1
Fork 0

Remove matroid thingy

This commit is contained in:
prescientmoon 2025-03-20 17:06:00 +01:00
parent 966f244e47
commit 325d12ba7e
Signed by: prescientmoon
SSH key fingerprint: SHA256:UUF9JT2s8Xfyv76b8ZuVL7XrmimH4o49p4b+iexbVH4

View file

@ -75,16 +75,7 @@ code-for-last-col = \color{blue}
\end{enumerate}
\end{frame}
% should we make is so that these bullet points appear one after another? Yes
\begin{frame}{Abstracting Independence - Motivation}
\begin{itemize}
\item 1
\item 2
\end{itemize}
\end{frame}
\include{prerequisites}
\include{isospectral}
\begin{frame}[fragile]{CMB Anisotropy of Homogeneous Spherical Spaces}
@ -169,20 +160,20 @@ code-for-last-col = \color{blue}
\end{frame}
\begin{frame}{The setup}
Real CMB observations are affected by instrumental noise and \textit{sky masking}. So, estimating $C_\ell$ accurately requires simulations.
Real CMB observations are affected by instrumental noise and \textit{sky masking}. So, estimating $C_\ell$ accurately requires simulations.
Given $C^{th}_\ell$, used to generate synthetic realizations of the CMB sky
\[
Given $C^{th}_\ell$, used to generate synthetic realizations of the CMB sky
\[
\textcolor{blue}{a_{\ell m}} \sim \mathcal{N} (0, C_\ell^{\text{th}}).
\]
However, this introduces bias, which must be corrected using a decorrelation matrix $W$, and a \textit{sky mask} matrix $M$ which accounts for issues caused by masking effects.
\]
However, this introduces bias, which must be corrected using a decorrelation matrix $W$, and a \textit{sky mask} matrix $M$ which accounts for issues caused by masking effects.
Giving us the test statistic (tests the assumption of statistical isotropy):
\[
Giving us the test statistic (tests the assumption of statistical isotropy):
\[
S_i = \sum_{j} W_{ij} M_j,
\]
Which examines $\langle \textcolor{blue}{a_{\ell m}} \rangle$ across multipole ranges. \\
\textbf{\textcolor{red}{Recall:}} $\langle a_{\ell m} \rangle \neq 0$, \textbf{suggests possible anisotropies or preferred directions in the universe}
\]
Which examines $\langle \textcolor{blue}{a_{\ell m}} \rangle$ across multipole ranges. \\
\textbf{\textcolor{red}{Recall:}} $\langle a_{\ell m} \rangle \neq 0$, \textbf{suggests possible anisotropies or preferred directions in the universe}
\end{frame}
@ -192,7 +183,7 @@ Which examines $\langle \textcolor{blue}{a_{\ell m}} \rangle$ across multipole r
\includegraphics[width=0.7\linewidth]{DSE-Test Graph}
\caption{The decorrelated band mean spectrum obtained by the seven-year WMAP data [9].}
\end{figure}
\textcolor{red}{Remark}In a positively curved space certain multipoles scales being preferred or suppressed in the CMB power spectrum.
\textcolor{red}{Remark}In a positively curved space certain multipoles scales being preferred or suppressed in the CMB power spectrum.
\end{frame}