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Parikh vectors
2JHC_1 6IRU_1 7PVD_1 Letter Amino acid
36 13 14 S Serine
22 13 15 T Threonine
28 6 10 Y Tyrosine
39 18 9 A Alanine
56 12 9 R Arginine
8 8 10 Q Glutamine
30 11 9 P Proline
39 12 15 I Isoleucine
40 16 9 V Valine
25 5 10 F Phenylalanine
15 2 5 W Tryptophan
49 13 16 D Aspartic acid
34 18 17 G Glycine
36 5 20 K Lycine
27 3 9 M Methionine
62 26 24 L Leucine
23 3 13 N Asparagine
5 2 9 C Cysteine
45 13 12 E Glutamic acid
25 9 9 H Histidine 

2JHC_1|Chain A|VP4 CORE PROTEIN|BLUETONGUE VIRUS 10 (ISOLATE USA) (10900)
>6IRU_1|Chains A, B, C|peptidase DR_1070|Deinococcus radiodurans (243230)
>7PVD_1|Chains A[auth a], B[auth b], C[auth c]|Glycoprotein G2|Lassa virus (strain Mouse/Sierra Leone/Josiah/1976) (11622)
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 \(w=f(c)\)
2JHC , Knot 256 644 0.85 40 285 599 
MPEPHAVLYVTNELSHIVKDGFLPIWKLTGDESLNDLWLENGKYATDVYAYGDVSKWTIRQLRGHGFIFISTHKNVQLADIIKTVDVRIPREVARSHDMKAFENEIGRRRIRMRKGFGDALRNYAFKMAIEFHGSEAETLNDANPRLHKIYGMPEIPPLYMEYAEIGTRFDDEPTDEKLVSMLDYIVYSAEEVHYIGCGDLRTLMQFKKRSPGRFRRVLWHVYDPIAPECSDPNVIVHNIMVDSKKDILKHMNFLKRVERLFIWDVSSDRSQMNDHEWETTRFAEDRLGEEIAYEMGGAFSSALIKHRIPNSKDEYHCISTYLFPQPGADADMYELRNFMRLRGYSHVDRHMHPDASVTKVVSRDVRKMVELYHGRDRGRFLKKRLFEHLHIVRKNGLLHESDEPRADLFYLTNRCNMGLEPSIYEVMKKSVIATAWVGRAPLYDYDDFALPRSTVMLNGSYRDIRILDGNGAILFLMWRYPDIVKKDLTYDPAWAMNFAVSLKEPIPDPPVPDISLCRFIGLRVESSVLRVRNPTLHETADELKRMGLDLSGHLYVTLMSGAYVTDLFWWFKMILDWSAQNREQKLRDLKRSAAEVIEWKEQMAERPWHVRNDLIAALREYKRKMGMREGASIDSWLELLRHL
6IRU , Knot 96 208 0.82 40 143 198 
MVRLLLTSFQHPSMAQFIGGKRVAYIPDAARSYADAPFVQKEREGLEKQGLELINLPLSHTDLAAVETTLNAVDGVYVAGGETFDLLQVLRSTGSDKVITRRVRQGLPYIGCSAGSVVAGPTIEAVSLMDSPDIAPDLKDYTGLGLTELAVIPHASGSISQFPIETIADTVRTYGERWPLCLLRDGQALWIEDGEVRLLNLEHHHHHH
7PVD , Knot 113 244 0.84 40 178 236 
GTFTWTLSDSEGKDTPGGYCLTRWMLIEAELKCFGNTAVAKCNEKHDEEFCDMLRLFDFNKQAIQRLKAEAQMSIQLINKAVNALINDQLIMKNHLRDIMGIPYCNYSKYWYLNHTTTGRTSLPKCWLVSNGSYLNETHFSDDIEQQADNMITEMLQKEYMERQGKTPLGLVDLFVFSTSFYLISIFLHLVKIPTHRHIVGKSCPKPHRLNHMGICSCGLYKQPGVPVKWKRGGGSDYKDDDDK

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 \(c\).

\(|P_{f(2JHC_1)}(2) \setminus P_{f(6IRU_1)}(2)|=174\), \(|P_{f(6IRU_1)}(2) \setminus P_{f(2JHC_1)}(2)|=32\). 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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
Pair \(Z_2\) Length of longest common subsequence
2JHC_1,6IRU_1 206 4
2JHC_1,7PVD_1 209 4
6IRU_1,7PVD_1 175 3

Newick tree

 
[
	2JHC_1:10.63,
	[
		6IRU_1:87.5,7PVD_1:87.5
	]:21.13
]

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 \((0.85)(0.8)(\frac{852 }{\log_{20} 852}-\frac{208}{\log_{20}208})=177.\)
Status Protein1 Protein2 d d1/2
Query variables 2JHC_1 6IRU_1 228 147.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]