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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