Antonino Ingargiola edited Concepts.tex  about 8 years ago

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$$n_t = n_a + \gamma\,n_d $$  The former includes all photons, while the latter only photons during   donor execitation excitation  periods. The inclusion of $\gamma$ factor allows to correct  bias when comparing the number of bursts accross across  several sub-populations. The results of burst search is a distribution of burst sizes that approximately   follows an exponential distribution.  Bursts with large size (which contain most of the information)  are much less frequent than bursts with smaller sizes. For this reason, it is   important to select burst sizes larger than a threshold in order  to properly characterize FRET populations(see populations (see  section~\ref{sec:burstsel}). Selecting bursts by size is a critically important step.  A too low threshold will broaden the FRET populations and introduce  artifacts (spurious peaks and patterns) due to the majority of bursts  having E and S computed from ratios of small integers.   Conversely Conversely,  a too high threshold will result in a lower number of bursts and possibly poor statistics in representing FRET populations.  When Additionally, when  selecting bursts (see section~~\ref{sec:burstsel}), section~\ref{sec:burstsel}),  it is important to use $\gamma$-corrected burst sizes,  in order to avoid under-representing some FRET sub-populations  due to different quantum yields between donor and acceptor dyes and/or  

The weighting can be used to build weighted histograms and Kernel Density   Estimation (KDE) plots. When using weights, the choice of a particular   burst size threshold affects less the shape of the burst distribution,  so lower thresholds can be used (better statistics) wihtout without  broadening the peaks of sub-populations (better population identification).  \subsubsection{Python details}  FRETBursts has the option to weight bursts using $\gamma$-corrected   burst sizes and to include the acceptor excitation photons \verb|naa|.  Passing A weight proportional to the burst size is applied by passing  the argument \verb|weights='size'| to histogram or KDE  plot functions. The \verb|weights|  keyword can be also passed to fitting  functions a weight proportional in order  to fit  the burst size is applied. Other weighted E or S distributions (see section~\ref{sec:fretfit}).  Several other  weighting functions (for example quadratical) are listed in the \href{http://fretbursts.readthedocs.org/en/latest/fret_fit.html#fretbursts.fret_fit.get_weights}{\texttt{fret\_fit.get\_weights} documentation}.  \subsection{Plotting "Data"}