phd-thesis-en/figures/complexification-ehresmann.tikz

\documentclass[crop,tikz]{standalone}
\input{common-headers}
\input{sigles}

\begin{document}

\tikzset{%
  neuron/.style={fill,black,circle,inner sep=0,minimum width=5pt},
  family/.style={draw,fill=white,circle,inner sep=0,minimum width=2cm},
  link/.style={-Stealth},
  transition/.style={thick, double,-Stealth},
  curly/.style={decorate,decoration={brace,amplitude=10pt}},
  curlyM/.style={decorate,decoration={brace,amplitude=10pt,mirror}},
  idq1/.style={magenta!60!white},
  idq2/.style={orange!60!white},
  idq3/.style={red!60!white},
  idn1/.style={fill,violet!70!white},
  idn2/.style={fill,blue!70!white},
  idn3/.style={fill,cyan!70!white},
}

\begin{tikzpicture}
  \draw (-1,1) rectangle (1,-2);
  \node[neuron] (A1) at (0   ,0)    {};
  \node[neuron] (B1) at (0.5 ,-1)   {};
  \node[neuron] (C1) at (0.2 ,-1.5) {};
  \node[neuron] (D1) at (-0.5,-1.1) {};
  \draw[link]   (A1) to (B1);
  \draw[link]   (A1) to (D1);
  \draw[link]   (C1) to (D1);
  \draw[link]   (B1) to (D1);

  \draw[transition] (1.5,-0.5) to node[auto] {$k_{t\rightarrow t'}$} (2.5,-0.5);

  \begin{scope}[xshift=4cm]
  \draw (-1,1) rectangle (1,-2);
  \node[neuron] (A2) at (0   ,0)    {};
  \node[neuron] (B2) at (0.5 ,-1)   {};
  \node[neuron] (C2) at (0.2 ,-1.5) {};
  \node[neuron] (D2) at (-0.5,-1.1) {};
  \draw[link]   (A2) to (B2);
  \draw[link]   (A2) to (D2);
  \draw[link]   (C2) to (D2);
  \draw[link]   (B2) to (D2);

  \draw[transition] (1.5,-0.5) to node[auto] {$k_{t'\rightarrow t''}$} (2.5,-0.5);
  \end{scope}

  \begin{scope}[xshift=8cm]
  \draw (-1,1) rectangle (1,-2);
  \node[neuron] (A3) at (0   ,0)    {};
  \node[neuron] (B3) at (0.5 ,-1)   {};
  \node[neuron] (C3) at (0.2 ,-1.5) {};
  \draw[link]   (A3) to (B3);
  \end{scope}

  \draw[dashed] (-2.5cm,-2.5cm) -- +(0.5cm,0cm);
  \draw[dashed] (  10cm,-2.5cm) -- +(0.5cm,0cm);
  \draw         (  -2cm,-2.5cm) --
                (  10cm,-2.5cm);
  \begin{scope}[yshift=-2.5cm]
  \foreach \x/\t in {0/$t$,4/$t'$,8/$t''$}
    \draw (\x,1pt) -- (\x,-3pt) node[anchor=north] {\t};
  \end{scope}
\end{tikzpicture}

\begin{tikzpicture}
  \node[neuron] (N1) at (0,0) {};
  \node[neuron] (N2) at (90:0.7cm) {};
  \node[neuron] (N3) at (10:0.5cm) {};
  \coordinate (Center) at (barycentric cs:N1=1,N2=1,N3=1);
  \draw[thin] (Center) circle (1cm);
  \node at ($(Center) + (-0.8,0)$) {$P$};


  \node[neuron] (N) at ($(Center) + ( 20:2.5cm)$) {};
  \node at ($(N.east) + (0.2,0)$) {$n_1$};
  \node[neuron] (D) at ($(Center) + (-20:2.5cm)$) {};
  \node at ($(D.east) + (0.2,0)$) {$n_2$};

  \draw[dashed] ($(Center) + (90:1cm)$) to (N);
  \draw[dashed] ($(Center) + (-50:1cm)$) to (N);

