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Parikh vectors
6STS_1 5JOV_1 2LTT_1 Letter Amino acid
4 31 2 M Methionine
2 64 1 Y Tyrosine
7 42 4 N Asparagine
5 42 0 Q Glutamine
9 72 12 E Glutamic acid
10 57 9 L Leucine
14 52 2 T Threonine
5 53 4 D Aspartic acid
0 20 7 H Histidine
18 63 9 K Lycine
1 48 2 P Proline
5 49 2 F Phenylalanine
8 48 4 S Serine
2 26 3 W Tryptophan
5 62 3 A Alanine
6 40 3 R Arginine
11 80 5 G Glycine
9 39 5 I Isoleucine
2 6 0 C Cysteine
10 61 3 V Valine 

6STS_1|Chains A, B|Myelin P2 protein|Homo sapiens (9606)
>5JOV_1|Chain A|Alpha-xylosidase BoGH31A|Bacteroides ovatus (28116)
>2LTT_1|Chains A, B|Putative uncharacterized protein ydbC|Lactococcus lactis subsp. lactis (272623)
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 \(w=f(c)\)
6STS , Knot 68 133 0.83 38 110 128 
GMSNKFLGTWKLVSSENFDDYMKALGVGLATQKLGNLAKPTVIISKKGDIITIRTESTFKNTEISFKLGQEFEETTADNRKTKSIVTLQRGSLNQVQRWDGKETTIKRKLVNGKMVAECKMKGVVCTRIYEKV
5JOV , Knot 360 955 0.86 40 333 901 
MGSSHHHHHHSSGLEVLFQGPASNKVYEKTGDSVIVKVQHKETGGPRLVRLQVMGDKLIHVSATADSKFADPQSLIVVPQKKQTSFAVVQNGDTITVSTEEVKASVLASTGEVWFTDKNGELILQENKGGGKTFTPIEVEGTKGYTVCQVFESPEDEAFYGLGQHQADEFNYKGKNEELFQYNTKVSVPFVVSNKNYGILLDSYSFCRFGNPNDYSQLNRIFKLYDKTGQEGALTGTYVPKKGETLVRREDSIYFENLKTIENLPKKLPLMGAKVTYEGEIEPAQTGEFKFILYYAGYVKVYLNNEPVVPERWRTAWNPNSYKFAAHLEAGKRVPLKIEWQPDGGQSYCGLRALTPVNPEEQGKQSWWSEMTKQLDYYFMAGENMDDVISGYRSLTGKSPVMPKWAMGFWQSREKYNTQEEMLGALKGFRDRKIPLDNIVLDWNHWPENAWGSHEFDKARFPDPKAMVDSIHAMHARMMISVWPKFYVTTEHFKEFDENGWMYQQSVKDSLKDWVGPGYHYGFYDAYDPDARKLFWKQMYEHYYPLGIDAWWMDASEPNVRDCTDLEYRKALCGPTALGSSTEFFNAYALMNAEAIYDGQRGVDNNKRVFLLTRSGFAGLQRYSTATWSGDIGTRWEDMKAQISAGLNFAMSGIPYWTMDIGGFCVENRYVAGQKQWNATKTENADYKEWRELNTRWYQFGAFVPLYRAHGQYPFREIWEIAPEGHPAYQSVVYYTKLRYNMMPYIYSLAGMTWFDDYTIMRPLVMDFTADAEVNDIGDQFMFGPSFMVSPVYRYGDRSREIYFPQAEGWYDFYSGKFQAGGERKVIEAPYERIPLYVRAGAIIPFGDDIQYTDEKPAEHIRLYIYQGADGEFTLYEDEGVNYNYEQGMYAMIPMKYDEATKTLVIGERQGEFPGMLKERTFTVVTVNKEKAQPFDLNAKGVTVKYNGSEQTLKL
2LTT , Knot 43 80 0.78 36 64 73 
MADKLKFEIIEELIVLSENAKGWRKELNRVSWNDAEPKYDIRTWSPDHEKMGKGITLSEEEFGVLLKELGNKLEHHHHHH

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 \(c\).

\(|P_{f(6STS_1)}(2) \setminus P_{f(5JOV_1)}(2)|=7\), \(|P_{f(5JOV_1)}(2) \setminus P_{f(6STS_1)}(2)|=230\). 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 1:1100011101011000010001011111110001101101011100010110100000100001010110010000100000001101001010010010100001000110101110001011100010001
Pair \(Z_2\) Length of longest common subsequence
6STS_1,5JOV_1 237 4
6STS_1,2LTT_1 110 3
5JOV_1,2LTT_1 275 6

Newick tree

 
[
	5JOV_1:14.76,
	[
		6STS_1:55,2LTT_1:55
	]:89.76
]

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 \((0.85)(0.8)(\frac{1088 }{\log_{20} 1088}-\frac{133}{\log_{20}133})=261.\)
Status Protein1 Protein2 d d1/2
Query variables 6STS_1 5JOV_1 333 188
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]