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Parikh vectors
7MVV_1 5TPU_1 4CIA_1 Letter Amino acid
89 10 32 G Glycine
72 10 21 K Lycine
37 5 11 M Methionine
166 9 24 A Alanine
58 15 33 N Asparagine
136 7 20 E Glutamic acid
239 13 53 L Leucine
79 6 23 F Phenylalanine
81 4 25 P Proline
38 8 28 Y Tyrosine
95 4 28 V Valine
103 10 24 D Aspartic acid
43 3 9 H Histidine
101 14 12 I Isoleucine
81 2 17 T Threonine
126 5 34 S Serine
25 1 8 W Tryptophan
99 9 18 R Arginine
32 3 9 C Cysteine
84 1 26 Q Glutamine 

7MVV_1|Chain A|Nucleoporin NUP192|Chaetomium thermophilum (strain DSM 1495 / CBS 144.50 / IMI 039719) (759272)
>5TPU_1|Chains A, B, C, D|Putative uncharacterized protein|Campylobacter jejuni (197)
>4CIA_1|Chain A|LYSOSOMAL PROTECTIVE PROTEIN|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 \(w=f(c)\)
7MVV , Knot 605 1784 0.84 40 359 1414 
GPLMSGLNDIFEAQKIEWHEGSAGGSGHMTDLRKLEALQALHAELVAVRQHRFEGLQVLETLLEEQTDAFKALIAKPARDTKDREALGKEPKKLKIGEEEYSLNEDFVNDCLKLADELDLNEKESARILIDCDAEGDVETQSRPLWECGVIRFHQERKYLLDCMRLILEIAADEDIDAGLQESFGVAAEDKIFGIPPPWERNKENQPTQVKKFIPRCMEAMKGVRSMLQCMADKANARNMLQQASLVRPLDNQETLDFSRLSLVEQHECLASILHAAVQRHHATIADFQDFIKILRKWDKYDHFLIHLIPVLAAYITEFGSPEGMGDLQQARRLNDFICKGGDEDSWALPVLGAAVRAWWIAEHNGFYLDDTVQDLRGINLDEEDEQRTKQFLDALKEGAFDFILSVAADCKAQEWQDPSQLGARQWLQRKIPSLPSEPFPFSHFLQHSLMVHLEGFVDATISNLPDVLRKLRTEEDEQRQLRPNHEQDMDLERFLIIISYAYEGRPDAAMSFWEDPDSNLAGFLQWASRRASTPLVSAFCEMLRCLADNEECATAAHNFLLDEGHQASGKMKRSQSLTWSQIFKELEYFTTKVCSERPNPPQASMHRPGRPGADPAEIEPESALMLECYLRLIAKLATESEIARKRLIMDEDFNLVDTILKLSVGVIPHRLRACIFYVLKALMIRKTHEELDAMWRWVEAWMTNPFSSLPGSQGAPQRISFLGQTPGPQECMEMMFREFGTGFEQSNAFIQLLTTLLVPPEGLNSLNDSVPFPEWLGSSIRTLGIEPYVDFVFDVFANRTKDISDPSQLRILRLSCLDFVMVCLVTFNEDLIVLGHESNISIDDAMAATNLATYVRLHPFSRVMEWLFNEKVITSLINTIHQDPISLGSASPDSPLVVSILRAIQVMIKALELQETYLHLVRPEVLRYQGEAGVRRKPVANAAYSAFEDGILSHLSLVVDLGKYCNLGHAELTLACLKLLEKISTSSRILSAWSPDSGRLGHRNKAIVQLERNGEGETISASLSASIMATLDPALAASGENYRVKLAILDFLYACLRATPDQPTIAHQLLGFHCELSKLGIEPKGPFDMQKSLFHSLLNVLITLTVSEEEQGMRGYLVTLKYRVLRILQLLWKSPLSASLVMDELRATNFLFHMLLREVQIQPQLPWDGQLVTGCEFLLSDASLAYIDYLASRAAIFEYIGKELCSVSQNRIPSIKRQIFDALNGQIFVDEEAPLTIPSIFDFFDFINTDYKWEEIPSPHFTYLKDLDLGPCILEHKYAGVHYDIRKAQEILALKRKEYEHSQLATPEFLETVELEEKVLIEWLTVRNRANLLLTARLNLLQAWANLLLVMIESNDFKSTPKMAFLLQALQAILPTLEAFSSLKSDEAFELARVAKVLLWKLDFSQDSDAGLDREQFTVGNLIGDKLFQLFQLCLSAISQCSGTPELRSLYYSICYRYLTAVVDNDATVAATPASSTIGPTRSVTNARARTLKAITLYGDRLLNVICDDAYGSDTTCQTAAMILLNALVHTSRASSAAGVSPADVDCPIIDALNRLNFIGVLVDSLKEILNEWLAPSSTFDPSLSTNASPSLPIPASPSQQYTSAKLALLLQLCQTRQGAKYVLQANLFRALEQSGVFAADPELVEVDSESGVPRVVALERHYALLVALARVVGAAVTARGAHNIVQGRKFLTQHRGLVVHVLKKNAGIGGGVVGNSLASSINGGSTATMTRRDEILAQQALEERIEELAEAFMLLITATGFLEYESEQVPSEQPRAHTTFFH
5TPU , Knot 71 139 0.84 40 105 135 
GGGHMIKNCKILNLRAIRDNRGSLIALENNKEVPFEIKRVYYIFDTDPNFPRGAHAHKNLEQVLIMMSGSCDIILNDGKNYEKICLNRPDIGLYIGKNMWREMKNFSYGAKLLVLASDFYDAAAYIRNYDEFLRNINDT
4CIA , Knot 190 455 0.85 40 245 431 
SRAPDQDEIQRLPGLAKQPSFRQYSGYLKGSGSKHLHYWFVESQKDPENSPVVLWLNGGPGCSSLDGLLTEHGPFLVQPDGVTLEYNPYSWNLIANVLYLESPAGVGFSYSDDKFYATNDTEVAQSNFEALQDFFRLFPEYKNNKLFLTGESYAGIYIPTLAVLVMQDPSMNLQGLAVGNGLSSYEQNDNSLVYFAYYHGLLGNRLWSSLQTHCCSQNKCNFYDNKDLECVTNLQEVARIVGNSGLNIYNLYAPCAGGVPSHFRYEKDTVVVQDLGNIFTRLPLKRMWHQALLRSGDKVRMDPPCTNTTAASTYLNNPYVRKALNIPEQLPQWDMCNFLVNLQYRRLYRSMNSQYLKLLSSQKYQILLYNGDVDMACNFMGDEWFVDSLNQKMEVQRRPWLVKYGDSGEQIAGFVKEFSHIAFLTIKGAGHMVPTDKPLAAFTMFSRFLNKQPYE

