Collected WDs TikZ Pictures wiring diagrams
<tex> \documentclass[11pt,oneside,article]{memoir}
\usepackage{amsthm} %\usepackage{xltxtra} %\usepackage{newpxtext} %\usepackage[varg,bigdelims]{newpxmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage[usenames,dvipsnames]{xcolor} \usepackage{tikz} \usetikzlibrary{
cd,
math, decorations.markings, decorations.pathreplacing, positioning, arrows.meta, circuits.logic.US, shapes, calc, fit,
quotes}
\newcommand{\tn}{\textnormal} \newcommand{\inp}[1]{#1^{\tn{in}}} \newcommand{\outp}[1]{#1^{\tn{out}}} \newcommand{\upd}[1]{#1^{\tn{upd}}} \newcommand{\rdt}[1]{#1^{\tn{rdt}}}
\tikzset{
oriented WD/.style={%everything after equals replaces "oriented WD" in key.
every to/.style={out=0,in=180,draw},
label/.style={
font=\everymath\expandafter{\the\everymath\scriptstyle},
inner sep=0pt,
node distance=2pt and -2pt},
semithick,
node distance=1 and 1,
decoration={markings, mark=at position \stringdecpos with \stringdec},
ar/.style={postaction={decorate}},
execute at begin picture={\tikzset{
x=\bbx, y=\bby,
every fit/.style={inner xsep=\bbx, inner ysep=\bby}}}
},
string decoration/.store in=\stringdec,
string decoration={\arrow{stealth};},
string decoration pos/.store in=\stringdecpos,
string decoration pos=.7,
bbx/.store in=\bbx,
bbx = 1.5cm,
bby/.store in=\bby,
bby = 1.5ex,
bb port sep/.store in=\bbportsep,
bb port sep=1.5,
% bb wire sep/.store in=\bbwiresep,
% bb wire sep=1.75ex,
bb port length/.store in=\bbportlen,
bb port length=4pt,
bb penetrate/.store in=\bbpenetrate,
bb penetrate=0,
bb min width/.store in=\bbminwidth,
bb min width=1cm,
bb rounded corners/.store in=\bbcorners,
bb rounded corners=2pt,
bb small/.style={bb port sep=1, bb port length=2.5pt, bbx=.4cm, bb min width=.4cm,
bby=.7ex}, bb medium/.style={bb port sep=1, bb port length=2.5pt, bbx=.4cm, bb min width=.4cm, bby=.9ex},
bb/.code 2 args={%When you see this key, run the code below:
\pgfmathsetlengthmacro{\bbheight}{\bbportsep * (max(#1,#2)+1) * \bby}
\pgfkeysalso{draw,minimum height=\bbheight,minimum width=\bbminwidth,outer
sep=0pt,
rounded corners=\bbcorners,thick,
prefix after command={\pgfextra{\let\fixname\tikzlastnode}},
append after command={\pgfextra{\draw
\ifnum #1=0{} \else foreach \i in {1,...,#1} {
($(\fixname.north west)!{\i/(#1+1)}!(\fixname.south west)$) +(-
\bbportlen,0)
coordinate (\fixname_in\i) -- +(\bbpenetrate,0) coordinate (\fixname_in\i')}\fi
%Define the endpoints of tickmarks
\ifnum #2=0{} \else foreach \i in {1,...,#2} {
($(\fixname.north east)!{\i/(#2+1)}!(\fixname.south east)$) +(-
\bbpenetrate,0)
coordinate (\fixname_out\i') -- +(\bbportlen,0) coordinate (\fixname_out\i)}\fi;
}}}
},
bb name/.style={append after command={\pgfextra{\node[anchor=north] at
(\fixname.north) {#1};}}} }
\tikzset{
unoriented WD/.style={
every to/.style={draw},
shorten <=-\penetration, shorten >=-\penetration,
label distance=-2pt,
thick,
node distance=\spacing,
execute at begin picture={\tikzset{
x=\spacing, y=\spacing}}
},
pack size/.store in=\psize,
pack size = 8pt,
spacing/.store in=\spacing,
spacing = 8pt,
link size/.store in=\lsize,
link size = 2pt,
penetration/.store in=\penetration, penetration = 2pt,
pack color/.store in=\pcolor,
pack color = blue,
pack inside color/.store in=\picolor,
pack inside color=blue!20,
pack outside color/.store in=\pocolor,
pack outside color=blue!50!black,
surround sep/.store in=\ssep,
surround sep=8pt,
link/.style={
circle,
draw=black,
fill=black,
inner sep=0pt,
minimum size=\lsize
},
pack/.style={
circle,
draw = \pocolor,
fill = \picolor,
inner sep = .25*\psize,
minimum size = \psize
},
outer pack/.style={
ellipse,
draw,
inner sep=\ssep,
color=\pocolor,
},
intermediate pack/.style={
ellipse,
dashed,
draw,
inner sep=\ssep,
color=\pocolor,
},
}
\tikzset{Yonepart/.pic={ \node[bb={1}{2},bb name = {\tiny$X_{11}$}] (X11) {}; \node[bb={2}{2},below right=of X11,bb name = {\tiny$X_{12}$}] (X12) {}; \node[bb={2}{1}, above right=of X12,bb name = {\tiny$X_{13}$}] (X13) {}; \node[bb={2}{2}, fit={($(X11.north west)+(.3,1.5)$) (X12) ($(X13.east)+(-.3,0)$)},bb name = {\scriptsize $Y_1$}] (Y1) {}; \draw (Y1_in1') to (X11_in1); \draw (Y1_in2') to (X12_in2); \draw (X11_out1) to (X13_in1); \draw (X11_out2) to (X12_in1); \draw (X12_out1) to (X13_in2); \draw (X12_out2) to (Y1_out2'); \draw (X13_out1) to (Y1_out1'); \coordinate (bottombox) at ($(X12.south)$); \coordinate (rightbox) at ($(X13.east)$); \coordinate (Y1northwest) at ($(Y1.north west)$); } }
\tikzset{Ytwopart/.pic={ \node[bb={2}{2}, bb name = {\tiny$X_{21}$}] (X21) {}; \node[bb={1}{2},above right=-1 and 1 of X21,bb name = {\tiny$X_{22}$}] (X22) {}; \node[bb={1}{2}, fit={($(X21.south west)+(-.25,0)$) ($(X22.north east)+(.25,3.5)$)},bb name = {\scriptsize$Y_2$}] (Y2){}; \draw (Y2_in1') to (X21_in2); \draw (X21_out1) to (X22_in1); \draw (X22_out2) to (Y2_out1'); \draw let \p1=(X22.south east), \p2=($(Y2_out2)$), \n1={\y1-\bby}, \n2=\bbportlen in (X21_out2) to (\x1+\n2,\n1) -- (\x1+\n2,\n1) to (Y2_out2'); \draw let \p1=(X22.north east), \p2=(X21.north west), \n1={\y1+\bby}, \n2=\bbportlen in
(X22_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X21_in1);
}
}
\tikzset{SmallNeuronPic/.pic={
\node[bb={3}{1}] (N1) {$\scriptstyle N_1$};
\node[bb={2}{1}, above right=.7 and 3.5 of N1] (N2) {$\scriptstyle N_2$};
\node[bb={2}{1}, below =of N2] (N3) {$\scriptstyle N_3$};
\node[bb={3}{1}, below =of N3] (N4) {$\scriptstyle N_4$};
\node[bb={6}{8}, fit={($(N1.west)-(.5,0)$) ($(N2.north)+(0,2)$) ($(N3.east)+(1.5,0)$) ($(N4.south)-(0,1)$)}, bb name={$\scriptstyle X$}] (X) {};
\draw (X_in1') to (N2_in1);
\draw (X_in2') to (N1_in1);
\draw (X_in3') to (N1_in2);
\draw (X_in4') to (N1_in3);
\draw (X_in6') to (N4_in2);
\draw (N1_out1) to (N2_in2);
\draw (N1_out1) to (N3_in1);
\draw (N1_out1) to (N4_in1);
\draw (N2_out1) to (X_out1');
\draw (N2_out1) to (X_out2');
\draw (N2_out1) to (X_out3');
\draw (N3_out1) to (X_out4');
\draw (N3_out1) to (X_out5');
\draw (N3_out1) to (X_out6');
\draw (N4_out1) to (X_out7');
\draw (N4_out1) to (X_out8');
\draw (X_in5') to[looseness=2] (N3_in2);
\draw let \p1=(N4.south east), \p2=(N4.south west), \n1={\y2-\bby}, \n2=\bbportlen in
(N3_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (N4_in3);
} }
\tikzset{SmallNeuronDashed/.pic={
\node[bb={3}{1}] (N1) {$\scriptstyle N_1$};
\node[bb={2}{1}, above right=.7 and 3.5 of N1] (N2) {$\scriptstyle N_2$};
\node[bb={2}{1}, below =of N2] (N3) {$\scriptstyle N_3$};
\node[bb={3}{1}, below =of N3] (N4) {$\scriptstyle N_4$};
\node[bb={6}{8}, fit={($(N1.west)-(.5,0)$) ($(N2.north)+(0,2)$) ($(N3.east)+(1.5,0)$) ($(N4.south)-(0,1)$)}, bb name={$\scriptstyle X$}] (X) {};
\draw[dashed] (X_in1') to (N2_in1);
\draw[dashed] (X_in2') to (N1_in1);
\draw[dashed] (X_in3') to (N1_in2);
\draw[dashed] (X_in4') to (N1_in3);
\draw[dashed] (X_in6') to (N4_in2);
\draw[dashed] (N1_out1) to (N2_in2);
\draw[dashed] (N1_out1) to (N3_in1);
\draw[dashed] (N1_out1) to (N4_in1);
\draw[dashed] (N2_out1) to (X_out1');
\draw[dashed] (N2_out1) to (X_out2');
\draw[dashed] (N2_out1) to (X_out3');
\draw[dashed] (N3_out1) to (X_out4');
\draw[dashed] (N3_out1) to (X_out5');
\draw[dashed] (N3_out1) to (X_out6');
\draw[dashed] (N4_out1) to (X_out7');
\draw[dashed] (N4_out1) to (X_out8');
\draw[dashed] (X_in5') to[looseness=2] (N3_in2);
\draw[dashed] let \p1=(N4.south east), \p2=(N4.south west), \n1={\y2-\bby}, \n2=\bbportlen in
(N3_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (N4_in3);
} }
\tikzset{SmallNestingPic/.pic={ \path (0,0) pic [purple] {Yonepart}; \path ($(rightbox)+(5,-5)$) pic [orange] {Ytwopart};
\node[bb={1}{2}, fit={($(Y1northwest)+(-.5,4)$) ($(Y2.south east)+(1,0)$)}, bb name={\small $Z$}] (Z) {}; \draw (Z_in1') to (Y1_in2); \draw let \p1=(Y2.north west),\p2=(Y2.north east),\n1={\y2+\bby},\n2=\bbportlen in
(Y1_out1) to (\x1+\n2,\n1)--(\x2+\n2,\n1) to (Z_out1');
\draw (Y1_out2) to (Y2_in1); \draw (Y2_out2) to (Z_out2'); \draw let \p1=(Y2.north east), \p2=(Y1.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(Y2_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (Y1_in1);
}
}
\tikzset{Zredgreen/.pic={ \node[bb={2}{2}, green!50!black, bb name = $\scriptstyle Y_1$] (YY1) {}; \node[bb={1}{2}, red, below right=-1 and 2 of YY1, bb name=$\scriptstyle Y_2$] (YY2) {}; \node[bb={1}{2}, fit={($(YY1.north west)+(-.5,4)$) ($(YY2.south east)+(.5,-2)$)}, bb name={\scriptsize $Z$}] (Z) {}; \draw (Z_in1') to (YY1_in2); \draw (YY1_out1) to (Z_out1'); \draw (YY1_out2) to (YY2_in1); \draw (YY2_out2) to (Z_out2'); \draw let \p1=(YY2.north east), \p2=(YY1.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(YY2_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (YY1_in1);
} }
\tikzset{Zcombined/.pic={ \node[bb={1}{2},green!25!black,bb name = {\tiny$X_{11}$}] (X11) {}; \node[bb={2}{2},green!25!black,below right=of X11,bb name = {\tiny$X_{12}$}] (X12) {}; \node[bb={2}{1}, green!25!black,above right=of X12,bb name = {\tiny$X_{13}$}] (X13) {}; \draw (X11_out1) to (X13_in1); \draw (X11_out2) to (X12_in1); \draw (X12_out1) to (X13_in2);
\node[bb={2}{2}, red!30!black, below right = 0 and 1.25 of X12, bb name = {\tiny$X_{21}$}] (X21) {}; \node[bb={1}{2}, red!30!black, above right=-1 and 1 of X21,bb name = {\tiny$X_{22}$}] (X22) {}; \draw (X21_out1) to (X22_in1); \draw let \p1=(X22.north east), \p2=(X21.north west), \n1={\y1+\bby}, \n2=\bbportlen in
(X22_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X21_in1);
\node[bb={1}{2}, fit = {($(X11.north east)+(-1,3)$) (X12) (X13) ($(X21.south)+(0,-1)$) ($(X22.east)+(.5,0)$)}, bb name ={\scriptsize $Z$}] (Z) {};
\draw (Z_in1') to (X12_in2); \draw (X13_out1) to (Z_out1'); \draw (X12_out2) to (X21_in2); \draw let \p1=(X22.south east),\n1={\y1-\bby}, \n2=\bbportlen in (X21_out2) to (\x1+\n2,\n1) to (Z_out2'); \draw let \p1=(X22.north east), \p2=(X11.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X22_out2) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X11_in1);
} }
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\setulmarginsandblock{1in}{1in}{*}
