implementations "of" to "for"

paper/paper.md

@@ -42,7 +42,7 @@ Furthermore, numerical integration methods typically suffer from the so-called \
 This phenomenon refers to the fact that the computational complexity of the integration grows exponentially with the number of dimensions [@CurseOfDim-Book]. Reducing the error of the integration value requires increasing the number of function evaluation points $N$ exponentially, which significantly increases the runtime of the computation, especially for higher dimensions.
 Previous work has demonstrated that this problem can be mitigated by leveraging the \textit{single instruction, multiple data} parallelization of GPUs [@ZMCintegral].
 
-Although GPU-based implementations of multidimensional numerical integration in \mbox{\texttt{Python}} exist, some of these packages do not allow fully automatic differentiation [@borowka2019gpu], which is crucial for many machine learning applications [@Baydin2018autodiffinML]. Recently, to fill this gap, the packages \texttt{VegasFlow} [@VegasFlow-Paper] and \mbox{\texttt{ZMCintegral}} [@ZMCintegral] were developed. Both of these implementations are, however, based on \texttt{TensorFlow} [@Tensorflow], and there are currently no packages available that enable more than one-dimensional integration in \texttt{PyTorch}.
+Although GPU-based implementations for multidimensional numerical integration in \mbox{\texttt{Python}} exist, some of these packages do not allow fully automatic differentiation [@borowka2019gpu], which is crucial for many machine learning applications [@Baydin2018autodiffinML]. Recently, to fill this gap, the packages \texttt{VegasFlow} [@VegasFlow-Paper] and \mbox{\texttt{ZMCintegral}} [@ZMCintegral] were developed. Both of these implementations are, however, based on \texttt{TensorFlow} [@Tensorflow], and there are currently no packages available that enable more than one-dimensional integration in \texttt{PyTorch}.
 Additionally, the available GPU-based \texttt{Python} packages that allow fully automatic differentiation rely solely on \texttt{Monte} \texttt{Carlo} methods [@ZMCintegral; @VegasFlow-Paper]. 
 Even though such methods offer good speed\textendash accuracy trade-offs for problems of high dimensionality $n_{\mathrm{d}}$, the efficiency of deterministic methods, such as the \texttt{Newton\textendash Cotes} formulas, is often superior for lower dimensionality [@Vegas-paper].