25 lines
753 B
TeX
25 lines
753 B
TeX
\part{Sequence alignment}
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\section{Simililarity between sequences}
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A function $d$ is a distance between two sequences $x$ and $y$ in an alphabet $\Sigma$ if
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\begin{itemize}
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\item $x, y \in \Sigma^{*}, d(x, x) = 0$
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\item $\forall x, y \in \Sigma^{*}$ $d(x,y) = d(y,x)$
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\item $\forall x, y, z \in \Sigma^{*}$ $d(x, z) \leq d(x, y) + d(x, z)$
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\end{itemize}
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Here we are interested by the distance that is able to represent the transformation of $x$ to $y$ using three types of basic operations:
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\begin{itemize}
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\item Substition
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\item Insertion
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\item Deletion
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\end{itemize}
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Example:
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\begin{itemize}
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\item $sub(a, b) = \begin{cases} 0 & \text{if} a = b \\ 1 &\text{otherwise} \end{cases}$.
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\item $del(a) = 1$
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\item $ins(a) = 1$
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\end{itemize}
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