\documentclass{article}

\title{Voynich Manuscript - Patterns of Co-occurrence}
\author{Sarah Goslee}
\date{2006-10-22}

\begin{document}

\maketitle

\section{Introduction}

These analyses continue using the three discrete subsets described in the first page:
an herbal subset (H) in Currier language A, and the recipe section (R) and the
balenological section (B), both in Currier language B.


<<label=subsets,echo=FALSE>>=

seth.char.pairs <- seth.page.chars
for(i in 1:length(seth.page.chars)) {
	temp <- seth.page.chars[[i]]
	seth.char.pairs[[i]] <- paste(temp[1:(length(temp)-1)], temp[2:length(temp)], sep="")
}
rm(i, temp)

seth.char.pairs.table <- table(unlist(seth.char.pairs))
seth.char.pairs.table <- data.frame(c1=substring(names(seth.char.pairs.table),1,1), c2=substring(names(seth.char.pairs.table),2,2), seth.char.pairs.table)
seth.char.pairs.table <- crosstab(seth.char.pairs.table$c1, seth.char.pairs.table$c2, seth.char.pairs.table$Freq)
seth.char.pairs.table <- seth.char.pairs.table[-match("*", rownames(seth.char.pairs.table)), -match("*", colnames(seth.char.pairs.table))]
seth.char.pairs.table <- seth.char.pairs.table[-match("X", rownames(seth.char.pairs.table)), -match("X", colnames(seth.char.pairs.table))]

setr.char.pairs <- setr.page.chars
for(i in 1:length(setr.page.chars)) {
	temp <- setr.page.chars[[i]]
	setr.char.pairs[[i]] <- paste(temp[1:(length(temp)-1)], temp[2:length(temp)], sep="")
}
rm(i, temp)

setr.char.pairs.table <- table(unlist(setr.char.pairs))
setr.char.pairs.table <- data.frame(c1=substring(names(setr.char.pairs.table),1,1), c2=substring(names(setr.char.pairs.table),2,2), setr.char.pairs.table)
setr.char.pairs.table <- crosstab(setr.char.pairs.table$c1, setr.char.pairs.table$c2, setr.char.pairs.table$Freq)
setr.char.pairs.table <- setr.char.pairs.table[-match("*", rownames(setr.char.pairs.table)), -match("*", colnames(setr.char.pairs.table))]
setr.char.pairs.table <- setr.char.pairs.table[-match("x", rownames(setr.char.pairs.table)), -match("x", colnames(setr.char.pairs.table))]

setb.char.pairs <- setb.page.chars
for(i in 1:length(setb.page.chars)) {
	temp <- setb.page.chars[[i]]
	setb.char.pairs[[i]] <- paste(temp[1:(length(temp)-1)], temp[2:length(temp)], sep="")
}
rm(i, temp)

setb.char.pairs.table <- table(unlist(setb.char.pairs))
setb.char.pairs.table <- data.frame(c1=substring(names(setb.char.pairs.table),1,1), c2=substring(names(setb.char.pairs.table),2,2), setb.char.pairs.table)
setb.char.pairs.table <- crosstab(setb.char.pairs.table$c1, setb.char.pairs.table$c2, setb.char.pairs.table$Freq)
setb.char.pairs.table <- setb.char.pairs.table[-match("*", rownames(setb.char.pairs.table)), -match("*", colnames(setb.char.pairs.table))]
setb.char.pairs.table <- rbind(setb.char.pairs.table[1:9,], rep(0, ncol(setb.char.pairs.table)), setb.char.pairs.table[10:nrow(setb.char.pairs.table),])
setb.char.pairs.table <- cbind(setb.char.pairs.table[,1:9], rep(0, nrow(setb.char.pairs.table)), setb.char.pairs.table[,10:ncol(setb.char.pairs.table)])
names(setb.char.pairs.table) <- names(seth.char.pairs.table)

write.table(seth.char.pairs.table, "hcharpair.csv", quote=FALSE)
write.table(setr.char.pairs.table, "rcharpair.csv", quote=FALSE)
write.table(setb.char.pairs.table, "bcharpair.csv", quote=FALSE)

seth.word.pairs <- seth.page.words
for(i in 1:length(seth.page.words)) {
	temp <- seth.page.words[[i]]
	seth.word.pairs[[i]] <- paste(temp[1:(length(temp)-1)], temp[2:length(temp)], sep=".")
}
rm(i, temp)

setr.word.pairs <- setr.page.words
for(i in 1:length(setr.page.words)) {
	temp <- setr.page.words[[i]]
	setr.word.pairs[[i]] <- paste(temp[1:(length(temp)-1)], temp[2:length(temp)], sep=".")
}
rm(i, temp)

setb.word.pairs <- setb.page.words
for(i in 1:length(setb.page.words)) {
	temp <- setb.page.words[[i]]
	setb.word.pairs[[i]] <- paste(temp[1:(length(temp)-1)], temp[2:length(temp)], sep=".")
}
rm(i, temp)


write.table(table(unlist(seth.word.pairs)), "hwordpair.csv", quote=FALSE)
write.table(table(unlist(setr.word.pairs)), "rwordpair.csv", quote=FALSE)
write.table(table(unlist(setb.word.pairs)), "bwordpair.csv", quote=FALSE)
@

Having found differences in character frequencies, I also wanted to look at patterns
of word beginnings and endings, and paragraph beginnings and endings. (Note that
"capital gallows characters" are by definition paragraph-initial.)

