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Parikh vectors
6FUT_1 1QUE_1 1IVE_1 Letter Amino acid
8 14 12 Q Glutamine
9 23 15 E Glutamic acid
2 6 5 M Methionine
14 18 15 P Proline
16 12 42 S Serine
8 18 24 T Threonine
18 13 26 R Arginine
16 16 27 D Aspartic acid
22 18 28 V Valine
4 15 12 Y Tyrosine
22 27 37 G Glycine
10 8 8 H Histidine
0 7 12 F Phenylalanine
5 11 25 N Asparagine
6 24 14 K Lycine
6 22 27 I Isoleucine
27 22 16 L Leucine
4 5 12 W Tryptophan
27 21 13 A Alanine
8 3 18 C Cysteine 

6FUT_1|Chain A|Complement factor D|Homo sapiens (9606)
>1QUE_1|Chain A|FERREDOXIN--NADP+ REDUCTASE|Nostoc sp. (1168)
>1IVE_1|Chains A, B|INFLUENZA A SUBTYPE N2 NEURAMINIDASE|Influenza A virus (strain A/Tokyo/3/1967 H2N2) (380960)
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 \(w=f(c)\)
6FUT , Knot 103 232 0.80 38 145 218 
ILGGREAEAHARPYMASVQLNGAHLCGGVLVAEQWVLSAAHCLEDAADGKVQVLLGAHSLSQPEPSKRLYDVLRAVPHPDSQPDTIDHDLLLLQLSEKATLGPAVRPLPWQRVDRDVAPGTLCDVAGWGIVNHAGRRPDSLQHVLLPVLDRATCNRRTHHDGAITERLMCAESNRRDSCKGDSGGPLVCGGVLEGVVTSGSRVCGNRKKPGIYTRVASYAAWIDSVLASAAA
1QUE , Knot 137 303 0.86 40 200 296 
TQAKAKHADVPVNLYRPNAPFIGKVISNEPLVKEGGIGIVQHIKFDLTGGNLKYIEGQSIGIIPPGVDKNGKPEKLRLYSIASTRHGDDVDDKTISLCVRQLEYKHPESGETVYGVCSTYLTHIEPGSEVKITGPVGKEMLLPDDPEANVIMLATGTGIAPMRTYLWRMFKDAERAANPEYQFKGFSWLVFGVPTTPNILYKEELEEIQQKYPDNFRLTYAISREQKNPQGGRMYIQDRVAEHADQLWQLIKNQKTHTYICGLRGMEEGIDAALSAAAAKEGVTWSDYQKDLKKAGRWHVETY
1IVE , Knot 168 388 0.86 40 224 369 
VEYRNWSKPQCQITGFAPFSKDNSIRLSAGGDIWVTREPYVSCDPVKCYQFALGQGTTLDNKHSNDTVHDRIPHRTLLMNELGVPFHLGTRQVCIAWSSSSCHDGKAWLHVCITGDDKNATASFIYDGRLVDSIGSWSQNILRTQESECVCINGTCTVVMTDGSASGRADTRILFIEEGKIVHISPLAGSAQHVEECSCYPRYPGVRCICRDNWKGSNRPVVDINMEDYSIDSSYVCSGLVGDTPRNDDRSSNSNCRDPNNERGTQGVKGWAFDNGNDLWMGRTISKDLRSGYETFKVIGGWSTPNSKSQINRQVIVDSDNRSGYSGIFSVEGKSCINRCFYVELIRGRKQETRVWWTSNSIVVFCGTSGTYGTGSWPDGANINFMPI

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 \(c\).

\(|P_{f(6FUT_1)}(2) \setminus P_{f(1QUE_1)}(2)|=61\), \(|P_{f(1QUE_1)}(2) \setminus P_{f(6FUT_1)}(2)|=116\). 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 1:1111001010101011010101101011111100111011001001101010111110010010100010011011101000100100011110100010111110111100100011110100111111100110010010011111100100000000011100011010000000001001111101111011100100101000011100011001111001110111
Pair \(Z_2\) Length of longest common subsequence
6FUT_1,1QUE_1 177 4
6FUT_1,1IVE_1 189 3
1QUE_1,1IVE_1 174 3

Newick tree

 
[
	6FUT_1:93.01,
	[
		1QUE_1:87,1IVE_1:87
	]:6.01
]

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 \((0.85)(0.8)(\frac{535 }{\log_{20} 535}-\frac{232}{\log_{20}232})=86.7\)
Status Protein1 Protein2 d d1/2
Query variables 6FUT_1 1QUE_1 113 97
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]