Update on Overleaf.

infrared-bookchapter.tex

@@ -389,7 +389,7 @@ To inform the choice of $X_i$ (before choosing $X_j$), we marginalize the sums o
 
 For sampling, the value of $X_i$ is selected with probability proportional
 to its corresponding partition function from the table. After $X_i$ is
-determined, the choice of $X_j$ becomes comparably simple. 
+determined, the choice of a value for $X_j$ becomes comparably simple. 
 
 For the previous examples, \Infrared's solving mechanism indeed boils down to fixing an arbitrary order of the variables and precomputing partition functions as described for the variables in base pairs. In the presence of more complex dependencies between variables, \Infrared still chooses values for the variables one-by-one in a predetermined optimized variable order. Given this order, it precomputes partial partition functions to derive the probabilities to choose values in order to sample from the desired Boltzmann distribution.
 The key for efficient uniform sampling is thus to precompute such partition functions as efficiently as possible. After the precomputation the choice for each variable is performed in constant time, resulting in linear time sampling. We are going to discuss further details of the \Infrared engine, when we progress to constraint network models with more complex dependencies as they result from simultaneously targeting several RNA structures.
@@ -402,15 +402,15 @@ sampler.set_target(0.75*n, 0.01*n, 'gc')
 samples = [sampler.targeted_sample() for _ in range(1000)]
 \end{Pythoncode}
 Note the use of \texttt{Sampler}'s method \texttt{targeted\_sample()} in place of \texttt{sample()}. This method provides access to an automatic mechanism that 
-returns only samples within the tolerance from the target. To make such a rejection strategy effective, we iteratively sample, estimate the current mean of the feature value and then update the feature weight. Concretely, \Infrared implements a form of multi-dimensional Boltzmann sampling~\cite{Bodini-Ponty-mdbs-2010} as applied in RNARedPrint~\cite{Hammer-RNARedPrint}.
+returns only samples within the tolerance from the target. To make such a rejection strategy effective, we iteratively sample, estimate the current mean of the feature value and then update the feature weight. Concretely, \Infrared implements a form of multi-dimensional Boltzmann sampling~\cite{Bodini-Ponty-mdbs-2010} as applied in RNARedPrint~\cite{hammer2019fixed}.
 
 \subsection{Controlling energy---Multiple features}
 
 While, for instructional purposes, we first presented how to target \GC content, an even more obvious target of RNA design is the energy of the target structure---or in other words, the affinity of the designs to the target structure. 
 
-Similar to the \GC content, RNA energy can be modeled as a sum of function values. This holds even for the detailed nearest-neighbor energy model of RNAs, where energy is composed of empirically determined or trained loop energies~\cite{NNDB, Andronescu}. Here, we focus on the much simpler base pair energy model, which has been demonstrated to be an effective proxy for the Turner (nearest neighbor) model in design applications~\cite{Hammer-RNARedPrint}.
+Similar to the \GC content, RNA energy can be modeled as a sum of function values. This holds even for the detailed nearest-neighbor energy model of RNAs, where energy is composed of empirically determined or trained loop energies~\cite{NNDB, Andronescu}. Here, we focus on the much simpler base pair energy model, which has been demonstrated to be an effective proxy for the Turner (nearest neighbor) model in design applications~\cite{hammer2019fixed}.
 
-In this simple model, every type of base pair (A-U, C-G or G-U) receives a different energy. To define the feature \texttt{energy}, we impose a function for each base pair \texttt{(i,j)} in the target structure and moreover distinguish terminal and non-terminal base pairs, simply by \texttt{(i-1, j+1) not in bps}. \Infrared provides a default parameterization, which has been originally trained for use with RNARedPrint~\cite{Hammer-RNARedPrint}.
+In this simple model, every type of base pair (A-U, C-G or G-U) receives a different energy. To define the feature \texttt{energy}, we impose a function for each base pair \texttt{(i,j)} in the target structure and moreover distinguish terminal and non-terminal base pairs, simply by \texttt{(i-1, j+1) not in bps}. \Infrared provides a default parameterization, which has been originally trained for use with RNARedPrint~\cite{hammer2019fixed}.
 \begin{Pythoncode}
     bps = parse(target)
     model.add_functions([BPEnergy(i, j, (i-1, j+1) not in bps)