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Parikh vectors
6KTV_1 8SAB_1 8ECC_1 Letter Amino acid
24 22 15 T Threonine
13 6 5 W Tryptophan
24 21 20 R Arginine
18 19 22 F Phenylalanine
24 14 43 K Lycine
10 11 5 M Methionine
26 12 16 P Proline
23 8 11 Y Tyrosine
5 6 8 C Cysteine
39 31 17 G Glycine
29 21 16 D Aspartic acid
41 21 38 E Glutamic acid
29 23 21 I Isoleucine
35 52 12 A Alanine
22 15 14 N Asparagine
26 40 40 L Leucine
25 23 25 S Serine
24 26 18 V Valine
7 13 11 Q Glutamine
16 19 7 H Histidine 

6KTV_1|Chain A|Sulfurtransferase|Chlorobium limicola (1092)
>8SAB_1|Chains A, B|Cystathionine beta-lyase|Klebsiella aerogenes KCTC 2190 (1028307)
>8ECC_1|Chains A, B[auth C]|Cyclic GMP-AMP synthase|Mus musculus (10090)
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 \(w=f(c)\)
6KTV , Knot 188 460 0.83 40 243 421 
GSEFQNKNFRAPQSEAIGILYKLIETGSKHKNMYDHTEITTDSLLALLGSEKVKIIDVRSADAYNGWRMRGEVRGGHIKGAKSLPAKWLTDPEWLNIVRFKQIRPEDAIVLYGYTPEECEQTATRFKENGYNNVSVFHRFHPDWTGNDAFPMDRLEQYNRLVPAEWVNGLISGEEIPEYDNDTFIVCHAHYRNRDAYLSGHIPGATDMDTLALESPETWNRRTPEELKKALEEHGITASTTVVLYGKFMHPDNADEFPGSAAGHIGAIRLAFIMMYAGVEDVRVLNGGYQSWTDAGFAISKDDVPKTTVPEFGAPIPSRPEFAVDIDEAKEMLQSEDSDLVCVRSYPEYIGEVSGYNYIKKKGRIPGAIFAECGSDAYHMENYRNHDHTTREYHEIEDIWAKSGIIPKKHLAFYCGTGWRGSEAWFNALLMGWPRVSVYDGGWFEWSNDPENPYETGVPK
8SAB , Knot 168 403 0.83 40 220 375 
MAHHHHHHMADKHLDTALVNAGRRKKYTQGSVNSVIQRASSLVFDTVEAKKHATRNRAKGELFYGRRGTLTHFSLQEAMCELEGGAGCALFPCGAAAVANTILAFVEQGDHVLMTNTAYEPSQDFCTKILAKLGVTTGWFDPLIGADIANLIQPNTKVVFLESPGSITMEVHDVPAIVAAVRRVAPEAIIMIDNTWAAGVLFKALDFGIDISIQAATKYLIGHSDGMIGTAVANARCWEQLCENAYLMGQMIDADTAYMTSRGLRTLGVRLRQHHESSLRVAEWLAQHPQVARVNHPALPGSKGHEFWKRDFSGSSGLFSFVLNKRLTDAELAAYLDNFSLFSMAYSWGGFESLILANQPEHIAAIRPEAEVDFSGTLIRLHIGLENVDDLLADLAAGFARIV
8ECC , Knot 156 364 0.84 40 198 344 
GTGPDKLKKVLDKLRLKRKDISEAAETVNKVVERLLRRMQKRESEFKGVEQLNTGSYYEHVKISAPNEFDVMFKLEVPRIELQEYYETGAFYLVKFKRIPRGNPLSHFLEGEVLSATKMLSKFRKIIKEEVKEIKDIDVSVEKEKPGSPAVTLLIRNPEEISVDIILALESKGSWPISTKEGLPIQGWLGTKVRTNLRREPFYLVPKNAKDGNSFQGETWRLSFSHTEKYILNNHGIEKTCCESSGAKCCRKECLKLMKYLLEQLKKEFQELDAFCSYHVKTAIFHMWTQDPQDSQWDPRNLSSCFDKLLAFFLECLRTEKLDHYFIPKFNLFSQELIDRKSKEFLSKKIEYERNNGFPIFDKL

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 \(c\).

\(|P_{f(6KTV_1)}(2) \setminus P_{f(8SAB_1)}(2)|=102\), \(|P_{f(8SAB_1)}(2) \setminus P_{f(6KTV_1)}(2)|=79\). 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 1:1001000010110001111100110010000010000010000111111000101101001010011010101011010110011101100101101101001010011110100100000010010001000101100101010100111100100000111101101110100110000001110010000001010101111001001110010010000100100110001101000111010110100100111011101111011111101110010110110001001111100001100011011111100101110100100110000001101000100110101000100010111111100100100100000000000000010011100111100011100101101001110111111101010011110100010010001110
Pair \(Z_2\) Length of longest common subsequence
6KTV_1,8SAB_1 181 4
6KTV_1,8ECC_1 161 5
8SAB_1,8ECC_1 176 3

Newick tree

 
[
	8SAB_1:91.99,
	[
		6KTV_1:80.5,8ECC_1:80.5
	]:11.49
]

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 \((0.85)(0.8)(\frac{863 }{\log_{20} 863}-\frac{403}{\log_{20}403})=123.\)
Status Protein1 Protein2 d d1/2
Query variables 6KTV_1 8SAB_1 154 145
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]