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Parikh vectors
6XOG_1 7OUO_1 5LMU_1 Letter Amino acid
31 0 0 E Glutamic acid
14 0 0 I Isoleucine
33 0 0 L Leucine
13 0 0 P Proline
16 0 0 T Threonine
8 2 428 C Cysteine
28 0 0 K Lycine
6 0 0 M Methionine
6 0 0 Y Tyrosine
31 0 0 V Valine
17 0 0 R Arginine
25 0 0 D Aspartic acid
2 0 0 W Tryptophan
24 1 311 A Alanine
10 0 0 N Asparagine
13 0 0 Q Glutamine
26 3 545 G Glycine
5 0 0 H Histidine
18 0 0 F Phenylalanine
20 0 0 S Serine

6XOG_1|Chain A|SUMO-activating enzyme subunit 1|Homo sapiens (9606)
>7OUO_1|Chains A[auth AAA], B[auth BBB]|RNA (5'-R(*UP*CP*GP*UP*GP*CP*GP*A)-3')|synthetic construct (32630)
>5LMU_1|Chain A|16S 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 \(w=f(c)\)
6XOG , Knot 148 346 0.83 40 189 327
MVEKEEAGGGISEEEAAQYDRQIRLWGLEAQKRLRASRVLLVGLKGLGAEIAKNLILAGVKGLTMLDHEQVTPEDPGAQFLIRTGSVGRNRAEASLERAQNLNPMVDVKVDTEDIEKKPESFFTQFDAVCLTCCSRDVIVKVDQICHKNSIKFFTGDVFGYHGYTFANLGEHEFVEEKTKVAKVSQGVEDGPDTKRAKLDSSETTMVKKKVVFCPVKEALEVDWSSEKAKAALKRTTSDYFLLQVLLKFRTDKGRDPSSDTYEEDSELLLQIRNDVLDSLGISPDLLPEDFVRYCFSEMAPVCAVVGGILAQEIVKALSQRDPPHNNFFFFDGMKGNGIVECLGPK
7OUO , Knot 5 8 0.43 8 6 6
UCGUGCGA
5LMU , Knot 274 1522 0.44 8 16 63
UUUGUUGGAGAGUUUGAUCCUGGCUCAGGGUGAACGCUGGCGGCGUGCCUAAGACAUGCAAGUCGUGCGGGCCGCGGGGUUUUACUCCGUGGUCAGCGGCGGACGGGUGAGUAACGCGUGGGUGACCUACCCGGAAGAGGGGGACAACCCGGGGAAACUCGGGCUAAUCCCCCAUGUGGACCCGCCCCUUGGGGUGUGUCCAAAGGGCUUUGCCCGCUUCCGGAUGGGCCCGCGUCCCAUCAGCUAGUUGGUGGGGUAAUGGCCCACCAAGGCGACGACGGGUAGCCGGUCUGAGAGGAUGGCCGGCCACAGGGGCACUGAGACACGGGCCCCACUCCUACGGGAGGCAGCAGUUAGGAAUCUUCCGCAAUGGGCGCAAGCCUGACGGAGCGACGCCGCUUGGAGGAAGAAGCCCUUCGGGGUGUAAACUCCUGAACCCGGGACGAAACCCCCGACGAGGGGACUGACGGUACCGGGGUAAUAGCGCCGGCCAACUCCGUGCCAGCAGCCGCGGUAAUACGGAGGGCGCGAGCGUUACCCGGAUUCACUGGGCGUAAAGGGCGUGUAGGCGGCCUGGGGCGUCCCAUGUGAAAGACCACGGCUCAACCGUGGGGGAGCGUGGGAUACGCUCAGGCUAGACGGUGGGAGAGGGUGGUGGAAUUCCCGGAGUAGCGGUGAAAUGCGCAGAUACCGGGAGGAACGCCGAUGGCGAAGGCAGCCACCUGGUCCACCCGUGACGCUGAGGCGCGAAAGCGUGGGGAGCAAACCGGAUUAGAUACCCGGGUAGUCCACGCCCUAAACGAUGCGCGCUAGGUCUCUGGGUCUCCUGGGGGCCGAAGCUAACGCGUUAAGCGCGCCGCCUGGGGAGUACGGCCGCAAGGCUGAAACUCAAAGGAAUUGACGGGGGCCCGCACAAGCGGUGGAGCAUGUGGUUUAAUUCGAAGCAACGCGAAGAACCUUACCAGGCCUUGACAUGCUAGGGAACCCGGGUGAAAGCCUGGGGUGCCCCGCGAGGGGAGCCCUAGCACAGGUGCUGCAUGGCCGUCGUCAGCUCGUGCCGUGAGGUGUUGGGUUAAGUCCCGCAACGAGCGCAACCCCCGCCGUUAGUUGCCAGCGGUUCGGCCGGGCACUCUAACGGGACUGCCCGCGAAAGCGGGAGGAAGGAGGGGACGACGUCUGGUCAGCAUGGCCCUUACGGCCUGGGCGACACACGUGCUACAAUGCCCACUACAAAGCGAUGCCACCCGGCAACGGGGAGCUAAUCGCAAAAAGGUGGGCCCAGUUCGGAUUGGGGUCUGCAACCCGACCCCAUGAAGCCGGAAUCGCUAGUAAUCGCGGAUCAGCCAUGCCGCGGUGAAUACGUUCCCGGGCCUUGUACACACCGCCCGUCACGCCAUGGGAGCGGGCUCUACCCGAAGUCGCCGGGAGCCUACGGGCAGGCGCCGAGGGUAGGGCCCGUGACUGGGGCGAAGUCGUAACAAGGUAGCUGUACCGGAAGGUGCGGCUGGAUCACCUCCUUUCU

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 \(c\).

\(|P_{f(6XOG_1)}(2) \setminus P_{f(7OUO_1)}(2)|=188\), \(|P_{f(7OUO_1)}(2) \setminus P_{f(6XOG_1)}(2)|=5\). 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 1:1100001111100001100000101111010001010011111101111011001111110110110000101001110111001011000101010010010111010100001000100110010110100000011101001000001011010111001001101100011000001101001100110000101000000110001110110011010100001011100000001110111010000100100000000001110100011001110101110011000100111101111111100110110000110001111011010111001110
Pair \(Z_2\) Length of longest common subsequence
6XOG_1,7OUO_1 193 2
6XOG_1,5LMU_1 193 4
7OUO_1,5LMU_1 10 7

Newick tree

 
[
	6XOG_1:11.39,
	[
		7OUO_1:5,5LMU_1:5
	]:10.39
]

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 \((0.85)(0.8)(\frac{354 }{\log_{20} 354}-\frac{8}{\log_{20}8})=115.\)
Status Protein1 Protein2 d d1/2
Query variables 6XOG_1 7OUO_1 147 75
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]