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摘要翻译：
RNA模体通常由短的、模块化的模式组成，包括在模块内和模块之间形成的碱基对。估计这些模式的丰度对于评估全基因组搜索中匹配的统计意义，以及预测给定的功能是在不同物种中多次进化还是来自单一的共同祖先具有根本的重要性。在这篇手稿中，我们以一个完整和独立的方式回顾了自动机理论、母函数和转移矩阵方法的一些基本概念，这些概念与生物序列的模式分析有关。我们在一个通用框架中形式化了马尔可夫链嵌入的概念，以分析由无记忆源产生的随机字符串中的模式。这种概念化，加上自动机识别复杂模式的能力，允许系统地分析与随机字符串中模式的出现和频率有关的问题。我们提出的应用集中于自动机的同步概念，以及用于在一般文本中搜索有限数量的关键字（包括根据基本配对规则生成的模式集）的自动机。
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英文标题：
《Multiple pattern matching: A Markov chain approach》
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作者：
Manuel Lladser, M. D. Betterton, Rob Knight
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Quantitative Biology 数量生物学
二级分类：Genomics 基因组学
分类描述：DNA sequencing and assembly; gene and motif finding; RNA editing and alternative splicing; genomic structure and processes (replication, transcription, methylation, etc); mutational processes.
DNA测序与组装；基因和基序的发现；RNA编辑和选择性剪接；基因组结构和过程（复制、转录、甲基化等）；突变过程。
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一级分类：Quantitative Biology 数量生物学
二级分类：Quantitative Methods 定量方法
分类描述：All experimental, numerical, statistical and mathematical contributions of value to biology
对生物学价值的所有实验、数值、统计和数学贡献
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches in genomewide searches, and for predicting whether a given function has evolved many times in different species or arose from a single common ancestor. In this manuscript, we review in an integrated and self-contained manner some basic concepts of automata theory, generating functions and transfer matrix methods that are relevant to pattern analysis in biological sequences. We formalize, in a general framework, the concept of Markov chain embedding to analyze patterns in random strings produced by a memoryless source. This conceptualization, together with the capability of automata to recognize complicated patterns, allows a systematic analysis of problems related to the occurrence and frequency of patterns in random strings. The applications we present focus on the concept of synchronization of automata, as well as automata used to search for a finite number of keywords (including sets of patterns generated according to base pairing rules) in a general text.
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PDF链接：
https://arxiv.org/pdf/704.3221
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