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Parikh vectors
8JYY_1 7HFS_1 4DZJ_1 Letter Amino acid
8 16 3 N Asparagine
13 6 12 E Glutamic acid
18 13 8 G Glycine
6 2 5 M Methionine
17 6 7 T Threonine
18 22 7 V Valine
11 2 10 R Arginine
4 3 2 C Cysteine
6 3 1 Q Glutamine
12 13 12 K Lycine
8 5 5 F Phenylalanine
14 5 8 P Proline
13 11 9 S Serine
12 6 7 I Isoleucine
5 0 2 W Tryptophan
11 15 17 A Alanine
10 9 12 D Aspartic acid
11 6 1 H Histidine
11 19 9 L Leucine
8 7 3 Y Tyrosine 

8JYY_1|Chains A, B, C, D, E, F, G, H, I, J|RCD-1-2|Neurospora crassa (5141)
>7HFS_1|Chains A, B|Non-structural protein 3|Severe acute respiratory syndrome coronavirus 2 (2697049)
>4DZJ_1|Chains A, B|Gene 1 protein|Shigella phage Sf6 (10761)
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 \(w=f(c)\)
8JYY , Knot 103 216 0.85 40 160 209 
SGRPMDNEEWFPLKQTHYPPPTIPSMKTGHPTGPISIGHIIPDLRHLDNVINCKGFEPFPPNMDVFTAHYEQCHFGDHLNSEFVVQAGLHHTNITSDRWEYDSVVEYAVYPTRQYIDRLLESKEVRQYIQASAALLGGWCVYMVTGIMVARGGGRNVTSEEKGAGVSGPEVGWDTKTKTKVNAHHTTDFVCAIRLVKIAKSGLRSSWTMKKVTREF
7HFS , Knot 80 169 0.81 38 119 162 
SMVNSFSGYLKLTDNVYIKNADIVEEAKKVKPTVVVNAANVYLKHGGGVAGALNKATNNAMQVESDDYIATNGPLKVGGSCVLSGHNLAKHCLHVVGPNVNKGEDIQLLKSAYENFNQHEVLLAPLLSAGIFGADPIHSLRVCVDTVRTNVYLAVFDKNLYDKLVSSFL
4DZJ , Knot 69 140 0.81 40 111 133 
MATEPKAGRPSDYMPEVADDICSLLSSGESLLKVCKRPGMPDKSTVFRWLAKHEDFRDEYAKATEARADSIFEEIFEIADNAIPDAAEVAKARLRVDTRKWALARMNPRKYGDKVTNELVGKDGGAIQIETSPMSTLFGK

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 \(c\).

\(|P_{f(8JYY_1)}(2) \setminus P_{f(7HFS_1)}(2)|=101\), \(|P_{f(7HFS_1)}(2) \setminus P_{f(8JYY_1)}(2)|=60\). 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 1:010110000111100000111011010010101110110111010010011000110111101011010000001100100011101110000100001000011001101000010011000010001010111111101011011111011100100000111101101110000000101000001101101101100110001010010001
Pair \(Z_2\) Length of longest common subsequence
8JYY_1,7HFS_1 161 3
8JYY_1,4DZJ_1 163 3
7HFS_1,4DZJ_1 134 4

Newick tree

 
[
	8JYY_1:85.15,
	[
		7HFS_1:67,4DZJ_1:67
	]:18.15
]

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 \((0.85)(0.8)(\frac{385 }{\log_{20} 385}-\frac{169}{\log_{20}169})=64.6\)
Status Protein1 Protein2 d d1/2
Query variables 8JYY_1 7HFS_1 85 73.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]