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Parikh vectors
9EWE_1 6GOH_1 2QRP_1 Letter Amino acid
14 2 36 P Proline
25 10 29 S Serine
28 12 63 A Alanine
20 2 65 E Glutamic acid
12 1 22 H Histidine
5 2 21 M Methionine
10 3 36 Y Tyrosine
7 14 46 N Asparagine
14 7 49 D Aspartic acid
27 12 48 G Glycine
15 6 50 I Isoleucine
4 6 12 W Tryptophan
18 6 62 V Valine
7 8 9 C Cysteine
14 3 30 Q Glutamine
34 8 79 L Leucine
11 3 38 F Phenylalanine
25 11 63 R Arginine
21 6 48 K Lycine
19 7 36 T Threonine 

9EWE_1|Chain A|DNA polymerase lambda|Homo sapiens (9606)
>6GOH_1|Chain A|Lysozyme C|Gallus gallus (9031)
>2QRP_1|Chain A|Glycogen phosphorylase, muscle form|Oryctolagus cuniculus (9986)
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 \(w=f(c)\)
9EWE , Knot 144 330 0.84 40 209 319 
GAQPSSQKATNHNLHITEKLEVLAKAYSVQGDKWRALGYAKAINALKSFHKPVTSYQEACSIPGIGKRMAEKIIEILESGHLRKLDHISESVPVLELFSNIWGAGTKTAQMWYQQGFRSLEDIRSQASLTTQQAIGLKHYSDFLERMPREEATEIEQTVQKAAQAFNSGLLCVACGSYRRGKATCGDVDVLITHPDGRSHRGIFSRLLDSLRQEGFLTDDLVKGETKYLGVCRLPGPGRRHRRLDIKVVPYSEFACALLYFTGSAHFNRSMRALAKTKGMSLSDHALSTAVVRNTHGCKVGPGRVLPTPTEKDVFRLLGLPYREPAERDW
6GOH , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL
2QRP , Knot 321 842 0.85 40 316 773 
SRPLSDQEKRKQISVRGLAGVENVTELKKNFNRHLHFTLVKDRNVATPRDYYFALAHTVRDHLVGRWIRTQQHYYEKDPKRIYYLSLEFYMGRTLQNTMVNLALENACDEATYQLGLDMEELEEIEEDAGLGNGGLGRLAACFLDSMATLGLAAYGYGIRYEFGIFNQKICGGWQMEEADDWLRYGNPWEKARPEFTLPVHFYGRVEHTSQGAKWVDTQVVLAMPYDTPVPGYRNNVVNTMRLWSAKAPNDFNLKDFNVGGYIQAVLDRNLAENISRVLYPNDNFFEGKELRLKQEYFVVAATLQDIIRRFKSSKFGCRDPVRTNFDAFPDKVAIQLNDTHPSLAIPELMRVLVDLERLDWDKAWEVTVKTCAYTNHTVLPEALERWPVHLLETLLPRHLQIIYEINQRFLNRVAAAFPGDVDRLRRMSLVEEGAVKRINMAHLCIAGSHAVNGVARIHSEILKKTIFKDFYELEPHKFQNKTNGITPRRWLVLCNPGLAEIIAERIGEEYISDLDQLRKLLSYVDDEAFIRDVAKVKQENKLKFAAYLEREYKVHINPNSLFDVQVKRIHEYKRQLLNCLHVITLYNRIKKEPNKFVVPRTVMIGGKAAPGYHMAKMIIKLITAIGDVVNHDPVVGDRLRVIFLENYRVSLAEKVIPAADLSEQISTAGTEASGTGNMKFMLNGALTIGTMDGANVEMAEEAGEENFFIFGMRVEDVDRLDQRGYNAQEYYDRIPELRQIIEQLSSGFFSPKQPDLFKDIVNMLMHHDRFKVFADYEEYVKCQERVSALYKNPREWTRMVIRNIATSGKFSSDRTIAQYAREIWGVEPSRQRLPAPDEKIP

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 \(c\).

\(|P_{f(9EWE_1)}(2) \setminus P_{f(6GOH_1)}(2)|=138\), \(|P_{f(6GOH_1)}(2) \setminus P_{f(9EWE_1)}(2)|=33\). 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 1:110100001000010100010111010010100101110101101100100110000010011111001100110110010100100100011110110011111000101100011001001000101000011110000011001100010010001001101100111011010000101001010111001010000111001100100011100011010000111001111100000101011100011011101010101000101110001101000110011100001001111011101000011011111000110001
Pair \(Z_2\) Length of longest common subsequence
9EWE_1,6GOH_1 171 3
9EWE_1,2QRP_1 167 4
6GOH_1,2QRP_1 246 3

Newick tree

 
[
	6GOH_1:11.40,
	[
		9EWE_1:83.5,2QRP_1:83.5
	]:28.90
]

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 \((0.85)(0.8)(\frac{459 }{\log_{20} 459}-\frac{129}{\log_{20}129})=98.4\)
Status Protein1 Protein2 d d1/2
Query variables 9EWE_1 6GOH_1 127 87
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]