Exact asymptotic results for the Bernoulli matching model of sequence alignment.

@article{Majumdar2005ExactAR,
  title={Exact asymptotic results for the Bernoulli matching model of sequence alignment.},
  author={Satya N. Majumdar and Sergei Nechaev},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2005},
  volume={72 2 Pt 1},
  pages={
          020901
        }
}
  • S. Majumdar, S. Nechaev
  • Published 11 October 2004
  • Computer Science, Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
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. We show that in the BM model, for all c , the distribution of the asymptotic length of the LCS, suitably scaled, is identical to the… 
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References

SHOWING 1-10 OF 75 REFERENCES
Extensive simulations for longest common subsequences . Finite size scaling, a cavity solution, and configuration space properties
Given two strings X and Y of N and M characters respectively, the Longest Common Subsequence (LCS) Problem asks for the longest sequence of (non-contiguous) matches between X and Y. Using extensive…
The Rate of Convergence of the Mean Length of the Longest Common Subsequence
Given two i.i.d. sequences of n letters from a finite alphabet, one can consider the length Ln of the longest sequence which is a subsequence of both the given sequences. It is known that ELn grows…
Mean-Field Approximations to the Longest Common Subsequence Problem
TLDR
This work describes a systematic way of incorporating correlations among the matches of two real sequences in the calculation, and obtains closer and closer approximations to the LCS problem.
Longest common subsequences of two random sequences
Given two random k-ary sequences of length n, what is f(n,k), the expected length of their longest common subsequence? This problem arises in the study of molecular evolution. We calculate f(n,k) for…
Some limit results for longest common subsequences
The longest common subsequence problem revisited
This paper re-examines, in a unified framework, two classic approaches to the problem of finding a longest common subsequence (LCS) of two strings, and proposes faster implementations for both. Letl…
Long Common Subsequences and the Proximity of two Random Strings.
Let $( x_1 ,x_2 , \cdots x_n )$ and $( x'_1 ,x'_2 , \cdots x'_n , )$ be two strings from an alphabet $mathcal{A}$, and let $L_n $ denote their longest common subsequence. The probabilistic behavior…
Alignment of molecular sequences seen as random path analysis.
TLDR
This work focuses on deriving a mathematically rigorous solution to RPA both in its combinatorial form and in its graphical representation, which puts DP in logical perspective under a more general conceptual framework.
Biological sequence analysis
TLDR
This talk will review a little over a decade's research on applying certain stochastic models to biological sequence analysis, and introduce the motif models in stages, beginning from very simple, non-stochastic versions, progressively becoming more complex, until they reach modern profile HMMs for motifs.
Identification of common molecular subsequences.
...
...