Math. Z. , 271 : 1141 – 1149 .
  • Bartho , P , Curto , C , Luczak , A , Marguet , S and Harris , KD . 2009 . Population coding of tone stimuli in auditory cortex: Dynamic rate vector analysis . Eur. J. Neurosci. , 30 : 1767 – 1778 .
  • Bernardi , A , Brachat , J , Comon , P and Mourrain , B . June 8–11 2011 . “ Multihomogeneous polynomial decomposition using moment matrices ” . In ISAAC 2011, Proceedings of the 36th International Symposium of Symbolic and Algebraic Computation , June 8–11 , 35 – 42 . Held in San Jose, CA , , USA : ACM New York .
  • Bernardi , A , Gimigliano , A and Idà , M . 2011 . On the stratification of secant varieties of Veronese varieties via symmetric rank . J. Symbolic. Comput. , 46 : 34 – 55 .
  • Bocci , C and Chiantini , L . On the identifiability of binary Segre products . J. Algebraic Geom. , in press, DOI: http://dx.doi.org/10.1090/S1056-3911-2011-00592-4
  • Brachat , J , Comon , P , Mourrain , B and Tsigaridas , EP . 2010 . Symmetric tensor decomposition . Linear Algebra Appl. , 433 : 851 – 1872 .
  • Bruno , W , Rota , G and Torney , D . 1999 . Probability set functions . Annals Combinatorics , 3 : 13 – 25 .
  • Buczyński , J , Ginensky , A and Landsberg , JM . Determinantal equations for secant varieties and the Eisenbud–Koh–Stillman conjecture , Preprint: arXiv:1007.0192v3 [math.AG]
  • Buczyński , J and Landsberg , JM . Ranks of tensors and a generalization of secant varieties , Linear Algebra Appl. (to appear). Preprint: arXiv:0909.4262 [math.AG]
  • Buczyński , J and Landsberg , JM . On the third secant variety , Preprint: arxiv:1111.7005 [math.AG]
  • Carlini , E . 2006 . “ Reducing the number of variables of a polynomial ” . In Algebraic Geometry and Geometric Modeling , Edited by: Elkadi , M , Mourrain , B and Piene , R . 237 – 247 . Berlin : Springer .
  • Comas , G and Seiguer , M . 2011 . On the rank of a binary form . Found. Comput. Math. , 11 : 65 – 78 .
  • Comon , P , Golub , G , Lim , L-H and Mourrain , B . 2008 . Symmetric tensors and symmetric tensor rank . SIAM J. Matrix Anal. Appl. , 30 : 1254 – 1279 .
  • Comon , P , Sorensen , M and Tsigaridas , E . Decomposing tensors with structured matrix factors reduces to rank-1 approximations, ICASSP'2010, Dallas, March 2010, pp. 14–19
  • de Almeida , ALF , Favier , G and Mota , JCM . 2007 . Parafac-based unified tensor modeling for wireless communication systems with application to blind multiuser equalization . Signal Process. , 87 : 337 – 351 .
  • Georgi , B and Schliep , A . 2006 . Context-specific independence mixture modeling for positional weight matrices, Bioinformatics , 22 : 166 – 173 .
  • Hà , HT . 2002 . Box shaped matrices and the defining ideal of certain blowup surface . J. Pure Appl. Algebra , 167 : 203 – 224 .
  • Landsberg , JM . Tensors: Geometry and Applications, Vol. 128, Graduate Studies in Mathematics . American Mathematical Society, Providence, RI , 2012
  • Landsberg , JM and Manivel , L . 2004 . On the ideals of secant varieties of Segre varieties . Found. Comput. Math. , 4 : 397 – 422 .
  • Landsberg , JM and Weyman , J . 2007 . On the ideals and singularities of secant varieties of Segre varieties . Bull. London Math. Soc. , 39 : 685 – 697 .
  • McCullagh , P . 1987 . Tensor Methods in Statistics, Monographs on Statistics and Applied Probability , London : Chapman and Hall .
  • Nion , D and De Lathauwer , L . 2008 . A block component model based blind DS-CDMA receiver . IEEE Trans. Signal Process. , 56 : 5567 – 5579 .
  • Oeding , L . Report on geometry and representation theory of tensors for computer science, statistics and other areas , Preprint: arXiv:0810.3940 [math.AG]
  • Oeding , L . 2011 . Set-theoretic defining equations of the tangential variety of the Segre variety . J. Pure Appl. Algebra , 215 : 1516 – 1527 .
  • Sturmfels , B and Zwiernik , P . Binary cumulant varieties , Annals Combinatorics, to appear (BAD Math Day Special Issue)
  • Sylvester , JJ . 1886 . Sur une extension d'un théorème de Clebsh relatif aux courbes du quatrième degré . Comptes Rendus, Math. Acad. Sci. Paris , 102 : 1532 – 1534 .
  • Torney , DC . 2000 . Binary cumulants . Adv. Appl. Math. , 25 : 34 – 40 .

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