% !TeX root = thesis.tex
% !TeX program = xelatex
\documentclass[a4paper,11pt,twoside]{thesis}

\usepackage[british]{babel}
\usepackage{csquotes}
\usepackage{debug}
\usepackage{sciencestuff}
\usepackage{import}

\author{Riccardo Finotello}
\title{D-branes and Deep Learning: \\ Theoretical and Computational Aspects In String Theory}
\advisor{Igor Pesando}
\institution{Università degli Studi di Torino}
\school{Scuola di Dottorato}
\specialisation{Dottorato in Fisica ed Astrofisica}
\logo{img/unito}

\renewcommand*{\bibfont}{\small}
\addbibresource{thesis.bib}

\fancyhead[L]{}
\fancyhead[R]{\rightmark}

\hypersetup{%
  pdftitle={D-branes and Deep Learning: Theoretical and Computational Aspects In String Theory},
  pdfauthor={Riccardo Finotello}
}

%---- abbreviations
\newcommand{\ml}{\textsc{ml}\xspace}
\newcommand{\fc}{\textsc{fc}\xspace}
\newcommand{\eda}{\textsc{eda}\xspace}
\newcommand{\pca}{\textsc{pca}\xspace}
\newcommand{\svm}{\textsc{svm}\xspace}
\newcommand{\bo}{\textsc{bo}\xspace}
\newcommand{\nbo}{\textsc{nbo}\xspace}
\newcommand{\gnbo}{\textsc{gnbo}\xspace}

%---- functions
\newcommand{\hyp}[4]{\ensuremath{\mathrm{F}\left( #1,\, #2;\, #3;\, #4 \right)}}
\newcommand{\poch}[2]{\ensuremath{\left( #1 \right)_{#2}}}
\newcommand{\gfun}[1]{\ensuremath{\Gamma\left( #1 \right)}}
\newcommand{\hodge}[2]{\ensuremath{h^{#1,#2}}}

%---- derivatives
\newcommand{\consprod}[2]{\left\langle #1, #2 \right\rangle}
\newcommand{\lconsprod}[2]{\left\langle\hspace{-0.25em}\left\langle #1\right.,\, #2 \right\rangle}
\newcommand{\dual}[1]{\tensor[^*]{#1}{}}

%---- integrals
\newcommand{\ddz}{\ensuremath{\frac{\mathrm{d}z}{2 \pi i}}}
\newcommand{\ddbz}{\ensuremath{\frac{\mathrm{d}\overline{z}}{2 \pi i}}}
\newcommand{\ddw}{\ensuremath{\frac{\mathrm{d}w}{2 \pi i}}}
\newcommand{\ddbw}{\ensuremath{\frac{\mathrm{d}\overline{w}}{2 \pi i}}}
\newcommand{\cint}[1]{\ensuremath{\oint\limits_{\ccC_{#1}}}}

%---- states
\newcommand{\regvacuum}{\ensuremath{\ket{0}_{\SL{2}{\R}}}\xspace}
\newcommand{\regvacuumin}{\ensuremath{\ket{0_{(\text{in})}}_{\SL{2}{\R}}}\xspace}
\newcommand{\regvacuumout}{\ensuremath{\ket{0_{(\text{out})}}_{\SL{2}{\R}}}\xspace}
\newcommand{\regvacuuminconj}{\ensuremath{\tensor[_{\SL{2}{\R}}]{\bra{0_{(\text{in})}}}{}}\xspace}
\newcommand{\regvacuumoutconj}{\ensuremath{\tensor[_{\SL{2}{\R}}]{\bra{0_{(\text{out})}}}{}}\xspace}
\newcommand{\twsvacket}{\ensuremath{\ket{\mathrm{T}}}\xspace}
\newcommand{\twsvacbra}{\ensuremath{\bra{\mathrm{T}}}\xspace}
\newcommand{\excvacket}{\ensuremath{\ket{T_{\rE,\, \brE}}}\xspace}
\newcommand{\excvacbra}{\ensuremath{\bra{T_{\rE,\, \brE}}}\xspace}
\newcommand{\eexcvacket}{\ensuremath{\ket{T_{\rE}}}\xspace}
\newcommand{\eexcvacbra}{\ensuremath{\bra{T_{\rE}}}\xspace}
\newcommand{\Gexcvac}{\ensuremath{\Omega_{\qty{x_{(t)},\, \rE_{(t)},\, \brE_{(t)}}}}}
\newcommand{\Gexcvacket}{\ensuremath{\ket{\Gexcvac}}}
\newcommand{\Gexcvacbra}{\ensuremath{\bra{\Gexcvac}}}
\newcommand{\GGexcvac}{\ensuremath{\Omega_{\qty{x_{(t)},\, \rE_{(t)}}}}}
\newcommand{\GGexcvacket}{\ensuremath{\ket{\GGexcvac}}}
\newcommand{\GGexcvacbra}{\ensuremath{\bra{\GGexcvac}}}
\newcommand{\cmode}[4]{\ensuremath{\mathfrak{C}_{#1}\qty(#2,\, \qty{#4,\, #3})}}

