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Parikh vectors
6LPX_1 7RTI_1 4WIG_1 Letter Amino acid
25 5 4 T Threonine
13 0 3 Y Tyrosine
28 0 12 R Arginine
15 0 2 Q Glutamine
23 0 4 H Histidine
17 0 0 K Lycine
9 0 3 M Methionine
25 0 7 P Proline
3 0 1 W Tryptophan
42 0 14 V Valine
13 0 4 N Asparagine
21 0 11 D Aspartic acid
10 5 7 C Cysteine
26 0 4 E Glutamic acid
16 0 1 I Isoleucine
16 0 2 F Phenylalanine
32 0 5 S Serine
34 3 15 A Alanine
50 2 16 G Glycine
63 0 18 L Leucine 

6LPX_1|Chains A, B|D-2-hydroxyglutarate dehydrogenase, mitochondrial|Homo sapiens (9606)
>7RTI_1|Chain A|DNA (5'-D(*AP*AP*TP*CP*TP*TP*TP*CP*CP*CP*AP*CP*GP*GP*T)-3')|Synthetic DNA (32630)
>4WIG_1|Chains A, B|Cytidine deaminase|Mycobacterium tuberculosis (1773)
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 \(w=f(c)\)
6LPX , Knot 192 481 0.82 40 228 450 
GPGSRYPVRRLPFSTVSKQDLAAFERIVPGGVVTDPEALQAPNVDWLRTLRGCSKVLLRPRTSEEVSHILRHCHERNLAVNPQGGNTGMVGGSVPVFDEIILSTARMNRVLSFHSVSGILVCQAGCVLEELSRYVEERDFIMPLDLGAKGSCHIGGNVATNAGGLRFLRYGSLHGTVLGLEVVLADGTVLDCLTSLRKDNTGYDLKQLFIGSEGTLGIITTVSILCPPKPRAVNVAFLGCPGFAEVLQTFSTCKGMLGEILSAFEFMDAVCMQLVGRHLHLASPVQESPFYVLIETSGSNAGHDAEKLGHFLEHALGSGLVTDGTMATDQRKVKMLWALRERITEALSRDGYVYKYDLSLPVERLYDIVTDLRARLGPHAKHVVGYGHLGDGNLHLNVTAEAFSPSLLAALEPHVYEWTAGQQGSVSAEHGVGFRKRDVLGYSKPPGALQLMQQLKALLDPKGILNPYKTLPSQAHHHHHH
7RTI , Knot 8 15 0.48 8 11 13 
AATCTTTCCCACGGT
4WIG , Knot 66 133 0.81 38 96 130 
MPDVDWNMLRGNATQAAAGAYVPYSRFAVGAAALVDDGRVVTGCNVDNVSYGLTLCAECAVVCALHSTGGGRLLALACVDGHGSVLMPCGRCRQVLLEHGGSELLIDHPVRPRRLGDLLPDAFGLDDLPRERR

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 \(c\).

\(|P_{f(6LPX_1)}(2) \setminus P_{f(7RTI_1)}(2)|=222\), \(|P_{f(7RTI_1)}(2) \setminus P_{f(6LPX_1)}(2)|=5\). 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 1:1110001100111001000011110011111110010110110101100101000111010000010011000000011101011001111101111001110010100110100101111001101100100010000111110111010001110110011110110010101011110111101011001001000001001001111001011110010110110101101111101111011001000011110110110110110101110010110110001101110001001100100110110011101110010110000010111110001001100010100001011100100110010101110100111010110101010101011010111110101001011001010100111100001110001111101100101110101110100011001000000
Pair \(Z_2\) Length of longest common subsequence
6LPX_1,7RTI_1 227 2
6LPX_1,4WIG_1 174 3
7RTI_1,4WIG_1 95 2

Newick tree

 
[
	6LPX_1:11.49,
	[
		4WIG_1:47.5,7RTI_1:47.5
	]:65.99
]

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 \((0.85)(0.8)(\frac{496 }{\log_{20} 496}-\frac{15}{\log_{20}15})=151.\)
Status Protein1 Protein2 d d1/2
Query variables 6LPX_1 7RTI_1 189 97.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]