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Parikh vectors
6FXC_1 2ZTT_1 7YLR_1 Letter Amino acid
0 10 29 R Arginine
415 3 43 A Alanine
0 2 19 P Proline
0 2 15 T Threonine
0 4 24 V Valine
0 10 24 E Glutamic acid
335 3 8 C Cysteine
0 0 10 H Histidine
0 7 13 I Isoleucine
0 5 6 K Lycine
0 4 9 M Methionine
0 2 5 Y Tyrosine
0 3 21 D Aspartic acid
0 4 11 Q Glutamine
453 3 32 G Glycine
0 3 34 L Leucine
0 5 10 F Phenylalanine
0 8 8 S Serine
0 0 2 W Tryptophan
0 1 7 N Asparagine 

6FXC_1|Chains AB[auth Ba], A[auth Aa]|16S ribosomal RNA|Staphylococcus aureus (1280)
>2ZTT_1|Chains A, C|RNA-directed RNA polymerase catalytic subunit|Influenza A virus (A/Puerto Rico/8/34(H1N1)) (211044)
>7YLR_1|Chain A|Ferredoxin|Variovorax paradoxus (34073)
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 \(w=f(c)\)
6FXC , Knot 292 1539 0.46 8 16 64 
AUGGAGAGUUUGAUCCUGGCUCAGGAUGAACGCUGGCGGCGUGCCUAAUACAUGCAAGUCGAGCGAACGGACGAGAAGCUUGCUUCUCUGAUGUUAGCGGCGGACGGGUGAGUAACACGUGGAUAACCUACCUAUAAGACUGGGAUAACUUCGGGAAACCGGAGCUAAUACCGGAUAAUAUUUUGAACCGCAUGGUUCAAAAGUGAAAGACGGUCUUGCUGUCACUUAUAGAUGGAUCCGCGCUGCAUUAGCUAGUUGGUAAGGUAACGGCUUACCAAGGCAACGAUGCAUAGCCGACCUGAGAGGGUGAUCGGCCACACUGGAACUGAGACACGGUCCAGACUCCUACGGGAGGCAGCAGUAGGGAAUCUUCCGCAAUGGGCGAAAGCCUGACGGAGCAACGCCGCGUGAGUGAUGAAGGUCUUCGGAUCGUAAAACUCUGUUAUUAGGGAAGAACAUAUGUGUAAGUAACUGUGCACAUCUUGACGGUACCUAAUCAGAAAGCCACGGCUAACUACGUGCCAGCAGCCGCGGUAAUACGUAGGUGGCAAGCGUUAUCCGGAAUUAUUGGGCGUAAAGCGCGCGUAGGCGGUUUUUUAAGUCUGAUGUGAAAGCCCACGGCUCAACCGUGGAGGGUCAUUGGAAACUGGAAAACUUGAGUGCAGAAGAGGAAAGUGGAAUUCCAUGUGUAGCGGUGAAAUGCGCAGAGAUAUGGAGGAACACCAGUGGCGAAGGCGACUUUCUGGUCUGUAACUGACGCUGAUGUGCGAAAGCGUGGGGAUCAAACAGGAUUAGAUACCCUGGUAGUCCACGCCGUAAACGAUGAGUGCUAAGUGUUAGGGGGUUUCCGCCCCUUAGUGCUGCAGCUAACGCAUUAAGCACUCCGCCUGGGGAGUACGACCGCAAGGUUGAAACUCAAAGGAAUUGACGGGGACCCGCACAAGCGGUGGAGCAUGUGGUUUAAUUCGAAGCAACGCGAAGAACCUUACCAAAUCUUGACAUCCUUUGACAACUCUAGAGAUAGAGCCUUCCCCUUCGGGGGACAAAGUGACAGGUGGUGCAUGGUUGUCGUCAGCUCGUGUCGUGAGAUGUUGGGUUAAGUCCCGCAACGAGCGCAACCCUUAAGCUUAGUUGCCAUCAUUAAGUUGGGCACUCUAAGUUGACUGCCGGUGACAAACCGGAGGAAGGUGGGGAUGACGUCAAAUCAUCAUGCCCCUUAUGAUUUGGGCUACACACGUGCUACAAUGGACAAUACAAAGGGCAGCGAAACCGCGAGGUCAAGCAAAUCCCAUAAAGUUGUUCUCAGUUCGGAUUGUAGUCUGCAACUCGACUACAUGAAGCUGGAAUCGCUAGUAAUCGUAGAUCAGCAUGCUACGGUGAAUACGUUCCCGGGUCUUGUACACACCGCCCGUCACACCACGAGAGUUUGUAACACCCGAAGCCGGUGGAGUAACCUUUUAGGAGCUAGCCGUCGAAGGUGGGACAAAUGAUUGGGGUGAAGUCGUAACAAGGUAGCCGUAUCGGAAGGUGCGGCUGGAU
2ZTT , Knot 43 79 0.79 36 67 75 
QRGVLEDEQMYQRCCNLFEKFFPSSSYRRPVGISSMVEAMVSRARIDARIDFESGRIKKEEFTEIMKICSTIEELRRQK
7YLR , Knot 138 330 0.80 40 186 312 
MTAPTATLQLRVAEARQLNPLIRMLRLCAEDGRALPGFAAGAHIRVQVSLPDGRTDWRHYSLINFATARNATNAPTEYVIAVRKEAEGRGGSRFMHEGLNEGDTLAIEAPKNDFPLHTGPGGSVLVAGGIGVTPLATMAARRRAEGAPVRMHYAGRSRELMAFLPELQALLGDDLRVHADAEAGAPLDIDALLDGVPAGDRLYVCGPKVMLDAVLARTQARGWEHDRVHFELFTEPVAEEGDQPFEVELAQSGQRFTVPAGQSILDCLIEHGCDPMFDCKRGECGVCAVPVLEGEIDHRDYVLTAREKAQGNVMQICISRAKGARLVLDI

