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Parikh vectors
6UED_1 9LSW_1 5DIS_1 Letter Amino acid
27 15 124 L Leucine
27 17 54 S Serine
3 4 13 W Tryptophan
28 14 76 V Valine
17 11 38 R Arginine
46 37 36 G Glycine
15 11 30 H Histidine
26 9 73 I Isoleucine
19 22 47 D Aspartic acid
9 5 59 N Asparagine
7 11 55 F Phenylalanine
11 12 36 P Proline
19 15 61 T Threonine
9 13 29 Y Tyrosine
55 13 57 A Alanine
15 11 65 Q Glutamine
14 25 76 E Glutamic acid
10 23 60 K Lycine
8 12 36 M Methionine
4 0 19 C Cysteine 

6UED_1|Chain A|UDP-3-O-acylglucosamine N-acyltransferase|Pseudomonas aeruginosa (strain ATCC 15692 / DSM 22644 / CIP 104116 / JCM 14847 / LMG 12228 / 1C / PRS 101 / PAO1) (208964)
>9LSW_1|Chains A, B, C, D, E, F, G, H, I, J|Red fluorescent protein,grafted calcium-binding sequence|Discosoma (86599)
>5DIS_1|Chain A|Exportin-1|Homo sapiens (9606)
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 \(w=f(c)\)
6UED , Knot 154 369 0.82 40 197 330 
MHHHHHHSSGRENLYFQGSTLSYTLGQLAAHVGAEVRGDADLPIQGLATLQEAGPAQLSFLANPQYRKYLPESRAGAVLLTAADADGFAGTALVVANPYLAYASLSHLFDRKPKAAAGIHPTAIVAADAEVDPSASVGAYAVIESGARIGAGVSIGAHCVIGARSVIGEGGWLAPRVTLYHDVTIGARVSIQSGAVIGGEGFGFANEKGVWQKIAQIGGVTIGDDVEIGANTTIDRGALSDTLIGNGVKLDNQIMIAHNVQIGDHTAMAACVGISGSAKIGRHCMLAGGVGLVGHIEICDNVFVTGMTMVTRSITEPGSYSSGTAMQPAAEWKKSAARIRQLDDMARRLQQLEKRLAAVTSSGDASSDA
9LSW , Knot 121 280 0.81 38 169 261 
MGGSHHHHHHGMASMTGGQQMGRDLYDDDDKDRWGSELASSEDVIKEFMRFKVRMEGSVNGHEFEIEGEGEGRPYEGTQTAKLKVTKGGPLPFAWDILSPQFQYGSKAYVKHPADIPDYLKLSFPEGFKWERVMNFEDGGVVTVTQDSSLQDGEFIYKVKLRGTNFPSDGPVMQKKTMGWEASTERMYPGDGDGDGEAELKGEIKMRLKLKDGGHYDAEVKTTYMAKKPVQLPGAYKTDIKLDITSHNEDYTIVEQYERAEGRHSTGAGGSGGSENLYFQ
5DIS , Knot 385 1044 0.85 40 330 922 
MTMLADHAARQLLDFSQKLDINLLDNVVNCLYHGEGAQQRMAQEVLTHLKEHPDAWTRVDTILEFSQNMNTKYYGLQILENVIKTRWKILPRNQCEGIKKYVVGLIIKTSSDPTCVEKEKVYIGKLNMILVQILKQEWPKHWPTFISDIVGASRTSESLCQNNMVILKLLSEEVFDFSSGQITQVKSKHLKDSMCNEFSQIFQLCQFVMENSQNAPLVHATLETLLRFLNWIPLGYIFETKLISTLIYKFLNVPMFRNVSLKCLTEIAGVSVSQYEEQFVTLFTLTMMQLKQMLPLNTNIRLAYSNGKDDEQNFIQNLSLFLCTFLKEHDQLIEKRLNLRETLMEALHYMLLVSEVEETEIFKICLEYWNHLAAELYRESPFSTSASPLLSGSQHFDVPPRRQLYLPMLFKVRLLMVSRMAKPEEVLVVENDQGEVVREFMKDTDSINLYKNMRETLVYLTHLDYVDTERIMTEKLHNQVNGTEWSWKNLNTLCWAIGSISGAMHEEDEKRFLVTVIKDLLGLCEQKRGKDNKAIIASNIMYIVGQYPRFLRAHWKFLKTVVNKLFEFMHETHDGVQDMACDTFIKIAQKCRRHFVQVQVGEVMPFIDEILNNINTIICDLQPQQVHTFYEAVGYMIGAQTDQTVQEHLIEKYMLLPNQVWDSIIQQATKNVDILKDPETVKQLGSILKTNVRACKAVGHPFVIQLGRIYLDMLNVYKCLSENISAAIQANGEMVTKQPLIRSMRTVKRETLKLISGWVSRSNDPQMVAENFVPPLLDAVLIDYQRNVPAAREPEVLSTMAIIVNKLGGHITAEIPQIFDAVFECTLNMINKDFEEYPEHRTNFFLLLQAVNSHCFPAFLAIPPTQFKLVLDSIIWAFKHTMRNVADTGLQILFTLLQNVAQEEAAAQSFYQTYFCDILQHIFSVVTDTSHTAGLTMHASILAYMFNLVEEGKISTSLNPGNPVNNQIFLQEYVANLLKSAFPHLQDAQVKLFVTGLFSLNQDIPAFKEHLRDFLVQIKEFAGEDTSDLFLEEREIALRQADEE

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 \(c\).

\(|P_{f(6UED_1)}(2) \setminus P_{f(9LSW_1)}(2)|=100\), \(|P_{f(9LSW_1)}(2) \setminus P_{f(6UED_1)}(2)|=72\). 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 1:100000000100010101001000110111011101010101110111010011110101110100000110001111110110101111011111010110101001100010111110101111101010101011101110011011111011100111100111011111101010001011101010011111101111100011100110111101100101110001001110001110110100011110010110001111011101010110001111111111010100011101101100010011000010110111010001101001001100100100011110001010001
Pair \(Z_2\) Length of longest common subsequence
6UED_1,9LSW_1 172 6
6UED_1,5DIS_1 177 4
9LSW_1,5DIS_1 201 4

Newick tree

 
[
	5DIS_1:97.41,
	[
		6UED_1:86,9LSW_1:86
	]:11.41
]

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 \((0.85)(0.8)(\frac{649 }{\log_{20} 649}-\frac{280}{\log_{20}280})=102.\)
Status Protein1 Protein2 d d1/2
Query variables 6UED_1 9LSW_1 125 110
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]