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 \(c\).

\(|P_{f(7MVV_1)}(2) \setminus P_{f(5TPU_1)}(2)|=257\), \(|P_{f(5TPU_1)}(2) \setminus P_{f(7MVV_1)}(2)|=3\). 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 1:11110110011010010100101110101001001011011010111100001011011001100000110111101100000001110010010110000010001100010110010100000101110001010100000111001110100000011001011101110001011100011111000111111110000000100100111001011011001100110010100110010110110000010100101100000110110111000010110100110110010000011101111111010011010111010010010011001100001111111111011111000110100010010110100000000001101100111011101110001001001001110011000110110011110011000111010111010100110110010000000001010000010100111110010010101110110010001111101100010011101100110011000001011001110010010101000001010011001001000100001011010100110111011010100111100010111011000011000111000101100110101111100101011011011110000001011101101110011001110011100101110011100010111001101100001110110011111011001000111101110010011101010111011100000100100101101001011110110100011111000010100111100110010101100110111000110011001000110110101001111011011011101101000010110101100010111000111011001100111001011101100001101010110101100100000110110100101100001110100010100101010101110101111101000010111101101010101001011001111000100111010111010001100110111010100000110101101000110110111001101011100101001110111001010101110101101001110010110100110011110011001001000011010001101101011100011101101101101100000100110101001001011101100001110001001001111000000000110101100101000111011010001011101010110111011111100001000101111101101111010110010000110110110111101010000011100001011011100110110101011000010101001000100001011100010111011000111000100101001011010100110110001010000000111111011100001001111011010011101100101111110010011001111000101010001010111110100000010111110100000110011010110110001111101011010000111011110000111111101111110101100110100110000111101100011111111100110010110010100000111001100010011011111101011100000011000101000110
Pair \(Z_2\) Length of longest common subsequence
7MVV_1,5TPU_1 260 4
7MVV_1,4CIA_1 150 4
5TPU_1,4CIA_1 212 3

Newick tree

 
[
	5TPU_1:12.93,
	[
		7MVV_1:75,4CIA_1:75
	]:54.93
]

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 \((0.85)(0.8)(\frac{1923 }{\log_{20} 1923}-\frac{139}{\log_{20}139})=460.\)
Status Protein1 Protein2 d d1/2
Query variables 7MVV_1 5TPU_1 583 313
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]