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

top
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

top

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

top
  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.  
  2. K.S. Alexander, The rate of convergence of the mean length of the longest common subsequence. Ann. Appl. Probab.4 (1994) 1074–1082.  
  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.  
  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.  
  5. V. Chvatal and D. Sankoff, Longest common subsequences of two random sequences. J. Appl. Probability12 (1975) 306–315.  
  6. P. Clote and R. Backofen, Computational molecular biology. An introduction. Wiley Series in Mathematical and Computational Biology. John Wiley & Sons Ltd., Chichester (2000).  
  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.  
  9. C.D. Howard and C.M. Newman, Geodesics and spanning trees for euclidian first-passage percolation. Ann. Probab.29 (2001) 577–623.  
  10. K. Johansson, Transversal fluctuations for increasing subsequences on the plane. Probab. Theory Related Fields116 (2000) 445–456.  
  11. J. Lember and H. Matzinger, Variance of the LCS for 0 and 1 with different frequencies. Submitted (2006).  
  12. C.M. Newman and M.S.T. Piza, Divergence of shape fluctuations in two dimensions. Ann. Probab.23 (1995) 977–1005.  
  13. P.A. Pevzner, Computational molecular biology. An algorithmic approach. Bradford Books, MIT Press, Cambridge, MA (2000).  
  14. M.J. Steele, An Efron-Stein inequality for non-symmetric statistics. Annals of Statistics14 (1986) 753–758.  
  15. M.S. Waterman, Estimating statistical significance of sequence alignments. Phil. Trans. R. Soc. Lond. B344 (1994) 383–390.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.