phd-thesis-fr/figures/complexification-ehresmann.tikz
2017-07-08 17:42:46 +02:00

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\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}