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Parikh vectors
6LRV_1 5EEX_1 7MFM_1 Letter Amino acid
18 4 32 L Leucine
7 1 15 M Methionine
10 4 28 D Aspartic acid
10 7 39 G Glycine
5 4 7 H Histidine
7 6 30 I Isoleucine
12 7 28 K Lycine
1 0 5 W Tryptophan
6 4 24 R Arginine
1 0 4 C Cysteine
18 6 32 E Glutamic acid
5 6 22 T Threonine
8 2 18 N Asparagine
12 2 9 Q Glutamine
4 0 16 P Proline
9 2 14 Y Tyrosine
6 7 34 V Valine
14 5 31 A Alanine
6 3 14 F Phenylalanine
11 4 22 S Serine 

6LRV_1|Chains A, B|Ferritin|Penaeus japonicus (27405)
>5EEX_1|Chains A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V|Transcription attenuation protein MtrB|Geobacillus stearothermophilus (1422)
>7MFM_1|Chains A, F[auth B], G[auth C], H[auth D], I[auth E], J[auth F]|Glutamate dehydrogenase|Bacillus subtilis (1423)
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 \(w=f(c)\)
6LRV , Knot 82 170 0.82 40 132 166 
MASQVRQNYHEDCEASINKQINMELYASYVYLSMAYYFERDDVALPGFAKFFKESSDEEREHAQTFMKYQNKRGGRIVLQQIAAPSMQEWGTGLEALQAALDLEKQVNQSLLELHSTASGNNDPHLTKLLEDEYLEEQVDSIKKIGDMITKLKRAGPHGLGEYMFDKELN
5EEX , Knot 42 74 0.81 34 63 72 
MYTNSDFVVIKALEDGVNVIGLTRGADTRFHHSEKLDKGEVLIAQFTEHTSAIKVRGKAYIQTRHGVIESEGKK
7MFM , Knot 176 424 0.83 40 219 397 
MAADRNTGHTEEDKLDVLKSTQTVIHKALEKLGYPEEVYELLKEPMRLLTVKIPVRMDDGSVKIFTGYRAQHNDSVGPTKGGIRFHPNVTEKEVKALSIWMSLKCGIIDLPYGGGKGGIVCDPRDMSFRELERLSRGYVRAISQIVGPTKDVPAPDVFTNSQIMAWMMDEYSRIDEFNSPGFITGKPLVLGGSHGRESATAKGVTICIKEAAKKRGIDIKGARVVVQGFGNAGSYLAKFMHDAGAKVVGISDAYGGLYDPEGLDIDYLLDRRDSFGTVTKLFNDTITNQELLELDCDILVPAAIENQITEENAHNIRAKIVVEAANGPTTLEGTKILSDRDILLVPDVLASAGGVTVSYFEWVQNNQGFYWSEEEVEEKLEKMMVKSFNNIYEMANNRRIDMRLAAYMVGVRKMAEASRFRGWI

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 \(c\).

\(|P_{f(6LRV_1)}(2) \setminus P_{f(5EEX_1)}(2)|=106\), \(|P_{f(5EEX_1)}(2) \setminus P_{f(6LRV_1)}(2)|=37\). 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 1:11001000000000101000101010100101011001000011111110110000000000100110000001101110011110100110110110111010001000110100010100010100110000100010010011011001001110111001100010
Pair \(Z_2\) Length of longest common subsequence
6LRV_1,5EEX_1 143 3
6LRV_1,7MFM_1 183 4
5EEX_1,7MFM_1 192 4

Newick tree

 
[
	7MFM_1:10.10,
	[
		6LRV_1:71.5,5EEX_1:71.5
	]:28.60
]

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 \((0.85)(0.8)(\frac{244 }{\log_{20} 244}-\frac{74}{\log_{20}74})=55.3\)
Status Protein1 Protein2 d d1/2
Query variables 6LRV_1 5EEX_1 72 50.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]