二值序列中约束长度模式的分布

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-21 DOI:10.1007/s11009-023-10068-5

Frosso S. Makri, Zaharias M. Psillakis

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引用次数: 0

摘要

在有限的二进制(0-1)试验序列上，我们定义了一个随机变量，列举了受一定约束的长度模式。对于独立同分布的二元试验序列，采用组合分析的方法建立了封闭形式的精确概率质量函数。得到了该随机变量均值的显式表达式。将有关概率质量函数的结果推广到可交换二元试验序列上。作为本研究的一个直接副产品，给出了在信息论中关于一类限行二进制序列计数的一个应用。数值算例进一步验证了结果。

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Distribution of Patterns of Constrained Length in Binary Sequences

On a finite sequence of binary (0-1) trials we define a random variable enumerating patterns of length subject to certain constraints. For sequences of independent and identically distributed binary trials exact probability mass functions are established in closed forms by means of combinatorial analysis. An explicit expression of the mean value of this random variable is obtained. The results associated with the probability mass functions are extended on sequences of exchangeable binary trials. An application in Information theory concerning counting of a class of run-length-limited binary sequences is provided as a direct byproduct of our study. Illustrative numerical examples exemplify further the results.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.