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Inequalities for the score constant in matching random sequences

Part of: Distribution theory Applications

Published online by Cambridge University Press:  14 July 2016

Yunshyong Chow  and
Yu Zhang
Yunshyong Chow*
Affiliation:
Academia Sinica
Yu Zhang*
Affiliation:
University of Colorado
*
∗Postal address: Institute of Mathematics, Academia Sinica, Taipei, Taiwan 11529. Research supported in part by NSC, Republic of China.
∗∗Postal address: Department of Mathematics, University of Colorado, Colorado Springs, CO 80933, USA.
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Abstract

We consider a sequence matching problem involving the optimal alignment score for contiguous sequences; rewarding matches and penalizing for deletions and mismatches. Arratia and Waterman conjectured in [1] that the score constant a(μ, δ) is a strictly monotone function (i) in δ for all positive δ and (ii) in μ if 0 ≤ μ ≤ 2δ. Here we prove that (i) is true for all δ and (ii) is true for some μ.

Keywords

Sequence matching

MSC classification

Primary: 62E20: Asymptotic distribution theory 62P10: Applications to biology and medical sciences
Type
Short Communications
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 601 - 606
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

Research supported in part by NSF grant DMS-9400467 and Grigsby.

References

Arratia, R., and Waterman, M. S. (1994). A phase transition for the score in matching random sequences allowing deletions. Ann. Appl. Prob. 4, 200–225.CrossRefGoogle Scholar