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\checkandfixthelayout
\setcounter{tocdepth}{1} \setcounter{secnumdepth}{1} \pagestyle{ruled} \renewcommand*{\chaptitlefont}{\bfseries\Large} \setsecheadstyle{\bfseries\large\raggedright} \setsubsecheadstyle{\bfseries\raggedright}
\begin{document}
\title{Collected Wiring diagrams} \author{David I. Spivak}
\maketitle
\begin{equation}\label{eqn.overview}\tag{overview}
\begin{tikzpicture}
\begin{scope}[font=\footnotesize, text height=1.5ex, text depth=.5ex]
\begin{scope}[oriented WD, bb port sep=1, bb port length=2.5pt, bb min width=.4cm, bby=.2cm, inner xsep=.2cm, x=.5cm, y=.3cm]
\node[bb={1}{1}] (Catf) {$f$};
\node[bb={1}{1}, right=1 of Catf] (Catg) {$g$};
\node[bb={0}{0}, fit=(Catf) (Catg)] (Cat) {};
\node[coordinate] at (Cat.west|-Catf_in1) (Cat_in1) {};
\node[coordinate] at (Cat.east|-Catg_out1) (Cat_out1) {};
\draw[shorten <=-2pt] (Cat_in1) -- (Catf_in1);
\draw (Catf_out1) -- (Catg_in1);
\draw[shorten >=-2pt] (Catg_out1) -- (Cat_out1);
%
\node[bb={1}{2}, above right=-1.5 and 4 of Catf] (Monf) {$f$};
\node[bb={2}{1}, below right=-1 and 1 of Monf] (Mong) {$g$};
\node[bb={0}{0}, fit=(Monf) (Mong)] (Mon) {};
\node[coordinate] at (Mon.west|-Monf_in1) (Mon_in1) {};
\node[coordinate] at (Mon.west|-Mong_in2) (Mon_in2) {};
\node[coordinate] at (Mon.east|-Monf_out1) (Mon_out1) {};
\node[coordinate] at (Mon.east|-Mong_out1) (Mon_out2) {};
\draw[shorten <=-2pt] (Mon_in1) -- (Monf_in1);
\draw[shorten >=-2pt] (Monf_out1) -- (Mon_out1);
\draw (Monf_out2) to (Mong_in1);
\draw[shorten <=-2pt] (Mon_in2) -- (Mong_in2);
\draw[shorten >=-2pt] (Mong_out1) -- (Mon_out2);
%
\node[bb={2}{1}, right= 4.5 of Monf] (Trf) {$f$};
\node[bb={2}{2}, below right=-1 and 1 of Trf] (Trg) {$g$};
\node[bb={0}{0}, fit={($(Trf.north west)+(-.5,1)$) ($(Trg.south east)+(.5,-1)$)}] (Tr) {};
\node[coordinate] at (Tr.west|-Trf_in2) (Tr_in1) {};
\node[coordinate] at (Tr.west|-Trg_in2) (Tr_in2) {};
\node[coordinate] at (Tr.east|-Trf_out1) (Tr_out1) {};
\node[coordinate] at (Tr.east|-Trg_out2) (Tr_out2) {};
\draw[shorten <=-2pt] (Tr_in1) -- (Trf_in2);
\draw (Trf_out1) to (Trg_in1);
\draw[shorten <=-2pt] (Tr_in2) -- (Trg_in2);
\draw[shorten >=-2pt] (Trg_out2) -- (Tr_out2);
\draw let \p1=(Trg.east), \p2=(Trf.north west), \n1=\bbportlen, \n2=\bby in
(Trg_out1) to[in=0] (\x1+\n1,\y2+\n2) -- (\x2-\n1,\y2+\n2) to[out=180] (Trf_in1);
%
\end{scope}
\begin{scope}[penetration=0, unoriented WD, pack outside color=black, pack inside color=white]
\node[pack, right=2.9 of Trf] (Hypf) {$f$};
\node[pack, below right=0 and .5 of Hypf] (Hypg) {$g$};
\node[outer pack, inner sep=5pt, fit=(Hypf) (Hypg)] (Hyp) {};
\node[coordinate] at ($(Hypg.-30)!.5!(Hyp.-30)$) (link) {};
\draw (Hypf) to[bend left] (Hypg);
\draw (Hypf) to[bend right] (Hypg);
\draw (Hypg) -- (link);
\draw[shorten >= -2pt] (link) to[bend left] (Hyp.-20);
\draw[shorten >= -2pt] (link) to[bend right] (Hyp.-45);
\draw[shorten >= -2pt] (Hypf) -- (Hyp);
\end{scope}
\begin{scope}[circuit logic US, thick, every to/.style={out=0,in=180}]
\node[and gate, draw, right=2.5 of Hypf] (Opdf) {$f$};
\node[and gate, draw, below right=0 and 0.5 of Opdf] (Opdg) {$g$};
\node[and gate, inner sep=1pt, draw, fit=(Opdf) (Opdg)] (Opd) {}; \draw[shorten <=-2pt] (Opd.input 1|-Opdf.west) to (Opdf.west); \draw[shorten <=-2pt] (Opd.input 1|-Opdg.input 2) to (Opdg.input 2); \draw (Opdf.output) to (Opdg.input 1); \draw[shorten >=-2pt] (Opdg.output) to (Opd.output);
\end{scope}
\node[below=.65 of Cat.south] (Cat name) {category}; \node[text width=1.5cm] at (Cat name-|Mon) {monoidal category}; \node[text width=2.5cm] at (Cat name-|Tr) {traced monoidal category}; \node[text width=2cm] at (Cat name-|Hyp) {hypergraph category}; \node at (Cat name-|Opd) {operad}; \end{scope} \end{tikzpicture} \end{equation}
%%%% Chapter %%%% \chapter{Boxes}
\begin{equation}\label{box1}\tag{box1} \begin{tikzpicture}[oriented WD, bbx = 1cm, bby =.5cm, bb min width=1cm, bb port length=4pt, bb port sep=1] \node[bb={1}{1}] (X) {$M$}; \draw[label] node [left=2pt of X_in1] {$A$} node [right=2pt of X_out1] {$B$} ; \end{tikzpicture} \end{equation}
\begin{equation}\label{box2}\tag{box2} \begin{tikzpicture}[oriented WD, bb small, bb port sep=2.2, baseline = (lone.center)] \node[bb={3}{1}, inner sep=10pt] (lone) {$\dot{u}$}; \node[above right=-3 and 1.5 of lone] (a) {}; \node[below right=-3 and 1.5 of lone] (b) {}; \draw (lone_out1) to (a); \draw (lone_out1) to (b); \draw [label] \foreach \i in {1,2,3} { node[anchor=east] at (lone_in\i) {\small $a_\i$} node[above right=1 and 0 of lone_out1] {\small $u$} } ; \end{tikzpicture} \end{equation}
\begin{equation}\label{box3}\tag{box3} \begin{tikzpicture}[oriented WD, bbx = .25cm, bby =.1cm, bb min width=.25cm, bb port length=2pt, bb port sep=1] \node[bb={1}{1}] (X) {}; \draw[label] node [left=2pt of X_in1] {$\inp{X}$} node [right=2pt of X_out1] {$\outp{X}$} ; \end{tikzpicture} \end{equation}
\begin{equation}\label{box32}\tag{box32} \begin{tikzpicture}[oriented WD, bbx = 1cm, bby =.3cm, bb min width=1cm, bb port length=4pt, bb port sep=1] \node[bb={2}{3}] (X) {}; \draw[label] node [left=2pt of X_in1] {$A$} node [left=2pt of X_in2] {$B$} node [right=2pt of X_out1] {$C$} node [right=2pt of X_out2] {$D$} node [right=2pt of X_out3] {$E$} ; \end{tikzpicture} \end{equation}
\begin{equation}\label{lots}\tag{lots} \begin{tikzpicture}[oriented WD, bb small] \node[bb={0}{0}] (00) {}; \node[bb={0}{1}, right=2 of 00] (01) {}; \node[bb={0}{2}, right=2 of 01] (02) {}; \node[bb={1}{0}, right=2 of 02] (10) {}; \node[bb={1}{1}, right=2 of 10] (11) {}; \node[bb={1}{2}, right=2 of 11] (12) {}; \node[bb={2}{0}, right=2 of 12] (20) {}; \node[bb={2}{1}, right=2 of 20] (21) {}; \node[bb={2}{2}, right=2 of 21] (22) {}; \node[ right=2 of 22] (dt) {$\cdots$}; \node[bb={3}{5}, right=2 of dt] (35) {}; \node[ right=2 of 35] (et) {etc.}; \end{tikzpicture} \end{equation}
%%%% Chapter %%%% \chapter{Simple Wiring Diagrams}
\begin{equation}\label{simple3}\tag{simple 3} \begin{tikzpicture}[oriented WD, bbx = .3cm, bby =.3cm, bb min width=.5cm, bb port length=2pt, bb port sep=1] \node[bb={1}{1}] (X1) {\tiny$\sigma_1$};
\node[bb={1}{1}, right=of X1] (X2) {\tiny$\sigma_2$};
\node[bb={1}{1}, right=of X2] (X3) {\tiny$\sigma_3$}; \node[bb={1}{1}, fit=(X1) (X2) (X3)] (Y) {}; \draw (Y_in1') to (X1_in1); \draw (X1_out1) to (X2_in1); \draw (X2_out1) to (X3_in1); \draw (X3_out1) to (Y_out1'); \end{tikzpicture} \end{equation}
\begin{equation}\label{no_exterior}\tag{no exterior} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex]
\node[bb={0}{1},bb name=$X_1$] (X1) {};
\node[bb={1}{0},right =2 of X1, bb name=$X_2$] (X2) {};
\draw[ar] (X1_out1) to (X2_in1);
\end{tikzpicture} \end{equation}
\begin{equation}\label{simple2}\tag{simple 2} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex]
\node[bb={1}{1},bb name=$X_1$] (X1) {};
\node[bb={1}{1},right =2 of X1, bb name=$X_2$] (X2) {};
\node[bb={1}{1}, fit={($(X1.north west)+(-1,3)$) ($(X1.south)+(0,-3)$) ($(X2.east)+(1,0)$)}, bb name = $Y$] (Y) {};
%
\draw[ar] (Y_in1') to (X1_in1); \draw[ar] (X1_out1) to (X2_in1); \draw[ar] (X2_out1) to (Y_out1'); \draw[label]
node at ($(Y_in1')!.5!(X1_in1)+(0,7pt)$) {$A$} node at ($(X1_out1)!.5!(X2_in1)+(0,7pt)$) {$B$} node at ($(X2_out1)!.5!(Y_out1')+(0,7pt)$) {$C$}; \end{tikzpicture} \end{equation}
\begin{equation}\label{no_passing_wires}\tag{no passing wires} \begin{tikzpicture}[oriented WD, bb small] \node[bb={1}{1}] (x) {}; \node[bb={2}{2}, fit={(x.north west) ($(x.south east)+(0,-2)$)}] (y) {}; \draw (y_in1') to (x_in1); \draw (x_out1) to (y_out1'); \draw (y_in2') to (y_out2'); \draw[red, thin] ($(y.north west)+(-1,1)$) -- ($(y.south east)+(1,-1)$); \draw[red, thin] ($(y.north east)+(1,1)$) -- ($(y.south west)+(-1,-1)$); \end{tikzpicture} \end{equation}
\begin{equation}\label{digging1}\tag{digging1} \begin{tikzpicture}[oriented WD] \node[bb={1}{0}] (shovel) {$\;shovel\;$}; \node[bb={1}{0}, below=2 of shovel] (person) {$\;person\;$}; \node[bb={1}{2}, left=4 of $(shovel)!.5!(person)$] (dig) {};
\draw[label] node [left=2pt of dig_in1] {digging} node [right=2pt of dig_out1] {scooping} node [right=2pt of dig_out2] {levering} node [left=2pt of shovel_in1] {scooping} node [left=2pt of person_in1] {levering} ; \end{tikzpicture} \end{equation}
\begin{equation}\label{digging2}\tag{digging2} \begin{tikzpicture}[oriented WD,bb small, font=\tiny] \node[bb={1}{0}] (shovel) {S}; \node[bb={1}{0}, below=2 of shovel] (person) {P}; \node[bb={1}{2}, left=3 of $(shovel)!.5!(person)$] (dig) {D}; \node[bb={1}{0}, fit=(dig) (shovel) (person)] (outer) {}; \draw (outer_in1') to (dig_in1); \draw (dig_out1) to (shovel_in1); \draw (dig_out2) to (person_in1); \end{tikzpicture} \end{equation}
%%%% Chapter %%%% \chapter{Oriented Wiring Diagrams}
% Section % \section{No Tracing}
\subsection{No splitting} \begin{equation}\label{parallel}\tag{parallel} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex]
\node[bb={1}{1},bb name=$X_1$] (X1) {};
\node[bb={1}{1},below =2 of X1, bb name=$X_2$] (X2) {};
\node[bb={2}{2}, fit={($(X1.north west)+(-1,3)$) ($(X2.south)+(0,-3)$) ($(X2.east)+(1,0)$)}, bb name = $Y$] (Y) {};
%
\draw[ar] (Y_in1') to (X1_in1); \draw[ar] (Y_in2') to (X2_in1); \draw[ar] (X1_out1) to (Y_out1'); \draw[ar] (X2_out1) to (Y_out2'); \draw[label]
node at ($(Y_in1')!.5!(X1_in1)+(0,7pt)$) {$A_1$} node at ($(Y_in2')!.5!(X2_in1)+(0,7pt)$) {$B_1$} node at ($(X1_out1)!.5!(Y_out1')+(0,7pt)$) {$A_2$} node at ($(X2_out1)!.5!(Y_out2')+(0,7pt)$) {$B_2$}; \end{tikzpicture} \end{equation}
\begin{equation}\label{junky}\tag{junky} \begin{tikzpicture}[oriented WD, bb min width =.6cm, bb port sep =.5, bby=.3cm, bbx=.6cm,bb port length=3pt]
\node[bb={1}{2}] (X1) {};
\node[bb={2}{1}, below right=-.5 and 1 of X1] (X2) {};
\node[bb={2}{2}, fit=(X1) (X2)] (Y) {};
\draw (Y_in1') to (X1_in1);
\draw (Y_in2') to (X2_in2);
\draw (X1_out1) to (Y_out1');
\draw (X1_out2) to (X2_in1);
\draw (X2_out1) to (Y_out2');