  \draw[link]   (N1) to (N2);
  \draw[link]   (N1) to (N3);
  \draw[link]   (N)  to node[auto] {$s_{12}$} (D);
  \draw[link]   (N1) to (D);
  \draw[link]   (N2) to (D);
  \draw[link]   (N3) to (D);
\end{tikzpicture}

\begin{tikzpicture}
  \node[neuron] (N1) at (0,0) {};
  \node[neuron] (N2) at (90:0.7cm) {};
  \node[neuron] (N3) at (10:0.5cm) {};
  \draw[link]   (N1) to (N2);
  \draw[link]   (N1) to (N3);

  \coordinate (Center) at (barycentric cs:N1=1,N2=1,N3=1);
  \draw[thin] (Center) circle (1cm);
  \node at ($(Center) + (-0.8,0)$) {$P$};

  \node[neuron] (N) at ($(Center) + ( 20:2.5cm)$) {};
  \node at ($(N.north) + (0,0.2)$) {$n$};

  \draw[dashed] ($(Center) + (90:1cm)$) to (N);
  \draw[dashed] ($(Center) + (-50:1cm)$) to (N);

  \coordinate (Center2) at ($(N) + (-20:2.5cm)$);

  \node[neuron] (N1') at ($(Center2) + (0,0)     $) {};
  \node[neuron] (N2') at ($(Center2) + (110:0.7cm)$) {};
  \node[neuron] (N3') at ($(Center2) + (30:0.5cm)$) {};
  \node[neuron] (N4') at ($(Center2) + (-130:0.5cm)$) {};

  \draw[link]   (N1') to (N2');
  \draw[link]   (N1') to (N3');
  \draw[link]   (N1') to (N4');
  \draw[link]   (N2') to (N3');

  \draw[thin] (Center2) circle (1cm);
  \node at ($(Center2) + (0.8,0)$) {$P'$};

  \draw[dashed] ($(Center2) + (  90:1cm)$) to (N);
  \draw[dashed] ($(Center2) + (-130:1cm)$) to (N);
\end{tikzpicture}


\begin{tikzpicture}
  \coordinate (cN1) at (0,0);
  \coordinate (cN2) at (90:0.7cm);
  \coordinate (cN3) at (10:0.5cm);
  \coordinate (Center) at (barycentric cs:N1=1,N2=1,N3=1);
  \coordinate (cN) at ($(Center) + ( 40:2.5cm)$);
  \coordinate (cN') at ($(cN) + (4cm,0)$);
  \coordinate (Center2) at ($(cN') + (-40:2.5cm)$);

  %Cluster
  \fill[black!20] ($(Center) + (0,1cm)$) rectangle ($(Center2) + (0,-1cm)$);


  %Bindings
  \filldraw[white,draw=black,dashed,opacity=0.6] ($(Center) + (110:1cm)$)
  -- (cN)
  -- ($(Center) + (-30:1cm)$)
  -- cycle;
  \filldraw[white,draw=black,dashed,opacity=0.6] ($(Center2) + (  70:1cm)$)
  -- (cN')
  -- ($(Center2) + (-150:1cm)$)
  -- cycle;

  %Circles
  \filldraw[white,draw=black,thin] (Center) circle (1cm);
  \filldraw[white,draw=black,thin] (Center2) circle (1cm);

  %IDs
  \node at ($(Center) + (-0.8,0)$) {$P$};
  \node at ($(Center2) + (0.8,0)$) {$P'$};

  %Network P
  \node[neuron] (N1) at (cN1) {};
  \node[neuron] (N2) at (cN2) {};
  \node[neuron] (N3) at (cN3) {};
  \draw[link]   (N1) to (N2);
  \draw[link]   (N1) to (N3);

