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Parikh vectors
6GRC_1 1VLP_1 1LCV_1 Letter Amino acid
10 17 2 H Histidine
22 20 2 F Phenylalanine
29 27 19 T Threonine
7 7 6 W Tryptophan
8 22 6 Y Tyrosine
36 14 4 R Arginine
31 25 4 D Aspartic acid
17 10 3 Q Glutamine
42 25 16 G Glycine
38 16 2 P Proline
41 25 16 A Alanine
6 2 0 C Cysteine
39 40 4 K Lycine
37 35 9 S Serine
30 21 7 V Valine
11 26 7 N Asparagine
39 32 4 E Glutamic acid
35 31 3 I Isoleucine
43 36 7 L Leucine
9 10 0 M Methionine 

6GRC_1|Chain A|Nuclease-like protein|Chaetomium thermophilum (strain DSM 1495 / CBS 144.50 / IMI 039719) (759272)
>1VLP_1|Chains A, B, C, D|nicotinate phosphoribosyltransferase|Saccharomyces cerevisiae (4932)
>1LCV_1|Chains A, B|streptavidin|Streptomyces avidinii (1895)
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 \(w=f(c)\)
6GRC , Knot 211 530 0.83 40 255 500 
MGIKGIYKEIGSGERISLCKLAIDHLEQHNRPLRLAIDMAIWQFQIQAARGGSNPAIRTLFYRFVRLLSLGIHPIFVFDGPNKPIFKRNRRSGTGNGVSTAMAKRLIRLFGFTAHDAPGEAEAECAYLEQQGIVDAVLSEDVDTIMFGSRVTLRDWSSEGSKGGPPTHVTLHDAKKIAEGPSGLDREGMVLVALMSGGDYLPDGIPGCGIKVACQAAKAGFGKELCRIKRADKEAITEWKQRLLHELRTNESGFFRTKHKALEIPENFPNMEVLRYYTHPVVSSPATIERLRQEFPPSSTVDIAGLREFTRETFDWTFRPGAIKLIKVLAPGLLVQRCLDRYVSGPRIDDPDLKKKEESTLVKGISMRREHFSTDATPELRVSFIPAELVGLDPGQEPEVQVEAFGRSGLALNSDDEFDEDISSSQKAPKKPFDPWQPDLAWVPETILKLGVPVTVEDWEEGQRSKGRAKEDKTAAKAKRKTKIIQSNMPAGALDKYVTVTKNISDTTVKSKESAPITIPSSPPKPSSQP
1VLP , Knot 182 441 0.83 40 233 410 
MGSDKIHHHHHHMSEPVIKSLLDTDMYKITMHAAVFTNFPDVTVTYKYTNRSSQLTFNKEAINWLKEQFSYLGNLRFTEEEIEYLKQEIPYLPSAYIKYISSSNYKLHPEEQISFTSEEIEGKPTHYKLKILVSGSWKDTILYEIPLLSLISEAYFKFVDIDWDYENQLEQAEKKAETLFDNGIRFSEFGTRRRRSLKAQDLIMQGIMKAVNGNPDRNKSLLLGTSNILFAKKYGVKPIGTVAHEWVMGVASISEDYLHANKNAMDCWINTFGAKNAGLALTDTFGTDDFLKSFRPPYSDAYVGVRQDSGDPVEYTKKISHHYHDVLKLPKFSKIICYSDSLNVEKAITYSHAAKENGMLATFGIGTNFTNDFRKKSEPQVKSEPLNIVIKLLEVNGNHAIKISDNLGKNMGDPATVKRVKEELGYTERSWSGDNEAHRWT
1LCV , Knot 56 121 0.74 36 85 115 
AGITGTWYNQLGSTFIVTAGADGALTGTYESAVGNAESRYVLTGRYDSAPATDGSGTALGWTVAWKNNYRNAHSATTWSGQYVGGAEARINTQWLLTSGTTEANAWKSTLVGHDTFTKVKP

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 \(c\).

\(|P_{f(6GRC_1)}(2) \setminus P_{f(1VLP_1)}(2)|=87\), \(|P_{f(1VLP_1)}(2) \setminus P_{f(6GRC_1)}(2)|=65\). 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 1:11101100011010010100111001000001101110111101010110110011100110011011011101111101100111000000101011001110011011110100111010100101000111011100010011110010100100010011110010100100110110110001111111101100110111101101100110111100100100100011001000110010000011100000110110011010110000011100110100100011100010111100100001010101111011011111111000100010110100101000000011011010000100010101010111101111011001010101110011110000010001000001100110110101111100110111110100100100001010000011010000011000111111000101000100001000001110110011010001
Pair \(Z_2\) Length of longest common subsequence
6GRC_1,1VLP_1 152 4
6GRC_1,1LCV_1 218 4
1VLP_1,1LCV_1 208 3

Newick tree

 
[
	1LCV_1:11.91,
	[
		6GRC_1:76,1VLP_1:76
	]:38.91
]

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 \((0.85)(0.8)(\frac{971 }{\log_{20} 971}-\frac{441}{\log_{20}441})=140.\)
Status Protein1 Protein2 d d1/2
Query variables 6GRC_1 1VLP_1 175 160.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]