\end{tikzpicture} \end{equation}
\begin{equation}\label{blue_sub}\tag{blue substitution} \begin{tikzpicture}[oriented WD,bb min width =.5cm, bbx=.5cm, bb port sep =1,bb port length=.08cm, bby=.15cm] \begin{scope}[blue!60!black] \node[bb={1}{2},bb name = {\tiny$X_{1}$}] (X11) {}; \node[bb={2}{2},below right=of X11,bb name = {\tiny$X_{2}$}] (X12) {}; \node[bb={2}{1}, above right=of X12,bb name = {\tiny$X_{3}$}] (X13) {}; \node[bb={2}{2}, fit={($(X11.north west)+(.3,1.5)$) (X12) ($(X13.east)+(-.3,0)$)},bb name = {\scriptsize $Y_3$}] (Y1) {}; \draw (Y1_in1') to (X11_in1); \draw (Y1_in2') to (X12_in2); \draw (X11_out1) to (X13_in1); \draw (X11_out2) to (X12_in1); \draw (X12_out1) to (X13_in2); \draw (X12_out2) to (Y1_out2'); \draw (X13_out1) to (Y1_out1'); \end{scope}
\node [bb={1}{2}, below left =1 and 9 of $(Y1.north west)$] (Y1) {\tiny $Y_1$}; \node [bb={1}{1},below=3 of Y1] (Y2) {\tiny $Y_2$}; \node [bb={2}{2}, blue!60!black,below right = 0 and 1 of Y1] (Y3) {\tiny $Y_3$}; \node [bb={2}{1},right=3 of Y1] (Y4) {\tiny $Y_4$}; \node [bb={1}{1},right=3 of Y2] (Y5) {\tiny $Y_5$}; \node [bb={1}{1},right=1of Y5] (Y6) {\tiny $Y_6$};
\node [bb={2}{2},fit={($(Y1.north)+(0,3)$) ($(Y2.south west)+(0,-3)$) (Y3) (Y4) (Y5) (Y6)}, bb name={\footnotesize $Z$}] (Z) {}; \draw (Z_in1') to (Y1_in1); \draw (Z_in2') to (Y2_in1); \draw (Y1_out1) to (Y4_in1); \draw (Y1_out2) to (Y3_in1); \draw (Y2_out1) to (Y3_in2); \draw (Y3_out1) to (Y4_in2); \draw (Y3_out2) to (Y5_in1); \draw (Y4_out1) to (Z_out1'); \draw (Y5_out1) to (Y6_in1); \draw (Y6_out1) to (Z_out2');
\end{tikzpicture} \end{equation}
\begin{equation}\label{terminate}\tag{terminate} \begin{tikzpicture}[oriented WD] \node[bb={1}{2}] (A) {}; \node[bb={2}{1}, below right=-1 and 1 of A] (B) {}; \node[bb={0}{0}, fit=(A) (B)] (outer) {}; \node[right=.6 of A_out1] (kill) {$\bullet$}; \draw (outer.west|-A_in1) -- (A_in1); \draw (outer.west|-B_in2) -- (B_in2); \draw (A_out1) to node[above, font=\footnotesize] {waste} (kill.center); \draw (A_out2) to (B_in1); \draw (B_out1) -- (B_out1-|outer.east); \end{tikzpicture} \end{equation}
\begin{equation}\label{IAN:feedforward}\tag{IAN: feedforward} \begin{tabular}{c|c|c} \small {Interfaces}&\small {Arrangements}&\small {Nesting}\\\hline ~&&\\ \parbox{.5in}{ \begin{tikzpicture}[oriented WD, bby=1ex]
\node[bb={3}{2}] (X1) {};
\node[bb={1}{1}, below=.4cm of X1] (X2) {};
\node[bb={0}{2}, below=.4cm of X2] (X3) {};
\end{tikzpicture} } & \parbox{1.3in}{ \begin{tikzpicture}[oriented WD,bb min width =.5cm, bbx=.5cm, bb port sep =1,bb port length=.08cm, bby=.15cm] \path (0,0) pic {Yonepart}; \end{tikzpicture} } & \parbox{2in}{ \begin{tikzpicture}[oriented WD, bb small]
\node[bb={1}{2}] (X1) {};
\node[bb={2}{1},right=9 of X1] (X2) {};
\node[bb={1}{2},below right = 2 and 2 of X1] (X11) {};
\node[bb={2}{2},below right=of X11] (X12) {};
\node[bb={2}{1}, above right=of X12] (X13) {};
\node[bb={2}{2}, dashed, fit={($(X11.north west)+(.3,1.5)$) (X12) ($(X13.east)+(-.3,0)$)}] (Y1) {};
\node[bb={2}{2}, fit={($(X1.north west)+(0,3)$) (Y1) (X2)}] (Z) {};
\draw (Y1_in1') to (X11_in1);
\draw (Y1_in2') to (X12_in2);
\draw (X11_out1) to (X13_in1);
\draw (X11_out2) to (X12_in1);
\draw (X12_out1) to (X13_in2);
\draw (X12_out2) to (Y1_out2');
\draw (X13_out1) to (Y1_out1');
\draw (Z_in1') to (X1_in1);
\draw (Z_in2') to (Y1_in2);
\draw (X1_out1) to (X2_in1);
\draw (X1_out2) to (Y1_in1);
\draw (Y1_out1) to (X2_in2);
\draw (Y1_out2) to (Z_out2');
\draw (X2_out1) to (Z_out1');
\end{tikzpicture} }\\ &&\parbox{1.7in}{(Getting a sense of how\\ fractals are a special case?)} \end{tabular} \end{equation}
\subsection{Splitting}
\begin{equation}\label{updrdt}\tag{upd and rdt} \begin{tikzpicture}[oriented WD, bbx=1.1em, bb min width=3.3em, bby=2ex, bb port sep = 1] \node[bb={2}{1}] (X1) {$\upd{f}$}; \node[bb={1}{1}, below right=-1 and 2 of X1] (X2) {$\rdt{f}$}; \node[bb={2}{1}, below right=-1.5 and 2 of X2] (X3) {$\upd{g}$}; \node[bb={3}{2}, fit={($(X1.north west)+(-1,0)$) (X2) ($(X3.south east)+(1,0)$)}, bb name = {$\upd{h}$}] (Y) {}; % \draw (Y_in1') to (X1_in1) ; \draw (Y_in2') to (X1_in2); \draw (X1_out1) to (Y_out1'); \draw (X1_out1) to (X2_in1); \draw (X2_out1) to (X3_in1); \draw (Y_in3') to (X3_in2); \draw (X3_out1) to (Y_out2'); \draw[label] node at ($(Y_in1)+(-.5,0)$) {$A$} node at ($(Y_in2)+(-.5,0)$) {$S$} node at ($(Y_in3)+(-.5,0)$) {$T$} node at ($(X1_out1)+(.3,.6)$) {$S$} node at ($(X2_out1)+(.3,.6)$) {$B$} node at ($(X3_out1)+(.3,.6)$) {$T$}; \end{tikzpicture} \qquad\qquad \begin{tikzpicture}[oriented WD, bbx=1.1em, bb min width=3.3em, bby=2ex, bb port sep = 1] \node[bb={1}{1}] (X) {$\rdt{g}$}; \node[bb={2}{1}, fit={($(X.north west)+(-1,1)$) ($(X.south east)+(1,-1)$)}, bb name={$\rdt{h}$}] (Y) {}; \node [circle,minimum size=4pt, inner sep=0, fill] (dot) at ($(Y_in1')+(.5,0)$) {}; % \draw (Y_in1') to (dot); \draw (Y_in2') to (X_in1); \draw (X_out1) to (Y_out1'); \draw[label] node at ($(Y_in1)-(.5,0)$) {$S$} node at ($(Y_in2)-(.5,0)$) {$T$} node at ($(X_out1)+(.3,.6)$) {$C$}; \end{tikzpicture} \end{equation}
\begin{equation}\label{split_leftright}\tag{split left/right} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex, bb port sep=3 pt]
\node[bb={1}{1},bb name=$X$] (X) {};
\node[bb={1}{2}, fit={(X) ($(X.north east)+(1.2,3)$) ($(X.south west)+(-1.2,-3)$)}, bb name = $Y$] (Y) {}; % \draw[ar] (Y_in1') to (X_in1); \draw[ar] (X_out1) to (Y_out1'); \draw[ar] (X_out1) to (Y_out2'); \draw[label] node at ($(Y_in1')!.5!(X_in1)+(0,7pt)$) {$A$} node at ($(X_out1)!.5!(Y_out1')+(0,7pt)$) {$B$} node at ($(X_out1)!.5!(Y_out2')-(0,7pt)$) {$B$}; \end{tikzpicture} \qquad\qquad \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex, bb port sep=2 pt]
\node[bb={2}{1},bb name=$X$] (X) {};
\node[bb={1}{1}, fit={(X) ($(X.north east)+(1.2,3)$) ($(X.south west)+(-1.2,-3)$)}, bb name = $Y$] (Y) {}; % \draw[ar] (Y_in1') to (X_in1); \draw[ar] (Y_in1') to (X_in2); \draw[ar] (X_out1) to (Y_out1'); \draw[label] node at ($(Y_in1')!.5!(X_in1)+(0,7pt)$) {$A$} node at ($(Y_in1')!.5!(X_in2)-(0,7pt)$) {$A$} node at ($(X_out1)!.5!(Y_out1')+(0,7pt)$) {$B$}; \end{tikzpicture} \end{equation}
\begin{equation}\label{split_and_terminate}\tag{split and terminate} \begin{tikzpicture}[oriented WD,bb min width =.5cm, bbx=.5cm, bb port sep =1,bb port length=0, bby=.15cm] \node [bb={1}{2}] (Y1) {\tiny $f_1$}; \node [bb={1}{2},below=3 of Y1] (Y2) {\tiny $f_2$}; \node [bb={2}{1},below right = 0 and 1 of Y1] (Y3) {\tiny $f_3$}; \node [bb={2}{1},right=3 of Y1] (Y4) {\tiny $f_4$}; \node [bb={1}{1},right=3 of Y2] (Y5) {\tiny $f_5$}; \node [bb={2}{2},fit={($(Y1.north)+(0,2)$) ($(Y2.south west)+(0,-2)$) (Y4) (Y5)}] (Z) {}; \node [circle, fill, inner sep=1pt] at ($(Y2_out2)+(0.5,0)$) (kill) {}; \draw (Z_in1'|-Y1_in1) to (Y1_in1); \draw (Z_in2'|-Y2_in1) to (Y2_in1); \draw (Y1_out1) to (Y4_in1); \draw (Y1_out2) to (Y3_in1); \draw (Y2_out1) to (Y3_in2); \draw (Y2_out2) to (kill); \draw (Y3_out1) to (Y4_in2); \draw (Y3_out1) to (Y5_in1); \draw (Y4_out1) to (Z_out1'|-Y4_out1); \draw (Y5_out1) to (Z_out2'|-Y5_out1); \end{tikzpicture} \end{equation}
\begin{equation}\label{meringue}\tag{meringue} \begin{tikzpicture}[oriented WD, align=center, bbx=1.2cm, bby=2ex] \node[bb={3}{1}, bb min width=.9in] (filling) {make\\lemon\\filling}; \node[bb={2}{1}, bb min width=.9in, below=of filling] (meringue) {make\\meringue}; \node at ($(filling.west)!.5!(meringue.west)$) (helper) {}; \node[bb={1}{2}, left = of helper] (separate) {separate\\egg}; \node[bb={2}{1}, above right = -2 and 1 of filling] (fill) {fill crust}; \node[bb={2}{1}, below right = of fill] (finish) {add\\meringue}; \node[bb={0}{0}, fit=(separate) (meringue) (fill) (finish)] (pie) {}; % \begin{scope}[font=\tiny] \draw (pie.west|-fill_in1) to node[above] {crust} (fill_in1); \draw (pie.west|-filling_in1) to node[above] {butter} (filling_in1); \draw (pie.west|-filling_in2) to node[above] {sugar} (filling_in2); \draw (pie.west|-separate_in1) to node[above] {egg} (separate_in1); \draw (pie.west|-meringue_in2) to node[above] {butter} (meringue_in2); \draw (separate_out1) to node[above] {yolk} (filling_in3); \draw (separate_out2) to node[fill=white, inner sep=0.8pt] {white} (meringue_in1); \draw (filling_out1) to node[fill=white, inner sep=0.8pt] {lemon\\filling} (fill_in2); \draw (fill_out1) to node[fill=white, inner sep=0.8pt] {lemon pie} (finish_in1); \draw let \p1=(fill.east|-meringue_out1), \n1=\bbportlen in (meringue_out1) to node[above] {meringue} (\x1+\n1,\y1) to (finish_in2); \draw (finish_out1) to node[above] {pie} (finish_out1-|pie.east); \end{scope} \end{tikzpicture} \end{equation}
% Section % \section{Tracing}
\subsection{No splitting}
\begin{equation}\label{minimal_feedback}\tag{minimal with feedback} \begin{tikzpicture}[oriented WD, bb small] \node[bb={1}{1}] (X) {}; \node[bb={0}{0},fit={($(X.north west)+(0,1)$) ($(X.south east)+(0,-1)$)}] (Y){}; \draw[ar] let \p1=(X.north west), \p2=(X.north east), \n1=\bbportlen, \n2={\y1+\bby} in (X_out1) to[in=0] (\x2+\n1,\n2) -- (\x1-\n1,\n2) to[out=180] (X_in1); \end{tikzpicture} \end{equation}
\begin{equation}\label{f_and_g}\tag{f and g} \begin{tikzpicture}[oriented WD, bb min width =.7cm, bby=1.6ex, bbx=.7cm,bb port length=3pt]
\node[bb port sep=1.6, bb={2}{2}, bb name=$f$] (X1) {};
\node[bb port sep=.8,bb={1}{1}, right=.7 of X1_out1, bb name=$g$] (X2) {};
\node[bb={1}{1}, fit={(X1) (X2) ($(X1.north)+(0,1)$)}] (Y) {};
\draw[ar] (Y_in1') to (X1_in2);
\draw[ar,pos=.8] (X1_out1) to (X2_in1);
\draw[ar] let \p1=(X2.south east), \n1={\y1-.8*\bby}, \n2=\bbportlen in
(X1_out2) -- (\x1+\n2,\n1) to (Y_out1');
\draw[ar] let \p1=(X2.north east), \p2=(X1.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X2_out1) to[in=0] (\x1+.7*\n2,\n1) -- (\x2-.7*\n2,\n1) to[out=180] (X1_in1);
\end{tikzpicture} \end{equation}