  %Network P'
  \node[neuron] (N1') at ($(Center2) + (0,0)     $) {};
  \node[neuron] (N2') at ($(Center2) + (110:0.7cm)$) {};
  \node[neuron] (N3') at ($(Center2) + (30:0.5cm)$) {};
  \node[neuron] (N4') at ($(Center2) + (-130:0.5cm)$) {};
  \draw[link]   (N2') to (N1');
  \draw[link]   (N1') to (N3');
  \draw[link]   (N1') to (N4');
  \draw[link]   (N3') to (N2');

  %Cat-neurons
  \node[neuron,label=above:$n_1$] (N) at (cN) {};
  \node[neuron,label=above:$n_2$] (N') at (cN') {};
  \draw[link]   (N) to node[auto]{\small{$(P,P')$}} (N');
\end{tikzpicture}


\begin{tikzpicture}
  \coordinate (Center)  at (0,0);
  \coordinate (cN)      at ($(Center) + ( 40:2.5cm)$);
  \coordinate (cM)      at ($(cN) + (4cm,0)$);
  \coordinate (cN')     at ($(cM) + (4cm,0)$);
  \coordinate (Center2) at ($(Center) + (4cm,0)$);
  \coordinate (Center3) at ($(cM) + (-40:2.5cm)$);
  \coordinate (Center4) at ($(Center3) + (4cm,0)$);

  %Cluster
  \fill[black!20] ($(Center) + (0,1cm)$) rectangle ($(Center2) + (0,-1cm)$);
  \fill[black!20] ($(Center3) + (0,1cm)$) rectangle ($(Center4) + (0,-1cm)$);

  %Bindings
  \filldraw[white,draw=black,dashed,opacity=0.6] ($(Center) + (110:1cm)$)
  -- (cN)
  -- ($(Center) + (-30:1cm)$)
  -- cycle;
  \filldraw[white,draw=black,dashed,opacity=0.6] ($(Center2) + (110:1cm)$)
  -- (cM)
  -- ($(Center2) + (-30:1cm)$)
  -- cycle;
  \filldraw[white,draw=black,dashed,opacity=0.6] ($(Center3) + (  70:1cm)$)
  -- (cM)
  -- ($(Center3) + (-150:1cm)$)
  -- cycle;
  \filldraw[white,draw=black,dashed,opacity=0.6] ($(Center4) + (  70:1cm)$)
  -- (cN')
  -- ($(Center4) + (-150:1cm)$)
  -- cycle;

  %Neuron nets
  \node[family] at (Center)  {$P$};
  \node[family] at (Center2) {$Q$};
  \node[family] at (Center3) {$Q'$};
  \node[family] at (Center4) {$P'$};

  %Cat-neurons
  \node[neuron,label=above:$n_1$] (N) at (cN) {};
  \node[neuron,label=above:$n_2$] (N') at (cN') {};
  \node[neuron,label=above:$n_3$] (M) at (cM) {};
  \draw[link]   (N) to node[auto]{\small{$(P,Q)$}} (M);
  \draw[link]   (M) to node[auto]{\small{$(Q',P')$}} (N');
  \draw[link,bend left]   (N) to (N');
\end{tikzpicture}

\begin{tikzpicture}

  \coordinate (Center)  at (0,0);
  \coordinate (cN)      at ($(Center) + ( 55:3cm)$);
  \coordinate (cM)      at ($(cN) + (4cm,0)$);
  \coordinate (cN')     at ($(cM) + (4cm,0)$);
  \coordinate (Center2) at ($(Center) + (4cm,0)$);
  \coordinate (Center3) at ($(cM) + (-55:3cm)$);
  \coordinate (Center4) at ($(Center3) + (4cm,0)$);

