Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\).
Let \(p_w(n)\) be the cardinality of \(P_w(n)\).
Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).
\(|P_{f(5TCV_1)}(2) \setminus P_{f(4HPW_1)}(2)|=90\),
\(|P_{f(4HPW_1)}(2) \setminus P_{f(5TCV_1)}(2)|=63\).
Let
\(
Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)|
\)
be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:1001111010010110011010110010001111011001110011001001001000001000100111001101101010010100011100111001001101000000110011001001100110110001110010100110100110110010001101010110110100011111111000010110110010110111100011101100101100100001100111000110101101001100111011111100010000010101110001010111010100101011011000101011101
Let d be the
Otu--Sayood
distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{629
}{\log_{20}
629}-\frac{310}{\log_{20}310})=88.7\)
Status
Protein1
Protein2
d
d1/2
Query variables
5TCV_1
4HPW_1
111
108
Was not able to put for d Was not able to put for d1
In notation analogous to
[Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]