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\title[MASH]{Mash: fast genome and metagenome distance estimation}
\author[Don Armstrong]{Don L. Armstrong}
\institute[IGB]{Institute for Genomic Biology, Computing Genomes 
  for Reproductive Health, University of Illinois, Urbana-Champaign}

\begin{document}

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  \begin{center}
    Code and slides are here: 
    
    \qrcode[padding]{http://dla2.us/p/mashminhash2016}
    
    \url{http://dla2.us/p/mashminhash2016}
   \end{center}
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  \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{mash_minhash_paper/paper_frontpage}
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\begin{frame}{MinHash Algorithm}
  \begin{columns}
    \column{0.3\textwidth}
    \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{mash_minhash_paper/fig_1.png}
    \column{0.7\textwidth}
    \begin{itemize}
    \item Decompose dataset into k-mers
      \only<2>{
        \begin{digression}{What about strandedness}
          \begin{itemize} 
          \item Take lexically lowest sequence
            \begin{itemize}
            \item Given 7-mers 5'-ACTGCAC-3' and its reverse complement, 5'-GTGCAGT-3'
            \item A $\lt$ G
            \item Use ACTGCAC
            \end{itemize}
          \item Because $S(A \cup B)$ is a random sample of $A \cup B$
            the fraction of elements in $S(A \cup B)$ which are shared
            by $S(A)$ and $S(B)$ is an unbiased estimate of $J(A,B)$
          \item $J(A,B) \approx \frac{|S(A \cup B) \cap S(A) \cap (B)}{|S(A \cup B)|}$
          \end{itemize}
        \end{digression}
      }
    \item Hash k-mers (32/64bit)
    \item Estimate Jaccard Index $J(A,B)$
      \only<3>{
        \begin{digression}{Estimating Jaccard Index}
          $J(A,B) = \frac{|A \cap B|}{|A \cup B|}$ 
          \begin{itemize} 
          \item Sample randomly from $A$ and $B$
          \item Because $S(A \cup B)$ is a random sample of $A \cup B$
            the fraction of elements in $S(A \cup B)$ which are shared
            by $S(A)$ and $S(B)$ is an unbiased estimate of $J(A,B)$
          \item $J(A,B) \approx \frac{|S(A \cup B) \cap S(A) \cap (B)}{|S(A \cup B)|}$
          \end{itemize}
        \end{digression}
      }
    \item<3-> How can we randomly sample?
    \item<3-> Properties of the hash!
    \end{itemize}
  \end{columns}
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\begin{frame}{Hash functions}
  
\end{frame}

\begin{frame}{MurmerHash3 -- properties}
\end{frame}

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  \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{mash_minhash_paper/fig_2.png}
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  \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{mash_minhash_paper/fig_4.png}
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  \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{mash_minhash_paper/fig_5.png}
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\section*{References}

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  \begin{center}
    \mbox{}\vspace{-\baselineskip}
    \printbibliography[heading=none]
  \end{center}
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\end{document}