\begin{equation}\label{little_trace}\tag{little trace} \begin{tikzpicture}[oriented WD,bb port sep=1, bb port length=2.5pt, bbx=.5cm, bb min width=.5cm, bby=1ex] \node[bb={2}{2}] (dom) {}; \node[bb={1}{1}, fit={(dom) ($(dom.north)+(0,1)$) ($(dom.south)-(0,2)$)}] (cod) {}; \draw[ar,pos=20] (cod_in1') to (dom_in2); \draw[ar,pos=2] (dom_out2) to (cod_out1'); \draw[ar] let \p1=(dom.north east), \p2=(dom.north west), \n1={\y2+\bby}, \n2=\bbportlen in (dom_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (dom_in1); \draw[label] node[below left=2pt and 3pt of dom_in2]{\tiny$X$} node[below right=2pt and 3pt of dom_out2]{\tiny$Y$} node[above left=1pt and 3pt of dom_in1] {\tiny$U$} node[above right=1pt and 3pt of dom_out1] {\tiny$U$}; \end{tikzpicture} \end{equation}
\begin{equation}\label{bigger_trace}\tag{bigger trace} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex] \node[bb={2}{2}, bb name=$X$] (dom) {}; \node[bb={1}{1}, fit={(dom) ($(dom.north east)+(1,4)$) ($(dom.south west)-(1,2)$)}, bb name = $Y$] (cod) {}; \draw[ar,pos=20] (cod_in1') to (dom_in2); \draw[ar,pos=2] (dom_out2) to (cod_out1'); \draw[ar] let \p1=(dom.north east), \p2=(dom.north west), \n1={\y2+\bby}, \n2=\bbportlen in (dom_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (dom_in1); \draw[label] node[below left=2pt and 3pt of dom_in2]{$A$} node[below right=2pt and 3pt of dom_out2]{$B$} node[above left=4pt and 6pt of dom_in1] {$C$} node[above right=4pt and 6pt of dom_out1] {$C$}; \end{tikzpicture} \end{equation}
\begin{align}\label{dia:series_parallel}\tag{series parallel} \begin{tikzpicture}[oriented WD, baseline=(Y.center), bbx=1em, bby=1ex] \node[bb={1}{1},bb name=$R_1$] (X1) {}; \node[bb={1}{1},right =2 of X1, bb name=$R_2$] (X2) {}; \node[bb={1}{1}, fit={($(X1.north west)+(-1,3)$) ($(X1.south)+(0,-3)$) ($(X2.east)+(1,0)$)}, bb name = $R_1R_2$] (Y) {}; % \draw[ar] (Y_in1') to (X1_in1); \draw[ar] (X1_out1) to (X2_in1); \draw[ar] (X2_out1) to (Y_out1'); \end{tikzpicture} \qquad\qquad \begin{tikzpicture}[oriented WD,baseline=(Y.center), bbx=1em, bby=1ex] \node[bb={1}{1},bb name=$R_1$] (X1) {}; \node[bb={1}{1},below =2 of X1, bb name=$R_2$] (X2) {}; \node[bb={2}{2}, fit={($(X1.north west)+(-1,3)$) ($(X2.south)+(0,-3)$) ($(X2.east)+(1,0)$)}, bb name = $R_1\otimes R_2$] (Y) {}; % \draw[ar] (Y_in1') to (X1_in1); \draw[ar] (Y_in2') to (X2_in1); \draw[ar] (X1_out1) to (Y_out1'); \draw[ar] (X2_out1) to (Y_out2'); \end{tikzpicture} \qquad\qquad \begin{tikzpicture}[oriented WD,baseline=(cod.center), bbx=1em, bby=1ex] \node[bb={2}{2}, bb name=$R$] (dom) {}; \node[bb={1}{1}, fit={(dom) ($(dom.north east)+(1,4)$) ($(dom.south west)-(1,2)$)}, bb name = $\tn{Tr}(R)$] (cod) {}; \draw[ar,pos=20] (cod_in1') to (dom_in2); \draw[ar,pos=2] (dom_out2) to (cod_out1'); \draw[ar] let \p1=(dom.north east), \p2=(dom.north west), \n1={\y2+\bby}, \n2=\bbportlen in (dom_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (dom_in1); \draw[label] node[below left=2pt and 3pt of dom_in2]{$A$} node[below right=2pt and 3pt of dom_out2]{$B$} node[above left=4pt and 6pt of dom_in1] {$C$} node[above right=4pt and 6pt of dom_out1] {$C$}; \end{tikzpicture} \end{align}
\begin{equation}\label{relations1}\tag{Relations 1} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex] \node[bb={1}{1},bb name=$R_1$] (R1) {};
\node[bb={2}{1}, above right = -2 and 1.5 of R1, bb name=$R_2$] (R2) {};
\node[bb={1}{2}, right = 1.5 of R2, bb name=$R_3$] (R3) {}; \node[bb={1}{1}, fit={($(R1.south west)+(-1,-1)$) (R2) ($(R3.north east)+(1,3)$)}, bb name = $S$] (S) {}; % \draw (S_in1') to (R2_in1); \draw (R1_out1) to (R2_in2); \draw (R2_out1) to (R3_in1); \draw (R3_out1) to (S_out1'); \draw let \p1=(R3.south east), \p2=(R1.south west), \n1={\y2-\bby}, \n2=\bbportlen in (R3_out2) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (R1_in1); % \draw [label] node[above left=.4 and 0 of R1_in1] {$x$} node[above right=.8 and -.1 of R1_out1] {$y$} node[above left=.4 and 0 of R2_in1] {$v$} node[above left=.4 and 0 of S_in1] {$v$} node[above right=.4 and 0 of R2_out1] {$w$} node[above right=.4 and 0 of R3_out1] {$z$} node[above right=.4 and 0 of S_out1] {$z$} node[above right=.4 and 0 of R3_out2] {$x$} ; \end{tikzpicture} \end{equation}
\begin{equation}\label{relations2}\tag{relations 2} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex]
\node[bb port sep=3,bb={1}{2}, bb name=$R'_2$] (R2) {};
\node[bb port sep=1.5, bb={1}{1}, right=1 of R2_out2] (R1) {$R'_1$}; \node[bb port sep=3,bb={2}{1}, right=5.5 of R2, bb name=$R'_3$] (R3) {}; \node[bb={1}{1}, fit={(R1) (R2) (R3)}, bb name = $S$] (S) {}; % \draw (S_in1') to (R2_in1); \draw (R2_out2) to (R1_in1); \draw (R2_out1) to (R3_in1); \draw (R3_out1) to (S_out1'); \draw (R1_out1) to (R3_in2); % \draw [label] node[above right=.4 and 0 of R2_out2] {$y$} node[above right=.4 and 0 of R1_out1] {$x$} node[above left=.4 and 0 of R2_in1] {$v$} node[above right=.4 and 0 of R2_out1] {$w$} node[above right=.4 and 0 of R3_out1] {$z$} ; \end{tikzpicture} \end{equation}
\begin{equation}\label{smallNestingPic}\tag{SmallNestingPic} \begin{tikzpicture}[oriented WD, bb min width =.5cm, bbx=.5cm, bb port sep =1,bb port length=.08cm, bby=.14cm] \path (0,0) pic {SmallNestingPic}; \end{tikzpicture} \end{equation}
\begin{equation}\label{Zcombined}\tag{Zcombined} \begin{tikzpicture}[oriented WD, bb min width =.5cm, bbx=.5cm, bb port sep =1,bb port length=.08cm, bby=.15cm] \path (0,0) pic {Zcombined}; \end{tikzpicture} \end{equation}
\begin{equation}\label{two_modules}\tag{two modules} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex]
\node[bb={3}{2},bb name=$X_1$] (X1) {};
\node[bb={2}{2},below right = -3 and 2 of X1, bb name=$X_2$] (X2) {};
\node[bb={3}{2}, fit={($(X1.north west)+(-1,2)$) ($(X2.south)+(0,-2)$) ($(X2.east)+(1,0)$)}, bb name = $Y$] (Y) {};
%
\draw[ar] (Y_in1') to (X1_in1); \draw[ar] (X1_out2) to (X2_in1); \draw[ar] (Y_in2') to (X1_in2); \draw[ar] (X1_out1) to (Y_out1'); \draw (X2_out1) to (Y_out2');
%
\draw[ar] let \p1=(X2.south east), \p2=(X1.south west), \n1={\y1-\bby}, \n2=\bbportlen in
(X2_out2) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X1_in3);
\draw[ar] let \p1=(X1.south west), \p2=(X1.south east), \n1={\y1-\bby}, \n2=\bbportlen in
(Y_in3') to (\x1-\n2,\n1) -- (\x2-\n2,\n1) to (X2_in2);
\end{tikzpicture} \end{equation}
\begin{equation}\label{pretty}\tag{pretty} \begin{tikzpicture}[oriented WD, bb min width =.5cm, bbx=.5cm, bb port sep =1,bb port length=.08cm, bby=.15cm] \node[bb={2}{2},green!25!black,bb name = {\tiny$X_1$}] (X11) {}; \node[bb={3}{3},green!25!black,below right=of X11,bb name = {\tiny$X_2$}] (X12) {}; \node[bb={2}{1}, green!25!black,above right=of X12,bb name = {\tiny$X_3$}] (X13) {}; \draw (X11_out1) to (X13_in1); \draw (X11_out2) to (X12_in1); \draw (X12_out1) to (X13_in2);
\node[bb={2}{2}, green!25!black, below right = -1 and 1.5 of X12, bb name = {\tiny$X_4$}] (X21) {}; \node[bb={1}{2}, green!25!black, above right=-1 and 1 of X21,bb name = {\tiny$X_5$}] (X22) {}; \draw (X21_out1) to (X22_in1); \draw let \p1=(X22.north east), \p2=(X21.north west), \n1={\y1+\bby}, \n2=\bbportlen in
(X22_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X21_in1);
\node[bb={2}{2}, fit = {($(X11.north east)+(-1,3)$) (X12) (X13) ($(X21.south)$) ($(X22.east)+(.5,0)$)}, bb name ={\scriptsize $Y$}] (Z) {};
\draw (Z_in1') to (X11_in2); \draw (Z_in2') to (X12_in2); \draw (X12_out2) to (X21_in2); \draw let \p1=(X22.south east),\n1={\y1-\bby}, \n2=\bbportlen in (X21_out2) to (\x1+\n2,\n1) to (Z_out2'); \draw let \p1=(X12.south east), \p2=(X12.south west), \n1={\y1-\bby}, \n2=\bbportlen in (X12_out3) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X12_in3); \draw let \p1=(X22.north east), \p2=(X11.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X22_out2) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X11_in1);
\draw let \p1=(X13_out1), \p2=(X22.north east), \n2=\bbportlen in (X13_out1) to (\x1+\n2,\y1) -- (\x2+\n2,\y1) to (Z_out1'); \end{tikzpicture} \end{equation}
\begin{equation}\label{prettier?}\tag{prettier?} \begin{tikzpicture}[oriented WD, bb min width =.5cm, bbx=.5cm, bb port sep =1,bb port length=0, bby=.15cm] \node[bb={2}{2}, green!25!black, bb name = {\tiny$X_1$}] (X11) {}; \node[bb={3}{3}, green!25!black, below right=of X11, bb name = {\tiny$X_2$}] (X12) {}; \node[bb={2}{1}, green!25!black, above right=of X12, bb name = {\tiny$X_3$}] (X13) {}; \node[bb={2}{2}, green!25!black, below right = -1 and 1.5 of X12, bb name = {\tiny$X_4$}] (X21) {}; \node[bb={1}{2}, green!25!black, above right=-1 and 1 of X21,bb name = {\tiny$X_5$}] (X22) {};
\node[bb={2}{2}, fit = {($(X11.north east)+(-1,2)$) (X12) (X13) ($(X21.south)$) ($(X22.east)+(.5,0)$)}] (Z) {};
\draw (X21_out1) to (X22_in1); \draw let \p1=(X22.north east), \p2=(X21.north west), \n1={\y1+\bby}, \n2=\bbportlen in
(X22_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X21_in1);
\draw (X11_out1) to (X13_in1); \draw (X11_out2) to (X12_in1); \draw (X12_out1) to (X13_in2); \draw (Z_in1'|-X11_in2) to (X11_in2); \draw (Z_in2'|-X12_in2) to (X12_in2); \draw (X12_out2) to (X21_in2); \draw (X21_out2) to (Z_out2'|-X21_out2); \draw let \p1=(X12.south east), \p2=(X12.south west), \n1={\y1-\bby}, \n2=\bbportlen in (X12_out3) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X12_in3); \draw let \p1=(X22.north east), \p2=(X11.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X22_out2) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X11_in1);
\draw (X13_out1) to (Z_out1'|-X13_out1); \end{tikzpicture} \end{equation}
\begin{equation}\label{pretty_no_num}\tag{pretty-no-num} \begin{tikzpicture}[oriented WD, bb min width =.5cm, bbx=.5cm, bb port sep =1,bb port length=.08cm, bby=.15cm] \node[bb={2}{2},green!25!black] (X11) {}; \node[bb={3}{3},green!25!black,below right=of X11] (X12) {}; \node[bb={2}{1}, green!25!black,above right=of X12] (X13) {}; \draw (X11_out1) to (X13_in1); \draw (X11_out2) to (X12_in1); \draw (X12_out1) to (X13_in2);
\node[bb={2}{2}, green!25!black, below right = -1 and 1.5 of X12] (X21) {}; \node[bb={1}{2}, green!25!black, above right=-1 and 1 of X21] (X22) {}; \draw (X21_out1) to (X22_in1); \draw let \p1=(X22.north east), \p2=(X21.north west), \n1={\y1+\bby}, \n2=\bbportlen in
