scholarly journals A distribution function from population genetics statistics using Stirling numbers of the first kind: Asymptotics, inversion and numerical evaluation

2021 ◽  
Author(s):  
Swaine Chen ◽  
Nico Temme
Keyword(s):  
Population Genetics ◽  
Distribution Function ◽  
Numerical Evaluation ◽  
Stirling Numbers

Analysis of the pore structure of adsorbents and its characterization by a numerical method

1984 ◽  
Vol 49 (12) ◽  
pp. 2721-2738 ◽  
Author(s):  
Ondřej Kadlec ◽  
Jerzy Choma ◽  
Helena Jankowska ◽  
Andrzej Swiatkowski
Keyword(s):  
Distribution Function ◽  
Pore Structure ◽  
Numerical Method ◽  
Active Carbon ◽  
Numerical Evaluation ◽  
Suggested Algorithm

This paper describes the algorithm of numerical evaluation of the parameters of the pore structure of adsorbents ( the micro, mezo and macropores). The structure of individual types of pores is described with the equation proposed by one of the present authors and giving the total distribution function of the pores with respect to their radii. The reliability of the suggested algorithm was verified in a number of calculations using a specially developed program. The results of the analysis and characterization of three different specimens of active carbon are shown as an example.

scholarly journals A faster and more accurate algorithm for calculating population genetics statistics requiring sums of Stirling numbers of the first kind

2020 ◽  
Author(s):  
Swaine L. Chen ◽  
Nico M. Temme
Keyword(s):  
Population Genetics ◽  
Dna Sequences ◽  
Cumulative Distribution Function ◽  
Beta Function ◽  
Stirling Numbers ◽  
Cumulative Distribution ◽  
Incomplete Beta Function ◽  
Improved Method ◽  
Direct Estimate ◽  
Improve Accuracy

AbstractStirling numbers of the first kind are used in the derivation of several population genetics statistics, which in turn are useful for testing evolutionary hypotheses directly from DNA sequences. Here, we explore the cumulative distribution function of these Stirling numbers, which enables a single direct estimate of the sum, using representations in terms of the incomplete beta function. This estimator enables an improved method for calculating an asymptotic estimate for one useful statistic, Fu’s Fs. By reducing the calculation from a sum of terms involving Stirling numbers to a single estimate, we simultaneously improve accuracy and dramatically increase speed.

Implementation of a Stirling number estimator enables direct calculation of population genetics tests for large sequence datasets

2018 ◽  
Vol 35 (15) ◽  
pp. 2668-2670 ◽  
Author(s):  
Swaine L Chen
Keyword(s):  
Population Genetics ◽  
Direct Calculation ◽  
Stirling Numbers ◽  
Stirling Number ◽  
Supplementary Information ◽  
Floating Point ◽  
Parameter Range ◽  
Recursive Method ◽  
Supplementary Data ◽  
Accurate Calculation

Abstract Motivation Stirling numbers enter into the calculation of several population genetics statistics, including Fu’s Fs. However, as alignments become large (≥50 sequences), the Stirling numbers required rapidly exceed the standard floating point range. Another recursive method for calculating Fu’s Fs suffers from floating point underflow issues. Results I implemented an estimator for Stirling numbers that has the advantage of being uniformly applicable to the full parameter range for Stirling numbers. I used this to create a hybrid Fu’s Fs calculator that accounts for floating point underflow. My new algorithm is hundreds of times faster than the recursive method. This algorithm now enables accurate calculation of statistics such as Fu’s Fs for very large alignments. Availability and implementation An R implementation is available at http://github.com/swainechen/hfufs. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals A Faster and More Accurate Algorithm for Calculating Population Genetics Statistics Requiring Sums of Stirling Numbers of the First Kind

2020 ◽  
Vol 10 (11) ◽  
pp. 3959-3967
Author(s):  
Swaine L. Chen ◽  
Nico M. Temme
Keyword(s):  
Population Genetics ◽  
Beta Function ◽  
Neutral Theory ◽  
Stirling Numbers ◽  
Cumulative Distribution ◽  
Direct Estimate ◽  
Theory Of Evolution ◽  
Sampling Formula ◽  
Improve Accuracy ◽  
Analytical Result

Ewen’s sampling formula is a foundational theoretical result that connects probability and number theory with molecular genetics and molecular evolution; it was the analytical result required for testing the neutral theory of evolution, and has since been directly or indirectly utilized in a number of population genetics statistics. Ewen’s sampling formula, in turn, is deeply connected to Stirling numbers of the first kind. Here, we explore the cumulative distribution function of these Stirling numbers, which enables a single direct estimate of the sum, using representations in terms of the incomplete beta function. This estimator enables an improved method for calculating an asymptotic estimate for one useful statistic, Fu’s Fs. By reducing the calculation from a sum of terms involving Stirling numbers to a single estimate, we simultaneously improve accuracy and dramatically increase speed.

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