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Parikh vectors
8CGU_1 6IGX_1 4WBE_1 Letter Amino acid
0 17 2 M Methionine
0 31 3 P Proline
0 3 1 W Tryptophan
388 58 2 A Alanine
353 17 1 C Cysteine
0 52 9 K Lycine
0 119 19 L Leucine
0 28 3 F Phenylalanine
0 70 17 E Glutamic acid
0 22 3 H Histidine
0 62 3 I Isoleucine
0 62 9 V Valine
0 42 9 D Aspartic acid
0 57 6 S Serine
0 18 5 Y Tyrosine
486 32 5 G Glycine
0 39 5 T Threonine
0 38 8 R Arginine
0 34 4 N Asparagine
0 38 6 Q Glutamine 

8CGU_1|Chain A|16S rRNA|Escherichia coli BW25113 (679895)
>6IGX_1|Chains A[auth B], C[auth D]|Condensin complex subunit 3|Homo sapiens (9606)
>4WBE_1|Chains A, B, C|Caprin-1|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 \(w=f(c)\)
8CGU , Knot 282 1540 0.44 8 16 64 
AAAUUGAAGAGUUUGAUCAUGGCUCAGAUUGAACGCUGGCGGCAGGCCUAACACAUGCAAGUCGAACGGUAACAGGAAGAAGCUUGCUUCUUUGCUGACGAGUGGCGGACGGGUGAGUAAUGUCUGGGAAACUGCCUGAUGGAGGGGGAUAACUACUGGAAACGGUAGCUAAUACCGCAUAACGUCGCAAGACCAAAGAGGGGGACCUUCGGGCCUCUUGCCAUCGGAUGUGCCCAGAUGGGAUUAGCUAGUAGGUGGGGUAACGGCUCACCUAGGCGACGAUCCCUAGCUGGUCUGAGAGGAUGACCAGCCACACUGGAACUGAGACACGGUCCAGACUCCUACGGGAGGCAGCAGUGGGGAAUAUUGCACAAUGGGCGCAAGCCUGAUGCAGCCAUGCCGCGUGUAUGAAGAAGCCCUUCGGGUUGUAAAGUACUUUCAGCGGGGAGGAAGGGAGUAAAGUUAAUACCUUUGCUCAUUGACGUUACCCGCAGAAGAAGCACCGGCUAACUCCGUGCCAGCAGCCGCGGUAAUACGGAGGGUGCAAGCGUUAAUCGGAAUUACUGGGCGUAAAGCGCACGCAGGCGGUUUGUUAAGUCAGAUGUGAAAUCCCCGGGCUCAACCUGGGAACUGCAUCUGAUACUGGCAAGCUUGAGUCUCGUAGAGGGGGGUAGAAUUCCAGGUGUAGCGGUGAAAUGCGUAGAGAUCUGGAGGAAUACCGGUGGCGAAGGCGGCCCCCUGGACGAAGACUGACGCUCAGGUGCGAAAGCGUGGGGAGCAAACAGGAUUAGAUACCCUGGUAGUCCACGCCGUAAACGAUGUCGACUUGGAGGUUGUGCCCUUGAGGCGUGGCUUCCGGAGCUAACGCGUUAAGUCGACCGCCUGGGGAGUACGGCCGCAAGGUUAAAACUCAAAUGAAUUGACGGGGGCCCGCACAAGCGGUGGAGCAUGUGGUUUAAUUCGAUGCAACGCGAAGAACCUUACCUGGUCUUGACAUCCACGGAAGUUUUCAGAGAUGAGAAUGUGCCUUCGGGAACCGUGAGACAGGUGCUGCAUGGCUGUCGUCAGCUCGUGUUGUGAAAUGUUGGGUUAAGUCCCGCAACGAGCGCAACCCUUAUCCUUUGUUGCCAGCGGUCCGGCCGGGAACUCAAAGGAGACUGCCAGUGAUAAACUGGAGGAAGGUGGGGAUGACGUCAAGUCAUCAUGGCCCUUACGACCAGGGCUACACACGUGCUACAAUGGCGCAUACAAAGAGAAGCGACCUCGCGAGAGCAAGCGGACCUCAUAAAGUGCGUCGUAGUCCGGAUUGGAGUCUGCAACUCGACUCCAUGAAGUCGGAAUCGCUAGUAAUCGUGGAUCAGAAUGCCACGGUGAAUACGUUCCCGGGCCUUGUACACACCGCCCGUCACACCAUGGGAGUGGGUUGCAAAAGAAGUAGGUAGCUUAACCUUCGGGAGGGCGCUUACCACUUUGUGAUUCAUGACUGGGGUGAAGUCGUAACAAGGUAACCGUAGGGGAACCUGCGGUUGGAUCACCUCCU
6IGX , Knot 314 839 0.84 40 295 730 
MGSSHHHHHHSQDPMGAERRLLSIKEAFRLAQQPHQNQAKLVVALSRTYRTMDDKTVFHEEFIHYLKYVMVVYKREPAVERVIEFAAKFVTSFHQSDMEDDEEEEDGGLLNYLFTFLLKSHEANSNAVRFRVCLLINKLLGSMPENAQIDDDVFDKINKAMLIRLKDKIPNVRIQAVLALSRLQDPKDDECPVVNAYATLIENDSNPEVRRAVLSCIAPSAKTLPKIVGRTKDVKEAVRKLAYQVLAEKVHMRAMSIAQRVMLLQQGLNDRSDAVKQAMQKHLLQGWLRFSEGNILELLHRLDVENSSEVAVSVLNALFSITPLSELVGLCKNNDGRKLIPVETLTPEIALYWCALCEYLKSKGDEGEEFLEQILPEPVVYADYLLSYIQSIPVVNEEHRGDFSYIGNLMTKEFIGQQLILIIKSLDTSEEGGRKKLLAVLQEILILPTIPISLVSFLVERLLHIIIDDNKRTQIVTEIISEIRAPIVTVGVAETLQKCLILCYELLKQMSISTGLSATMNGIIESLILPGIISIHPVVRNLAVLCLGCCGLQNQDFARKHFVLLLQVLQIDDVTIKISALKAIFDQLMTFGIEPFKTKKIKTLHCEGTEINSDDEQESKEVEETATAKNVLKLLSDFLDSEVSELRTGAAEGLAKLMFSGLLVSSRILSRLILLWYNPVTEEDVQLRHCLGVFFPVFAYASRTNQECFEEAFLPTLQTLANAPASSPLAEIDITNVAELLVDLTRPSGLNPQAKTSQDYQALTVHDNLAMKICNEILTSPCSPEIRVYTKALSSLELSSHLAKDLLVLLNEILEQVKDRTCLRALEKIKIQLEKGNKE
4WBE , Knot 61 120 0.81 40 95 118 
RREQLMREEAEQKRLKTVLELQYVLDKLGDDEVRTDLKQGLNGVPILSEEELSLLDEFYKLVDPERDMSLRLNEQYEHASIHLWDLLEGKEKPVCGTTYKVLKEIVERVFQSNYFDSTHN

