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Parikh vectors
6DPP_1 9HUA_1 3PFW_1 Letter Amino acid
3 16 9 Q Glutamine
16 17 16 E Glutamic acid
10 32 19 L Leucine
14 15 18 K Lycine
5 17 16 Y Tyrosine
6 27 15 N Asparagine
10 21 26 G Glycine
2 17 8 H Histidine
7 23 25 S Serine
6 8 3 W Tryptophan
6 10 17 R Arginine
7 21 19 D Aspartic acid
0 0 5 C Cysteine
10 14 18 T Threonine
9 24 38 V Valine
6 24 34 A Alanine
11 28 19 I Isoleucine
1 8 11 M Methionine
2 17 12 F Phenylalanine
5 15 18 P Proline 

6DPP_1|Chain A|Ribonuclease H|Bacillus halodurans (strain ATCC BAA-125 / DSM 18197 / FERM 7344 / JCM 9153 / C-125) (272558)
>9HUA_1|Chains A, B, C, D|Glucosyltransferase 3|Limosilactobacillus reuteri (1598)
>3PFW_1|Chains A[auth O], B[auth P]|Glyceraldehyde-3-phosphate dehydrogenase, testis-specific|Homo sapiens (9606)
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 \(w=f(c)\)
6DPP , Knot 65 136 0.78 38 108 134 
EEIIWESLSVDVGSQGNPGIVEYKGVDTKTGEVLFEREPIPIGTNNMGEFLAIVHGLRYLKERNSRKPIYSDSQTAIKWVKDKKAKSTLVRNEETALIWKLVDEAEEWLNTHTYETPILKWQTDKWGEIKADYGRK
9HUA , Knot 150 354 0.83 38 217 335 
MGSSHHHHHHSSGLVPRGSHLTVHITNLYGQSFQSTAQIAQNQIAKIGRELGFNELGIYSYNWPDEPSVALDTRFDGIIASVSNNDTVIFQSPTWNSIEWDQAFIDHLAPYNVKKIIFIHDIIPLMFESNRYLLPQFIDYYNKADLIIAPSQPMVDFLRANGLTVEKVVLQHMWDHYASVDFTVTPQNTGVINLAGNLEKFQLVGHWHYPNNPLYAFAKVIDIEPTDNIKFMGWQSDPVLLSKLRHNGGFGLVWSNESYWKNYMHLNANHKLSTYLAAGLPVIVNENIAESETILRKGLGIVADNLDEAIEKVQGMDDQSYNEMVQRVDDFARLIREGYFAKKALTEAVFNLYY
3PFW , Knot 148 346 0.83 40 210 332 
MVSVARELTVGINGFGRIGRLVLRACMEKGVKVVAVNDPFIDPEYMVYMFKYDSTHGRYKGSVEFRNGQLVVDNHEISVYQCKEPKQIPWRAVGSPYVVESTGVYLSIQAASDHISAGAQRVVISAPSPDAPMFVMGVNENDYNPGSMNIVSNASCTTNCLAPLAKVIHERFGIVEGLMTTVHSYTATQKTVDGPSRKAWRDGRGAHQNIIPASTGAAKAVTKVIPELKGKLTGMAFRVPTPDVSVVDLTCRLAQPAPYSAIKEAVKAAAKGPMAGILAYTEDEVVSTDFLGDTHSSIFDAKAGIALNDNFVKLISWYDNEYGYSHRVVDLLRYMFSRDAENLYFQ

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 \(c\).

\(|P_{f(6DPP_1)}(2) \setminus P_{f(9HUA_1)}(2)|=39\), \(|P_{f(9HUA_1)}(2) \setminus P_{f(6DPP_1)}(2)|=148\). 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 1:0011100101011001011110001100001011100011111000110111110110010000000110000001101100001000110000011110110010011000000011101000011010100100
Pair \(Z_2\) Length of longest common subsequence
6DPP_1,9HUA_1 187 3
6DPP_1,3PFW_1 176 4
9HUA_1,3PFW_1 155 4

Newick tree

 
[
	6DPP_1:94.80,
	[
		3PFW_1:77.5,9HUA_1:77.5
	]:17.30
]

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 \((0.85)(0.8)(\frac{490 }{\log_{20} 490}-\frac{136}{\log_{20}136})=104.\)
Status Protein1 Protein2 d d1/2
Query variables 6DPP_1 9HUA_1 133 90
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]