Exact Asymptotic Results for a Model of Sequence Alignment
Satya N. Majumdar, Sergei Nechaev
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 large c limit. 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 Tracy-Widom distribution of the largest eigenvalue of a random matrix whose entries are drawn from a Gaussian unitary ensemble. In particular, in the large c limit, this provides an exact expression for the asymptotic length distribution in the original LCS problem.
Create a lesson
Related papers
Large Language Model Agents for Evidence Based Genetic Disease Severity Classification
Tohid Ghasemnejad, Ahmadreza Argha, Mark Grosser et al.
STUART: Sequence Triage and qUAntification of Read Transcripts for Rapid Ionizing Radiation Exposure Assessment
Tomasz Strzoda, Lourdes Cruz-Garcia, Mustafa Najim et al.
PlainMap: a lightweight, restartable mapping pipeline for ancient and modern DNA
Michael V. Westbury
Democratizing Clinical Tumor Whole Genome Sequencing: 18-hour End-to-end Analysis via Trillion-parameter Large Language Models Locally Deployed on Consumer-grade Hardware
Rui Xiao, Yili Xu
Structure is not mechanism: high-gain gated-FFN rows across text and genomic foundation models
Alexandros Tzanakakis, Aris Karatzikos, Ilias Georgakopoulos-Soares
RAGCell: Retrieval-Augmented Generation as Supervision for Versatile Single-cell Analysis
Tianyu Liu, Fan Zhang, Jiayuan Chen et al.