(X22_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X21_in1);
\node[bb={2}{2}, fit = {($(X11.north east)+(-1,3)$) (X12) (X13) ($(X21.south)$) ($(X22.east)+(.5,0)$)}] (Z) {};
\draw (Z_in1') to (X11_in2); \draw (Z_in2') to (X12_in2); \draw (X12_out2) to (X21_in2); \draw let \p1=(X22.south east),\n1={\y1-\bby}, \n2=\bbportlen in (X21_out2) to (\x1+\n2,\n1) to (Z_out2'); \draw let \p1=(X12.south east), \p2=(X12.south west), \n1={\y1-\bby}, \n2=\bbportlen in (X12_out3) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X12_in3); \draw let \p1=(X22.north east), \p2=(X11.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X22_out2) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X11_in1);
\draw let \p1=(X13_out1), \p2=(X22.north east), \n2=\bbportlen in (X13_out1) to (\x1+\n2,\y1) -- (\x2+\n2,\y1) to (Z_out1'); \end{tikzpicture} \end{equation}
\begin{equation}\label{cobordism_equation}\tag{cobordism equation} \begin{tikzpicture}[oriented WD, bb min width =.7cm, bby=1.6ex, bbx=.7cm,bb port length=3pt,baseline=(current bounding box.center)] \node[bb port sep=1.6, bb={2}{2}, bb name=$f$] (X1) {}; \node[bb port sep=.8,bb={1}{1}, right=.7 of X1_out1, bb name=$g$] (X2) {}; \node[bb={1}{1}, fit={(X1) (X2) ($(X1.north)+(0,1)$)}] (Y) {}; \draw[ar] (Y_in1') to (X1_in2); \draw[ar,pos=.8] (X1_out1) to (X2_in1); \draw[ar] let \p1=(X2.south east), \n1={\y1-.8*\bby}, \n2=\bbportlen in (X1_out2) -- (\x1+\n2,\n1) to (Y_out1'); \draw[ar] let \p1=(X2.north east), \p2=(X1.north west), \n1={\y2+\bby}, \n2=\bbportlen in (X2_out1) to[in=0] (\x1+.7*\n2,\n1) -- (\x2-.7*\n2,\n1) to[out=180] (X1_in1); \end{tikzpicture} \quad = \quad \begin{tikzpicture}[oriented WD, bb min width =.7cm, bby=1.6ex, bbx=.7cm,bb port length=3pt,baseline=(current bounding box.center)] \node[bb port sep=1.6, bb={2}{2}, bb name=$f$] (X1) {}; \node[bb port sep=.8,bb={1}{1}, left=.7 of X1_in1, bb name=$g$] (X2) {}; \node[bb={1}{1}, fit={(X2) (X1) ($(X1.north)+(0,1)$)}] (Y) {}; \draw[ar] (X1_out2) to (Y_out1'); \draw[ar,pos=.8] (X2_out1) to (X1_in1); \draw[ar] let \p1=(X2.south west), \n1={\y1-.8*\bby}, \n2=\bbportlen in (Y_in1') to (\x1-\n2,\n1) -- (X1_in2); \draw[ar] let \p1=(X2.north west), \p2=(X1.north east), \n1={\y2+\bby}, \n2=\bbportlen in (X1_out1) to[in=0] (\x2+.7*\n2,\n1) -- (\x1-.7*\n2,\n1) to[out=180] (X2_in1); \end{tikzpicture} \end{equation}
\begin{equation}\label{cobordism}\tag{cobordism} \parbox{2in}{ \begin{tikzpicture}[oriented WD, bb min width =.7cm, bby=1.2ex, bbx=1.1cm,bb port length=3pt, label/.append style={node distance=1pt and -3pt}]
\node[bb={2}{1},, bb name={\tiny $X_1$}] (X1) {};
\node[bb={1}{2}, right=.7 of X1_out1, bb name={\tiny $X_2$}] (X2) {};
\node[bb={2}{2}, fit={(X1) (X2) ($(X1.south)-(0,3)$) ($(X1.north)+(0,5)$)}, bb name={\footnotesize$Y$}] (Y) {};
\draw (Y_in1') to[in looseness=1.25] (X1_in2);
\draw[ar,pos=.8] (X1_out1) to (X2_in1);
\draw (X2_out2) to[out looseness=1.25] (Y_out1');
\draw[ar] let \p1=(X1.south west), \p2=(X2.south east), \n1={\y2-2*\bby}, \n2=\bbportlen in
(Y_in2') to[in looseness=1.5] (\x1-\n2,\n1) -- (\x2+\n2,\n1) to[out looseness=1.5] (Y_out2');
\draw[ar] let \p1=(X2.north east), \p2=(X1.north west), \n1={\y2+2*\bby}, \n2=\bbportlen in
(X2_out1) to[in=0, looseness=1.5] (\x1+.7*\n2,\n1) -- (\x2-.7*\n2,\n1) to[out=180, looseness=1.5] (X1_in1);
\draw[label]
node[above left=2pt and -3pt of X1_in1] {\tiny$X_{1a}$}
node[below left=of X1_in2] {\tiny$X_{1b}$}
node[above right=of X1_out1] {\tiny$X_{1c}$}
node[above left=of X2_in1] {\tiny$X_{2a}$}
node[above right=2pt and -3pt of X2_out1] {\tiny$X_{2b}$}
node[below right=of X2_out2] {\tiny$\outp{X}_{2c}$}
node[below left=of Y_in1] {\tiny$Y_{a}$}
node[below left=of Y_in2] {\tiny$Y_{b}$}
node[below right=of Y_out1] {\tiny$Y_{c}$}
node[below right=of Y_out2] {\tiny$Y_{d}$}
;
\end{tikzpicture} } \qquad \parbox{1.8in}{ \begin{tikzpicture}[x=1cm,y=1ex,node distance=1 and 1,semithick,every label quotes/.style={font=\everymath\expandafter{\the\everymath\scriptstyle}},every to/.style={out=0,in=180},baseline=(current bounding box.center)]
\node ["$X_{1a}$" left] (X1a) {$-$};
\node [below=0 of X1a, "$X_{1b}$" left] (X1b) {$-$};
\node [below=0 of X1b, "$X_{1c}$" left] (X1c) {$+$};
\node [below=1.5 of X1c, "$X_{2a}$" left] (X2a) {$-$};
\node [below=0 of X2a, "$X_{2b}$" left] (X2b) {$+$};
\node [below=0 of X2b, "$X_{2c}$" left] (X2c) {$+$};
\node [below right=-1 and 2 of X1a, "$Y_a$" right] (Ya) {$-$};
\node [below=1.5 of Ya, "$Y_b$" right] (Yb) {$-$};
\node [below=1.5 of Yb, "$Y_c$" right] (Yc) {$+$};
\node [below=1.5 of Yc, "$Y_d$" right] (Yd) {$+$};
\draw (X1a) to[in=0] (X2b);
\draw (X1b) to (Ya);
\draw (X1c) to[in=0] (X2a);
\draw (X2c) to (Yc);
\draw (Yb) to[out=180] (Yd);
\end{tikzpicture} } \end{equation}
\begin{equation}\label{tensor_first}\tag{tensor first} \begin{tikzpicture}[oriented WD,baseline=(Y.center), bbx=1em, bby=1.2ex]
\node[bb={2}{2},bb name=$X_1$] (X1) {};
\node[bb={2}{1},below right = -3 and 3 of X1, bb name=$X_2$] (X2) {};
\node[bb={2}{2}, fit={($(X1.north west)+(-1,2)$) ($(X2.south)+(0,-2)$) ($(X2.east)+(1,0)$)}, bb name = $Y$] (Y) {};
%
\draw[ar] (Y_in1') to (X1_in1); \draw[ar] (X1_out2) to (X2_in1); \draw[ar] (Y_in2') to (X2_in2); \draw[ar] (X1_out1) to (Y_out1'); \draw (X2_out1) to (Y_out2');
%
\draw[ar] let \p1=(X2.south east), \p2=(X1.south west), \n1={\y1-\bby}, \n2=\bbportlen in
(X2_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X1_in2);
%
\draw [label]
node[above left=.4 and 0 of X1_in1] {$a$}
node[above left=.4 and 0 of X1_in2] {$b$} node[above left=.4 and 0 of X2_in1] {$c$} node[above left=.2 and 0 of X2_in2] {$d$} node[above right=.4 and 0 of X1_out1] {$e$} node[above right=.4 and 0 of X1_out2] {$f$} node[above right=.4 and 0 of X2_out1] {$g$} node[above left=.4 and 0 of Y_in1] {$h$} node[above left=.4 and 0 of Y_in2] {$i$} node[above right=.4 and 0 of Y_out1] {$j$} node[above right=.4 and 0 of Y_out2] {$k$}; \end{tikzpicture} \qquad\qquad \begin{tikzpicture}[oriented WD,baseline=(Y.center), bbx=2em, bby=1.2ex, bb port sep=1] \begin{scope}[bbx=.25em, bb min width=.25em, bby=.5em, bb port sep=1, black!20!white] \node[bb={2}{2}] (X1) {$\scriptstyle X_1$}; \node[bb={2}{1}, below =of X1] (X2) {$\scriptstyle X_2$}; \end{scope} \node[bb={4}{3}, fit={($(X1.north)+(0,2)$) (X2)}, bb name=$X_1\boxplus X_2$] (X) {}; \begin{scope}[black!20!white] \draw (X_in1') to (X1_in1); \draw (X_in2') to (X1_in2); \draw (X_in3') to (X2_in1); \draw (X_in4') to (X2_in2); \draw (X1_out1) to (X_out1'); \draw (X1_out2) to (X_out2'); \draw (X2_out1) to (X_out3'); \end{scope} \node[bb={2}{2}, fit={($(X.north east)+(.5,3)$) ($(X.south west)-(.5,2)$)}, bb name = $Y$] (Y) {}; % \draw[ar] (Y_in1') to (X_in1); \draw[ar] (Y_in2') to (X_in4); \draw[ar] (X_out1) to (Y_out1'); \draw[ar] (X_out3) to (Y_out2'); % \draw[ar] let \p1=(X.south east), \p2=(X.south west), \n1={\y1-\bby}, \n2=\bbportlen in (X_out2) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X_in3); \draw[ar] let \p1=(X.south east), \p2=(X.south west), \n1={\y1-2*\bby}, \n2={\bbportlen} in (X_out3) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X_in2); % \draw [label]
node[above left=.4 and 0 of X_in1] {$a$}
node[above left=.4 and 0 of X_in2] {$b$} node[above left=.4 and 0 of X_in3] {$c$} node[above left=.2 and 0 of X_in4] {$d$} node[above right=.4 and 0 of X_out1] {$e$} node[above right=.4 and 0 of X_out2] {$f$} node[above right=.4 and 0 of X_out3] {$g$} node[above left=.4 and 0 of Y_in1] {$h$} node[above left=.4 and 0 of Y_in2] {$i$} node[above right=.4 and 0 of Y_out1] {$j$} node[above right=.4 and 0 of Y_out2] {$k$}; \end{tikzpicture} \end{equation}
\begin{equation}\label{empty_nest}\tag{empty nest} \begin{tikzpicture}[oriented WD, bbx = .5cm, bby =.8ex, bb min width=.5cm, bb port length=2pt, bb port sep=1]
\node[bb={1}{3}] (X11) {};
\node[bb={2}{1}, right=1.5 of X11] (X12) {};
\node[bb={3}{2}, below right=of X12] (X13) {};
\node[bb={2}{2}, fit={(X11) (X12) (X13) ($(X12.north)+(0,2)$) ($(X13.east)+(.5,0)$)}, dashed] (Y1) {};
\node[bb={2}{1}, below left=6 and 0 of X13] (X21) {};
\node[bb={0}{2},below left=of X21] (X22) {};
\node[bb={1}{2}, fit=(X21) (X22), dashed] (Y2) {};
\node[bb={2}{3}, fit={($(Y1.north)+(0,1)$) ($(Y2.south)-(0,1)$) ($(Y1.west)-(.25,0)$) ($(Y1.east)+(.25,0)$)}] (Z) {};
\begin{scope}[gray]
\draw[ar] (Z_in1') to (Y1_in1);
\draw[ar] (Z_in2') to (Y2_in1);
\draw (Y2_in1') to[in looseness=2] (X21_in1);
\draw[ar] (X22_out1) to (X21_in2);
\draw (X22_out2) to (Y2_out2');
\draw[ar] (Y2_out2) to (Z_out3');
\draw (Y1_in1') to (X11_in1);
\draw (X13_out2) to (Y1_out2');
\draw (Y1_in2') to[in looseness=2] (X13_in3);
\draw (X11_out3) to[in looseness=2] (X13_in2);%
\draw (X12_out1) to (X13_in1);
\draw (X11_out2) to (X12_in2);
\draw (Y1_out1) to (Z_out1');
\draw[ar] (Y1_out2) to (Z_out2');
\draw (X21_out1) to (Y2_out1');
\draw[ar] let \p1=(Y2.north east), \p2=(Y1.south west), \n1={\y1+2*\bby}, \n2=\bbportlen in
(Y2_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (Y1_in2);
\draw[ar] let \p1=(X13.north east), \p2=(X12.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X13_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X12_in1);
\draw let \p1=(X12.north west), \p2=(X13.north east), \n1={\y1+2*\bby}, \n2=\bbportlen in
(X11_out1) to (\x1-2*\n2,\n1) -- (\x2+2*\n2,\n1) to[out=0] (Y1_out1');
\end{scope}
\end{tikzpicture}
\end{equation}
\begin{equation}\label{empty_nest_red_egg}\tag{empty nest red egg} \begin{tikzpicture}[oriented WD, bbx = .5cm, bby =.8ex, bb min width=.5cm, bb port length=2pt, bb port sep=1]
\node[bb={1}{3}] (X11) {};
\node[bb={2}{1}, right=1.5 of X11] (X12) {};
\node[bb={3}{2}, red, below right=of X12] (X13) {};
\node[bb={2}{2}, fit={(X11) (X12) (X13) ($(X12.north)+(0,2)$) ($(X13.east)+(.5,0)$)}, dashed] (Y1) {};
\node[bb={2}{1}, below left=6 and 0 of X13] (X21) {};
\node[bb={0}{2},below left=of X21] (X22) {};
\node[bb={1}{2}, fit=(X21) (X22), dashed] (Y2) {};
