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Parikh vectors
1URQ_1 7OGB_1 7RQE_1 Letter Amino acid
3 15 0 V Valine
4 11 0 R Arginine
1 11 0 Q Glutamine
6 11 0 L Leucine
1 5 0 F Phenylalanine
1 11 0 T Threonine
0 3 795 C Cysteine
5 8 0 K Lycine
4 4 0 M Methionine
7 8 0 S Serine
0 4 0 N Asparagine
6 13 0 E Glutamic acid
8 11 1065 G Glycine
1 11 0 I Isoleucine
1 9 0 Y Tyrosine
9 11 636 A Alanine
3 14 0 D Aspartic acid
3 3 0 H Histidine
0 3 0 P Proline
0 0 0 W Tryptophan 

1URQ_1|Chain A|M-TOMOSYN ISOFORM|RATTUS NORVEGICUS (10116)
>7OGB_1|Chain A|GTPase HRas|Homo sapiens (9606)
>7RQE_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 \(w=f(c)\)
1URQ , Knot 34 63 0.74 32 56 61 
GSHGGIEGVKGAASGVVGELARARLALDERGQKLSDLEERTAAMMSSADSFSKHAHEMMLKYK
7OGB , Knot 79 166 0.81 38 130 163 
MTEYKLVVVGAGGVGKSALTIQLIQNHFVDEYDPTIEDSYRKQVVIDGETCLLDILDTAGQEEYSAMRDQYMRTGEGFLCVFAINNTKSFEDIHQYREQIKRVKDSDDVPMVLVGNKCDLAARTVESRQAQDLARSYGIPYIETSAKTRQGVEDAFYTLVREIRQH
7RQE , 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 \(c\).

\(|P_{f(1URQ_1)}(2) \setminus P_{f(7OGB_1)}(2)|=28\), \(|P_{f(7OGB_1)}(2) \setminus P_{f(1URQ_1)}(2)|=102\). 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 1:100111011011101111011010111000100100100001111001001000100111000
Pair \(Z_2\) Length of longest common subsequence
1URQ_1,7OGB_1 130 3
1URQ_1,7RQE_1 66 3
7OGB_1,7RQE_1 138 4

Newick tree

 
[
	7OGB_1:75.01,
	[
		1URQ_1:33,7RQE_1:33
	]:42.01
]

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 \((0.85)(0.8)(\frac{229 }{\log_{20} 229}-\frac{63}{\log_{20}63})=54.8\)
Status Protein1 Protein2 d d1/2
Query variables 1URQ_1 7OGB_1 69 47
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

Graphviz Engine:
Graphviz Engine: