Lab 6 - Quarto Presentation.qmd

---
title: "Lab 6: Quarto Presentation"
author: "Brandon Imstepf"
format: revealjs
editor: visual
bibliography: references.bib
---

## Some Important Literature

-   This reference contains cool stuff about Physics Informed Neural Networks (PINNs) [@raissi_physics-informed_2019]

-   This is a paper from a collaborator I'm working with, and we're solving the PDE described in this paper using machine learning! [@torok_emergence_2021]

-   This paper is very well structured and relevant to my research in Alzheimer's Disease [@thompson_alzheimers_2024]

## Some Cool Equations

$$
\begin{equation*}
            \vec{\textbf{x}}(t) = \vec{\textbf{x}}_{0}  e^{- \beta H t} = \underbrace{Ue^{-\Lambda \beta t}U^{H}\vec{\textbf{x}}_{0}}_{\text{Diagonalization}} = \underbrace{\sum_{i=1}^{N}(e^{(-\beta \lambda_{i} t)}\vec{\textbf{u}}_{i}^{H}\vec{\textbf{x}}_{0})\vec{\textbf{u}}_{i}}_{\text{Eigendecomposition}}
\end{equation*}
$$

## References