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Parikh vectors
2LYN_1 6KRT_1 6BIN_1 Letter Amino acid
6 20 15 F Phenylalanine
2 28 7 S Serine
4 4 4 W Tryptophan
12 13 8 R Arginine
7 24 16 D Aspartic acid
8 21 9 I Isoleucine
11 34 15 L Leucine
6 19 13 P Proline
5 18 13 T Threonine
10 20 4 Y Tyrosine
9 48 8 A Alanine
0 2 2 C Cysteine
3 10 3 Q Glutamine
5 30 19 E Glutamic acid
8 48 8 G Glycine
7 5 3 M Methionine
11 43 17 V Valine
6 11 9 N Asparagine
3 4 6 H Histidine
13 33 10 K Lycine 

2LYN_1|Chains A, B, C, D|SPERM LYSIN|Haliotis rufescens (6454)
>6KRT_1|Chains A, B|monodehydroascorbate reductase|Deschampsia antarctica (159298)
>6BIN_1|Chain A|HLA class II histocompatibility antigen, DR alpha chain|Homo sapiens (9606)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
2LYN , Knot 70 136 0.84 38 110 133 
RSWHYVEPKFLNKAFEVALKVQIIAGFDRGLVKWLRVHGRTLSTVQKKALYFVNRRYMQTHWANYMLWINKKIDALGRTPVVGDYTRLGAEIGRRIDMAYFYDFLKDKNMIPKYLPYMEEINRMRPADVPVKYMGK
6KRT , Knot 183 435 0.85 40 216 408 
MATEKHFKYVVLGGGVAGGYAAREFAKQGVQPGELAIISREAVAPYERPALSKAYLFPQNPARLPGFHVCVGSGGERLLPEWYSEKGIELILNTEIVKADLASKTLTSAAGATFTYEILLIATGSSVIKLSDFGTQGADSNNILYLREVDDADKLYAAIQAKKGGKAVVVGGGYIGLELSAVLKMNNLDVTMVFPEPWCMPRLFTAEIAAFYESYYTNKGVKIVKGTVAVGFDADANGDVTAVKLKDGSVLEADIVVVGVGGRPLTTLFKGQVAEEKGGIKTDASFETSVPGVYAVGDVATFPMKIYNDVRRVEHVDHSRKSAEQAVKAIKGKESGEAVPEYDYLPYFYSRSFDLSWQFYGDNVGEAVLFGDSDPASAKPKFGSYWIKDGKVVGAFLEGGSGDENGLIAKVARAQPPVSSIEELKQDGLLFASKI
6BIN , Knot 88 189 0.81 40 143 184 
IKEEHVIIQAEFYLNPDQSGEFMFDFDGDEIFHVDMAKKETVWRLEEFGRFASFEAQGALANIAVDKANLEIMTKRSNYTPITNVPPEVTVLTNSPVELREPNVLICFIDKFTPPVVNVTWLRNGKPVTTGVSETVFLPREDHLFRKFHYLPFLPSTEDVYDCRVEHWGLDEPLLKHWEFDTSGDDDDK

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 \(c\).

\(|P_{f(2LYN_1)}(2) \setminus P_{f(6KRT_1)}(2)|=40\), \(|P_{f(6KRT_1)}(2) \setminus P_{f(2LYN_1)}(2)|=146\). 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 1:0010010101100110111010111110011101101010010010001101100001000110011110001011100111100001110110010110100110000111001101001001011011100110
Pair \(Z_2\) Length of longest common subsequence
2LYN_1,6KRT_1 186 4
2LYN_1,6BIN_1 155 3
6KRT_1,6BIN_1 157 4

Newick tree

 
[
	6KRT_1:88.72,
	[
		2LYN_1:77.5,6BIN_1:77.5
	]:11.22
]

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 \((0.85)(0.8)(\frac{571 }{\log_{20} 571}-\frac{136}{\log_{20}136})=126.\)
Status Protein1 Protein2 d d1/2
Query variables 2LYN_1 6KRT_1 165 106.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]