\node[bb={2}{3}, fit={($(Y1.north)+(0,1)$) ($(Y2.south)-(0,1)$) ($(Y1.west)-(.25,0)$) ($(Y1.east)+(.25,0)$)}] (Z) {};
\begin{scope}[gray]
\draw[ar] (Z_in1') to (Y1_in1);
\draw[ar] (Z_in2') to (Y2_in1);
\draw (Y2_in1') to[in looseness=2] (X21_in1);
\draw[ar] (X22_out1) to (X21_in2);
\draw (X22_out2) to (Y2_out2');
\draw[ar] (Y2_out2) to (Z_out3');
\draw (Y1_in1') to (X11_in1);
\draw (X13_out2) to (Y1_out2');
\draw (Y1_in2') to[in looseness=2] (X13_in3);
\draw (X11_out3) to[in looseness=2] (X13_in2);%
\draw (X12_out1) to (X13_in1);
\draw (X11_out2) to (X12_in2);
\draw (Y1_out1) to (Z_out1');
\draw[ar] (Y1_out2) to (Z_out2');
\draw (X21_out1) to (Y2_out1');
\draw[ar] let \p1=(Y2.north east), \p2=(Y1.south west), \n1={\y1+2*\bby}, \n2=\bbportlen in
(Y2_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (Y1_in2);
\draw[ar] let \p1=(X13.north east), \p2=(X12.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X13_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X12_in1);
\draw let \p1=(X12.north west), \p2=(X13.north east), \n1={\y1+2*\bby}, \n2=\bbportlen in
(X11_out1) to (\x1-2*\n2,\n1) -- (\x2+2*\n2,\n1) to[out=0] (Y1_out1');
\end{scope}
\end{tikzpicture}
\end{equation}
\begin{equation}\label{two_clusters1}\tag{two clusters 1} \begin{tikzpicture}[oriented WD, bbx = .5cm, bby =.8ex, bb min width=.5cm, bb port length=2pt, bb port sep=1]
\node[bb={1}{3}] (X11) {$\scriptstyle X_{11}$};
\node[bb={2}{1}, right=1.5 of X11] (X12) {$\scriptstyle X_{12}$};
\node[bb={3}{2}, below right=of X12] (X13) {$\scriptstyle X_{13}$};
\node[bb={2}{2}, fit={(X11) (X12) (X13) ($(X12.north)+(0,2)$) ($(X13.east)+(.5,0)$)}, dashed] (Y1) {};
\node[bb={2}{1}, below left=6 and 0 of X13] (X21) {$\scriptstyle X_{21}$};
\node[bb={0}{2},below left=of X21] (X22) {$\scriptstyle X_{22}$};
\node[bb={1}{2}, fit=(X21) (X22), dashed] (Y2) {};
\node[bb={2}{3}, fit={($(Y1.north)+(0,1)$) ($(Y2.south)-(0,1)$) ($(Y1.west)-(.25,0)$) ($(Y1.east)+(.25,0)$)}] (Z) {};
\draw[label]
node at ($(Y1.north west)+(.5,-2)$) {$Y_1$} node at ($(Y2.north west)+(.5,-2)$) {$Y_2$} node at ($(Z.north west)+(.5,-2)$) {$Z$};
\begin{scope}[gray]
\draw[ar] (Z_in1') to (Y1_in1);
\draw[ar] (Z_in2') to (Y2_in1);
\draw (Y2_in1') to[in looseness=2] (X21_in1);
\draw[ar] (X22_out1) to (X21_in2);
\draw (X22_out2) to (Y2_out2');
\draw[ar] (Y2_out2) to (Z_out3');
\draw (Y1_in1') to (X11_in1);
\draw (X13_out2) to (Y1_out2');
\draw (Y1_in2') to[in looseness=2] (X13_in3);
\draw (X11_out3) to[in looseness=2] (X13_in2);%
\draw (X12_out1) to (X13_in1);
\draw (X11_out2) to (X12_in2);
\draw (Y1_out1) to (Z_out1');
\draw[ar] (Y1_out2) to (Z_out2');
\draw (X21_out1) to (Y2_out1');
\draw[ar] let \p1=(Y2.north east), \p2=(Y1.south west), \n1={\y1+2*\bby}, \n2=\bbportlen in
(Y2_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (Y1_in2);
\draw[ar] let \p1=(X13.north east), \p2=(X12.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X13_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X12_in1);
\draw let \p1=(X12.north west), \p2=(X13.north east), \n1={\y1+2*\bby}, \n2=\bbportlen in
(X11_out1) to (\x1-2*\n2,\n1) -- (\x2+2*\n2,\n1) to[out=0] (Y1_out1');
\end{scope}
\end{tikzpicture}
\end{equation}
\begin{equation}\label{two_clusters2}\tag{two clusters 2} \begin{tikzpicture}[oriented WD, bbx = .5cm, bby =.8ex, bb min width=.5cm, bb port length=2pt, bb port sep=1]
\node[bb={1}{3}] (X11) {$X_{11}$};
\node[bb={2}{1}, right=1.5 of X11] (X12) {$X_{12}$};
\node[bb={3}{2}, below right=of X12] (X13) {$X_{13}$};
\node[bb={2}{2}, fit={(X11) (X12) (X13) ($(X12.north)+(0,5)$) ($(X13.east)+(.5,0)$)}, dashed, bb name={$Y_1$}] (Y1) {};
\node[bb={2}{1}, below left=9 and 0 of X13] (X21) {$X_{21}$};
\node[bb={0}{2},below left=of X21] (X22) {$X_{22}$};
\node[bb={1}{2}, fit={($(X21.north east)+(0,3)$) (X22)}, dashed, bb name={$Y_2$}] (Y2) {};
\node[bb={2}{3}, fit={($(Y1.north)+(0,3)$) ($(Y2.south)-(0,1)$) ($(Y1.west)-(.25,0)$) ($(Y1.east)+(.25,0)$)}, bb name={$Z$}] (Z) {};
\begin{scope}[gray]
\draw[ar] (Z_in1') to (Y1_in1);
\draw[ar] (Z_in2') to (Y2_in1);
\draw (Y2_in1') to[in looseness=2] (X21_in1);
\draw[ar] (X22_out1) to (X21_in2);
\draw (X22_out2) to (Y2_out2');
\draw[ar] (Y2_out2) to (Z_out3');
\draw (Y1_in1') to (X11_in1);
\draw (X13_out2) to (Y1_out2');
\draw (Y1_in2') to[in looseness=2] (X13_in3);
\draw (X11_out3) to[in looseness=2] (X13_in2);%
\draw (X12_out1) to (X13_in1);
\draw (X11_out2) to (X12_in2);
\draw (Y1_out1) to (Z_out1');
\draw[ar] (Y1_out2) to (Z_out2');
\draw (X21_out1) to (Y2_out1');
\draw[ar] let \p1=(Y2.north east), \p2=(Y1.south west), \n1={\y1+2*\bby}, \n2=\bbportlen in
(Y2_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (Y1_in2);
\draw[ar] let \p1=(X13.north east), \p2=(X12.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X13_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X12_in1);
\draw let \p1=(X12.north west), \p2=(X13.north east), \n1={\y1+2*\bby}, \n2=\bbportlen in
(X11_out1) to (\x1-2*\n2,\n1) -- (\x2+2*\n2,\n1) to[out=0] (Y1_out1');
\end{scope}
\end{tikzpicture}
\end{equation}
\begin{equation}\label{Andrea}\tag{Andrea} \begin{tikzpicture}[oriented WD, bb min width =.7cm, bby=1.6ex, bbx=.7cm,bb port length=3pt]
\node[bb port sep=.8, bb={2}{1}, bb name=$\Sigma$] (Sigma1) {};
\node[bb port sep=1.6,bb min width=4.3em, bb={2}{3}, below right=-2.5 and 1 of Sigma1.south east, bb name=Chassis] (Chassis) {};
\node[bb port sep=.9,bb min width=4.3em, bb={2}{4}, below right=-3 and 2 of Chassis_out2, bb name=Motor] (Motor) {};
\node[bb port sep=.8, bb={2}{1}, right= of Motor.south east, bb name=$\Sigma$] (Sigma2) {};
\node[bb={2}{3}, fit={($(Sigma1.north west)+(0,1)$) (Chassis) (Motor) (Sigma2)}] (Y) {};
\draw[ar] (Y_in1') to (Sigma1_in2);
\draw[ar] (Y_in2') to (Chassis_in2);
\draw[ar] (Sigma1_out1) to (Chassis_in1);
\draw[ar] (Chassis_out1) to (Motor_in1);
\draw[ar] (Chassis_out2) to (Motor_in2);
\draw[ar] let \p1=(Motor.south west), \p2=(Motor.south east), \n1={\y1-\bby},\n2=\bbportlen in
(Chassis_out3) to (\x1-\n2,\n1) -- (\x2+\n2,\n1) to (Sigma2_in2);
\draw[ar] (Motor_out2) to (Y_out1');
\draw[ar] (Motor_out3) to (Y_out2');
\draw[ar] (Motor_out4) to (Sigma2_in1);
\draw[ar] (Sigma2_out1) to (Y_out3');
\draw[ar] let \p1=(Motor.north east), \p2=(Sigma1.north west), \n1={\y2+\bby},\n2=\bbportlen in
(Motor_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (Sigma1_in1);
\draw[label] node[left=.3 of Y_in1] {\footnotesize Extra payload} node[left=.3 of Y_in2] {\footnotesize Velocity} node[right=.3 of Y_out1] {\footnotesize Voltage} node[right=.3 of Y_out2] {\footnotesize Current} node[right=.3 of Y_out3] {\footnotesize Cost \$} node[above right=.2 and 0 of Chassis_out1] {\tiny Torque} node[above right=.2 and 0 of Chassis_out2] {\tiny Speed} node[above right=.2 and 0 of Chassis_out3] {\tiny Cost \$} node[above right=.3 and .3 of Motor_out1, align=center, font=\tiny] {Motor\\weight} ; \end{tikzpicture} \end{equation}
\begin{equation}\label{string decoration}\tag{string decoration} \begin{tikzpicture} [oriented WD, bb min width =.5cm, bby=2ex, bbx=.6cm, bb port length=3pt, string decoration = {\node[circle, inner sep=0pt, fill=white, font=\fontsize{5}{5}\selectfont] {$\leq$};}, baseline=(Y)]
\node[bb port sep=.8, bb={3}{1}] (Sigma1) {$\Sigma$};
\node[bb port sep=2,bb min width=4.3em, bb={2}{3}, below right=-3 and 1 of Sigma1.south east] (Chassis) {Chassis};
\node (Chassis 15) at ($(Chassis_out1)!.5!(Chassis_out2)$) {};
\node[bb port sep=2*3/5,bb min width=4.3em, bb={2}{4}, right=2 of Chassis 15] (Motor) {Motor};
\node[bb port sep=2*3/5, bb={2}{2}, bb min width=4.3em, right=2 of Motor] (Battery) {Battery};
\node[bb port sep=.8, bb={3}{1}, below right=-.5 and 1 of Battery] (Sigma2) {$\Sigma$};
\node[bb={0}{0}, fit={($(Sigma1.north west)+(-.5,2)$) (Chassis) (Motor) (Sigma2)}] (Y) {};
\node[coordinate] (Y_in1) at (Y.west|-Sigma1_in3) {}; \node[coordinate] (Y_in2) at (Y.west|-Chassis_in2) {}; \node[coordinate] (Y_out1) at (Y.east|-Sigma2_out1) {};
\draw[ar] (Y_in1) to (Sigma1_in3);
\draw[ar] (Y_in2) to (Chassis_in2);
\draw[ar] (Sigma1_out1) to (Chassis_in1);
\draw[ar] (Chassis_out1) to (Motor_in1);
\draw[ar] (Chassis_out2) to (Motor_in2);
\draw[ar] let \p1=(Motor.west), \p2=(Sigma2_in3), \n1=\bbportlen in
(Chassis_out3) to (\x1-\n1,\y2) -- (Sigma2_in3);
\draw[ar] (Motor_out2) to node[above=-1pt, font=\tiny] {Voltage} (Battery_in1);
\draw[ar] (Motor_out3) to node[above=-1pt, font=\tiny] {Current} (Battery_in2);
\draw[ar] let \p1=(Battery.west), \p2=(Sigma2_in2), \n1=\bbportlen in
(Motor_out4) to node[pos=.4, above=1pt, font=\tiny] {Cost \$} (\x1-\n1, \y2) -- (Sigma2_in2);
\draw[ar] (Battery_out2) to (Sigma2_in1);
\draw[ar, string decoration pos=.5] (Sigma2_out1) to (Y_out1);
\draw[ar, string decoration = {\node[circle, inner sep=0pt, fill=white, font=\fontsize{5}{5}\selectfont] {$\geq$};}, string decoration pos=.5] let \p1=(Motor.north east), \p2=(Sigma1.north west), \n1={\y2+\bby},\n2=\bbportlen in
(Motor_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (Sigma1_in1);
\draw[ar, string decoration = {\node[circle, inner sep=0pt, fill=white, font=\fontsize{5}{5}\selectfont] {$\geq$};}, string decoration pos=.5] let \p1=(Battery.north east), \p2=(Sigma1.north west), \n1={\y2+\bby+\bby},\n2=\bbportlen in
(Battery_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (Sigma1_in2);
% \draw[label] node[left=.3 of Y_in1] {\footnotesize Extra payload} node[left=.3 of Y_in2] {\footnotesize Velocity} node[right=.3 of Y_out1] {\footnotesize Cost \$} node[above right=.2 and 0 of Chassis_out1] {\tiny Torque} node[above right=.2 and 0 of Chassis_out2] {\tiny Speed} node[above right=.2 and 0 of Chassis_out3] {\tiny Cost \$} node[above right=.3 and .5 of Motor_out1, align=left, font=\tiny] {Motor\\Weight} node[above right=.3 and .8 of Battery_out1, align=left, font=\tiny] {Battery\\Weight} node[above right=.2 and 0 of Battery_out2, font=\tiny] {Cost \$} ; \end{tikzpicture} \end{equation}
\subsection{Diverging}
