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Parikh vectors
5MIB_1 4JLK_1 6CNV_1 Letter Amino acid
41 13 22 I Isoleucine
35 28 21 S Serine
43 15 35 T Threonine
16 13 14 R Arginine
10 29 14 E Glutamic acid
17 12 10 H Histidine
40 11 25 P Proline
36 13 21 V Valine
28 13 11 Q Glutamine
47 13 35 G Glycine
3 17 29 K Lycine
9 7 4 W Tryptophan
13 12 11 Y Tyrosine
52 11 18 A Alanine
36 13 20 N Asparagine
4 7 4 M Methionine
30 12 7 F Phenylalanine
38 11 11 D Aspartic acid
8 2 11 C Cysteine
40 28 24 L Leucine 

5MIB_1|Chain A|Laccase 2|Steccherinum murashkinskyi (2721089)
>4JLK_1|Chains A, B|Deoxycytidine kinase|Homo sapiens (9606)
>6CNV_1|Chain A|Hemagglutinin|Influenza B virus (1275762)
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 \(w=f(c)\)
5MIB , Knot 211 546 0.81 40 234 496 
MASFKSIAALIALIFAVNAAQIGPVTDLHITNANISPDGFSRPAVLAGGTFPGPTIAGNTGDNFQITVFNDLTDPSMLTDTSIHWHGLFQKGTNWADGPAFVTQCPIITGQSFDYNFNVPGQAGTFWYHSHLSTQYCDGLRGPFVVYDPNDPNASLYDVDDDTTIITLADWYHTLAQQEPIGAAITADATLINGLGRSFTNTTASPLSVITVQSGKRYRMRLVSISCDPNYLFSIDGHDMTIIEVDGVNSQQLTVDQIQIFAAQRYSFVLNANQPVGNYWIRAQPNSGGQGFDGGINSAILRYEGATVEDPTTTAPTTFSNPLVETDLHPLADLGVPGQPFRGGADDPLVLNLAFANGRFSIDGVSFVPPTVPVLLQILSGAQNAQDLLPAGSVISLPSNSVIEVALPAGAAGGPHPFHLHGHNFAVVQSANNATPNYVNPIWRDTVSIGGTGDNVTIRFTTNNPGPWFLHCHIDWHLEAGFAIVFAEDIPDTASANPVPQAWSDLCPAYDQAHNISTATRQDFQILCICGILHVNFRQEERCGIS
4JLK , Knot 126 280 0.84 40 186 268 
MGSSHHHHHHSSGLVPRGSHMATPPKRSSPSFSASSEGTRIKKISIEGNIAAGKSTFVNILKQLSEDWEVVPEPVARWSNVQSTQDEFEELTMEQKNGGNVLQMMYEKPERWSFTFQTYACLSRIRAQLASLNGKLKDAEKPVLFFERSVYSDRYIFASNLYESESMNETEWTIYQDWHDWMNNQFGQSLELDGIIYLQATPETCLHRIYLRGRNEEQGIPLEYLEKLHYKHESWLLHRTLKTNFDYLQEVPILTLDVNEDFKDKYESLVEKVKEFLSTL
6CNV , Knot 150 347 0.84 40 203 328 
DRICTGITSSNSPHVVKTATQGEVNVTGVIPLTTTPTKSHFANLKGTETRGKLCPKCLNCTDLDVALGRPKCTGKIPSARVSILHEVRPVTSGCFPIMHDRTKIRQLPNLLRGYEHIRLSTHNVINAENAPGGPYKIGTSGSCPNITNGNGFFATMAWAVPKNDKNKTATNPLTIEVPYICTEGEDQITVWGFHSDNETQMAKLYGDSKPQKFTSSANGVTTHYVSQIGGFPNQTEDGGLPQSGRIVVDYMVQKSGKTGTITYQRGILLPQKVWCASGRSKVIKGSLPLIGEADCLHEKYGGLNKSKPYYTGEHAKAIGNCPIWVKTPLKLANGTKYRPPAKLLKER

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 \(c\).

\(|P_{f(5MIB_1)}(2) \setminus P_{f(4JLK_1)}(2)|=117\), \(|P_{f(4JLK_1)}(2) \setminus P_{f(5MIB_1)}(2)|=69\). 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 1:110100111111111110110111100101001010101100111111101111011100100101011001001011000010101110010011011111000111010010001011101101100001000000110111110010010101001000001101101000110001111110101011011100100001011011010010000101101000100110101001011010110000101001011110000111010011100110101001101101110011100011010010001100100111000101110111110110111001111011110101010110111101111101101100100111110110110001101111111111101101010011110010010100101110001011101001010100001111110001010101111111100110010101110110010110001001001000010110101110101000000110
Pair \(Z_2\) Length of longest common subsequence
5MIB_1,4JLK_1 186 4
5MIB_1,6CNV_1 167 4
4JLK_1,6CNV_1 177 3

Newick tree

 
[
	4JLK_1:93.07,
	[
		5MIB_1:83.5,6CNV_1:83.5
	]:9.57
]

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 \((0.85)(0.8)(\frac{826 }{\log_{20} 826}-\frac{280}{\log_{20}280})=149.\)
Status Protein1 Protein2 d d1/2
Query variables 5MIB_1 4JLK_1 187 143
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]