capitalize Monte Carlo

latex/tex/abstract.tex

@@ -2,7 +2,7 @@
 
 The analytical cross section for the parton-level \(\qqgg\) diphoton
 process is calculated.  With the application to this in mind, some
-monte carlo integration and sampling methods are studied, implemented
+Monte Carlo integration and sampling methods are studied, implemented
 and compared. Proton-Proton scattering is simulated on the partonic
 level through the use of parton density functions. Throughout,
 obtained results are verified through comparison with the \sherpa\
@@ -15,7 +15,7 @@ including parton showers, hadronization and multiple interactions at
 
 Der analytische wirkungsquerschnitt fuer den \(\qqgg\) diphoton prozess
 wird berechnet. Mit hinblick auf die Anwendung auf diesen Prozess
-werden monte carlo Methoden untersucht, implementiert und
+werden Monte Carlo Methoden untersucht, implementiert und
 verglichen. Proton-Proton Streuung wird auf der partonischen ebene
 mithilfe von parton-density Funktionen simuliert.  Gewonnene resultate
 werden durchweg mit dem \sherpa\ event generator verifiziert. Zuletzt

latex/tex/introduction.tex

@@ -4,11 +4,11 @@
 Monte carlo methods have been and still are one of the most important
 tools for theoretical calculations in particle physics. Be it for
 validating the well established standard model or for making
-predictions about new theories, monte carlo simulations are the
+predictions about new theories, Monte Carlo simulations are the
 crucial interface of theory and experimental data, making them
 directly comparable. Furthermore horizontal scaling is almost trivial
-to implement in monte carlo algorithms, making them well adapted to
-modern parallel computing. In this the thesis, the use of monte carlo
+to implement in Monte Carlo algorithms, making them well adapted to
+modern parallel computing. In this the thesis, the use of Monte Carlo
 methods will be traced through from simple integration to the
 simulation of proton-proton scattering.
 
@@ -22,11 +22,11 @@ scope of this thesis. The differential and total cross section of this
 process is being calculated in leading order in \cref{chap:qqgg} and
 the obtained result is compared to the total cross section obtained
 with the \sherpa~\cite{Gleisberg:2008ta} event generator, used as
-matrix element integrator. In \cref{chap:mc} some simple monte carlo
+matrix element integrator. In \cref{chap:mc} some simple Monte Carlo
 methods are discussed, implemented and their results compared. First
-monte carlo integration is studies and the \vegas\
+Monte Carlo integration is studies and the \vegas\
 algorithm~\cite{Lepage:19781an} is implemented and
-evaluated. Subsequently monte carlo sampling methods are explored and
+evaluated. Subsequently Monte Carlo sampling methods are explored and
 the output of \vegas\ is used to improve the sampling
 efficiency. Histograms of observables are generated and compared to
 histograms from \sherpa using the \rivet~\cite{Bierlich:2019rhm}

latex/tex/monte-carlo/integration.tex

@@ -9,7 +9,7 @@ probability density on
 with a \(1\) in the fashion of \cref{eq:baseintegral}, the Integral
 of \(f\) over \(\Omega\) can be interpreted as the expected value
 \(\EX{F/\Rho}\) of the random variable \(F/\Rho\) under the
-distribution \(\rho\). This is the key to most monte carlo methods.
+distribution \(\rho\). This is the key to most Monte Carlo methods.
 
 \begin{equation}
   \label{eq:baseintegral}
@@ -77,9 +77,9 @@ The convergence of \cref{eq:approxexp} is not dependent on the
 dimensionality of the integration volume as opposed to many other
 numerical integration algorithms (trapezoid rule, Simpsons rule) that
 usually converge like \(N^{-\frac{k}{n}}\) with \(k\in\mathbb{N}\) as
-opposed to \(N^{-\frac{k}{n}}\) with monte carlo. Because integrals in
-particle physics usually have a high dimensionality, monte carlo
-integration is suitable there. When implementing monte carlo methods,
+opposed to \(N^{-\frac{k}{n}}\) with Monte Carlo. Because integrals in
+particle physics usually have a high dimensionality, Monte Carlo
+integration is suitable there. When implementing Monte Carlo methods,
 the random samples can be obtained through hardware or software random
 number generators (RNGs). Most implementations utilize software RNGs
 because supply pseudo-random numbers in a reproducible way, which

latex/tex/pdf/results.tex

@@ -97,7 +97,7 @@ stratified sampling (as discussed in \cref{sec:stratsamp-real}) and
 the hit-or-miss method. Because the stratified sampling requires very
 accurate upper bounds, they have been overestimated by
 \result{xs/python/pdf/overesimate}, which lowers the efficiency
-slightly but reduces bias. The monte carlo integrator was used to
+slightly but reduces bias. The Monte Carlo integrator was used to
 estimate the location of the maximum in each hypercube and then this
 estimate was improved by gradient ascend\footnote{Which becomes
   problematic, when performed close to a cut.}.

latex/tex/qqgammagamma/comparison.tex

@@ -2,7 +2,7 @@
 \label{sec:compsher}
 
 The result obtained in \cref{sec:qqggcalc} shall now be verified by the
-monte carlo event generator \sherpa{}~\cite{Gleisberg:2008ta}. To
+Monte Carlo event generator \sherpa{}~\cite{Gleisberg:2008ta}. To
 facilitate this, an expression for the total cross section for a range
 of \(\theta\) or \(\eta\) has to be obtained. Using the golden rule
 for \(2\rightarrow 2\) processes and observing that the initial and
@@ -86,7 +86,7 @@ an interval of \([-\eta, \eta]\), is dominated by the linear
 contributions in \cref{eq:total-crossec} and would result in an
 infinity if no cut on \(\eta\) would be made.  Choosing
 \(\eta\in [-2.5,2.5]\) and \(\ecm=\SI{100}{\giga\electronvolt}\) the
-process was monte carlo integrated in \sherpa\ using the runcard
+process was Monte Carlo integrated in \sherpa\ using the runcard
 in \cref{sec:qqggruncard}. This runcard describes the exact same (first
 order) process as the calculated cross section.