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Parikh vectors
3QVI_1 5NVN_1 4CBF_1 Letter Amino acid
31 12 30 E Glutamic acid
24 14 55 G Glycine
31 12 45 T Threonine
4 6 10 W Tryptophan
35 7 47 V Valine
8 15 20 R Arginine
7 6 14 H Histidine
7 7 18 M Methionine
36 12 30 S Serine
13 9 30 A Alanine
4 2 13 C Cysteine
47 9 31 K Lycine
28 13 25 I Isoleucine
40 15 34 L Leucine
36 9 20 F Phenylalanine
16 10 15 P Proline
22 6 10 Y Tyrosine
33 8 16 N Asparagine
22 8 20 D Aspartic acid
7 9 12 Q Glutamine 

3QVI_1|Chains A, B, C, D|Histo-aspartic protease|Plasmodium falciparum (5833)
>5NVN_1|Chains A, C|Eukaryotic translation initiation factor 4E type 2|Homo sapiens (9606)
>4CBF_1|Chains A, C, E|ENVELOPE PROTEIN E|DENGUE VIRUS 2 (11060)
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 \(w=f(c)\)
3QVI , Knot 180 451 0.81 40 217 424 
MNLTIKEEDFTNTFMKNEESFNTFRVTKVKRWNAKRLFKILFVTVFIVLAGGFSYYIFENFVFQKNRKINHIIKTSKYSTVGFNIENSYDRLMKTIKEHKLKNYIKESVKLFNKGLTKKSYLGSEFDNVELKDLANVLSFGEAKLGDNGQKFNFLFHTASSNVWVPSIKCTSESCESKNHYDSSKSKTYEKDDTPVKLTSKAGTISGIFSKDLVTIGKLSVPYKFIEMTEIVGFEPFYSESDVDGVFGLGWKDLSIGSIDPYIVELKTQNKIEQAVYSIYLPPENKNKGYLTIGGIEERFFDGPLNYEKLNHDLMWQVDLDVHFGNVSSKKANVILDSATSVITVPTEFFNQFVESASVFKVPFLSLYVTTCGNTKLPTLEYRSPNKVYTLEPKQYLEPLENIFSALCMLNIVPIDLEKNTFVLGDPFMRKYFTVYDYDNHTVGFALAKNL
5NVN , Knot 94 189 0.87 40 148 185 
GPHMLEAEHPLQYNYTFWYSRRTPGRPTSSQSYEQNIKQIGTFASVEQFWRFYSHMVRPGDLTGHSDFHLFKEGIKPMWEDDANKNGGKWIIRLRKGLASRCWENLILAMLGEQFMVGEEICGAVVSVRFQEDIISIWNKTASDQATTARIRDTLRRVLNLPPNTIMEYKTHTDSIKMPGRLGPQRLLF
4CBF , Knot 199 495 0.83 40 250 463 
MRCVGVGNRDFVEGVSGGAWVDLVLEHGGCVTTMAQGKPTLDFELTKTTAKEVALLRTYCIEASISNITTATRCPTQGEPYLKEEQDQQYICRRDVVDRGWGNGCGLFGKGGVVTCAKFLCSGKITGNLVQIENLEYTVAVTVHNGDTHAVGNDTSSHGVTATITPRSPSVEVKLPDYGELTLDCEPRSGIDFNEMILMKMKKKTWLVHKQWFLDLPLPWTAGADTSEVHWNHKERMVTFKVPHAKRQDVTVLGSQEGAMHSALAGATEVDSGDGNHMFAGHLKCKVRMEKLRIKGMSYTMCSGKFSIDKEMAETQHGTTVVKVKYEGAGAPCKVPIEIRDVNKEKVVGRIISSTPFAENTNSVTNIELEPPFGDSYIVIGVGESALTLHWFRKGSSIGKMFESTYRGAKRMAILGETAWDFGSVGGLFTSLGKAVHQVFGSVYTTMFGGVSWMVRILIGFLVLWIGTNSRNTSMAMTCIAVGGITLFLGFTVQA

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 \(c\).

\(|P_{f(3QVI_1)}(2) \setminus P_{f(5NVN_1)}(2)|=126\), \(|P_{f(5NVN_1)}(2) \setminus P_{f(3QVI_1)}(2)|=57\). 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 1:1010100001000110000010010100100101001101111011111111100011001110000010011000000011101000000110010000100010001011001100000110010010100110110110101100100101110010001111010000000000000000000000000011010001101011100011011010110011010011110110000010111111100101101010110100000100110010111000001010111100011011100001000111010101011010000101110010011011001100110010110111101010001000110100001001001010001011001101101101111010000111101110001010000000111111001
Pair \(Z_2\) Length of longest common subsequence
3QVI_1,5NVN_1 183 3
3QVI_1,4CBF_1 161 4
5NVN_1,4CBF_1 192 3

Newick tree

 
[
	5NVN_1:97.80,
	[
		3QVI_1:80.5,4CBF_1:80.5
	]:17.30
]

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 \((0.85)(0.8)(\frac{640 }{\log_{20} 640}-\frac{189}{\log_{20}189})=128.\)
Status Protein1 Protein2 d d1/2
Query variables 3QVI_1 5NVN_1 160 115
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]