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Parikh vectors
5LSQ_1 8ZNZ_1 6JCE_1 Letter Amino acid
10 19 0 Y Tyrosine
17 45 0 V Valine
19 21 0 R Arginine
18 32 0 D Aspartic acid
14 16 0 Q Glutamine
17 13 0 H Histidine
20 21 0 F Phenylalanine
30 24 12 T Threonine
23 27 0 A Alanine
13 31 0 N Asparagine
9 11 0 M Methionine
23 24 0 P Proline
19 34 0 S Serine
7 5 0 W Tryptophan
7 8 0 C Cysteine
25 29 0 E Glutamic acid
29 49 0 L Leucine
19 35 0 K Lycine
27 46 17 G Glycine
13 34 0 I Isoleucine 

5LSQ_1|Chain A|Ethylene Forming Enzyme|Pseudomonas syringae (317)
>8ZNZ_1|Chains A, F[auth B]|5'-nucleotidase|Homo sapiens (9606)
>6JCE_1|Chain A|29-mer DNA|synthetic construct (32630)
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 \(w=f(c)\)
5LSQ , Knot 157 359 0.85 40 223 349 
MNHKVHHHHHHNLQTFELPTEVTGCAADISLGRALIQAWQKDGIFQIKTDSEQDRKTQEAMAASKQFCKEPLTFKSSCVSDLTYSGYVASGEEVTAGKPDFPEIFTVCKDLSVGDQRVKAGWPCHGPVPWPNNTYQKSMKTFMEELGLAGERLLKLTALGFELPINTFTDLTRDGWHHMRVLRFPPQTSTLSRGIGAHTDYGLLVIAAQDDVGGLYIRPPVEGEKRNRNWLPGESSAGMFEHDEPWTFVTPTPGVWTVFPGDILQFMTGGQLLSTPHKVKLNTRERFACAYFHEPNFEASAYPLFEPSANERIHYGEHFTNMFMRCYPDRITTQRINKENRLAHLEDLKKYSDTRATGS
8ZNZ , Knot 217 524 0.86 40 261 495 
AWELTILHTNDVHSRLEQTSEDSSKCVNASRCMGGVARLFTKVQQIRRAEPNVLLLDAGDQYQGTIWFTVYKGAEVAHFMNALRYDAMALGNHEFDNGVEGLIEPLLKEAKFPILSANIKAKGPLASQISGLYLPYKVLPVGDEVVGIVGYTSKETPFLSNPGTNLVFEDEITALQPEVDKLKTLNVNKIIALGHSGFEMDKLIAQKVRGVDVVVGGHSNTFLYTGNPPSKEVPAGKYPFIVTSDDGRKVPVVQAYAFGKYLGYLKIEFDERGNVISSHGNPILLNSSIPEDPSIKADINKWRIKLDNYSTQELGKTIVYLDGSSQSCRFRECNMGNLICDAMINNNLRHTDEMFWNHVSMCILNGGGIRSPIDERNNGTITWENLAAVLPFGGTFDLVQLKGSTLKKAFEHSVHRYGQSTGEFLQVGGIHVVYDLSRKPGDRVVKLDVLCTKCRVPSYDPLKMDEVYKVILPNFLANGGDGFQMIKDELLRHDSGDQDINVVSTYISKMKVIYPAVEGRIKFS
6JCE , Knot 8 29 0.31 4 4 6 
GGTTGGTGTGGTTGGTTGTGGTGGTGGTG

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 \(c\).

\(|P_{f(5LSQ_1)}(2) \setminus P_{f(8ZNZ_1)}(2)|=61\), \(|P_{f(8ZNZ_1)}(2) \setminus P_{f(5LSQ_1)}(2)|=99\). 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 1:10001000000010010110010101101011011101100011101000000000000111100010001101000010010001011010010110101101101000101100010111100111111000000010011001111100110101111011100100100011001011011100001001111000011111110001111010111010000001111000111100001101101011110111101101101101100100101000001101010010101010111010100010010010011100010010000100000110100100000001010
Pair \(Z_2\) Length of longest common subsequence
5LSQ_1,8ZNZ_1 160 3
5LSQ_1,6JCE_1 221 3
8ZNZ_1,6JCE_1 259 3

Newick tree

 
[
	6JCE_1:13.09,
	[
		5LSQ_1:80,8ZNZ_1:80
	]:51.09
]

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 \((0.85)(0.8)(\frac{883 }{\log_{20} 883}-\frac{359}{\log_{20}359})=140.\)
Status Protein1 Protein2 d d1/2
Query variables 5LSQ_1 8ZNZ_1 179 150.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]