feat(thesis): refactor preliminaries to separate file and fill with first drafts

src/thesis/Thesis_408230.tex

@@ -66,7 +66,7 @@
 % \allowdisplaybreaks
 
 % Define more theorem environments.
-\newtheorem{definition}{Definition}[subsection]
+\newtheorem{definition}{Definition}[section]
 \newtheorem{theorem}[definition]{Theorem}
 \newtheorem{proposition}[definition]{Proposition}
 \newtheorem{lemma}[definition]{Lemma}
@@ -79,6 +79,8 @@
 \newtheorem{remark}[definition]{Remark}
 \newtheorem{algorithm}[definition]{Algorithm}
 
+\newcommand{\uc}{u_{\mathsf{c}}}
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%    End of preamble   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{document}
@@ -207,23 +209,7 @@
   Afterwards we will apply an existing robustness verification method to our network
   ary measure its performance.
 
-
-  \chapter{Preliminaries}\label{ch:preliminaries}
-
-  \begin{definition}[Standard uncertainty]
-    \label{def:standard-uncertainty}
-
-  \end{definition}
-
-  \begin{definition}[Combined standard uncertainty]
-    \label{def:combined-standard-uncertainty}
-
-  \end{definition}
-
-  \begin{definition}[Expanded uncertainty]
-    \label{def:expanded-uncertainty}
-
-  \end{definition}
+  \include{preliminaries}
 
 
   \chapter{Uncertainty propagation in NN}\label{ch:uncertainty-propagation-in-nn}
@@ -295,5 +281,4 @@
   \clearpage
 
   \printbibliography
-  ~\nocite{*}
 \end{document}

src/thesis/preliminaries.tex

+\chapter{Preliminaries}\label{ch:preliminaries}
+
+The following definitions are taken from the \enquote{Guide to
+the expression of uncertainty in measurement (GUM)}~\citep{jcgm_guide_2020} which
+in turn is based on the \enquote{International vocabulary of metrology — Basic and
+general concepts and associated terms (VIM)}~\citep{jcgm_international_2012}
+regarding those definitions.
+
+
+\section{Terms related to measurement uncertainty}\label{sec:terms-related-to
+-measurement-uncertainty}
+
+\begin{definition}
+  [uncertainty]\label{def:uncertainty}
+  (or \enquote*{measurement uncertainty} or \enquote*{uncertainty of measurement})
+  (non-negative) parameter, associated with the result of a measurement, that
+  characterizes the dispersion of the values that could reasonably be attributed to
+  the measurand
+\end{definition}
+
+
+\begin{definition}[Standard uncertainty]
+  \label{def:standard-uncertainty}
+  (or \enquote*{standard measurement uncertainty} or \enquote*{standard uncertainty
+  of measurement})
+  uncertainty of the result of a measurement expressed as a standard deviation $u$
+\end{definition}
+
+\begin{definition}[Combined standard uncertainty]
+  \label{def:combined-standard-uncertainty}
+  (or \enquote*{combined standard measurement uncertainty})
+  standard uncertainty $\uc$ of the result of a measurement when that result is
+  obtained from the values of a number of other quantities, equal to the positive
+  square root of a sum of terms, the terms being the variances or covariances of
+  these other quantities weighted according to how the measurement result varies
+  with changes in these quantities
+\end{definition}
+
+\begin{definition}[Coverage factor]
+  \label{def:coverage-factor}
+  (or \enquote*{expanded measurement uncertainty})
+  numerical factor $k$, typically in the range 2 to 3, used as a multiplier of the
+  combined standard uncertainty in order to obtain an expanded uncertainty
+\end{definition}
+
+\begin{definition}[Expanded uncertainty]
+  \label{def:expanded-uncertainty}
+  (or \enquote*{expanded measurement uncertainty})
+  quantity $U$ defining an interval about the result of a measurement that may be
+  expected to encompass a large fraction of the distribution of values that could
+  reasonably be attributed to the measurand, which is obtained by multiplying the
+  combined standard uncertainty $\uc$ by a coverage factor $k$
+\end{definition}
\ No newline at end of file