diff --git a/report_thesis/src/sections/problem_definition.tex b/report_thesis/src/sections/problem_definition.tex
index fa840370..94422e71 100644
--- a/report_thesis/src/sections/problem_definition.tex
+++ b/report_thesis/src/sections/problem_definition.tex
@@ -1,6 +1,6 @@
 \section{Problem Definition}\label{sec:problem_definition}
 The objective of this research is to predict major oxide compositions from \gls{libs} data.
-We aim to enhance the accuracy and robustness of these predictions by developing and validating a computational methodology that addresses the challenges of such quantification of elements in soil samples from \gls{libs} data. 
+We aim to enhance the accuracy and robustness of these predictions by developing and validating a computational methodology that addresses the challenges of such quantification of elements in soil samples from \gls{libs} data.
 This objective presents several significant challenges, including the high dimensionality of spectral data, multicollinearity, matrix effects, and limited data availability.
 
 A fundamental premise of this research posits that by effectively addressing these challenges, the accuracy and robustness of predicting elemental concentrations from \gls{libs} data can be significantly enhanced. This assumption is supported by several key studies in the field.
@@ -70,4 +70,4 @@ \subsubsection{Data Availability}
 Due to the high cost of data collection, datasets are often small. This limits the number of samples available for evaluation, affecting the generalizability and robustness of the models\cite{p9_paper}.
 
 \subsection{Problem Formulation}
-The objective of this research is to develop a computational model, denoted as $\mathcal{F}: \mathbb{R}^N \rightarrow \mathbb{R}^{n_o}$, to predict major oxide concentrations in geological samples from processed \gls{libs} spectral data. 
+The objective of this research is to develop a computational model, denoted as $\mathcal{F}: \mathbb{R}^N \rightarrow \mathbb{R}^{n_o}$, to predict major oxide concentrations in geological samples from processed \gls{libs} spectral data, that maintains accuracy and exhibits robustness against the challenges posed by the high dimensionality of the data, multicollinearity among spectral features, matrix effects, and the limited availability of data.