cchar, v. 1.6: Count characters in sequence data.
cpg, v. 0.7: Compute the CpG content of DNA sequences.
cutSeq, v. 0.11: Cut regions from molecular sequences.
generateQuerySbjct, v. 0.4: Generate pairs of homologous DNA sequences.
gd, v. 0.12: Calculate genetic diversity (pi, S, and Tajima's D) from aligned DNA sequences with or without sliding window.
getSeq, v. 0.4: Get specific sequences from a FASTA file containing multiple entries.
ms2dna, v. 1.16: Generate samples of homologous DNA sequences evolved under defined evolutionary scenarios by converting the output of Richard Hudson's coalescent simulation program ms. As of version 1.11, it can also deal with output generated by Gary Chen's fast coalescent simulator MaCS using the pipeline macs [options] | msformatter | ms2dna -a.
randomizeSeq, v. 0.8: Randomize sequences.
sequencer, v. 1.14: Simulate shotgun sequencing with paired (as of version 1.11) or unpaired reads and a user-defined error rate.
simK, v. 0.4: Simulate pair of sequences with given number of substitutions/site (K).
W. Feller. Proceedings of the conference on differential equations
(dedicated to A. Weinstein), стр. 251--270. University of Maryland Book Store, College Park, Md., (1956)
W. Feller. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, стр. 227--246. Berkeley and Los Angeles, University of California Press, (1951)
D. Kendall. Biometrika, (1948)The author discusses a ``birth-and-death process'' for which the Kolmogorov differential equations assume the form $$ P_n'(t)=-n(a+b)+cP_n(t)+(n-1)a+cP_n-1(t)\\ +(n+1)bP_n+1(t), $$ where $P_n(t)$ is the probability of a population size $n$. The case $c0$ corresponds to mortality and fertility proportional to the actual population size. The $c$-term accounts for an increase by immigration. The generating function of $P_n(t)$ is obtained and it is shown that for small $c$ one obtains approximations to R. A. Fisher's ``logarithmic series distribution'' which has found several applications in biology..
A. Kolmogorov. Izv. Akad. Nauk SSSR, Ser. Math, (1937)Computes density of fairly general Johnson-Mehl crystals and the probability that a point is not in a crystal yet..
J. Neyman, и E. Pearson. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, (1933)