%---- operators
\newcommand{\noE}[1]{\ccN_{\rE,\, \brE}\qty[ #1 ]}

%---- coordinates
\newcommand{\pX}{\ensuremath{X'}\xspace}
\newcommand{\kmr}{\ensuremath{\qty{k_+,\, k_-,\, l,\, r}}}
\newcommand{\kmkr}{\ensuremath{\qty{k_+,\, l,\, \vec{k},\, r}}}
\newcommand{\kmkrN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, l_{\qty(#1)},\, \vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}}
\newcommand{\kmrN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, k_{\qty(#1)\, -},\,l_{\qty(#1)},\, r_{\qty(#1)}}}}
\newcommand{\mkmkr}{\ensuremath{\qty{-k_+,\, -l,\, -\vec{k},\, r}}}
\newcommand{\mkmkrN}[1]{\ensuremath{\qty{-k_{\qty(#1)\, +},\, -l_{\qty(#1)},\, -\vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}}
\newcommand{\kmkrgen}{\ensuremath{\qty{k_+,\, p,\, l,\, \vec{k},\, r}}}
\newcommand{\kmkrgenN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, p_{\qty(#1)},\, l_{\qty(#1)},\, \vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}}
\newcommand{\mkmkrgen}{\ensuremath{\qty{-k_+,\, -p,\, -l,\, -\vec{k},\, r}}}
\newcommand{\mkmkrgenN}[1]{\ensuremath{\qty{-k_{\qty(#1)\, +},\, -p_{\qty(#1)},\, -l_{\qty(#1)},\, -\vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}}
\newcommand{\lkrsi}{\ensuremath{\qty{l,\, \vec{k},\, r,\, \sigma_-}}}
\newcommand{\lsi}{\ensuremath{l\, \hsigma_-}}
\newcommand{\lsiN}[1]{\ensuremath{l_{\qty(#1)}\, \hsigma_{-\, \qty(#1)}}}
\newcommand{\pol}[1]{\ensuremath{\mathcal{E}_{\kmkr\, \underline{#1}}}}
\newcommand{\polN}[2]{\ensuremath{\mathcal{E}_{\kmkrN{#2}\, \underline{#1}}}}
\newcommand{\polabbrN}[2]{\ensuremath{\mathcal{E}_{\qty(#2)\, \underline{#1}}}}
\newcommand{\genpolN}[1]{\ensuremath{\mathcal{E}_{\kmkrN{#1}}}}

%---- BEGIN DOCUMENT

\begin{document}

%---- TITLE
\maketitlepage{}
\cleardoubleplainpage{}

%---- FRONTESPICE
\makefrontespice{}
\cleardoubleplainpage{}

%---- ABSTRACT
\begin{abstractpage}
  \input{sec/abstract.tex}
\end{abstractpage}
\cleardoubleplainpage{}

%---- ACKNOWLEDGENTS
\begin{acknowledgmentspage}
  \input{sec/acknowledgments.tex}
\end{acknowledgmentspage}
\cleardoubleplainpage{}

%---- TOC AND OUTLINE
\plaintoc{}
\outline{Outline}
\input{sec/outline.tex}

%---- PARTICLE PHYSICS
\thesispart{Conformal Symmetry and Geometry of the Worldsheet}
\label{part:cft}
\section{Introduction}
\input{sec/part1/introduction.tex}
\section{D-branes Intersecting at Angles}
\input{sec/part1/dbranes.tex}
\section{Fermions With Boundary Defects}
\input{sec/part1/fermions.tex}
\section{Summary and Conclusion}
\input{sec/part1/conclusion.tex}

%---- COSMOLOGY
\thesispart{Cosmological Backgrounds and Divergences}
\label{part:cosmo}
\section{Introduction}
\input{sec/part2/introduction.tex}
\section{Time Dependent Orbifolds}
\input{sec/part2/divergences.tex}
\section{Summary and Conclusion}
\input{sec/part2/conclusion.tex}

%---- DEEP LEARNING
\thesispart{Deep Learning the Geometry of String Theory}
\label{part:deeplearning}
\section{Introduction}
\input{sec/part3/introduction.tex}
\section{Machine Learning and Deep Learning for CICY Manifolds}
\input{sec/part3/ml.tex}
\section{Summary and Conclusion}
\label{sec:conclusion}
\input{sec/part3/conclusion.tex}


%---- APPENDIX
\thesispart{Appendix}
\label{part:appendix}
\appendix
\section{The Isomorphism in Details}
\label{sec:isomorphism}
\input{sec/app/isomorphism.tex}

\section{The Parameters of the Hypergeometric Function}
\label{sec:parameters}
\input{sec/app/parameters.tex}

\section{Reflection Conditions on the Vacuum}
\label{sec:details_reflection}
\input{sec/app/reflection.tex}

\section{Tensor Wave Functions on NBO}
\label{sec:NO_tensor_wave}
\input{sec/app/tensor_wave.tex}

\section{Overlap of Second Level Massive States on NBO}
\label{sec:NO_full_TTS}
\input{sec/app/massive.tex}

\section{Machine Learning Algorithms}
\label{app:ml-algo}
\input{sec/app/ml.tex}


%---- BIBLIOGRAPHY
\cleardoubleplainpage{}
\printbibliography[heading=bibintoc]

\end{document}

% vim: ft=tex