deletions | additions       diff --git a/Concepts.tex b/Concepts.tex  index 07a541d..23c6d6a 100644  --- a/Concepts.tex  +++ b/Concepts.tex 
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Identifying single-molecule bursts in the stream of photons is  one of the most crucial steps in the analysis of freely-diffusing single-molecule FRET data.  The widely used "sliding window" ``sliding window''  algorithm, introduced by the Seidel group in 1998 (\cite{Eggeling_1998}, \cite{Fries_1998}), involves searching for  $m$ consecutive photons detected during a period shorter than  $\Delta t$. In other words, bursts are regions of the photon stream where the  local rate (computed using $m$ photons) is above a minimal rate chosen as a  threshold. minimum threshold rate.  Eggeling did not provide any criteria a criterion  on how to choose the rate threshold and the number of photons $m$ and as therefore and, therefore,  it has become a common practice to manually adjust those parameters for each specific measurement.  A more general approach consists in taking into account the background rate of 
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during acceptor  excitation (\verb|Ph_sel(Aex='Aem')|).  After each burst search, it is useful necessary  to select bursts having a minimum number of photons (burst size). In the most  basic form, this selection can be performed during burst search by discarding  bursts with size smaller than a threshold $L$, as originally proposed by  Eggeling~\textit{et al.}~\cite{Eggeling_1998}.  This method, however, neglects the effect  of background and gamma γ  factor on the burst size and can lead to a selection bias of certain channels and/or sub-populations.  For this reason we encourage performing a burst size selection after background  correction, possibly taking into account the gamma γ  factor, as discussed in sections~\ref{sec:burstsizeweights} and~\ref{sec:burstsel}.  \subsection{γ-corrected burst sizes and weights} 
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The number of photon detected during a burst is commonly called the ``burst size''.  Bursts sizes are usually computed using either all photons, or photons detected   during donor excitation period. To compute the  burst size, size $n_t$,  FRETBursts uses one of the following formulas:  \begin{equation} 
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n_t = n_a + \gamma\,n_d + n_{aa}  \end{equation}  The former \noindent where $n_d$, $n_a$ and $n_aa$ have are the background-corrected  burst counts in different channels and excitation periods (section~\ref{sec:data_intro})  Eq.~\ref{eq:burstsize_dex}  includes only photons during donor excitation periods, while the latter eq.~\ref{eq:burstsize_allph}  includes all photons. The inclusion of $\gamma$ γ  factor allows to obtain a ``fair threshold'' and to correct bias when comparing the number of bursts across several sub-populations.  The results of burst search is a distribution of burst sizes that approximately  
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different photon detection efficiencies of donor and acceptor emission.  A simple way to mitigate the dependence on the burst size threshold is  weight weighting  bursts according to their size (i.e. their information content) so that the biggest bursts will have the highest weights.  The weighting can be used to build weighted histograms and Kernel Density   Estimation (KDE) plots. When using weights, the choice of a particular