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Add new figures in Tikz

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Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
This commit is contained in:
Riccardo
2020-10-16 19:01:42 +02:00
parent 0f00e28fe5
commit 6f6c909341
45 changed files with 823 additions and 727 deletions
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64
sec/part1/dbranes.tex
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@@ -381,8 +381,7 @@ We thus translated the rotations of the D-branes encoded in the matrices $R_{(t)
\begin{figure}[tbp]
\centering
\def\svgwidth{0.5\textwidth}
\import{img}{branchcuts.pdf_tex}
\import{tikz}{branchcuts.pgf}
\caption{%
Branch cut structure of the complex plane with $N_B = 4$.
Cuts are pictured as solid coloured blocks running from one intersection point to another at finite.
@@ -599,8 +598,7 @@ We choose $\bart = 1$ in what follows.
\begin{figure}[tbp]
\centering
\def\svgwidth{0.35\linewidth}
\import{img}{threebranes_plane.pdf_tex}
\import{tikz}{threebranes_plane.pgf}
\caption{%
Fixing the \SL{2}{\R} invariance for $N_B = 3$ and $\bart = 1$ leads to a cut structure with all the cuts defined on the real axis towards $\omega_{\bart} = \infty$.}
\label{fig:hypergeometric_cuts}
@@ -2111,23 +2109,41 @@ Here we compute the parameter $\vec{n}_{1}$ given two Abelian rotation in $\omeg
Results are shown in~\Cref{tab:Abelian_composition}.
\begin{figure}[tbp]
\centering
\begin{subfigure}[b]{0.45\linewidth}
\centering
\def\svgwidth{0.8\textwidth}
\import{img}{abelian_angles_case1.pdf_tex}
\caption{%
The Abelian limit when the triangle has all acute angles.
This corresponds to the cases $n_{0} + n_{\infty}< \frac{1}{2}$ and $n_{0}< n_{\infty}$ which are exchanged under the parity $P_2$.}
\label{fig:Abelian_angles_1}
\import{tikz}{abelian_angles_case1_a.pgf}
\caption{Case 1.}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.45\linewidth}
\centering
\import{tikz}{abelian_angles_case1_b.pgf}
\caption{Case 2.}
\end{subfigure}
\caption{%
The Abelian limit when the triangle has all acute angles.
This corresponds to the cases $n_{0} + n_{\infty}< \frac{1}{2}$ and $n_{0}< n_{\infty}$ which are exchanged under the parity $P_2$.}
\label{fig:Abelian_angles_1}
\end{figure}
\begin{figure}[tbp]
\centering
\begin{subfigure}[b]{0.45\linewidth}
\centering
\def\svgwidth{0.8\textwidth}
\import{img}{abelian_angles_case2.pdf_tex}
\caption{%
The Abelian limit when the triangle has one obtuse angle.
This corresponds to the cases $n_{0} + n_{\infty}> \frac{1}{2}$ and $n_{0}> n_{\infty}$ which are exchanged under the parity $P_2$.}
\label{fig:Abelian_angles_2}
\import{tikz}{abelian_angles_case2_a.pgf}
\caption{Case 1.}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.45\linewidth}
\centering
\import{tikz}{abelian_angles_case2_b.pgf}
\caption{Case 2.}
\end{subfigure}
\caption{%
The Abelian limit when the triangle has one obtuse angle.
This corresponds to the cases $n_{0} + n_{\infty}> \frac{1}{2}$ and $n_{0}> n_{\infty}$ which are exchanged under the parity $P_2$.}
\label{fig:Abelian_angles_2}
\end{figure}
Under the parity transformation $P_2$ the previous four cases are grouped
@@ -2151,8 +2167,17 @@ when all $m = 0$.
\begin{figure}[tbp]
\centering
\def\svgwidth{0.8\textwidth}
\import{img}{usual_abelian_angles.pdf_tex}
\begin{subfigure}[b]{0.45\linewidth}
\centering
\import{tikz}{usual_abelian_angles_a.pgf}
\caption{Case 1.}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.45\linewidth}
\centering
\import{tikz}{usual_abelian_angles_b.pgf}
\caption{Case 2.}
\end{subfigure}
\caption{%
The geometrical angles used in the usual geometrical approach to the Abelian configuration do not distinguish among the possible branes orientations.
In fact we have $0 \le \alpha < 1$ and $0 < \varepsilon < 1$.
@@ -2552,8 +2577,7 @@ Each term of the action can be interpreted again as an area of a triangle where
\begin{figure}[tbp]
\centering
\def\svgwidth{0.35\textwidth}
\import{img/}{brane3d.pdf_tex}
\import{tikz}{brane3d.pgf}
\caption{%
Pictorial $3$-dimensional representation of two D2-branes intersecting in the Euclidean space $\R^3$ along a line (in $\R^4$ the intersection is a point since the co-dimension of each D-brane is 2): since it is no longer constrained on a bi-dimensional plane, the string must be deformed in order to stretch between two consecutive D-branes.
Its action can be larger than the planar area.

