deletions | additions       diff --git a/time_series_convergence.tex b/time_series_convergence.tex  index 2c53eed..b89de63 100644  --- a/time_series_convergence.tex  +++ b/time_series_convergence.tex 
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After \texttt{eq\_min\_ptiter} steps we call the \texttt{pymbar.detectEquilibration} function to find the initial burnout region of the time series to discard. \texttt{pymbar.detectEquilibration} loops over ever shorter segments of the time series looking for the one that gives the largest number of effectively uncorrelated samples, that being the equilibrated set of data, and it returns an equilibration time. From this point on we will only consider points in the timeseries past this equilibration time.  We would now expect to be dealing with a stationary time series while, as a matter of fact, the system is probably still slowly drifting. In any case, we want to estimate the integrate integrated  autocorrelation time which depends strongly on the length of the time series. When truncating the time series we might have been left with only a short array of point. For this reason we return as the predicted number of PT iterations \texttt{eq\_max\_ptiter}. When the time series is at least $1e5$ in length we then start updating the number of predicted PT iterations from Eq.~(\ref{eq:ptiter_prediction}). Since all replicas run for the same amount of time we take the largest number of steps from one of the replicas, typically the one corresponding to $k=0$. \end{document}