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 \(c\).

\(|P_{f(8CGU_1)}(2) \setminus P_{f(6IGX_1)}(2)|=9\), \(|P_{f(6IGX_1)}(2) \setminus P_{f(8CGU_1)}(2)|=288\). 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 1:1110011111100011001011000111001110100110110111000110101010111001110110110111111111000100000001001101110110111011101110110100011111100100011011111111101100100111110110110011010010101101001011110011111111111000001110000001001001110101000111011110011001101110111101101100010001110110110000011001100011111110110011001010011110011110101100011100000101111110110110111111010010101101110101110001101011001010010101010111111100000011100101111010000011011111111111111011110011010000010001001101001000101111111101001100110000101001101100101101101011111101011101001100111100100111010111101010101110110001001110011101011110000011100011000111110010100011010011011100011100001011111111101111000011101011011011110101011111000111111101001101101111101100000011101111100110100011101011111010111111011101111001110100001101100010100101110110100110001111100101000001111010110000011110011010100111001100100011111101011001011110011110001110111001101111100010101110110111101010110001100011010110101111110000100011000011010001011111000001111101111101010000011111001011110111010010101100100100110001010010111101001110011100001011011101011000001000000100100110110001100111110001111111100100110110111001111111110111110110100111001001011000001011001111001010101010010110110101010111111111011000010111110111011100001011110101001011000111001111000101100011000010111100111100100110110010111001111010010110111010100000111000010101010010001001010010111110111001011111111011101100011000001111111010001001000010110001011001111011110010110111101100101111111000101100111001000000
Pair \(Z_2\) Length of longest common subsequence
8CGU_1,6IGX_1 297 4
8CGU_1,4WBE_1 109 2
6IGX_1,4WBE_1 228 4

Newick tree

 
[
	6IGX_1:14.58,
	[
		8CGU_1:54.5,4WBE_1:54.5
	]:95.08
]

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 \((0.85)(0.8)(\frac{2379 }{\log_{20} 2379}-\frac{839}{\log_{20}839})=369.\)
Status Protein1 Protein2 d d1/2
Query variables 8CGU_1 6IGX_1 311 296
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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