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Parikh vectors
7LQP_1 6QRT_1 5RLI_1 Letter Amino acid
14 48 46 A Alanine
6 37 29 D Aspartic acid
16 37 32 G Glycine
4 23 24 F Phenylalanine
5 10 30 N Asparagine
2 1 26 C Cysteine
8 11 18 Q Glutamine
6 10 12 H Histidine
13 11 34 K Lycine
14 20 53 V Valine
8 39 50 L Leucine
3 8 8 M Methionine
8 11 40 S Serine
11 16 50 T Threonine
4 35 30 R Arginine
14 26 23 E Glutamic acid
15 11 29 I Isoleucine
5 19 30 P Proline
3 6 3 W Tryptophan
4 9 34 Y Tyrosine 

7LQP_1|Chains A, B|Integrase|Human immunodeficiency virus 1 (11676)
>6QRT_1|Chain A|Xylose isomerase|Streptomyces rubiginosus (1929)
>5RLI_1|Chains A, B|Helicase|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
7LQP , Knot 80 163 0.83 40 123 161 
MHGEVDSSPGIWQLDCTHLEGKVILVAVHVASGYIEAEVIPAETGQETAYFLLKLAGRWPVKTVHTDNGSNFTSTTVKAACEWAGIKQEFGIPYNPQSQGVIESMNKELKKIIGQVRDQAEHLKTAVQMAVFIHNKKRKGGIGGYSAGERIVDIIATDIETKE
6QRT , Knot 161 388 0.82 40 206 357 
MNYAPTPVDRFTFGLWTVGWQGRDPFGDATRRALDPVESVRRLAELGAHGVTFHDDDLIPFGSSDSEREEHVKRFRQALDDTGMKVPMATTNLFTHPVFKDGGFTANDRDVRRYALRKTIRNIDLAVELGAETYVAWGGREGAESGGAKDVRDALDRMKEAFDLLGEYVTSQGYDIRFAIEPKPNQPRGDILLPTVGHALAFIERLERPELYGVNPEVGHEQMAGLNFPHGIAQALWAGKLFHIDLNGQNGIKYDQDLRFGAGDLRAAFWLVDLLESAGYSGPRHFDFKPPRTEDFDGVWASAAGCMRNYLILKERAAAFRADPEVQEALRASRLDELARPTAADGLQALLDDRSAFEEFDVDAAAARGMAFERLDQLAMDHLLGARG
5RLI , Knot 238 601 0.84 40 268 568 
AVGACVLCNSQTSLRCGACIRRPFLCCKCCYDHVISTSHKLVLSVNPYVCNAPGCDVTDVTQLYLGGMSYYCKSHKPPISFPLCANGQVFGLYKNTCVGSDNVTDFNAIATCDWTNAGDYILANTCTERLKLFAAETLKATEETFKLSYGIATVREVLSDRELHLSWEVGKPRPPLNRNYVFTGYRVTKNSKVQIGEYTFEKGDYGDAVVYRGTTTYKLNVGDYFVLTSHTVMPLSAPTLVPQEHYVRITGLYPTLNISDEFSSNVANYQKVGMQKYSTLQGPPGTGKSHFAIGLALYYPSARIVYTACSHAAVDALCEKALKYLPIDKCSRIIPARARVECFDKFKVNSTLEQYVFCTVNALPETTADIVVFDEISMATNYDLSVVNARLRAKHYVYIGDPAQLPAPRTLLTKGTLEPEYFNSVCRLMKTIGPDMFLGTCRRCPAEIVDTVSALVYDNKLKAHKDKSAQCFKMFYKGVITHDVSSAINRPQIGVVREFLTRNPAWRKAVFISPYNSQNAVASKILGLPTQTVDSSQGSEYDYVIFTQTTETAHSCNVNRFNVAITRAKVGILCIMSDRDLYDKLQFTSLEIPRRNVATLQ

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 \(c\).

\(|P_{f(7LQP_1)}(2) \setminus P_{f(6QRT_1)}(2)|=42\), \(|P_{f(6QRT_1)}(2) \setminus P_{f(7LQP_1)}(2)|=125\). 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 1:1010100011110100001010111111011010101011110010001011101110111001000010010000101100111100011110010001110010001001110100010010011011111000000111110011001101110010000
Pair \(Z_2\) Length of longest common subsequence
7LQP_1,6QRT_1 167 3
7LQP_1,5RLI_1 211 4
6QRT_1,5RLI_1 178 3

Newick tree

 
[
	5RLI_1:10.86,
	[
		7LQP_1:83.5,6QRT_1:83.5
	]:18.36
]

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 \((0.85)(0.8)(\frac{551 }{\log_{20} 551}-\frac{163}{\log_{20}163})=112.\)
Status Protein1 Protein2 d d1/2
Query variables 7LQP_1 6QRT_1 136 97
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]