Remove matroid thingy
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main.tex
31
main.tex
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@ -75,16 +75,7 @@ code-for-last-col = \color{blue}
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\end{enumerate}
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\end{frame}
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% should we make is so that these bullet points appear one after another? Yes
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\begin{frame}{Abstracting Independence - Motivation}
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\begin{itemize}
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\item 1
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\item 2
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\end{itemize}
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\end{frame}
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\include{prerequisites}
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\include{isospectral}
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\begin{frame}[fragile]{CMB Anisotropy of Homogeneous Spherical Spaces}
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@ -169,20 +160,20 @@ code-for-last-col = \color{blue}
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\end{frame}
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\begin{frame}{The setup}
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Real CMB observations are affected by instrumental noise and \textit{sky masking}. So, estimating $C_\ell$ accurately requires simulations.
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Real CMB observations are affected by instrumental noise and \textit{sky masking}. So, estimating $C_\ell$ accurately requires simulations.
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Given $C^{th}_\ell$, used to generate synthetic realizations of the CMB sky
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\[
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Given $C^{th}_\ell$, used to generate synthetic realizations of the CMB sky
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\[
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\textcolor{blue}{a_{\ell m}} \sim \mathcal{N} (0, C_\ell^{\text{th}}).
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\]
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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.
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\]
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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.
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Giving us the test statistic (tests the assumption of statistical isotropy):
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\[
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Giving us the test statistic (tests the assumption of statistical isotropy):
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\[
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S_i = \sum_{j} W_{ij} M_j,
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\]
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Which examines $\langle \textcolor{blue}{a_{\ell m}} \rangle$ across multipole ranges. \\
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\textbf{\textcolor{red}{Recall:}} $\langle a_{\ell m} \rangle \neq 0$, \textbf{suggests possible anisotropies or preferred directions in the universe}
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\]
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Which examines $\langle \textcolor{blue}{a_{\ell m}} \rangle$ across multipole ranges. \\
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\textbf{\textcolor{red}{Recall:}} $\langle a_{\ell m} \rangle \neq 0$, \textbf{suggests possible anisotropies or preferred directions in the universe}
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\end{frame}
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@ -192,7 +183,7 @@ Which examines $\langle \textcolor{blue}{a_{\ell m}} \rangle$ across multipole r
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\includegraphics[width=0.7\linewidth]{DSE-Test Graph}
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\caption{The decorrelated band mean spectrum obtained by the seven-year WMAP data [9].}
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\end{figure}
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\textcolor{red}{Remark}In a positively curved space certain multipoles scales being preferred or suppressed in the CMB power spectrum.
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\textcolor{red}{Remark}In a positively curved space certain multipoles scales being preferred or suppressed in the CMB power spectrum.
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\end{frame}
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