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 \(c\).

\(|P_{f(6FXC_1)}(2) \setminus P_{f(2ZTT_1)}(2)|=15\), \(|P_{f(2ZTT_1)}(2) \setminus P_{f(6FXC_1)}(2)|=66\). 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 1:101111110001100001100011110111010011011010100011010101011100111011101110111111000100000001101001101101110111011101101010111011000100010111100111101100001111110011110011010011101101000011100101011000111110111111011000010010010001011101110001010010100110011001101111011011000100111101101101010110011000111111101100110010100111100111101011000111000001011111101101101111110000001011011101111100011011110110100101011101101111100000111001011110000100100111111111010101010111011001010101000011011010001100111111001011001100101010011011001011011010101110110111010010001111001001110101111010101011101100000011100011010111110001011000110010111111001001111100111111000111010111111111111011110000101010110110111101010111110101111111010011011011111011000000110001011001101001101010111110101111100111011110011101000011011000101001011101101110100111010011111100000100000011010010110011010100111010000100011111101011001011110011110001111111001101111100010101110110111101010110001100011110110101111110000100111000011010000001101100001111101111000000000001111110111101101110110101011001001001100010100101111010011100111000010110111010110000011100011001001001001110011101000011100110010011011011100111111111011111011010011100100101000000101100011100101010101001011011101101011111101101111001011110011101110000101111001000001100011100101100010110001100101011110011110010011011001011100110101001011011101010000011100001010101001000100101001011111000101101000111100110111101100000011111001100100111110111101110110011110111100101101111011001010011111101011001110
Pair \(Z_2\) Length of longest common subsequence
6FXC_1,2ZTT_1 81 2
6FXC_1,7YLR_1 188 4
2ZTT_1,7YLR_1 183 3

Newick tree

 
[
	7YLR_1:10.52,
	[
		6FXC_1:40.5,2ZTT_1:40.5
	]:64.02
]

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 \((0.85)(0.8)(\frac{1618 }{\log_{20} 1618}-\frac{79}{\log_{20}79})=409.\)
Status Protein1 Protein2 d d1/2
Query variables 6FXC_1 2ZTT_1 291 166.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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