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Parikh vectors
8DAU_1 1TQR_1 8XZK_1 Letter Amino acid
4 3 16 C Cysteine
73 0 0 E Glutamic acid
23 0 0 M Methionine
18 0 0 Y Tyrosine
64 0 0 V Valine
51 0 0 R Arginine
69 0 0 D Aspartic acid
60 4 17 G Glycine
51 0 0 I Isoleucine
28 0 0 F Phenylalanine
41 0 0 P Proline
39 4 0 T Threonine
3 0 0 W Tryptophan
81 6 8 A Alanine
12 0 0 H Histidine
69 0 0 L Leucine
41 0 0 S Serine
42 0 0 N Asparagine
49 0 0 K Lycine
20 0 0 Q Glutamine 

8DAU_1|Chains A, B, C, D, E, F|Cell division control protein 48|Saccharomyces cerevisiae (4932)
>1TQR_1|Chain A|DNA HIV-1 U5 LTR extremity|null
>8XZK_1|Chain A|RNA (53-MER)|unidentified eubacterium clone A70 (41312)
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 \(w=f(c)\)
8DAU , Knot 307 838 0.82 40 276 732 
GSHMGEEHKPLLDASGVDPREEDKTATAILRRKKKDNMLLVDDAINDDNSVIAINSNTMDKLELFRGDTVLVKGKKRKDTVLIVLIDDELEDGACRINRVVRNNLRIRLGDLVTIHPCPDIKYATRISVLPIADTIEGITGNLFDVFLKPYFVEAYRPVRKGDHFVVRGGMRQVEFKVVDVEPEEYAVVAQDTIIHWEGEPINREDEENNMNEVGYDDIGGCRKQMAQIREMVELPLRHPQLFKAIGIKPPRGVLMYGPPGTGKTLMARAVANETGAFFFLINGPEVMSKMAGESESNLRKAFEEAEKNAPAIIFIDEIDSIAPKRDKTNGEVERRVVSQLLTLMDGMKARSNVVVIAATNRPNSIDPALRRFGRFDREVDIGIPDATGRLEVLRIHTKNMKLADDVDLEALAAETHGYVGADIASLCSEAAMQQIREKMDLIDLDEDEIDAEVLDSLGVTMDNFRFALGNSNPSALRETVVESVNVTWDDVGGLDEIKEELKETVEYPVLHPDQYTKFGLSPSKGVLFYGPPGTGKTLLAKAVATEVSANFISVKGPELLSMWYGESESNIRDIFDKARAAAPTVVFLDELDSIAKARGGSLGDAGGASDRVVNQLLTEMDGMNAKKNVFVIGATNRPDQIDPAILRPGRLDQLIYVPLPDENARLSILNAQLRKTPLEPGLELTAIAKATQGFSGADLLYIVQRAAKYAIKDSIEAHRQHEAEKEVKVEGEDVEMTDEGAKAEQEPEVDPVPYITKEHFAEAMKTAKRSVSDAELRRYEAYSQQMKASRGQFSNFNFNDAPLGTTATDNANSNNSAPSGAGAAFGSNAEEDDDLYS
1TQR , Knot 7 17 0.38 8 11 13 
GGAAAATCTCTAGCAGT
8XZK , Knot 19 53 0.47 8 15 38 
GGGUGUGUACCGUUCAACUCGUCCCAGCUUCGACUGGGACUACGGGAGCGCCU

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 \(c\).

\(|P_{f(8DAU_1)}(2) \setminus P_{f(1TQR_1)}(2)|=268\), \(|P_{f(1TQR_1)}(2) \setminus P_{f(8DAU_1)}(2)|=3\). 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 1:1001100001110101101000000101110000000111100110000011110000100101101001110100000011111100010011001001100010101101101010101001001011111001011010110111010110100110010011101110010101101010001111000110101011000000001001100011100001101001101110010110111101101111011110100111011100011111110110110011100000100110010001111111001001110000001010001100110110110100011111100010010111001101000101111010101011010000101100101011110001011101101000111001000101101000010101100111010010111100010110001100101010011110010001000100111010000011101001111011110100111011100101011010110110110100000100110010111101111001001101011011011110001100110010110100011111100010010111101101001101111000101011010100011011101011101001101101101100110011000101000001000101010010100011010001010111010000110110010001001010000100001010010100101001111001000100000110111111100100000100
Pair \(Z_2\) Length of longest common subsequence
8DAU_1,1TQR_1 271 3
8DAU_1,8XZK_1 279 3
1TQR_1,8XZK_1 14 3

Newick tree

 
[
	8DAU_1:15.73,
	[
		1TQR_1:7,8XZK_1:7
	]:15.73
]

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 \((0.85)(0.8)(\frac{855 }{\log_{20} 855}-\frac{17}{\log_{20}17})=245.\)
Status Protein1 Protein2 d d1/2
Query variables 8DAU_1 1TQR_1 303 154
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]