  % Specific identity
  \coordinate (silb1) at ($(cN) + (-1cm,2cm)$);
  \coordinate (silb2) at ($(Center) + (-1.5cm,-2cm)$);
  \coordinate (corner1) at ($(cN') + (1cm,-0.5cm)$);
  \coordinate (corner2) at ($(Center4) + (1.5cm,1.5cm)$);
  \coordinate (lalb1) at ($(corner1) + (0,2.5cm)$);
  \coordinate (lalb2) at ($(corner2) + (0,-3.5cm)$);
  \coordinate (IQde) at ($(corner2) + (-1cm,0.1cm)$);
  \coordinate (IQa)  at ($(corner1) + (0.1cm,1cm)$);
  \coordinate (centerSep) at (barycentric cs:cM=4,Center2=1,Center3=1);
  \coordinate (levelCue) at ($ (centerSep) + (-8cm,0cm) $);
  \coordinate (curlyCue) at ($ (centerSep) +  (7cm,0cm) $);
  %\draw[thick] (silb1) rectangle (corner1);
  %\draw[thick] (silb2) rectangle (corner2);
  %\node at (silb1) [label=south east:{Identité spécifique}] {};
  %\node at (silb2) [label=north east:{Identité spécifique}] {};
  \node at (levelCue) [label=north east:{Niveau $n+1$},yshift=-1mm] {};
  \node at (levelCue) [label=south east:{Niveau $n$},yshift=1mm] {};

  \draw[double] (levelCue) -- (curlyCue) -- ($ (curlyCue) + (3.2cm,0cm) $);

  % Curlies
  \draw[curlyM] ($ (curlyCue) + (0cm,0.05cm) $) -- +(0cm,1.5cm)
  node (idnh) [midway,anchor=west,xshift=0.4cm] {Identité spécifique};
  \draw[curly ] ($ (curlyCue) + (0cm,-0.05cm) $) -- +(0cm,-3cm)
  node (idnb) [midway,anchor=west,xshift=0.4cm] {Identité spécifique};

  %\draw[-Stealth, thick] ([xshift=-1cm]idnb.north) -- ([xshift=-1cm]idnh.south)
  %node [midway,auto,swap,text width={width("Identification")},align=center,
  %fill=white] {Identification\\ qualitative};


  %Cluster
  \fill[black,opacity=0.4] ($(Center) + (0,1cm)$) rectangle ($(Center2) + (0,-1cm)$);
  \fill[black,opacity=0.4] ($(Center3) + (0,1cm)$) rectangle ($(Center4) + (0,-1cm)$);

  %Bindings
  \filldraw[idq1,dashed,opacity=0.6] ($(Center) + (110:1cm)$)
  -- (cN)
  -- ($(Center) + (-30:1cm)$)
  -- cycle;
  \filldraw[idq2,dashed,opacity=0.6] ($(Center2) + (110:1cm)$)
  -- (cM)
  -- ($(Center2) + (-30:1cm)$)
  -- cycle;
  \filldraw[idq2,dashed,opacity=0.6] ($(Center3) + (  70:1cm)$)
  -- (cM)
  -- ($(Center3) + (-150:1cm)$)
  -- cycle;
  \filldraw[idq3,dashed,opacity=0.6] ($(Center4) + (  70:1cm)$)
  -- (cN')
  -- ($(Center4) + (-150:1cm)$)
  -- cycle;

  %Neuron nets
  \node[family,idq1] at (Center)  {$P$};
  \node[family,idq2] at (Center2) {$Q$};
  \node[family,idq2] at (Center3) {$Q'$};
  \node[family,idq3] at (Center4) {$P'$};

  %Cat-neurons
  \node[neuron,idq1,label=above:$n_1$] (N) at (cN) {};
  \node[neuron,idq2,label=above:$n_2$] (M) at (cM) {};
  \node[neuron,idq3,label=above:$n_3$] (N') at (cN') {};
  \draw[link]   (N) to node[auto]{\small{$(P,Q)$}} (M);
  \draw[link]   (M) to node[auto]{\small{$(Q',P')$}} (N');

  % Identité numérique
  \begin{scope}[on background layer]
    \node[fit=(N) (M) (N'),inner sep=5mm,idn1,rounded corners] {};
    \node[fit=(Center) (Center2), inner sep=1.2cm,idn2,rounded corners] {};
    \node[fit=(Center3) (Center4), inner sep=1.2cm,idn3,rounded corners] {};
  \end{scope}
\end{tikzpicture}

\end{document}