6
sec/part1/fermions.tex
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@@ -95,7 +95,7 @@ Their solutions are the ``holomorphic'' functions $\psi_{+}^i(\xi_+)$ and $\psi_
}
\begin{figure}[tbp]
\centering
\includegraphics[width=0.4\linewidth]{img/point-like-defects}
\import{tikz}{defects.pgf}
\caption{Propagation of the string in the presence of the worldsheet defects.}
\label{fig:point-like-defects}
\end{figure}
@@ -838,7 +838,7 @@ Finally we get the anti-commutation relations as
\begin{figure}[tbp]
\centering
\includegraphics[width=0.5\linewidth]{img/complex-plane}
\import{tikz}{complex_plane_defects.pgf}
\caption{%
Fields are glued on the $x < 0$ semi-axis with non trivial discontinuities for $x_{(t)} < x < x_{(t-1)}$ for $t = 1,\, 2,\, \dots,\, N$ and where $x_{(t)} = \exp( \htau_{E,\, (t)} )$.
}
@@ -1636,7 +1636,7 @@ Moreover notice that for $\rL \le -1$ both $b^{(\rE)}_{\rL \le n \le 0}$ and $b^
\begin{figure}[tbp]
\centering
\includegraphics[width=0.5\linewidth]{img/in-annihilators.pdf}
\import{tikz}{inconsistent_theories.pgf}
\caption{As a consistency condition, we have to exclude the values of
$\rL$ for which both $b^{(
E)}_n$ and $b^{*\, ( \brE )}_{\rL + 1 - n}$ are in-annihilators

6
sec/part3/introduction.tex
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@@ -59,7 +59,7 @@ Thus getting also \hodge{2}{1} from \ml techniques is an important first step to
Finally regression is also more useful for extrapolating results: a classification approach assumes that we already know all the possible values of the Hodge numbers and has difficulties to predict labels which do not appear in the training set.
This is necessary when we move to a dataset for which not all topological quantities have been computed, for instance CY constructed from the Kreuzer--Skarke list of polytopes~\cite{Kreuzer:2000:CompleteClassificationReflexive}.
The data analysis and \ml are programmed in Python using open-source packages: \texttt{pandas}~\cite{WesMcKinney:2010:DataStructuresStatistical}, \texttt{matplotlib}~\cite{Hunter:2007:Matplotlib2DGraphics}, \texttt{seaborn}~\cite{Waskom:2020:MwaskomSeabornV0}, \texttt{scikit-learn}~\cite{Pedregosa:2011:ScikitlearnMachineLearning}, \texttt{scikit-optimize}~\cite{Head:2020:ScikitoptimizeScikitoptimize}, \texttt{tensorflow}~\cite{Abadi:2015:TensorFlowLargescaleMachine} (and its high level API \emph{Keras}).
The data analysis and \ml are programmed in Python using known open-source packages such as \texttt{pandas}~\cite{WesMcKinney:2010:DataStructuresStatistical}, \texttt{matplotlib}~\cite{Hunter:2007:Matplotlib2DGraphics}, \texttt{seaborn}~\cite{Waskom:2020:MwaskomSeabornV0}, \texttt{scikit-learn}~\cite{Pedregosa:2011:ScikitlearnMachineLearning}, \texttt{scikit-optimize}~\cite{Head:2020:ScikitoptimizeScikitoptimize}, \texttt{tensorflow}~\cite{Abadi:2015:TensorFlowLargescaleMachine} (and its high level API \emph{Keras}).
Code is available on \href{https://thesfinox.github.io/ml-cicy/}{Github}.
@@ -192,14 +192,14 @@ Below we show a list of the \cicy properties and of their configuration matrices
\begin{figure}[tbp]
\centering
\begin{subfigure}[c]{.45\linewidth}
\begin{subfigure}[b]{.45\linewidth}
\centering
\includegraphics[width=\linewidth, trim={0 0.45in 6in 0}, clip]{img/label-distribution_orig}
\caption{\hodge{1}{1}}
\label{fig:data:hist-h11}
\end{subfigure}
\hfill
\begin{subfigure}[c]{.45\linewidth}
\begin{subfigure}[b]{.45\linewidth}
\centering
\includegraphics[width=\linewidth, trim={6in 0.45in 0 0}, clip]{img/label-distribution_orig}
\caption{\hodge{2}{1}}

8
sec/part3/ml.tex
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@@ -1020,7 +1020,7 @@ Using the same network we also achieve \SI{97}{\percent} of accuracy in the favo
\centering
\begin{subfigure}[c]{0.475\linewidth}
\centering
\includegraphics[width=\linewidth]{img/fc}
\import{tikz}{fc.pgf}
\caption{Architecture of the network.}
\label{fig:nn:dense}
\end{subfigure}
@@ -1099,7 +1099,7 @@ The convolution layers have $180$, $100$, $40$ and $20$ units each.
\begin{figure}[tbp]
\centering
\includegraphics[width=0.75\linewidth]{img/ccnn}
\import{tikz}{ccnn.pgf}
\caption{%
Pure convolutional neural network for redicting \hodge{1}{1}.
It is made of $4$ modules composed by convolutional layer, ReLU activation, batch normalisation (in this order), followed by a dropout layer, a flatten layer and the output layer (in this order).
@@ -1204,7 +1204,7 @@ The callbacks helped to contain the training time (without optimisation) under 5
\begin{figure}[tbp]
\centering
\includegraphics[width=0.9\linewidth]{img/icnn}
\resizebox{\linewidth}{!}{\import{tikz}{icnn.pgf}}
\caption{%
In each concatenation module (here shown for the ``old'' dataset) we operate with separate convolution operations over rows and columns, then concatenate the results.
The overall architecture is composed of 3 ``inception'' modules made by two separate convolutions, a concatenation layer and a batch normalisation layer (strictly in this order), followed by a dropout layer, a flatten layer and the output layer with ReLU activation (in this order).
@@ -1374,7 +1374,7 @@ Another reason is that the different algorithms may perform similarly well in th
\begin{figure}[tbp]
\centering
\includegraphics[width=0.65\linewidth]{img/stacking}
\resizebox{0.65\linewidth}{!}{\import{tikz}{stacking.pgf}}
\caption{Stacking ensemble learning with two level learning.}
\label{fig:stack:def}
\end{figure}