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Parikh vectors
6FUV_1 6TOF_1 6TKU_1 Letter Amino acid
15 4 24 Q Glutamine
41 4 24 K Lycine
18 3 21 P Proline
23 3 13 Y Tyrosine
42 8 48 A Alanine
29 7 39 N Asparagine
38 8 31 D Aspartic acid
0 5 5 C Cysteine
31 6 19 E Glutamic acid
33 5 63 G Glycine
15 15 42 L Leucine
16 6 12 M Methionine
19 9 40 S Serine
29 7 47 T Threonine
4 9 27 R Arginine
4 3 9 H Histidine
24 9 30 I Isoleucine
14 7 28 F Phenylalanine
9 0 8 W Tryptophan
23 10 54 V Valine 

6FUV_1|Chain A|Solute Binding Protein, BlMnBP1 in complex with mannotriose|Bifidobacterium (1678)
>6TOF_1|Chain A|B-cell lymphoma 6 protein|Homo sapiens (9606)
>6TKU_1|Chain A|depolymerase KP32gp38|Klebsiella phage KP32 (674082)
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 \(w=f(c)\)
6FUV , Knot 177 427 0.83 38 204 402 
NNKAGVTYPEIKLGETGKDLKATITFFNGRTDMGLASYPGKNWDAYIKEFNAMYPNITVKVQTDSNYADSALTRLQANNDSWDIMMIPAVDRSEFSNYFVSYGKTEDMDKEIKLANEKAYDGQTYGVATDGQTSGVVYNAKVFKEAGINELPKTPEEFQAALKAIKEKTKAVPLYTNFAEEWAMGAWDQYIGGNATGDPKFMNQIMPHDKTPFAKDDKAPDTHPYAVYKTLYDAVANGYTEEDYSTTDWESSKGKMNNGEIATMVLGAWAVPQMKQAGEHADDVQYMPFPITVDGKQYATLAGNYSMGINKNSDKDRQEAAMIFVKWMTEKSGYSKNEGGIPIVKNDDSYPDTYEHFKDVELIVDAPAKEGEEDLFADINSDSELGINNGNGKKIQDIVVDAANKTKTIDQIMGEWDQKWGKAVESE
6TOF , Knot 65 128 0.82 38 98 125 
GPGADSCIQFTRHASDVLLNLNRLRSRDILTDVVIVVSREQFRAHKTVLMACSGLFYSIFTDQLKCNLSVINLDPEINPEGFCILLDFMYTSRLNLREGNIMAVMATAMYLQMEHVVDTCRKFIKASE
6TKU , Knot 230 584 0.83 40 254 541 
MLDNFNQPKGSTIGVLKDGRTIQEAFDSLPRLESFSGSTATDKLRAAITLGVSEVAIGPVEGNGGRPYEFGDVVIPYPLRIVGCGSQGINVTKGTVLKRSAGASFMFHFTGEGQAQRPMGGGLFNINLNGDTATALGDIIKVTQWSYFKANNCAFQNMAGWGIRLKDVMESNISGNLFRRLGGPSGGGILFDDVRSAVTDNVNNLHIEDNTFALMSGPWIGSTANSNPDLIWIVRNKFEFDGTPAAPNTVDSYVLDFQQLSRAFIQDNGFTHFTTERNRYVGVLRVGATAVGTIKFEDNLLFACESAGLIAGGIVVSRGNVNNQGSATTAIKQFTNTSSKLCKLERVINVQSNGNVSVGQQILPDGYINMAELPGNTRLPSEYDADGETTSVLRVPANTQVRQWSVPKMYKDGLTVTKVTVRAKGAAAGAILSLQSGSTVLSTKSIDAGVWKNYVFYVKANQLQETLQLRNTGTADVLADGMVFGKVDYIDWDFAIAPGTLAAGAKYTTPNQSYLDVAGMRVQAVSIPMFDGPTTGLQVWVEATSANGSFVVVMKNDTGSELVTTVTRCRVRAFVSKGHHHHHH

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 \(c\).

\(|P_{f(6FUV_1)}(2) \setminus P_{f(6TOF_1)}(2)|=152\), \(|P_{f(6TOF_1)}(2) \setminus P_{f(6FUV_1)}(2)|=46\). 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 1:0001110010101100100101010110100011110011001010100101101010101000000100110010100001011111110000100011001000010001011000100100011100100011100101100111001100100101110110000011110001100111111000111010101011001110000111000011000101100010011101000000000010000101001011011111111101001100100100111110101000101110001110000000000111111011000010000011111100000010000010010111011100100011101000001110010100100111011000001001110100011011000
Pair \(Z_2\) Length of longest common subsequence
6FUV_1,6TOF_1 198 3
6FUV_1,6TKU_1 164 3
6TOF_1,6TKU_1 212 5

Newick tree

 
[
	6TOF_1:10.55,
	[
		6FUV_1:82,6TKU_1:82
	]:26.55
]

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 \((0.85)(0.8)(\frac{555 }{\log_{20} 555}-\frac{128}{\log_{20}128})=125.\)
Status Protein1 Protein2 d d1/2
Query variables 6FUV_1 6TOF_1 159 104
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]