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Parikh vectors
8JLK_1 2ZJQ_1 3NGP_1 Letter Amino acid
16 0 3 N Asparagine
7 688 0 C Cysteine
22 0 5 E Glutamic acid
16 906 4 G Glycine
20 0 2 S Serine
21 0 5 V Valine
18 0 4 T Threonine
30 737 2 A Alanine
31 0 2 R Arginine
28 0 5 D Aspartic acid
25 0 2 I Isoleucine
22 0 8 K Lycine
7 0 1 M Methionine
18 0 1 F Phenylalanine
16 0 3 Y Tyrosine
19 0 2 Q Glutamine
6 0 0 H Histidine
27 0 9 L Leucine
8 0 2 P Proline
4 0 2 W Tryptophan 

8JLK_1|Chain A|mGs|Homo sapiens (9606)
>2ZJQ_1|Chain A[auth X]|ribosomal 23S RNA|Deinococcus radiodurans (1299)
>3NGP_1|Chain A|Spectrin alpha chain, brain|Gallus gallus (9031)
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 \(w=f(c)\)
8JLK , Knot 157 361 0.85 40 219 345 
MGCTLSAEDKAAVERSKMIEKQLQKDKQVYRATHRLLLLGADNSGKSTIVKQMRIYHVNGYSEEECKQYKAVVYSNTIQSIIAIIRAMGRLKIDFGDSARADDARQLFVLAGAAEEGFMTAELAGVIKRLWKDSGVQACFNRSREYQLNDSAAYYLNDLDRIAQPNYIPTQQDVLRTRVKTSGIFETKFQVDKVNFHMFDVGAQRDERRKWIQCFNDVTAIIFVVDSSDYNRLQEALNDFKSIWNNRWLRTISVILFLNKQDLLAEKVLAGKSKIEDYFPEFARYTTPEDATPEPGEDPRVTRAKYFIRDEFLRISTASGDGRHYCYPHFTCSVDTENARRIFNDCRDIIQRMHLRQYELL
2ZJQ , Knot 483 2880 0.44 8 16 64 
GGUCAAGAUAGUAAGGGUCCACGGUGGAUGCCCUGGCGCUGGAGCCGAUGAAGGACGCGAUUACCUGCGAAAAGCCCCGACGAGCUGGAGAUACGCUUUGACUCGGGGAUGUCCGAAUGGGGAAACCCACCUCGUAAGAGGUAUCCGCAAGGAUGGGAACUCAGGGAACUGAAACAUCUCAGUACCUGAAGGAGAAGAAAGAGAAUUCGAUUCCGUUAGUAGCGGCGAGCGAACCCGGAUCAGCCCAAACCGAAACGCUUGCGUUUCGGGGUUGUAGGACCAGUUUUUAAGAUUCAACCCCUCAAGCCGAAGUGGCUGGAAAGCUACACCUCAGAAGGUGAGAGUCCUGUAGGCGAACGAGCGGUUGACUGUACUGGCACCUGAGUAGGUCGUUGUUCGUGAAACGAUGACUGAAUCCGCGCGGACCACCGCGCAAGGCUAAAUACUCCCAGUGACCGAUAGCGCAUAGUACCGUGAGGGAAAGGUGAAAAGAACCCCGGGAGGGGAGUGAAAGAGAACCUGAAACCGUGGACUUACAAGCAGUCAUGGCACCUUAUGCGUGUUAUGGCGUGCCUAUUGAAGCAUGAGCCGGCGACUUAGACCUGACGUGCGAGCUUAAGUUGAAAAACGGAGGCGGAGCGAAAGCGAGUCCGAAUAGGGCGGCAUUAGUACGUCGGGCUAGACUCGAAACCAGGUGAGCUAAGCAUGACCAGGUUGAAACCCCCGUGACAGGGGGCGGAGGACCGAACCGGUGCCUGCUGAAACAGUCUCGGAUGAGUUGUGUUUAGGAGUGAAAAGCUAACCGAACCUGGAGAUAGCUAGUUCUCCCCGAAAUGUAUUGAGGUACAGCCUCGGAUGUUGACCAUGUCCUGUAGAGCACUCACAAGGCUAGGGGGCCUACCAGCUUACCAAACCUUAUGAAACUCCGAAGGGGCACGCGUUUAGUCCGGGAGUGAGGCUGCGAGAGCUAACUUCCGUAGCCGAGAGGGAAACAACCCAGACCAUCAGCUAAGGUCCCUAAAUGAUCGCUCAGUGGUUAAGGAUGUGUCGUCGCAUAGACAGCCAGGAGGUUGGCUUAGAAGCAGCCACCCUUCAAAGAGUGCGUAAUAGCUCACUGGUCGAGUGACGAUGCGCCGAAAAUGAUCGGGGCUCAAGUGAUCUACCGAAGCUAUGGAUUCAACUCGCGAAGCGAGUUGUCUGGUAGGGGAGCGUUCAGUCCGCGGAGAAGCCAUACCGGAAGGAGUGGUGGAGCCGACUGAAGUGCGGAUGCCGGCAUGAGUAACGAUAAAAGAAGUGAGAAUCUUCUUCGCCGUAAGGACAAGGGUUCCUGGGGAAGGGUCGUCCGCCCAGGGAAAGUCGGGACCUAAGGUGAGGCCGAACGGCGCAGCCGAUGGACAGCAGGUCAAGAUUCCUGCACCGAUCAUGUGGAGUGAUGGAGGGACGCAUUACGCUAUCCAAUGCCAAGCUAUGGCUAUGCUGGUUGGUACGCUCAAGGGCGAUCGGGUCAGAAAAUCUACCGGUCACAUGCCUCAGACGUAUCGGGAGCUUCCUCGGAAGCGAAGUUGGAAACGCGACGGUGCCAAGAAAAGCUUCUAAACGUUGAAACAUGAUUGCCCGUACCGCAAACCGACACAGGUGUCCGAGUGUCAAUGCACUAAGGCGCGCGAGAGAACCCUCGUUAAGGAACUUUGCAAUCUCACCCCGUAACUUCGGAAGAAGGGGUCCCCACGCUUCGCGUGGGGCGCAGUGAAUAGGCCCAGGCGACUGUUUACCAAAAUCACAGCACUCUGCCAACACGAACAGUGGACGUAUAGGGUGUGACGCCUGCCCGGUGCCGGAAGGUCAAGUGGAGCGGUGCAAGCUGCGAAAUGAAGCCCCGGUGAACGGCGGCCGUAACUAUAACGGUCCUAAGGUAGCGAAAUUCCUUGUCGGGUAAGUUCCGACCUGCACGAAAGGCGUAACGAUCUGGGCGCUGUCUCAACGAGGGACUCGGUGAAAUUGAAUUGGCUGUAAAGAUGCGGCCUACCCGUAGCAGGACGAAAAGACCCCGUGGAGCUUUACUAUAGUCUGGCAUUGGGAUUCGGGUUUCUCUGCGUAGGAUAGGUGGGAGCCUGCGAAACUGGCCUUUUGGGGUCGGUGGAGGCAACGGUGAAAUACCACCCUGAGAAACUUGGAUUUCUAACCUGAAAAAUCACUUUCGGGGACCGUGCUUGGCGGGUAGUUUGACUGGGGCGGUCGCCUCCCAAAAUGUAACGGAGGCGCCCAAAGGUCACCUCAAGACGGUUGGAAAUCGUCUGUAGAGCGCAAAGGUAGAAGGUGGCUUGACUGCGAGACUGACACGUCGAGCAGGGAGGAAACUCGGGCUUAGUGAACCGGUGGUACCGUGUGGAAGGGCCAUCGAUCAACGGAUAAAAGUUACCCCGGGGAUAACAGGCUGAUCUCCCCCGAGAGUCCAUAUCGGCGGGGAGGUUUGGCACCUCGAUGUCGGCUCGUCGCAUCCUGGGGCUGAAGAAGGUCCCAAGGGUUGGGCUGUUCGCCCAUUAAAGCGGCACGCGAGCUGGGUUCAGAACGUCGUGAGACAGUUCGGUCUCUAUCCGCUACGGGCGCAGGAGAAUUGAGGGGAGUUGCUCCUAGUACGAGAGGACCGGAGUGAACGGACCGCUGGUCUCCCUGCUGUCGUACCAACGGCACAUGCAGGGUAGCUAUGUCCGGAACGGAUAACCGCUGAAAGCAUCUAAGCGGGAAGCCAGCCCCAAGAUGAGUUCUCCCACUGUUUAUCAGGUAAGACUCCCGGAAGACCACCGGGUUAAGAGGCCAGGCGUGCACGCAUAGCAAUGUGUUCAGCGGACUGGUGCUCAUCAGUCGAGGUCUUGACCACUC
3NGP , Knot 36 62 0.79 36 56 59 
MDETGKELVLVLYDYQEKSPRELTVKKGDILTLLNSTNKDWWKIEVNGRQGFVPAAYLKKLD

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 \(c\).

\(|P_{f(8JLK_1)}(2) \setminus P_{f(2ZJQ_1)}(2)|=214\), \(|P_{f(2ZJQ_1)}(2) \setminus P_{f(8JLK_1)}(2)|=11\). 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 1:1100101000111000011000100000100100011111100010001100101001010000000000111000010011111011101010110010100100111111110011101011111001100011010100000001000110010010011010011000011000100011100010100101011011100000001100100101111110000000100110010011000110010111110000111001111000100011011000010010101100101001001100011010010101000001010001000010011000001100101000011
Pair \(Z_2\) Length of longest common subsequence
8JLK_1,2ZJQ_1 225 4
8JLK_1,3NGP_1 201 3
2ZJQ_1,3NGP_1 70 2

Newick tree

 
[
	8JLK_1:12.50,
	[
		3NGP_1:35,2ZJQ_1:35
	]:86.50
]

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 \((0.85)(0.8)(\frac{3241 }{\log_{20} 3241}-\frac{361}{\log_{20}361})=691.\)
Status Protein1 Protein2 d d1/2
Query variables 8JLK_1 2ZJQ_1 480 315.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]