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Parikh vectors
7JXQ_1 1QDP_1 8UVS_1 Letter Amino acid
13 2 0 Y Tyrosine
20 2 636 A Alanine
25 2 0 I Isoleucine
33 1 0 L Leucine
13 3 0 T Threonine
17 1 0 R Arginine
8 3 0 N Asparagine
26 1 0 E Glutamic acid
6 2 0 W Tryptophan
18 1 0 P Proline
22 0 0 V Valine
21 1 0 D Aspartic acid
23 6 0 K Lycine
13 1 0 M Methionine
8 1 0 F Phenylalanine
18 1 0 S Serine
6 8 795 C Cysteine
12 3 0 Q Glutamine
21 3 1065 G Glycine
8 0 0 H Histidine 

7JXQ_1|Chains A, B, C, D|Epidermal growth factor receptor|Homo sapiens (9606)
>1QDP_1|Chain A|ROBUSTOXIN|Atrax robustus (6903)
>8UVS_1|Chains A[auth 1A], EB[auth 2A]|23S Ribosomal RNA|Thermus thermophilus HB8 (300852)
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 \(w=f(c)\)
7JXQ , Knot 148 331 0.86 40 211 325 
GSTSGEAPNQALLRILKETEFKKIKVLGSGAFGTVYKGLWIPEGEKVKIPVAIKELREATSPKANKEILDEAYVMASVDNPHVCRLLGICLTSTVQLIMQLMPFGCLLDYVREHKDNIGSQYLLNWCVQIAKGMNYLEDRRLVHRDLAARNVLVKTPQHVKITDFGLAKLLGAEEKEYHAEGGKVPIKWMALESILHRIYTHQSDVWSYGVTVWELMTFGSKPYDGIPASEISSILEKGERLPQPPICTIDVYMIMRKCWMIDADSRPKFRELIIEFSKMARDPQRYLVIQGDERMHLPSPTDSNFYRALMDEEDMDDVVDADEYLIPQQG
1QDP , Knot 28 42 0.83 36 38 40 
CAKKRNWCGKNEDCCCPMKCIYAWYNQQGSCQTTITGLFKKC
8UVS , Knot 480 2915 0.43 8 16 64 
GUCAAGAUGGUAAGGGCCCACGGUGGAUGCCUCGGCACCCGAGCCGAUGAAGGACGUGGCUACCUGCGAUAAGCCAGGGGGAGCCGGUAGCGGGCGUGGAUCCCUGGAUGUCCGAAUGGGGGAACCCGGCCGGCGGGAACGCCGGUCACCGCGCUUUUGCGCGGGGGGAACCUGGGGAACUGAAACAUCUCAGUACCCAGAGGAGAGGAAAGAGAAAUCGACUCCCUGAGUAGCGGCGAGCGAAAGGGGACCAGCCUAAACCGUCCGGCUUGUCCGGGCGGGGUCGUGGGGCCCUCGGACACCGAAUCCCCAGCCUAGCCGAAGCUGUUGGGAAGCAGCGCCAGAGAGGGUGAAAGCCCCGUAGGCGAAAGGUGGGGGGAUAGGUGAGGGUACCCGAGUACCCCGUGGUUCGUGGAGCCAUGGGGGAAUCUGGGCGGACCACCGCCUAAGGCUAAGUACUCCGGGUGACCGAUAGCGCACCAGUACCGUGAGGGAAAGGUGAAAAGAACCCCGGGAGGGGAGUGAAAUAGAGCCUGAAACCGUGGGCUUACAAGCAGUCACGGCCCCGCAAGGGGUUGUGGCGUGCCUAUUGAAGCAUGAGCCGGCGACUCACGGUCGUGGGCGAGCUUAAGCCGUUGAGGCGGAGGCGUAGGGAAACCGAGUCCGAACAGGGCGCAAGCGGGCCGCACGCGGCCCGCAAAGUCCGCGGCCGUGGACCCGAAACCGGGCGAGCUAGCCCUGGCCAGGGUGAAGCUGGGGUGAGACCCAGUGGAGGCCCGAACCGGUGGGGGAUGCAAACCCCUCGGAUGAGCUGGGGCUAGGAGUGAAAAGCUAACCGAGCCCGGAGAUAGCUGGUUCUCCCCGAAAUGACUUUAGGGUCAGCCUCAGGCGCUGACUGGGGCCUGUAGAGCACUGAUAGGGCUAGGGGGCCCACCAGCCUACCAAACCCUGUCAAACUCCGAAGGGUCCCAGGUGGAGCCUGGGAGUGAGGGCGCGAGCGAUAACGUCCGCGUCCGAGCGCGGGAACAACCGAGACCGCCAGCUAAGGCCCCCAAGUCUGGGCUAAGUGGUAAAGGAUGUGGCGCCGCGAAGACAGCCAGGAGGUUGGCUUAGAAGCAGCCAUCCUUUAAAGAGUGCGUAAUAGCUCACUGGUCGAGUGGCGCCGCGCCGAAAAUGAUCGGGGCUUAAGCCCAGCGCCGAAGCUGCGGGUCUGGGGGAUGACCCCAGGCGGUAGGGGAGCGUUCCCGAUGCCGAUGAAGGCCGACCCGCGAGGGCGGCUGGAGGUAAGGGAAGUGCGAAUGCCGGCAUGAGUAACGAUAAAGAGGGUGAGAAUCCCUCUCGCCGUAAGCCCAAGGGUUCCUACGCAAUGGUCGUCAGCGUAGGGUUAGGCGGGACCUAAGGUGAAGCCGAAAGGCGUAGCCGAAGGGCAGCCGGUUAAUAUUCCGGCCCUUCCCGCAGGUGCGAUGGGGGGACGCUCUAGGCUAGGGGGACCGGAGCCAUGGACGAGCCCGGCCAGAAGCGCAGGGUGGGAGGUAGGCAAAUCCGCCUCCCAACAAGCUCUGCGUGGUGGGGAAGCCCGUACGGGUGACAACCCCCCGAAGCCAGGGAGCCAAGAAAAGCCUCUAAGCACAACCUGCGGGAACCCGUACCGCAAACCGACACAGGUGGGCGGGUGCAAGAGCACUCAGGCGCGCGGGAGAACCCUCGCCAAGGAACUCUGCAAGUUGGCCCCGUAACUUCGGGAGAAGGGGUGCUCCCUGGGGUGAUGAGCCCCGGGGAGCCGCAGUGAACAGGCUCUGGCGACUGUUUACCAAAAACACAGCUCUCUGCGAACUCGUAAGAGGAGGUAUAGGGAGCGACGCUUGCCCGGUGCCGGAAGGUCAAGGGGAGGGGUGCAAGCCCCGAACCGAAGCCCCGGUGAACGGCGGCCGUAACUAUAACGGUCCUAAGGUAGCGAAAUUCCUUGUCGGGUAAGUUCCGACCUGCACGAAAAGCGUAACGACCGGAGCGCUGUCUCGGCGAGGGACCCGGUGAAAUUGAACUGGCCGUGAAGAUGCGGCCUACCCGUGGCAGGACGAAAAGACCCCGUGGAGCUUUACUGCAGCCUGGUGUUGGCUCUUGGUCGCGCCUGCGUAGGAUAGGUGGGAGCCUGUGAACCCCCGCCUCCGGGUGGGGGGGAGGCGCCGGUGAAAUACCACCCUGGCGCGGCUGGGGGCCUAACCCUCGGAUGGGGGGACAGCGCUUGGCGGGCAGUUUGACUGGGGCGGUCGCCUCCUAAAAGGUAACGGAGGCGCCCAAAGGUCCCCUCAGGCGGGACGGAAAUCCGCCGGAGAGCGCAAGGGUAGAAGGGGGCCUGACUGCGAGGCCUGCAAGCCGAGCAGGGGCGAAAGCCGGGCCUAGUGAACCGGUGGUCCCGUGUGGAAGGGCCAUCGAUCAACGGAUAAAAGUUACCCCGGGGAUAACAGGCUGAUCUCCCCCGAGCGUCCACAGCGGCGGGGAGGUUUGGCACCUCGAUGUCGGCUCGUCGCAUCCUGGGGCUGAAGAAGGUCCCAAGGGUUGGGCUGUUCGCCCAUUAAAGCGGCACGCGAGCUGGGUUCAGAACGUCGUGAGACAGUUCGGUCUCUAUCCGCCACGGGCGCAGGAGGCUUGAGGGGGGCUCUUCCUAGUACGAGAGGACCGGAAGGGACGCACCUCUGGUUUCCCAGCUGUCCCUCCAGGGGCAUAAGCUGGGUAGCCAUGUGCGGAAGGGAUAACCGCUGAAAGCAUCUAAGCGGGAAGCCCGCCCCAAGAUGAGGCCUCCCACGGCGUCAAGCCGGUAAGGACCCGGGAAGACCACCCGGUGGAUGGGCCGGGGGUGUAAGCGCCGCGAGGCGUUGAGCCGACCGGUCCCAAUCGUCCGAGGUCUUGACCCCUCC

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 \(c\).

\(|P_{f(7JXQ_1)}(2) \setminus P_{f(1QDP_1)}(2)|=194\), \(|P_{f(1QDP_1)}(2) \setminus P_{f(7JXQ_1)}(2)|=21\). 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 1:1000101100111011000010010111011110100111110100101111100100100101000110010111010010100111101000101110111110110010000001100011010101101100100001100011100111001001010011110111100000010110111011110011001000000110011011011011001001111001001100100110111001010111000111010001010011101001100100011101000101101000010011100001001101000111001
Pair \(Z_2\) Length of longest common subsequence
7JXQ_1,1QDP_1 215 3
7JXQ_1,8UVS_1 219 2
1QDP_1,8UVS_1 48 3

Newick tree

 
[
	7JXQ_1:12.52,
	[
		1QDP_1:24,8UVS_1:24
	]:10.52
]

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 \((0.85)(0.8)(\frac{373 }{\log_{20} 373}-\frac{42}{\log_{20}42})=105.\)
Status Protein1 Protein2 d d1/2
Query variables 7JXQ_1 1QDP_1 137 76
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]