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Parikh vectors
9KMJ_1 9NDI_1 2CWB_1 Letter Amino acid
43 0 2 S Serine
33 0 3 Y Tyrosine
18 0 2 M Methionine
44 0 3 F Phenylalanine
51 4 10 G Glycine
32 1 11 T Threonine
20 0 2 W Tryptophan
50 0 4 V Valine
34 4 13 A Alanine
19 4 0 C Cysteine
13 0 10 Q Glutamine
6 0 6 H Histidine
69 0 10 L Leucine
27 0 6 K Lycine
35 0 2 P Proline
17 0 3 N Asparagine
18 0 9 D Aspartic acid
44 0 3 I Isoleucine
21 0 2 R Arginine
26 0 7 E Glutamic acid 

9KMJ_1|Chain A|Sodium- and chloride-dependent taurine transporter|Homo sapiens (9606)
>9NDI_1|Chain A|DNA (5'-D(P*AP*CP*GP*GP*AP*CP*AP*GP*CP*GP*TP*CP*A)-3')|synthetic construct (32630)
>2CWB_1|Chain A|Immunoglobulin G-binding protein G,Ubiquitin-like protein 7|Streptococcus sp. group G (1320)
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 \(w=f(c)\)
9KMJ , Knot 244 620 0.84 40 276 577 
MATKEKLQCLKDFHKDILKPSPGKSPGTRPEDEAEGKPPQREKWSSKIDFVLSVAGGFVGLGNVWRFPYLCYKNGGGAFLIPYFIFLFGSGLPVFFLEIIIGQYTSEGGITCWEKICPLFSGIGYASVVIVSLLNVYYIVILAWATYYLFQSFQKELPWAHCNHSWNTPHCMEDTMRKNKSVWITISSTNFTSPVIEFWERNVLSLSPGIDHPGSLKWDLALCLLLVWLVCFFCIWKGVRSTGKVVYFTATFPFAMLLVLLVRGLTLPGAGAGIKFYLYPDITRLEDPQVWIDAGTQIFFSYAICLGAMTSLGSYNKYKYNSYRDCMLLGCLNSGTSFVSGFAIFSILGFMAQEQGVDIADVAESGPGLAFIAYPKAVTMMPLPTFWSILFFIMLLLLGLDSQFVEVEGQITSLVDLYPSFLRKGYRREIFIAFVCSISYLLGLTMVTEGGMYVFQLFDYYAASGVCLLWVAFFECFVIAWIYGVNRFSEDIRDMIGYRPGPWMKYSWAVITPVLCVGCFIFSLVKYVPLTYNKTYVYPNWAIGLGWSLALSSMLCVPLVIVIRLCQTEGPFLVRVKYLLTPREPNRWAVEREGATPYNSRTVMNGALVKPTHIIVETMM
9NDI , Knot 8 13 0.52 8 9 11 
ACGGACAGCGTCA
2CWB , Knot 53 108 0.76 38 82 103 
MHHHHHHQYKLALNGKTLKGETTTEAVDAATAEKVFKQYANDNGVDGEWTYDDATKTFTVTEGSQWQPQLQQLRDMGIQDDELSLRALQATGGDIQAALELIFAGGAP

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 \(c\).

\(|P_{f(9KMJ_1)}(2) \setminus P_{f(9NDI_1)}(2)|=270\), \(|P_{f(9NDI_1)}(2) \setminus P_{f(9KMJ_1)}(2)|=3\). 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 1:11000010010010001101011001100100010101100001000101110111111111011011010000111111110111111011111110111100000111001001011101110101111011010011111110001100100011110000010010010001000001110100001001110110001101011100110101011101111111011011011000101101010111111111110110111111110101010100100101110110011100110111100110000000000000111101001001101111101111110001101101100111111110101101111101101111111111110001101010100110101011001000011111100100111101100111011011000110110111111100111111011001000100111001111100011110111011011101100111000000101011111110111001101111111010000111110100110100100111000110100000110111101001110011
Pair \(Z_2\) Length of longest common subsequence
9KMJ_1,9NDI_1 273 3
9KMJ_1,2CWB_1 246 4
9NDI_1,2CWB_1 85 3

Newick tree

 
[
	9KMJ_1:14.00,
	[
		2CWB_1:42.5,9NDI_1:42.5
	]:10.50
]

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 \((0.85)(0.8)(\frac{633 }{\log_{20} 633}-\frac{13}{\log_{20}13})=189.\)
Status Protein1 Protein2 d d1/2
Query variables 9KMJ_1 9NDI_1 240 122.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]