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Parikh vectors
6RYV_1 1OSZ_1 1AKI_1 Letter Amino acid
17 8 1 H Histidine
24 17 3 Y Tyrosine
38 7 14 N Asparagine
51 15 7 D Aspartic acid
39 6 6 I Isoleucine
51 11 10 S Serine
12 4 2 M Methionine
28 6 3 F Phenylalanine
41 13 2 P Proline
13 9 6 W Tryptophan
63 19 12 A Alanine
25 13 3 Q Glutamine
62 23 12 G Glycine
38 26 8 L Leucine
53 16 6 V Valine
56 19 7 T Threonine
30 21 11 R Arginine
17 5 8 C Cysteine
35 25 2 E Glutamic acid
21 11 6 K Lycine 

6RYV_1|Chain A|Kelch domain-containing protein|Colletotrichum graminicola (strain M1.001 / M2 / FGSC 10212) (645133)
>1OSZ_1|Chain A|MHC CLASS I H-2KB HEAVY CHAIN|Mus musculus (10090)
>1AKI_1|Chain A|LYSOZYME|Gallus gallus (9031)
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 \(w=f(c)\)
6RYV , Knot 277 714 0.85 40 285 641 
EFAITSCPNNETVWETPIGVKYTLCPGSDYQNGGASLQTVRDIQSSLECAKICDSDARCNRAVYDNVNKACDVKNSTNPMQWAADDRFETIRLTNDLPEGAFISTCSFNETSYRVPETNAEYRICPDTDYTGVNAKVVEGVTTIQACAELCSNTQDCRKSVFDHINNACAIKAAEPATSIFWVQDKQFSTIRLPENIDPAVKGKWGDLIRLPVIPVAAYIVPSYPEPSRLLFFSSWSNDAFSGASGMTQFGDYDFATGAISQRTVTNTHHDMFCPGISQLEDGRILIQGGSDADTVSIYDPATNEFTRGPNMTLARGYQTSCTLSNGKVFTIGGAYSGERVGKNGEVYDPVANAWTYLPGADFRPMLTNDHEGIWREDNHAWLFGWKNGSIFQAGPSKDQHWYGIQGNGTVAKAATRDDDDAMCGVWVMYDAVAGKIFSAGGSPDYTDSPATQRAHITTIGEPNTPAEVERVADMGFPRGFANAVVLPDGQVLVTGGQRMSLVFTNTDGILVAELFNPETREWKQMAPMAVPRNYHSVSILLPDATVFSGGGGMCWVQNVGDSTAGCDKTVDHSDGEIFEPPYLFNEDGSRAARPVISAISADPIKAGATLTFTVEGVEGQGTAALIRLGSVTHSVNSDQRRVPLNVTVSGNEYSATLPDDYGILLPGYYYLFVSTPQGTPSIAKTVHVILGLEQKLISEEDLNSAVDHHHHHH
1OSZ , Knot 122 274 0.83 40 175 264 
GPHSLRYFVTAVSRPGLGEPRYMEVGYVDDTEFVRFDSDAENPRYEPRARWMEQEGPEYWERETQKAKGNEQSFRVDLRTLLGYYNQSKGGSHTIQVISGCEVGSDGRLLRGYQQYAYDGCDYIALNEDLKTWTAADMAALITKHKWEQAGEAERLRAYLEGTCVEWLRRYLKNGNATLLRTDSPKAHVTHHSRPEDKVTLRCWALGFYPADITLTWQLNGEELIQDMELVETRPAGDGTFQKWASVVVPLGKEQYYTCHVYHQGLPEPLTLRW
1AKI , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL

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 \(c\).

\(|P_{f(6RYV_1)}(2) \setminus P_{f(1OSZ_1)}(2)|=144\), \(|P_{f(1OSZ_1)}(2) \setminus P_{f(6RYV_1)}(2)|=34\). 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 1:011100010000110011110001011000001110100100100010010100001000011000100100100000110111000100101000110111100001000000110001000101000001101011011001010101000000000011001001011011011001111000010010110010111010110110111111110111001010011110010001101101100110001101110000100000011011100100101110110010010100110001001101011010000001001011011110010011001010011101100111101011100000111000001111110010110111000001011010101101100000011011111001111011011101000001100010100110100110100110111101110111110101110110010111000011111011010000100111111100000101111010110111110110011000110000100001011011011000100110111011010110111010101011010101111011010001000000111010101000010110001111110001110010101011001011111000110000100110000000
Pair \(Z_2\) Length of longest common subsequence
6RYV_1,1OSZ_1 178 4
6RYV_1,1AKI_1 225 5
1OSZ_1,1AKI_1 201 3

Newick tree

 
[
	1AKI_1:11.94,
	[
		6RYV_1:89,1OSZ_1:89
	]:22.94
]

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 \((0.85)(0.8)(\frac{988 }{\log_{20} 988}-\frac{274}{\log_{20}274})=192.\)
Status Protein1 Protein2 d d1/2
Query variables 6RYV_1 1OSZ_1 243 166.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]