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Parikh vectors
9CRB_1 2WLB_1 5EFW_1 Letter Amino acid
1 3 2 H Histidine
0 8 11 I Isoleucine
5 5 5 P Proline
1 0 1 W Tryptophan
0 2 2 M Methionine
0 3 7 F Phenylalanine
2 5 11 R Arginine
6 4 0 C Cysteine
0 1 8 Q Glutamine
1 14 13 E Glutamic acid
6 10 8 G Glycine
0 12 13 L Leucine
3 4 5 S Serine
0 1 3 Y Tyrosine
1 5 10 A Alanine
2 10 11 D Aspartic acid
0 3 7 N Asparagine
0 2 9 K Lycine
0 4 11 T Threonine
0 7 8 V Valine 

9CRB_1|Chain A|Avt1 peptide|Aulactinia veratra (1730095)
>2WLB_1|Chains A, B|ELECTRON TRANSFER PROTEIN 1, MITOCHONDRIAL|SCHIZOSACCHAROMYCES POMBE (4896)
>5EFW_1|Chain A|NPH1-1|Avena sativa (4498)
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 \(w=f(c)\)
9CRB , Knot 17 28 0.67 20 23 26 
SCARGCGGDSDCPCPGWHCPSPGGRCEP
2WLB , Knot 52 103 0.78 38 81 98 
GTGIKVFFVTPEGREIMIEGNEGDSILDLAHANNIDLEGACEGSVACSTCHVIVDPEHYELLDPPEEDEEDMLDLAFGLEETSRLGCQVLLRKDLDGIRVRIP
5EFW , Knot 72 145 0.82 38 119 140 
GSLATTLERIEKNFVITDPRLPDNPIIFASDSFLQLTEYSREEILGRNARFLQGPETDRATVRKIRDAIDNQTEVTVQLINYTKSGKKFWNLFHLQPMRDQKGDVQYFIGVQLDGTEHVRDAAEREGVMLIKKTAENIDEAAKEL

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 \(c\).

\(|P_{f(9CRB_1)}(2) \setminus P_{f(2WLB_1)}(2)|=18\), \(|P_{f(2WLB_1)}(2) \setminus P_{f(9CRB_1)}(2)|=76\). 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 1:0010101100001011100101110001
Pair \(Z_2\) Length of longest common subsequence
9CRB_1,2WLB_1 94 3
9CRB_1,5EFW_1 132 2
2WLB_1,5EFW_1 128 3

Newick tree

 
[
	5EFW_1:69.98,
	[
		9CRB_1:47,2WLB_1:47
	]:22.98
]

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 \((0.85)(0.8)(\frac{131 }{\log_{20} 131}-\frac{28}{\log_{20}28})=37.6\)
Status Protein1 Protein2 d d1/2
Query variables 9CRB_1 2WLB_1 47 29
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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