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Parikh vectors
2YGW_1 7XPW_1 2JXA_1 Letter Amino acid
11 7 9 D Aspartic acid
13 4 0 H Histidine
60 9 6 L Leucine
8 2 4 M Methionine
19 8 4 F Phenylalanine
8 2 0 W Tryptophan
16 7 5 N Asparagine
17 4 4 I Isoleucine
19 10 4 K Lycine
21 7 9 P Proline
38 11 6 A Alanine
7 6 8 C Cysteine
24 5 5 Q Glutamine
33 6 3 S Serine
29 4 6 R Arginine
35 14 7 E Glutamic acid
36 6 7 G Glycine
20 3 3 T Threonine
14 2 7 Y Tyrosine
32 10 9 V Valine 

2YGW_1|Chains A, B|MALONYL-COA DECARBOXYLASE, MITOCHONDRIAL|HOMO SAPIENS (9606)
>7XPW_1|Chain A|Thioredoxin domain-containing protein 17|Oncomelania hupensis (56141)
>2JXA_1|Chain A|Latrophilin 1|Mus musculus (10090)
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 \(w=f(c)\)
2YGW , Knot 187 460 0.83 40 229 438 
GTENLYFQSMDELLRRAVPPTPAYELRAATPAPAEGQCADFVSFYGGLAETAQRAELLGRLARGFGVDHGQVAEQSAGVLHLRQQQREAAVLLQAEDRLRYALVPRYRGLFHHISKLDGGVRFLVQLRADLLEAQALKLVEGPDVREMNGVLKGMLSEWFSSGFLNLERVTWHSPCEVLQKISEAEAVHPVKNWMDMKRRVGPYRRCYFFSHCSTPGEPLVVLHVALTGDISSNIQAIVKEHPPSETAAANKITAAIFYSISLTQQGLQGVELGTFLIKRVVKELQREFPHLGVFSSLSPIPGFTKWLLGLLNSQTKEHGRNELFTDSECKEISEITGGPINETLKLLLSSSEWVQSEKLVRALQTPLMRLCAWYLYGEKHRGYALNPVANFHLQNGAVLWRINWMADVSLRGITGSCGLMANYRYFLEETGPNSTSYLGSKIIKASEQVLSLVAQFQKN
7XPW , Knot 65 127 0.82 40 106 125 
MVKEIHVEGFEAYSKAAEENNGKNIFALFCGSKDANGESWCPDCVTAEPVIARNLKYAPADSVFIHCSVGERAFWKDQSNVFRKDPVLKLKCVPTLLKPGTPQRLEEEQCADDNLVQMFFQEELEHH
2JXA , Knot 53 106 0.77 36 80 101 
GLPFGLMRRELACEGYPIELRCPGSDVIMVENANYGRTDDKICDADPFQMENVQCYLPDAFKIMSQRCNNRTQCVVVAGSDAFPDPCPGTYKYLEVQYDCVPYKVE

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 \(c\).

\(|P_{f(2YGW_1)}(2) \setminus P_{f(7XPW_1)}(2)|=159\), \(|P_{f(7XPW_1)}(2) \setminus P_{f(2YGW_1)}(2)|=36\). 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 1:1000101001001100111101100101101111010010110101111001001011101101111001011000111101000000111110100010011110001110010010111011101010110101101101101001011101110011001110100101001001100100101101100110100011100000110000011011111011101010001011100011000111001011110010100011011011011100110010001101111001011111001111110000000100011000000010010111100010111000011000011011001110101101010000101101110101001111101011101010110100111100001100011000001100110100011011101000
Pair \(Z_2\) Length of longest common subsequence
2YGW_1,7XPW_1 195 4
2YGW_1,2JXA_1 219 3
7XPW_1,2JXA_1 128 3

Newick tree

 
[
	2YGW_1:11.86,
	[
		7XPW_1:64,2JXA_1:64
	]:49.86
]

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 \((0.85)(0.8)(\frac{587 }{\log_{20} 587}-\frac{127}{\log_{20}127})=134.\)
Status Protein1 Protein2 d d1/2
Query variables 2YGW_1 7XPW_1 169 107.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]