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Parikh vectors
4ADP_1 9DYZ_1 1GDL_1 Letter Amino acid
9 0 3 W Tryptophan
43 0 1 R Arginine
14 0 0 C Cysteine
33 4 7 G Glycine
15 0 7 F Phenylalanine
34 0 5 P Proline
49 0 9 S Serine
30 0 14 E Glutamic acid
26 0 9 I Isoleucine
29 0 14 K Lycine
16 0 1 M Methionine
56 0 21 A Alanine
25 0 6 D Aspartic acid
17 0 5 H Histidine
34 4 17 V Valine
25 0 2 Y Tyrosine
14 0 6 N Asparagine
12 0 4 Q Glutamine
55 0 14 L Leucine
43 0 8 T Threonine 

4ADP_1|Chain A|RNA-DIRECTED RNA POLYMERASE|HEPATITIS C VIRUS (3052230)
>9DYZ_1|Chain A[auth AAA]|VVGG(DVA)(DVA)GG|synthetic construct (32630)
>1GDL_1|Chain A|LEGHEMOGLOBIN (NITROGEN MONOXY)|Lupinus luteus (3873)
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 \(w=f(c)\)
4ADP , Knot 228 579 0.83 40 254 538 
MASMSYSWTGALITPCSPEEEKLPINPLSNSLLRYHNKVYCTTTKSASLRAKKVTFDRMQVLDSYYDSVLKDIKLAASKVTARLLTMEEACQLTPPHSARSKYGFGAKEVRSLSGRAVNHIKSVWKDLLEDSETPIPTTIMAKNEVFCVDPTKGGKKAARLIVYPDLGVRVCEKMALYDITQKLPQAVMGASYGFQYSPAQRVEFLLKAWAEKKDPMGFSYDTRCFDSTVTERDIRTEESIYRACSLPEEAHTAIHSLTERLYVGGPMFNSKGQTCGYRRCRASGVLTTSMGNTITCYVKALAACKAAGIIAPTMLVCGDDLVVISESQGTEEDERNLRAFTEAMTRYSAPPGDPPRPEYDLELITSCSSNVSVALGPQGRRRYYLTRDPTTPIARAAWETVRHSPINSWLGNIIQYAPTIWARMVLMTHFFSILMAQDTLDQNLNFEMYGAVYSVSPLDLPAIIERLHGLDAFSLHTYTPHELTRVASALRKLGAPPLRAWKSRARAVRASLISRGGRAAVCGRYLFNWAVKTKLKLTPLPEARLLDLSSWFTVGAGGGDIYHSVSRARPRSHHHHHH
9DYZ , Knot 4 8 0.34 4 4 4 
VVGGVVGG
1GDL , Knot 76 153 0.83 38 115 151 
GALTESQAALVKSSWEEFNANIPKHTHRFFILVLEIAPAAKDLFSFLKGTSEVPQNNPELQAHAGKVFKLVYEAAIQLEVTGVVVTDATLKNLGSVHVSKGVADAHFPVVKEAILKTIKEVVGAKWSEELNSAWTIAYDELAIVIKKEMDDAA

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 \(c\).

\(|P_{f(4ADP_1)}(2) \setminus P_{f(9DYZ_1)}(2)|=250\), \(|P_{f(9DYZ_1)}(2) \setminus P_{f(4ADP_1)}(2)|=0\). 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 1:110100010111101001000011101100011000001000000010101001010010110000001100101110010101101001001011001000011110010010101100100110011000001110011100011010100110011011101011101000111001000110111110011000110010111011100001111000000100010000100000100100110010011001000101111110001000100000101110001100100010111100111111101110100111100001000000010110011000011110110100010110000001011111010000010001001110111001000110011101100110111011110011011110001000101010111001011011111001011011010000100100110110011111101100010110101100110111010011011100010101110101101001101111110100010010100000000
Pair \(Z_2\) Length of longest common subsequence
4ADP_1,9DYZ_1 250 3
4ADP_1,1GDL_1 193 3
9DYZ_1,1GDL_1 113 3

Newick tree

 
[
	4ADP_1:12.74,
	[
		1GDL_1:56.5,9DYZ_1:56.5
	]:68.24
]

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 \((0.85)(0.8)(\frac{587 }{\log_{20} 587}-\frac{8}{\log_{20}8})=179.\)
Status Protein1 Protein2 d d1/2
Query variables 4ADP_1 9DYZ_1 226 114
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]