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Table 2 q-gram profiles of strings \(x_1\), \(x_2\), \(y_1\), and \(y_2\); q-gram distance between \(x_1\) and \(y_1\); and q-gram distance between \(x_2\) and \(y_2\), giving \(D_{\beta ,q}(x, y) = 8\)

From: Circular sequence comparison: algorithms and applications

(a) \(G_q(x_1)\)
 \(\texttt {AAA}\) 0
 \(\texttt {AGC}\) 0
 \(\texttt {AGT}\) 0
 \(\texttt {CCC}\) 0
 \(\texttt {CTA}\) 0
 \(\texttt {GAG}\) 1
 \(\texttt {GCG}\) 0
 \(\texttt {GGA}\) 1
 \(\texttt {GGG}\) 0
 \(\texttt {GTC}\) 0
 \(\texttt {TAG}\) 0
 \(\texttt {TCT}\) 0
 \(\texttt {TTC}\) 0
 \(\texttt {TTT}\) 0
(b) \(G_q(y_1)\)
 \(\texttt {AAA}\) 0
 \(\texttt {AGC}\) 0
 \(\texttt {AGT}\) 0
 \(\texttt {CCC}\) 0
 \(\texttt {CTA}\) 0
 \(\texttt {GAG}\) 0
 \(\texttt {GCG}\) 0
 \(\texttt {GGA}\) 0
 \(\texttt {GGG}\) 0
 \(\texttt {GTC}\) 0
 \(\texttt {TAG}\) 0
 \(\texttt {TCT}\) 1
 \(\texttt {TTC}\) 1
 \(\texttt {TTT}\) 0
(c) \(D_{q}(x_1, y_1)\)
 \(\texttt {AAA}\) 0
 \(\texttt {AGC}\) 0
 \(\texttt {AGT}\) 0
 \(\texttt {CCC}\) 0
  \(\texttt {CTA}\) 0
 \(\texttt {GAG}\) 1
 \(\texttt {GCG}\) 0
 \(\texttt {GGA}\) 1
 \(\texttt {GGG}\) 0
 \(\texttt {GTC}\) 0
 \(\texttt {TAG}\) 0
 \(\texttt {TCT}\) 1
 \(\texttt {TTC}\) 1
 \(\texttt {TTT}\) 0
(d) \(G_q(x_2)\)
 \(\texttt {AAA}\) 0
 \(\texttt {AGC}\) 0
 \(\texttt {AGT}\) 0
 \(\texttt {CCC}\) 0
 \(\texttt {CTA}\) 1
 \(\texttt {GAG}\) 0
 \(\texttt {GCG}\) 0
 \(\texttt {GGA}\) 0
 \(\texttt {GGG}\) 0
 \(\texttt {GTC}\) 0
 \(\texttt {TAG}\) 0
 \(\texttt {TCT}\) 1
 \(\texttt {TTC}\) 0
 \(\texttt {TTT}\) 0
(e) \(G_q(y_2)\)
 \(\texttt {AAA}\) 0
 \(\texttt {AGC}\) 1
 \(\texttt {AGT}\) 0
 \(\texttt {CCC}\) 0
 \(\texttt {CTA}\) 0
 \(\texttt {GAG}\) 0
 \(\texttt {GCG}\) 1
 \(\texttt {GGA}\) 0
 \(\texttt {GGG}\) 0
 \(\texttt {GTC}\) 0
 \(\texttt {TAG}\) 0
 \(\texttt {TCT}\) 0
 \(\texttt {TTC}\) 0
 \(\texttt {TTT}\) 0
(f) \(D_{q}(x_2, y_2)\)
 \(\texttt {AAA}\) 0
 \(\texttt {AGC}\) 1
 \(\texttt {AGT}\) 0
 \(\texttt {CCC}\) 0
 \(\texttt {CTA}\) 1
 \(\texttt {GAG}\) 0
 \(\texttt {GCG}\) 1
 \(\texttt {GGA}\) 0
 \(\texttt {GGG}\) 0
 \(\texttt {GTC}\) 0
 \(\texttt {TAG}\) 0
 \(\texttt {TCT}\) 1
 \(\texttt {TTC}\) 0
 \(\texttt {TTT}\) 0