text: user240: Chromosome capture experiments, like Hi-C, typically bin the genome into distinct bins. A contact matrix, $M$, is given by $M_{i,j} = |\{pairs | mate_1 \in bin_i, mate_2 \in bin_j\}|$.
  If one of the read mates spans a bin boundary, where should that pair be assigned?
  For example, if $mate_1$ overlaps $bin_i$ and $mate_2$ overlaps both $bin_j$ and $bin_{j+1}$, should this read pair be assigned to $M_{i,j}$ or $M_{i,j+1}$? Should it be randomly assigned to either bin with equal probability? Should it be assigned to both?
  I know this may be a rare event, but if Hi-C datasets are generated using billions of reads (such as Rao et al., Cell, 2014), this is bound to happen.
  
  user2108: [Old question, but possibly still relevant to answer.]
  This will not necessarily be rare. One or the other of the mates could span the ligation junction itself, in which case your read start and end could be entirely different chromosomes. In fact, some tools specifically measure the quality of Hi-C libraries by measuring the number of such ligations directly observable within reads. This will be a much larger number of reads than bin-crossing reads.
  The safest thing to do in all such cases (IMO) is to take the read start position as the location of interest for each mate. That way, if a junction does occur, you still have an unambiguous position which is your best guess of where each end of the ligation product actually originates. This gets around both the minor issue of the bin-crossing problem and the major issue of the ligation junction problem. There is probably some imprecision here and you throw out some information, but sorting out the complex possible situations otherwise seems like a lot of hassle for minimal gain.
  
original_text: 240: <p>Chromosome capture experiments, like Hi-C, typically bin the genome into distinct bins. A contact matrix, <span class="math-container">$M$</span>, is given by <span class="math-container">$M_{i,j} = |\{pairs | mate_1 \in bin_i, mate_2 \in bin_j\}|$</span>.</p>
  
  <p>If one of the read mates spans a bin boundary, where should that pair be assigned?</p>
  
  <p>For example, if <span class="math-container">$mate_1$</span> overlaps <span class="math-container">$bin_i$</span> and <span class="math-container">$mate_2$</span> overlaps both <span class="math-container">$bin_j$</span> and <span class="math-container">$bin_{j+1}$</span>, should this read pair be assigned to <span class="math-container">$M_{i,j}$</span> or <span class="math-container">$M_{i,j+1}$</span>? Should it be randomly assigned to either bin with equal probability? Should it be assigned to both?</p>
  
  <p>I know this may be a rare event, but if Hi-C datasets are generated using billions of reads (such as <a href="https://doi.org/10/xqj" rel="nofollow noreferrer">Rao <em>et al.</em>, Cell, 2014</a>), this is bound to happen.</p>
   2108: <p>[Old question, but possibly still relevant to answer.]</p>
  <p>This will not necessarily be rare. One or the other of the mates could span the ligation junction itself, in which case your read start and end could be entirely different chromosomes. In fact, <a href="https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008839" rel="nofollow noreferrer">some tools</a> specifically measure the quality of Hi-C libraries by measuring the number of such ligations directly observable within reads. This will be a much larger number of reads than bin-crossing reads.</p>
  <p>The safest thing to do in all such cases (IMO) is to take the read start position as the location of interest for each mate. That way, if a junction does occur, you still have an unambiguous position which is your best guess of where each end of the ligation product actually originates. This gets around both the minor issue of the bin-crossing problem and the major issue of the ligation junction problem. There is probably some imprecision here and you throw out some information, but sorting out the complex possible situations otherwise seems like a lot of hassle for minimal gain.</p>
  