Macroscopic non-uniqueness and transversal fluctuation in optimal random sequence alignment

Saba Amsalu; Heinrich Matzinger; Serguei Popov

ESAIM: Probability and Statistics (2007)

  • Volume: 11, page 281-300
  • ISSN: 1292-8100

Abstract

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We investigate the optimal alignment of two independent random sequences of length n. We provide a polynomial lower bound for the probability of the optimal alignment to be macroscopically non-unique. We furthermore establish a connection between the transversal fluctuation and macroscopic non-uniqueness.

How to cite

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Amsalu, Saba, Matzinger, Heinrich, and Popov, Serguei. "Macroscopic non-uniqueness and transversal fluctuation in optimal random sequence alignment." ESAIM: Probability and Statistics 11 (2007): 281-300. <http://eudml.org/doc/250100>.

@article{Amsalu2007,
abstract = { We investigate the optimal alignment of two independent random sequences of length n. We provide a polynomial lower bound for the probability of the optimal alignment to be macroscopically non-unique. We furthermore establish a connection between the transversal fluctuation and macroscopic non-uniqueness. },
author = {Amsalu, Saba, Matzinger, Heinrich, Popov, Serguei},
journal = {ESAIM: Probability and Statistics},
keywords = {Longest common subsequence; path property; longitudinal fluctuation; transversed fluctuation.; longest common subsequence; transversed fluctuation},
language = {eng},
month = {6},
pages = {281-300},
publisher = {EDP Sciences},
title = {Macroscopic non-uniqueness and transversal fluctuation in optimal random sequence alignment},
url = {http://eudml.org/doc/250100},
volume = {11},
year = {2007},
}

TY - JOUR
AU - Amsalu, Saba
AU - Matzinger, Heinrich
AU - Popov, Serguei
TI - Macroscopic non-uniqueness and transversal fluctuation in optimal random sequence alignment
JO - ESAIM: Probability and Statistics
DA - 2007/6//
PB - EDP Sciences
VL - 11
SP - 281
EP - 300
AB - We investigate the optimal alignment of two independent random sequences of length n. We provide a polynomial lower bound for the probability of the optimal alignment to be macroscopically non-unique. We furthermore establish a connection between the transversal fluctuation and macroscopic non-uniqueness.
LA - eng
KW - Longest common subsequence; path property; longitudinal fluctuation; transversed fluctuation.; longest common subsequence; transversed fluctuation
UR - http://eudml.org/doc/250100
ER -

References

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  1. D. Aldous and P. Diaconis, Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem. Bull. Amer. Math. Soc. (N.S.)36 (1999) 413–432.  Zbl0937.60001
  2. K.S. Alexander, The rate of convergence of the mean length of the longest common subsequence. Ann. Appl. Probab.4 (1994) 1074–1082.  Zbl0812.60014
  3. R. Arratia and M.S. Waterman, A phase transition for the score in matching random sequences allowing deletions. Ann. Appl. Probab.4 (1994) 200–225.  Zbl0809.62008
  4. J. Baik, P. Deift and K. Johansson, On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc.12 (1999) 1119–1178.  Zbl0932.05001
  5. V. Chvatal and D. Sankoff, Longest common subsequences of two random sequences. J. Appl. Probability12 (1975) 306–315.  Zbl0313.60008
  6. P. Clote and R. Backofen, Computational molecular biology. An introduction. Wiley Series in Mathematical and Computational Biology. John Wiley & Sons Ltd., Chichester (2000).  Zbl0955.92013
  7. R. Hauser and H. Matzinger, Local uniqueness of alignments with af fixed proportion of gaps. Submitted (2006).  
  8. C.D. Howard, Models of first-passage percolation, in Probability on discrete structures, Encyclopaedia Math. Sci.110, Springer, Berlin (2004) 125–173.  Zbl1206.82048
  9. C.D. Howard and C.M. Newman, Geodesics and spanning trees for euclidian first-passage percolation. Ann. Probab.29 (2001) 577–623.  Zbl1062.60099
  10. K. Johansson, Transversal fluctuations for increasing subsequences on the plane. Probab. Theory Related Fields116 (2000) 445–456.  Zbl0960.60097
  11. J. Lember and H. Matzinger, Variance of the LCS for 0 and 1 with different frequencies. Submitted (2006).  Zbl1111.60081
  12. C.M. Newman and M.S.T. Piza, Divergence of shape fluctuations in two dimensions. Ann. Probab.23 (1995) 977–1005.  Zbl0835.60087
  13. P.A. Pevzner, Computational molecular biology. An algorithmic approach. Bradford Books, MIT Press, Cambridge, MA (2000).  Zbl0972.92011
  14. M.J. Steele, An Efron-Stein inequality for non-symmetric statistics. Annals of Statistics14 (1986) 753–758.  Zbl0604.62017
  15. M.S. Waterman, Estimating statistical significance of sequence alignments. Phil. Trans. R. Soc. Lond. B344 (1994) 383–390.  

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