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Parikh vectors
4EDB_1 2RPD_1 6IFW_1 Letter Amino acid
9 1 1 C Cysteine
11 0 4 H Histidine
18 0 23 I Isoleucine
18 0 21 K Lycine
10 0 11 F Phenylalanine
21 0 27 V Valine
13 0 10 R Arginine
17 1 14 T Threonine
32 0 13 S Serine
11 0 13 D Aspartic acid
8 0 13 Q Glutamine
22 0 25 E Glutamic acid
24 1 12 G Glycine
3 0 6 M Methionine
14 0 6 Y Tyrosine
18 1 20 A Alanine
28 0 28 L Leucine
21 0 12 P Proline
6 0 0 W Tryptophan
26 0 15 N Asparagine 

4EDB_1|Chains A, C, E|Hemagglutinin|Influenza A virus (457457)
>2RPD_1|Chain A|DNA (5'-D(*DTP*DAP*DCP*DG)-3')|null
>6IFW_1|Chains A, B|Ribosomal RNA small subunit methyltransferase A|Bacillus subtilis (strain 168) (224308)
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 \(w=f(c)\)
4EDB , Knot 142 330 0.83 40 202 309 
ADPGDTICIGYHANNSTDTVDTVLEKNVTVTHSVNLLEDSHNGKLCLLKGIAPLQLGNCSVAGWILGNPECELLISKESWSYIVEKPNPENGTCYPGHFADYEELREQLSSVSSFERFEMFPKESSWPNHTVTGVSASCSHNGKSSFYKNLLWLTGKNGLYPNLSKSYANNKEKEVLVLWGVHHPPNIGDQRALYHTENAYVSVVSSHYSRKFTPEIAKRPKVRDQEGRINYYWTLLEPGDTIIFEANGNLIAPRYAFALSRGFGSGIINSNAPMDECDAKCQTPQGAINSSLPFQNVHPVTIGECPKYVRSAKLRMVTGLRNIPSIQSR
2RPD , Knot 4 4 0.46 8 3 2 
TACG
6IFW , Knot 119 274 0.81 38 168 262 
MNEKNIKHGQNFLIDTNILNRIVDHAEVTEKTGVIEIGPGIGALTEQLAKRAKKVVAFEIDQRLLPILKDTLSPYENVTVIHQDVLKADVKSVIEEQFQDCDEIMVVANLPYYVTTPIIMKLLEEHLPLKGIVVMLQKEVAERMAADPSSKEYGSLSIAVQFYTEAKTVMIVPKTVFVPQPNVDSAVIRLILRDGPAVDVENESFFFQLIKASFAQRRKTLLNNLVNNLPEGKAQKSTIEQVLEETNIDGKRRGESLSIEEFAALSNGLYKALF

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 \(c\).

\(|P_{f(4EDB_1)}(2) \setminus P_{f(2RPD_1)}(2)|=202\), \(|P_{f(2RPD_1)}(2) \setminus P_{f(4EDB_1)}(2)|=3\). 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 1:101100101100100000010011000101000101100000101011011111011000111111101000111000010011001010010001101100001000100100100101110000110001011010000010001000111101001101010000100000011111110011011000110000010101100000001010110010100001010001011011001110101011110011110011101110001110000100001011100011100101101100100100101011011001101000
Pair \(Z_2\) Length of longest common subsequence
4EDB_1,2RPD_1 205 1
4EDB_1,6IFW_1 160 4
2RPD_1,6IFW_1 171 1

Newick tree

 
[
	2RPD_1:98.71,
	[
		4EDB_1:80,6IFW_1:80
	]:18.71
]

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 \((0.85)(0.8)(\frac{334 }{\log_{20} 334}-\frac{4}{\log_{20}4})=111.\)
Status Protein1 Protein2 d d1/2
Query variables 4EDB_1 2RPD_1 139 70.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]