\begin{equation}\tag{kitchen sink} \begin{tikzpicture}[oriented WD,baseline=(Y.center), bbx=2em, bby=1.2ex, bb port sep=1.2] \node[bb={5}{5}] (X) {}; \node[bb={2}{3}, fit={($(X.north east)+(0.7,1.7)$) ($(X.south west)-(.7,.7)$)}] (Y) {}; \node [circle,minimum size=4pt, inner sep=0, fill] (dot1) at ($(Y_in1')+(.5,0)$) {}; \node [circle,minimum size=4pt, inner sep=0, fill] (dot2) at ($(X_out4)+(.5,0)$) {}; \draw[ar] (Y_in1') to (dot1); \draw[ar] (X_out4) to (dot2); \draw[ar] (Y_in2') to (X_in5); \draw[ar] (Y_in2') to (X_in4); \draw[ar] (X_out5) to (Y_out3'); \draw[ar] (X_out2) to (Y_out1'); \draw[ar] (X_out2) to (Y_out2'); % \draw[ar] let \p1=(X.north west), \p2=(X.north east), \n1={\y1+\bby}, \n2=\bbportlen in (X_out1) to[in=0] (\x2+\n2,\n1) -- (\x1-\n2,\n1) to[out=180] (X_in1); \draw[ar] let \p1=(X.north west), \p2=(X.north east), \n1={\y1+2*\bby}, \n2=\bbportlen in (X_out1) to[in=0] (\x2+\n2,\n1) -- (\x1-\n2,\n1) to[out=180] (X_in2); % \draw [label] node at ($(X.east)+(1.2,4.5)$) {$Y$}
node at ($(X.west)+(.6,0)$) {$X$}
node[left=.1 of X_in3] {$\dotso$} node[right=.1 of X_out3] {$\dotso$}; \end{tikzpicture} \end{equation}
\begin{equation}\label{kitchen sink 2}\tag{kitchen sink 2} \begin{tikzpicture}[oriented WD, baseline=(Y.center), bb port sep=1.2, bb port length=0]
\node[bb={6}{6}] (X) {};
\node[bb={1}{0}, fit={($(X.north east)+(0.7,1.7)$) ($(X.south west)-(.7,.7)$)}] (Y) {};
\node [circle, minimum size=4pt, inner sep=0, fill] (dot1) at ($(Y_in1')+(.5,0)$) {};
\node [circle, minimum size=4pt, inner sep=0, fill] (dot2) at ($(X_in5)+(-.5,0)$) {};
\draw[ar] (Y.west|-dot1) to (dot1);
\draw[ar] (Y.west|-X_in6) to (X_in6);
\draw[ar] (dot2) to (X_in5);
\draw[ar] (X_out2) to (X_out2-|Y.east);
\draw[ar] (X_out5) to (X_out6-|Y.east);
\draw[ar] (X_out6) to (X_out6-|Y.east);
%
\draw[ar] let \p1=(X.north west), \p2=(X.north east), \n1={\y1+\bby}, \n2=\bbportlen in
(X_out1) to[in=0] (\x2+\n2,\n1) -- (\x1-\n2,\n1) to[out=180] (X_in1);
\draw[ar] let \p1=(X.north west), \p2=(X.north east), \n1={\y1+2*\bby}, \n2=\bbportlen in
(X_out1) to[in=0] (\x2+\n2,\n1) -- (\x1-\n2,\n1) to[out=180] (X_in2);
%
\draw [label]
node[left=.1 of X_in3] {$\vdots$} node[right=.1 of X_out3] {$\vdots$}; \draw[red, shorten <=-.5cm, shorten >=-.5cm] (Y.north west) -- (Y.south east); \draw[red, shorten <=-.5cm, shorten >=-.5cm] (Y.north east) -- (Y.south west); \end{tikzpicture} \end{equation}
\begin{equation}\label{simple_2}\tag{simple 2} \begin{tikzpicture}[oriented WD, bb min width=.6cm, bb port sep=1, bbx=.6cm, bby=1ex, bb port length=2.5pt]
\node[bb port sep=2, bb={2}{2}] (X1) {};
\node[bb={1}{1}, right=.7 of X1_out1] (X2) {};
\node[bb={1}{2}, fit={(X1) (X2) ($(X1.north)+(0,1)$)}] (Y) {};
\draw[ar] (Y_in1') to (X1_in2);
\draw[ar] (X1_out1) to (X2_in1);
\draw (X2_out1) to[in looseness=1] (Y_out1');
\draw[ar] (X1_out2) to (Y_out2');
\draw[ar] let \p1=(X2.north east), \p2=(X1.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X2_out1) to[in=0,in looseness=.9] (\x1+.7*\n2,\n1) -- (\x2-.7*\n2,\n1) to[out=180] (X1_in1);
\end{tikzpicture}
\end{equation}
\begin{equation}\label{split_trace}\tag{split trace} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex] \node[bb={1}{1},bb name=$M_1$] (M1) {}; \node[bb={1}{1},right=2 of M1,bb name=$M_2$] (M2) {}; \node[bb={0}{1},fit={($(M1.north west)+(-.5,1)$) ($(M2.south east)+(.5,-1)$)}] (Y) {}; \draw[ar] (M1_out1) to (M2_in1); \draw (M2_out1) to (Y_out1'); \draw[ar] let \p1=(M2.south east), \p2=(M1.south west),\n1=\bbportlen,\n2={\y1-\bby} in (M2_out1) to[in=0] (\x1+\n1,\n2) -- (\x2-\n1,\n2) to[out=180] (M1_in1); \end{tikzpicture} \end{equation}
\begin{equation}\label{numbers}\tag{numbers} \parbox{1.85in}{ \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex] \node[bb={1}{1},bb name=$M_1$] (M1) {}; \node[bb={1}{1},right=1 of M1,bb name=$M_2$] (M2) {}; \node[bb={1}{2},dashed, fit={(M1) (M2)}] (dashed) {}; \node[bb={0}{1},fit={($(dashed.north west)+(-.5,1)$) ($(dashed.south east)+(.5,-1)$)}] (Y) {}; \draw[ar] (M1_out1) to (M2_in1); \draw (M2_out1) to (dashed_out1'); \draw (M2_out1) to (dashed_out2'); \draw (dashed_in1') to (M1_in1); \draw (dashed_out1) to (Y_out1'); \draw[ar] let \p1=(dashed.south east), \p2=(dashed.south west),\n1=\bbportlen,\n2={\y1-\bby} in (dashed_out2) to[in=0] (\x1+\n1,\n2) -- (\x2-\n1,\n2) to[out=180] (dashed_in1); \draw[label] node[above right=.5 and 0 of M1_out1] {$3$} node[above right=.5 and 0 of dashed_out1] {$2$} node[above left=.5 and 0 of M1_in1] {$2$} ; \end{tikzpicture} } \qquad \parbox{2.1in}{ \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex] \node[bb={1}{1},bb name=$M_1$] (M1) {}; \node[bb={1}{1},left=2 of M1.north west,bb name=$M_2$] (M2) {}; \node[bb={1}{2},dashed, fit={($(M2.north west)+(-.5,2)$) ($(M1.south east)+(.5,-1)$)}] (dashed) {}; \node[bb={0}{1},fit={($(dashed.north west)+(-.75,1)$) ($(dashed.south east)+(.75,-1)$)}] (Y) {}; \draw[ar] (M2_out1) to (M1_in1); \draw[ar] (M1_out1) to (dashed_out2'); \draw[ar] (dashed_in1') to (M2_in1); \draw[ar] (dashed_out1) to (Y_out1'); \draw[ar] let \p1=(M1.north west), \p2=(dashed_out1), \n2=\bbportlen in (M2_out1) to (\x1-\n2,\y2) -- (dashed_out1'); \draw[ar] let \p1=(dashed.south east), \p2=(dashed.south west), \n1=\bbportlen, \n2={\y1-\bby} in (dashed_out2) to[in=0] (\x1+\n1,\n2) -- (\x2-\n1,\n2) to[out=180] (dashed_in1); \draw[label] node[above right=.5 and .5 of M1_out1] {$3$} node[right=.8 of M2_out1] {$2$} node[above left=.5 and .1 of M2_in1] {$3$} ; \end{tikzpicture} } \qquad \parbox{1.5in}{ \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex, bb port sep=1.3] \node[bb={0}{2},bb name=$M_1$] (M1) {}; \node[bb={2}{0},right=2 of M1,bb name=$M_2$] (M2) {}; \node[bb={0}{1},fit={($(M1.north west)+(0.5,2.5)$) ($(M2.south east)+(0.5,0)$)}] (Y) {}; \draw (M1_out1) to (M2_in1); \draw[ar] (M1_out2) to (M2_in2); \draw[ar] let \p1=(M2.north west), \p2=(M2.north east), \n1=\bbportlen, \n2={\y1+\bby} in (M1_out1) to (\x1-\bbportlen,\n2) -- (\x2+\bbportlen,\n2) to (Y_out1'); \draw[label] node[above right=.3 and 0 of M1_out1] {$2$} node[below right=.3 and 0 of M1_out2] {$3$} ; \end{tikzpicture} } \end{equation}
\begin{equation}\label{neuron1}\tag{neuron1} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex, bb port sep=1]
\node[bb={2}{1}] (N1) {$\scriptstyle N_1$};
\node[bb={1}{1}, below = 1 of N1] (N2) {$\scriptstyle N_2$};
\node[bb={3}{1}, below=1 of N2] (N3) {$\scriptstyle N_3$};
\node[bb={3}{1}, above right = -3 and 3.5 of N3] (N6) {$\scriptstyle N_6$};
\node[bb={2}{1}, above =of N6] (N5) {$\scriptstyle N_5$};
\node[bb={2}{1}, above= of N5] (N4) {$\scriptstyle N_4$};
\node[bb={4}{4}, fit={($(N2.west)-(.5,0)$) ($(N4.north)+(0,2)$) ($(N5.east)+(1.5,0)$) ($(N3.south)-(0,1)$)}, bb name={$\scriptstyle X$}] (X) {};
\draw (X_in1') to (N1_in2);
\draw (X_in2') to (N2_in1);
\draw (X_in3') to (N3_in1);
\draw (X_in4') to (N3_in2);
\draw (N1_out1) to (N4_in1);
\draw (N2_out1) to (N4_in2);
\draw (N2_out1) to (N5_in1);
\draw (N2_out1) to (N6_in1);
\draw (N4_out1) to (X_out1');
\draw (N3_out1) to (N6_in2);
\draw (N5_out1) to (X_out2');
\draw (N6_out1) to (X_out3');
\draw (N6_out1) to (X_out4');
\draw let \p1=(N2.south east), \p2=(N3_out1),\n2=\bbportlen in
(N3_out1) -- (\x1+\n2,\y2) to (N5_in2);
\draw let \p1=(N6.south east), \p2=(N3.south west), \n1={\y2-\bby}, \n2=\bbportlen in
(N5_out1) to[in=0, looseness=.8] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (N3_in3);
\draw let \p1=(N6.south east), \p2=(N6.south west), \n1={\y2-\bby}, \n2=\bbportlen in
(N6_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (N6_in3);
\draw let \p1=(N1.north east), \p2=(N1.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(N1_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (N1_in1);
\end{tikzpicture} \end{equation}
\begin{equation}\label{neuron2}\tag{neuron2} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex, bb port sep=1]
\node[bb={3}{1}] (N0) {$\scriptstyle N_0$};
\node[bb={3}{1}, below = 1 of N0] (N1) {$\scriptstyle N_1$};
\node[bb={2}{1}, right= 3.5 of N0] (N2) {$\scriptstyle N_2$};
\node[bb={3}{1}, below=1 of N1] (N3) {$\scriptstyle N_3$};
\node[bb={2}{1}, below =of N2] (N4) {$\scriptstyle N_4$};
\node[bb={3}{1}, below =of N4] (N5) {$\scriptstyle N_5$};
\node[bb={7}{8}, fit={($(N1.west)-(.5,0)$) ($(N2.north)+(0,2)$) ($(N4.east)+(1.5,0)$) ($(N3.south)-(0,1)$)}, bb name={$\scriptstyle X$}] (X) {};
\draw (X_in1') to (N0_in2);
\draw (X_in2') to (N0_in3);
\draw (X_in3') to (N1_in1);
\draw (X_in4') to (N1_in2);
\draw (X_in5') to (N1_in3);
\draw (X_in6') to (N3_in1);
\draw (X_in7') to (N3_in2);
\draw (N0_out1) to (N2_in1);
\draw (N1_out1) to (N2_in2);
\draw (N1_out1) to (N4_in1);
\draw (N1_out1) to (N5_in1);
\draw (N2_out1) to (X_out1');
\draw (N2_out1) to (X_out2');
\draw (N2_out1) to (X_out3');
\draw (N3_out1) to (N5_in2);
\draw (N4_out1) to (X_out4');
\draw (N4_out1) to (X_out5');
\draw (N4_out1) to (X_out6');
\draw (N5_out1) to (X_out7');
\draw (N5_out1) to (X_out8');
\draw let \p1=(N1.south east), \p2=(N3_out1),\n2=\bbportlen in
(N3_out1) -- (\x1+\n2,\y2) to (N4_in2);
\draw let \p1=(N5.south east), \p2=(N3.south west), \n1={\y2-\bby}, \n2=\bbportlen in
(N4_out1) to[in=0, looseness=.8] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (N3_in3);
\draw let \p1=(N5.south east), \p2=(N5.south west), \n1={\y2-\bby}, \n2=\bbportlen in
(N5_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (N5_in3);
\draw let \p1=(N0.north east), \p2=(N0.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(N0_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (N0_in1);
\end{tikzpicture} \end{equation}
