2005
DOI: 10.1103/physreve.72.020901
|View full text |Cite
|
Sign up to set email alerts
|

Exact asymptotic results for the Bernoulli matching model of sequence alignment

Abstract: Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the distribution of the LCS in a simpler, yet nontrivial, variant of the original model called the Bernoulli matching (BM) model which reduces to the original model in the c → ∞ limit. We show that in the BM model, for all c, the distribution of the asymptotic length of the LCS, su… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1

Citation Types

9
76
1

Year Published

2006
2006
2021
2021

Publication Types

Select...
6
2

Relationship

2
6

Authors

Journals

citations
Cited by 62 publications
(86 citation statements)
references
References 35 publications
9
76
1
Order By: Relevance
“…, has been derived in terms of the optimal fluctuation approach [50][51][52], where it has been demonstrated that both asymptotics (left and right) of the function P * (f ) are consistent with the Tracy-Widom distribution [1] which was known to describe the statistical properties of many other systems [2][3][4][5][6][7].…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…, has been derived in terms of the optimal fluctuation approach [50][51][52], where it has been demonstrated that both asymptotics (left and right) of the function P * (f ) are consistent with the Tracy-Widom distribution [1] which was known to describe the statistical properties of many other systems [2][3][4][5][6][7].…”
Section: Discussionmentioning
confidence: 99%
“…Nowadays we have got rather comprehensive list of various systems (both purely mathematical and physical) whose macroscopic statistical properties are described by the same universal Tracy-Widom (TW) distribution function. These systems are: the longest increasing subsequences (LIS) model [2] (Section I.A) zero-temperature lattice directed polymers with geometric disorder [3] the polynuclear growth (PNG) system [4], (Section I.B) the oriented digital boiling model [5], the ballistic decomposition model [6], the longest common subsequences (LCS) [7], the onepoint distribution of the solutions of the KPZ equation [8] (which describes the motion of an interface separating two homogeneous bulk phases) in the long time limit [9,10], and finally finite temperature directed polymers in random potentials with short-range correlations [11][12][13][14]. It should be noted that directed polymers in a quenched random potential have been the subject of intense investigations during the past three decades (see e.g.…”
mentioning
confidence: 99%
“…Amazingly, the Tracy-Widom distribution has since emerged in a number of seemingly unrelated problems such as the longest increasing subsequence problem [4], directed polymers in (1 + 1)-dimensions [5], various (1 + 1)-dimensional growth models [6], a class of sequence alignment problems [7] and in finance [8]. Recently, it has been shown that the statistics of the largest eigenvalue is also of importance in population growth of organisms in fluctuating environments [9].…”
mentioning
confidence: 99%
“…The Bernoulli Matching model for this problem has been considered in details in [35]. An example of the random matrix with the optimal path is outlined by the bold line in Fig.4 (only filled circles, i.e.…”
Section: Expectations Of Lcs Energy For General Cost Functionsmentioning
confidence: 99%
“…The ground state energy, E m,n (a = 0), has a meaning of the LIS length of "1" (see [35]). The mean value E m,n in the thermodynamic limit n = m → ∞ equals to…”
Section: Expectations Of Lcs Energy For General Cost Functionsmentioning
confidence: 99%