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Parikh vectors
7JYB_1 4RNY_1 6JLU_1 Letter Amino acid
46 20 2 A Alanine
28 18 1 R Arginine
37 25 2 G Glycine
39 41 7 L Leucine
14 18 4 F Phenylalanine
10 16 4 N Asparagine
22 13 0 D Aspartic acid
27 17 1 E Glutamic acid
17 22 1 I Isoleucine
23 14 2 P Proline
1 0 0 C Cysteine
11 17 1 Q Glutamine
18 20 0 H Histidine
14 34 1 K Lycine
6 1 1 W Tryptophan
6 6 1 M Methionine
26 29 3 S Serine
16 16 2 T Threonine
13 23 2 Y Tyrosine
30 21 3 V Valine 

7JYB_1|Chains A, B, C, D, E, F, G, H|Alkanesulfonate monooxygenase|Pseudomonas fluorescens (205922)
>4RNY_1|Chains A, B|Conserved hypothetical secreted protein|Helicobacter pylori (85962)
>6JLU_12|Chains KA[auth L], L[auth l]|PsbL|Chaetoceros gracilis (240364)
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 \(w=f(c)\)
7JYB , Knot 167 404 0.82 40 218 383 
MGSSHHHHHHSSGLVPRGSHMASMDVFWFLPTHGDGHYLGTTQGARPVTLNYLKQVAQAADSLGYHGVLIPTGRSCEDSWVIASALVPLTERLRYLVAIRPGIISPTVSARMAATLDRLSNGRLLINVVTGGDPDENRGDGSFLSHSERYEVTDEFLKIWRRVLQGEAVDFEGKHLKVQNAKALYPPVQKPYPPLYFGGSSDAAHDLAAEQVDVYLTWGEPPAAVAEKLADVRERAARHGRKVKFGIRLHVIVRETAEEAWKAADKLIEHISDETIEAAQKSFSRFDSEGQRRMAALHDGRRDNLEIAPNLWAGVGLVRGGSGTALVGDPQQVAARIKEYADLGIESFIFSGYPHLEEAYRFAELVFPLLPEPYASLAGRGVTNLTGPFGEMIANDVLPAKANA
4RNY , Knot 157 371 0.83 38 209 343 
MERLVWDKLTLLGFLEKNHIPQKLYYNLSSQDKELSAEIQSNVTYYTLRDANNTLIQALIPISQDLQIHIYKKGEDYFLDFIPIIFTRKEKTLLLSLQTSPYQDIIKATNDPLLANQLMNAYKKSVPFKRLVKNDKIAIVYTRDYRVGQAFGQPTIKMAMVSSRSNQYYLFSHSNGHYYDSKAQEVAGFLLETPVKYTRISSPFSYGRFHPVLKVRRPHYGVDYAAKHGSLIHSASDGRVGFMGVKAGYGKVVEIHLNELRLVYAHMSAFANGLKKGSFVKKGQIIGRVGSTGLSTGPHLHFGVYKNSRPINPLGYIRTAKSKLHGKQREVFLEKAQRSKQKLEELLKTHSFEKNSFYLLEGFLEHHHHHH
6JLU , Knot 24 38 0.76 34 33 36 
MTGPNPNKQAVELNRTSLYWGLLLIFVLAVLFSSYFFN

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 \(c\).

\(|P_{f(7JYB_1)}(2) \setminus P_{f(4RNY_1)}(2)|=76\), \(|P_{f(4RNY_1)}(2) \setminus P_{f(7JYB_1)}(2)|=67\). 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 1:11000000000011110100110101111110010100110001101101001001101100110011111010000001111011111000100111101111010101011101001001011101101101000010101100000001000110110011010110101001010010110111001011101110001100111001010101101111110011010001100100101110101110001001101100110010000101100010010001000111100100001011101111111101101011110100111010001011100111010101001001101111111010101110110010111101110011110101
Pair \(Z_2\) Length of longest common subsequence
7JYB_1,4RNY_1 143 6
7JYB_1,6JLU_1 209 3
4RNY_1,6JLU_1 194 3

Newick tree

 
[
	6JLU_1:10.85,
	[
		7JYB_1:71.5,4RNY_1:71.5
	]:37.35
]

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 \((0.85)(0.8)(\frac{775 }{\log_{20} 775}-\frac{371}{\log_{20}371})=109.\)
Status Protein1 Protein2 d d1/2
Query variables 7JYB_1 4RNY_1 137 131
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]