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 \(c\).
\(|P_{f(4EOR_1)}(2) \setminus P_{f(2ZNB_1)}(2)|=93\),
\(|P_{f(2ZNB_1)}(2) \setminus P_{f(4EOR_1)}(2)|=66\).
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 1:0100100100110100111001000101011110010100000111001100101100100101101101100000101110110001001101011011111110001101101111000001100010100111000111011011110111111000000110110011011110000001101101101110110001111100010011011001101001111110011000101101100010011111000100110011000100010101111011100100111010
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 \((0.85)(0.8)(\frac{530
}{\log_{20}
530}-\frac{232}{\log_{20}232})=85.3\)
Status
Protein1
Protein2
d
d1/2
Query variables
4EOR_1
2ZNB_1
105
93.5
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)],
\[
\delta=
\alpha \mathrm{min} + (1-\alpha) \mathrm{max}=
\begin{cases}
d &\alpha=0,\\
d_1/2 &\alpha=1/2
\end{cases}
\]