deletions | additions       diff --git a/Burst_Variance_Analysis.tex b/Burst_Variance_Analysis.tex  index 0cd2f62..7dfc5bb 100644  --- a/Burst_Variance_Analysis.tex  +++ b/Burst_Variance_Analysis.tex 
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\end{equation}  \subsection{BVA Implementation}  BVA analysis consists of four steps: 1) slicing bursts into sub-bursts containing a constant number of consecutive photons,~\textit{n}, 2) computing FRET efficiencies of each sub-burst, 3) calculating the empirical standard deviation ($s_E$) of sub-burst FRET efficiencies over the whole burst, and 4) comparing $s_E$ to the expected standard deviation of a shot-noise limited distribution~(eq.~\ref{eq:binom_std}). In order If, as in figure~\ref{fig:bva_static}, the observed FRET efficiency distribution   originates from a static mixture of FRET efficiency sub-populations (of different   non-interconverting molecules),   $s_E$ of each burst is only affected by shot noise and will follow the expected standard deviation curve based on eq.~\ref{eq:binom_std}.   Conversely, if the observed distribution originates from biomolecules of a single specie, which   interconverts between different FRET sub-populations in (times comparable to diffusion   time), as in figure~\ref{fig:bva_dynamic}, $s_E$ of each burst will be larger than the expected   shot-noise-limited standard deviation, hence it will be placed above the shot-noise standard   deviation curve (right panel on figure~\ref{fig:bva_dynamic}).  For implementation details please refer  to perform the  BVA using notebook included with FRETBursts  (\href{http://nbviewer.jupyter.org/github/tritemio/FRETBursts_notebooks/blob/master/notebooks/Example%20-%20Burst%20Variance%20Analysis.ipynb}{link}).  \paragraph{Python details}  With  FRETBursts, first, one has to obtain a user can easily get  the photon mask data needed  for each channel BVA analysis.   For start, we need two photon streams: photon during donor excitation (Dex) and acceptor photon during donor excitation (AemDex). These selections are obtained  by \verb|Data.get_ph_times| (see in 4.7) computing photon masks  as follows. follows (see section~\ref{sec:burststimes}):  \begin{lstlisting}  AemDex_mask = ds.get_ph_mask(ph_sel=Ph_sel(Dex='Aem'))   Dex_mask = ds.get_ph_mask(ph_sel=Ph_sel(Dex='DAem'))   AemDex_mask = ds.get_ph_mask(ph_sel=Ph_sel(Dex='Aem'))  AemDex_mask_d = AemDex_mask[Dex_mask]  \end{lstlisting}  Note that a Here, the first two variables (\verb|Dex_mask| and \verb|AemDex_mask|) select  photon time stamp array by \verb|Data.mburst| is streams  from µs-ALEX the all-photons timestamps arrays,  while BVA is based upon a single laser excitation. In this regards, to implement BVA for µs-ALEX data, one needs to reduce \verb|AemDex_mask_d|, selects acceptor photons from  the Dex  photon time stamp array as if it only contains photon data stream. As shown below, this selection is  needed to count acceptor photons in sub-bursts  during donor excitation by using \verb|Data.recompute_index_reduce|. In addition, the photon BVA analysis.  Next, we need burst  data array for accepter emission during relative to  donor excitation (AemDex_mask) has stream (by default   burst start-stop index refer  to be further selected accordingly. all-photons timestamps array).  \begin{lstlisting}  bursts = ds_FRET.mburst[0]  ph_d = ds_FRET.get_ph_times(ph_sel=Ph_sel(Dex='DAem'))  bursts = ds_FRET.mburst[0]  bursts_d = bursts.recompute_index_reduce(ph_d)  AemDex_mask_d = AemDex_mask[Dex_mask]  \end{lstlisting}  Using \verb|AemDex_mask_d[start:stop].sum| one can count Here, \verb|ph_d| contains  the number of photons emitted from acceptor in each sub-burst containing a constant number of consecutive photons,~\textit{n}. Then, FRET efficiencies (E_small) of sub-bursts are calculated and used to obtain Dex timestamps, \verb|bursts|  the empirical standard deviation ($s_E$) of sub-burst FRET efficiencies over original burst data and   \verb|bursts_d|  thewhole  burst as follows. data with start-stop index relative to \verb|ph_d|.  \begin{lstlisting}  n=7 Finally, once previous variables are computed, we can easily implement the BVA algorithm  by computing the $\sigma_E$ quantity for each burst.  Std_small=[] \begin{lstlisting}  n = 7  E_sub_std = []  for burst in bursts_d:  E_small=[] E_sub = []  startlist = range(burst.istart, burst.istop + 2 - n, n)  stoplist = [i + n for i in startlist]  for start, stop in zip(startlist, stoplist):   A_D = AemDex_mask_d[start:stop].sum()  E = A_D / n  E_small.append(E)  Std_small.append(np.std(E_small)) E_sub.append(E)  E_sub_std.append(np.std(E_sub))  \end{lstlisting}  After computations, one can plot $s_E$ and Here \verb|n| is  the expected standard deviation curve (according to~ eq.~\ref{eq:binom_std}; red curve) with BVA parameter defining  the respect to each burst's FRET efficiency as shown in the right panels number  of figure ~\ref{fig:bva_static} & ~\ref{fig:bva_dynamic}. photons in each sub-burst.  Finally, by plotting the 2D distribution of $s_E$ (i.e. \verb|E_sub_std|) versus the average (uncorrected) E   we obtain the BVA plot of figure~\ref{fig:bva_static} and~\ref{fig:bva_dynamic}.  If, as in figure~\ref{fig:bva_static}, the observed FRET efficiency distribution   originates from a static mixture of FRET efficiency sub-populations (of different   non-interconverting molecules),   $s_E$ of each burst is only affected by shot noise and will follow the expected standard deviation curve based on eq.~\ref{eq:binom_std}.   Conversely, if the observed distribution originates from biomolecules of a single specie, which   interconverts between different FRET sub-populations in (times comparable to diffusion   time), as in figure~\ref{fig:bva_dynamic}, $s_E$ of each burst will be larger than the expected   shot-noise-limited standard deviation, hence it will be placed above the shot-noise standard   deviation curve (right panel on figure~\ref{fig:bva_dynamic}).  For implementation details please refer to the BVA notebook included with FRETBursts  (\href{http://nbviewer.jupyter.org/github/tritemio/FRETBursts_notebooks/blob/master/notebooks/Example%20-%20Burst%20Variance%20Analysis.ipynb}{link}).