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Parikh vectors
2NTX_1 9BUP_1 2DMA_1 Letter Amino acid
11 7 4 F Phenylalanine
14 2 0 P Proline
7 4 2 Y Tyrosine
21 12 20 R Arginine
18 11 9 G Glycine
4 1 0 H Histidine
27 27 17 K Lycine
33 4 9 S Serine
18 8 8 T Threonine
21 10 11 V Valine
25 3 5 D Aspartic acid
27 8 37 E Glutamic acid
41 12 15 L Leucine
24 7 18 A Alanine
19 5 23 I Isoleucine
14 3 5 M Methionine
8 0 1 W Tryptophan
11 7 8 N Asparagine
1 0 0 C Cysteine
21 2 6 Q Glutamine 

2NTX_1|Chains A, B|Emb|CAB41934.1|Arabidopsis thaliana (3702)
>9BUP_1|Chain A[auth S1]|40S ribosomal protein S24|Plasmodium falciparum 3D7 (36329)
>2DMA_1|Chain A|V-type ATP synthase subunit E|Pyrococcus horikoshii (70601)
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 \(w=f(c)\)
2NTX , Knot 158 365 0.85 40 210 349 
GKRSERQQADMEMMKDRFAKLLLGEDMSGGGKGVSSALALSNAITNLAASIFGEQTKLQPMPQDRQARWKKEIDWLLSVTDHIVEFVPSQQTSKDGVCTEIMVTRQRGDLLMNIPALRKLDAMLIDTLDNFRGHNEFWYVSRDSEEGQQARNDRTNDKWWLPPVKVPPGGLSEPSRRMLYFQKDSVTQVQKAAMAINAQVLSEMEIPESYIDSLPKNGRASLGDSIYKSITEEWFDPEQFLAMLDMSTEHKVLDLKNRIEASVVIWKRKLHTKDTKSSWGSAVSLEKRELFEERAETILVLLKQKFPGLPQSSLDISKIQFNKDVGQAVLESYSRILESLAYTVMSRIEDVLYTDTLALKQTLLA
9BUP , Knot 63 133 0.77 36 94 125 
MTDQFTIRVKKYMSNPLLRRKQFALEILHPNKGSVAKKEVKERLAKMYKLNNVNTIVLFGFKTLFGGGRTKGFGLIYKNVDAVKKFEKKYRLVREGLIDKETKAGRRASKELKNRRKKVRGTEKTKVSGAKKK
2DMA , Knot 84 198 0.74 34 111 184 
MNGAELIIQEINKEAERKIEYILNEARQQAEKIKEEARRNAEAKAEWIIRRAKTQAELEKQRIIANARLEVRRKRLAIQEEIISSVLEEVKRRLETMSEDEYFESVKALLKEAIKELNEKKVRVMSNEKTLGLIASRIEEIKSELGDVSIELGETVDTMGGVIVETEDGRIRIDNTFEARMERFEGEIRSTIAKVLFG

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 \(c\).

\(|P_{f(2NTX_1)}(2) \setminus P_{f(9BUP_1)}(2)|=146\), \(|P_{f(9BUP_1)}(2) \setminus P_{f(2NTX_1)}(2)|=30\). 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 1:10000000101011000110111100101110110011110011001110111000010111000010100010111010001101110000000110001110000101110111100101111001001010001101000000100100000000111111011111100100011010000100100111110101100101100010011001010110010001000110100111110100000110100010101111000100000000110110100001100010011111000111110001010010100011011100000110011001100100110000111000111
Pair \(Z_2\) Length of longest common subsequence
2NTX_1,9BUP_1 176 4
2NTX_1,2DMA_1 141 4
9BUP_1,2DMA_1 103 4

Newick tree

 
[
	2NTX_1:87.13,
	[
		2DMA_1:51.5,9BUP_1:51.5
	]:35.63
]

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 \((0.85)(0.8)(\frac{498 }{\log_{20} 498}-\frac{133}{\log_{20}133})=107.\)
Status Protein1 Protein2 d d1/2
Query variables 2NTX_1 9BUP_1 142 94
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]