\begin{figure}
\begin{center}
<<label=begincode,fig=TRUE,echo=FALSE>>=

seth.char.begin <- seth.char.pairs.table[1:3,-c(1:3)]
seth.char.begin <- apply(seth.char.begin, 2, sum)
seth.char.begin <- seth.char.begin/sum(seth.char.begin)
seth.char.pbegin <- seth.char.pairs.table[3,-c(1:3)]
seth.char.pbegin <- seth.char.pbegin/sum(seth.char.pbegin)

seth.char.end <- seth.char.pairs.table[-c(1:3), 1:3]
seth.char.end <- apply(seth.char.end, 1, sum)
seth.char.end <- seth.char.end/sum(seth.char.end)
seth.char.pend <- seth.char.pairs.table[-c(1:3),3]
seth.char.pend <- seth.char.pend/sum(seth.char.pend)


setr.char.begin <- setr.char.pairs.table[1:3,-c(1:3)]
setr.char.begin <- apply(setr.char.begin, 2, sum)
setr.char.begin <- setr.char.begin/sum(setr.char.begin)
setr.char.pbegin <- setr.char.pairs.table[3,-c(1:3)]
setr.char.pbegin <- setr.char.pbegin/sum(setr.char.pbegin)

setr.char.end <- setr.char.pairs.table[-c(1:3), 1:3]
setr.char.end <- apply(setr.char.end, 1, sum)
setr.char.end <- setr.char.end/sum(setr.char.end)
setr.char.pend <- setr.char.pairs.table[-c(1:3),3]
setr.char.pend <- setr.char.pend/sum(setr.char.pend)


setb.char.begin <- setb.char.pairs.table[1:3,-c(1:3)]
setb.char.begin <- apply(setb.char.begin, 2, sum)
setb.char.begin <- setb.char.begin/sum(setb.char.begin)
setb.char.pbegin <- setb.char.pairs.table[3,-c(1:3)]
setb.char.pbegin <- setb.char.pbegin/sum(setb.char.pbegin)

setb.char.end <- setb.char.pairs.table[-c(1:3), 1:3]
setb.char.end <- apply(setb.char.end, 1, sum)
setb.char.end <- setb.char.end/sum(setb.char.end)
setb.char.pend <- setb.char.pairs.table[-c(1:3),3]
setb.char.pend <- setb.char.pend/sum(setb.char.pend)

plot(1:length(seth.char.begin), seth.char.begin, type="b", pch=names(seth.char.begin), col="green", xlab="Character", ylab="Frequency", main="Word beginnings")
lines(1:length(setr.char.begin), setr.char.begin, type="b", pch=names(setr.char.begin), col="darkgoldenrod2")
lines(1:length(setb.char.begin), setb.char.begin, type="b", pch=names(setb.char.begin), col="purple")

@
\caption{Frequencies of characters beginning words.}
\label{fig:begin}
\end{center}
\end{figure}

Set H is the only group where d was an extremely frequent word-initial character, and t and y were also more frequent in this position in set H than the other two (Fig. \ref{fig:begin}). The characters o, q and especially l were less common as word-initials in set H. Sets R and B were similar, although there are differences in the frequency of a and d between the two sets.

\begin{figure}
\begin{center}
<<label=pbegincode,fig=TRUE,echo=FALSE>>=
plot(1:length(seth.char.pbegin), seth.char.pbegin, type="b", pch=names(seth.char.pbegin), col="green", xlab="Character", ylab="Frequency", main="Paragraph beginnings", ylim=c(0, .7))
lines(1:length(setr.char.pbegin), setr.char.pbegin, type="b", pch=names(setr.char.pbegin), col="darkgoldenrod2")
lines(1:length(setb.char.pbegin), setb.char.pbegin, type="b", pch=names(setb.char.pbegin), col="purple")
@
\caption{Frequencies of characters beginning paragraphs.}
\label{fig:pbegin}
\end{center}
\end{figure}

Paragraph-initial characters were mainly the gallows characters F, K, P, T, and q and o were also found (Fig. \ref{fig:pbegin}). In set R, d was found as a paragraph-initial character. F and K were more common in set H, and P was less common.

\begin{figure}
\begin{center}
<<label=endcode,fig=TRUE,echo=FALSE>>=
plot(1:length(seth.char.end), seth.char.end, type="b", pch=names(seth.char.end), col="green", xlab="Character", ylab="Frequency", main="Word endings", ylim=c(0,.6))
lines(1:length(setr.char.end), setr.char.end, type="b", pch=names(setr.char.end), col="darkgoldenrod2")
lines(1:length(setb.char.end), setb.char.end, type="b", pch=names(setb.char.end), col="purple")
@
\caption{Frequencies of characters ending words.}
\label{fig:end}
\end{center}
\end{figure}

Word-ending characters were similar in all three sets, and only four characters were commonly found: l, n, r and y (Fig. \ref{fig:end}). The same characters were found in the paragraph-final position, but frequencies among sets were more variable (Fig. \ref{fig:pend}).

\begin{figure}
\begin{center}
<<label=pendcode,fig=TRUE,echo=FALSE>>=
plot(1:length(seth.char.pend), seth.char.pend, type="b", pch=names(seth.char.pend), col="green", xlab="Character", ylab="Frequency", main="Paragraph endings", ylim=c(0, .7))
lines(1:length(setr.char.pend), setr.char.pend, type="b", pch=names(setr.char.pend), col="darkgoldenrod2")
lines(1:length(setb.char.pend), setb.char.pend, type="b", pch=names(setb.char.pend), col="purple")
@
\caption{Frequencies of characters ending paragraphs.}
\label{fig:pend}
\end{center}
\end{figure}


\end{document}