\begin{equation}\label{nnet}\tag{nnet} \begin{tikzpicture}[oriented WD, bb port sep=1.5, scale=2] \tikzmath{ int \hidden, \depth, \hiddeninc, \incsqrd; \hidden=3; %Set this \depth=3; %Set this \hiddeninc=\hidden+1; \incsqrd = \hiddeninc*\hiddeninc; } \foreach \j in {1,...,\depth} { \node[bb={0}{1}] (N0\j) at (0,\incsqrd-\hiddeninc*\j) {}; } \foreach \i [remember=\i as \lasti (initially 0)] in {1,...,\hidden} { \foreach \j in {1,...,\depth} { \node[bb={\depth}{1}] (N\i\j) at (\i,\incsqrd-\hiddeninc*\j) {}; \foreach \jj in {1,...,\depth} { \draw (N\lasti\jj_out1) to[looseness=0.2] (N\i\j_in\jj); \node [right=6pt, font=\tiny] at (N\i\j_in\jj) {$w^\i_{\j,\jj}$}; } } } \foreach \j in {1,...,\depth} { \node[bb={\depth}{1}] (N\hiddeninc\j) at (\hiddeninc,\incsqrd-\hiddeninc*\j) {}; \foreach \jj in {1,...,\depth} { \draw (N\hidden\jj_out1) to[looseness=0.2] (N\hiddeninc\j_in\jj); \node [right=6pt, font=\tiny] at (N\hiddeninc\j_in\jj) {$w^\hiddeninc_{\j,\jj}$}; } } \end{tikzpicture} \end{equation}
\begin{equation}\label{NAS network}\tag{NAS network} \begin{tikzpicture}[oriented WD, inner sep=3pt, bb small, baseline=(RadSig), font=\small] \node[bb={1}{2}] (plane1) {plane 1}; \node[bb={2}{1}, right=5 of plane1] (plane2) {plane 2}; \node[bb={1}{1}, text width=2cm, align=center] at ($(plane1)!.5!(plane2)+(0,20)$) (radar) {radar satellite}; \node[bb={0}{0}, fit={($(plane1)+(-4,-5)$) ($(plane2)+(4,5)$) (radar)}] {}; \draw[ar] (plane1_out1) to node [above=2pt] {1-TCAS} (plane2_in1); \draw[ar] (plane2_in2) to node [below=2pt] {2-TCAS}(plane1_out2); \draw[ar] (plane2_out1) to[in=0, out=0, looseness=1] node [above right=-.2 and -.2] {2-Altd} (radar_out1); \draw[ar] (plane1_in1) to[in=180, out=180, looseness=1] node [above left=-.2 and -.2] {1-Altd} (radar_in1); \draw[ar] (radar.270) to[out=270, in=90] node[below=6, pos=0] (RadSig) {RadSig} (plane1.north); \draw[ar] (radar.270) to[out=270, in=90] (plane2.north); \end{tikzpicture} \end{equation}
\begin{equation}\label{zooming into plane1}\tag{zooming into plane1} \begin{tikzpicture}[oriented WD, bb port sep=1, bb port length=2.5pt, bbx=1cm, bb min width=.4cm, bby=1.5ex, font=\footnotesize] \node[bb={2}{1}] (TCAS) {Onboard TCAS}; \node[bb={1}{1}, below right=0 and 1 of TCAS] (pilot) {pilot}; \node[bb={1}{1}, right=1 of pilot] (surface) {jets\&wings}; \node[bb={2}{2}, fit={($(TCAS.north west)+(-.5,0)$) ($(surface.south east)+(.5,0)$)}] (plane) {}; \draw[ar] (plane_in1') to node[above=0pt] {2-TCAS} (TCAS_in1); \draw[ar] (plane_in2') to node[below=3pt] {RadSig} (TCAS_in2); \draw[ar] (TCAS_out1) to (pilot_in1); \draw[ar] (TCAS_out1) to node[above=0pt] {1-TCAS} (plane_out1'); \draw[ar] (pilot_out1) to node[below=0pt] {yoke} (surface_in1); \draw[ar] (surface_out1) to node[above=0pt] {altitude} (plane_out2'); \end{tikzpicture} \end{equation}
\begin{equation}\label{NAS-blue}\tag{NAS-blue} \begin{tikzpicture}[oriented WD, inner sep=3pt, bb small, baseline=(RadSig), font=\small] \node[bb={1}{2}, fill=blue!20] (plane1) {plane 1}; \node[bb={2}{1}, fill=blue!20, right=10 of plane1] (plane2) {plane 2\ }; \node[bb={1}{1}, fill=blue!20, text width=2cm, align=center] at ($(plane1)!.5!(plane2)+(0,25)$) (radar) {radar satellite}; \node[bb={0}{0}, fit={($(plane1)+(-6,-5)$) ($(plane2)+(6,5)$) ($(radar.north)+(0,5)$)}, bb name=National Airspace System] {}; \draw[ar] (plane1_out1) to node [above=2pt] {1-TCAS} (plane2_in1); \draw[ar] (plane2_in2) to[out=180, in =0] node [below=2pt] {2-TCAS} (plane1_out2); \draw[ar] (plane2_out1) to[in=0, out=0, looseness=1] node [above right=-.2 and -.2] {2-altitude} (radar_out1); \draw[ar] (plane1_in1) to[in=180, out=180, looseness=1] node [above left=-.2 and -.2] {1-altitude} (radar_in1); \draw[ar] (radar.270) to[out=270, in=90] node[below=5, pos=0, text width=.6in, align=center] (RadSig) {radar\\[-3pt]signal} (plane1.north); \draw[ar] (radar.270) to[out=270, in=90] (plane2.north); \end{tikzpicture} \end{equation}
\begin{equation}\label{single plane-blue}\tag{single plane-blue} \begin{tikzpicture}[oriented WD, bb port sep=1, bb port length=2.5pt, bbx=1.5cm, bb min width=.4cm, bby=1.5ex, font=\footnotesize] \node[bb={2}{1}, fill=blue!20, text width=1.25cm] (TCAS) {onboard TCAS}; \node[bb={1}{1}, fill=blue!20, below right=-1.5 and 1 of TCAS] (pilot) {pilot}; \node[bb={1}{1}, fill=blue!20, right=-.5 and 2 of pilot] (surface) {jets\&wings}; \node[bb={2}{2}, fit={($(TCAS.north west)+(-.5,3)$) ($(surface.south east)+(.5,-1.75)$)}, bb name=plane 1] (plane) {}; \draw[ar] (plane_in1') to node[above=3pt, text width=.8in, align=left] {their TCAS\\[-3pt] command} (TCAS_in1); \draw[ar] (plane_in2') to node[below=3pt] {radar signal} (TCAS_in2); \draw[ar] (TCAS_out1) to (pilot_in1); \draw[ar] let \p1=(pilot.north west), \p2=(plane_out1), \n1=\bbportlen in (TCAS_out1) to (\x1-\n1,\y2) -- node[above=0pt] {our TCAS command} (plane_out1'); \draw[ar] (pilot_out1) to node[below=0pt, align=left] {yoke \& throttle} (surface_in1); \draw[ar] (surface_out1) to node[below=0pt] {altitude} (plane_out2'); \end{tikzpicture} \end{equation}
\begin{equation}\label{IAN_feedback}\tag{IAN feedback} \begin{tabular}{c|c|c} \small Interfaces&\small Arrangements&\small Nesting\\\hline ~&&\\ \parbox{.5in}{ \begin{tikzpicture}[oriented WD, bby=1ex]
\node[bb={3}{2}] (X1) {};
\node[bb={1}{1}, below=.4cm of X1] (X2) {};
\node[bb={0}{2}, below=.4cm of X2] (X3) {};
\end{tikzpicture} } & \;\;\parbox{1.45in}{ \begin{tikzpicture}[oriented WD,bb min width =.7cm, bb port sep =1, bbx=.6cm,bb port length=3pt]
\node[bb port sep=1.6, bb={2}{2}, bb name=$f$] (X1) {};
\node[bb port sep=.8,bb={1}{1}, right=.7 of X1_out1, bb name=$g$] (X2) {};
\node[bb={1}{2}, fit={(X1) (X2) ($(X1.north)+(0,1)$)}] (Y) {};
\draw[ar] (Y_in1') to (X1_in2);
\draw[ar,pos=.8] (X1_out1) to (X2_in1);
\draw (X2_out1) to (Y_out1');
\draw[ar] (X1_out2) to (Y_out2');
\draw[ar] let \p1=(X2.north east), \p2=(X1.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X2_out1) to[in=0] (\x1+.7*\n2,\n1) -- (\x2-.7*\n2,\n1) to[out=180] (X1_in1);
\end{tikzpicture} } & \;\;\parbox{1.2in}{ \begin{tikzpicture}[oriented WD, bb small]
\node[bb={2}{2}] (X1) {};
\node[bb={1}{1}, fit={(X1) ($(X1.north)+(0,1)$)}, dashed] (Y1) {};
\node[bb={2}{1}, below right=4 and 0 of X1] (X2) {};
\node[bb={0}{2},below left=of X2] (X3) {};
\node[bb={1}{2}, fit=(X2) (X3), dashed] (Y2) {};
\node[bb={1}{2}, fit=(Y1) (Y2)] (Z) {};
\draw[ar] (Z_in1') to (Y2_in1);
\draw[ar] (Y2_in1') to (X2_in1);
\draw[ar] (X3_out1) to (X2_in2);
\draw[ar] (X3_out2) to (Y2_out2');
\draw (Y2_out2) to (Z_out2');
\draw[ar] (Y1_in1') to (X1_in2);
\draw (X1_out2) to (Y1_out1');
\draw[ar] (Y1_out1) to (Z_out1');
\draw (X2_out1) to (Y2_out1');
\draw[ar] let \p1=(Y2.north east), \p2=(Y1.south west), \n1={\y1+\bby}, \n2=\bbportlen in
(Y2_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (Y1_in1);
\draw[ar] let \p1=(X1.north east), \p2=(X1.north west), \n1={\y1+\bby}, \n2=\bbportlen in
(X1_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X1_in1);
\end{tikzpicture} } \end{tabular} \end{equation}
\subsection{Converging}
\begin{equation}\label{converging}\tag{converging} \begin{tikzpicture}[oriented WD, bbx=1em, bby=1ex]
\node[bb={2}{2},bb name=$X_1$] (X1) {};
\node[bb={2}{2},below right = -3 and 2 of X1, bb name=$X_2$] (X2) {};
\node[bb={3}{2}, fit={($(X1.north west)+(-1,2)$) ($(X2.south)+(0,-2)$) ($(X2.east)+(1,0)$)}, bb name = $Y$] (Y) {};
%
\draw[ar] (Y_in1') to (X1_in1); \draw[ar] (X1_out2) to (X2_in1); \draw[ar] (Y_in3') to (X2_in2); \draw[ar] (Y_in2') to (X1_in2); \draw[ar] (X1_out1) to (Y_out1'); \draw (X2_out1) to (Y_out2');
%
\draw[ar] let \p1=(X2.south east), \p2=(X1.south west), \n1={\y1-\bby}, \n2=\bbportlen in
(X2_out2) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X1_in2);
\end{tikzpicture} \end{equation}
%%%% Chapter %%%%
\chapter{Unoriented Wiring diagrams}
% Section % \section{Circles}
\begin{equation}\label{pack2}\tag{pack2} \begin{tikzpicture}[unoriented WD, link size = 0pt] \node[pack, pack size=3pt] (p1) {}; \node[link, right=.2 of p1] (l1) {}; \node[link, left=.2 of p1] (m1) {}; \draw (p1) to (l1); \draw (p1) to (m1); \node[pack, right=4 of p1, pack size=9pt] (p2) {}; \node[link, right=.2 of p2] (l2) {}; \node[link, left=.2 of p2] (m2) {}; \draw (p2) to (l2); \draw (p2) to (m2); \node[pack, right=4 of p2, pack size=27pt] (p3) {}; \node[link, right=.2 of p3] (l3) {}; \node[link, left=.2 of p3] (m3) {}; \draw (p3) to (l3); \draw (p3) to (m3); \end{tikzpicture} \end{equation}
\begin{equation}\label{white pack}\tag{white pack} \begin{tikzpicture}[unoriented WD, link size = 0pt, pack outside color=black, pack inside color=white] \node[pack, pack size=20pt] (p) {}; \draw (p) to["$S_2$" right] +(1.5,0); \draw (p) to["$S_1$" left] +(-1.5,0); \end{tikzpicture} \end{equation}
\begin{equation}\label{labels?}\tag{labels?} \begin{tikzpicture} [unoriented WD, spacing=10pt, link size=1pt, pack size=12pt, surround sep=3pt, font=\tiny] \node[pack] (f) {}; \node[pack,right=3 of f] (g) {}; \node[pack, right=3 of g] (h) {}; \node[pack, right=3 of h] (i) {}; \draw (g) to["$S$" right] +(.5,0); \draw (h) to["$S_2$" right] +(.5,0); \draw (h) to["$S_1$" left] +(-.5,0); \draw (i) to["$S_1$" above] +(-.2,.4); \draw (i) to["$S_2$" below] +(-.2,-.4); \draw (i) to["$S_3$" right] +(.5,0); \node[font=\footnotesize, above=of g] (labels) {some typed finite sets shown with labels}; % \node[pack,right=7 of i] (ff) {}; \node[pack,right=3 of ff] (gg) {}; \node[pack, right=3 of gg] (hh) {}; \node[pack, right=3 of hh] (ii) {}; \draw (gg) -- +(.5,0); \draw (hh) -- +(.5,0); \draw (hh) -- +(-.5,0); \draw (ii) -- +(-.2,.4); \draw (ii) -- +(-.2,-.4); \draw (ii) -- +(.5,0); \node[font=\footnotesize] at (labels-|gg) (no labels) {some typed finite sets shown without labels}; \end{tikzpicture} \end{equation}
% Section % \section{Functional cospans}
\begin{equation}\label{functional1}\tag{functional} \begin{tikzpicture}[unoriented WD, spacing=16pt, surround sep=2pt, every label/.style={font=\small}] \node[pack] (X1) {$X_1$}; \node[pack, right=2 of X1] (X2) {$X_2$}; \node[pack, below=1.5 of $(X1)!.5!(X2)$] (X3) {$X_3$}; \node[link, above=2 of X3] (L123) {}; \node[link, below left=.5 of $(X1)!.5!(X3)$] (L13) {}; \node[link, below right=.5 of X2] (L2) {}; \node[link, below right=0 and 1.5 of X3] (Lout) {}; \node[outer pack, fit=(X1) (X2) (X3) (L123) (L13) (L2)] (outer) {}; \draw (X1) -- (L13); \draw (L13) -- (X3); \draw (L13) -- (outer); \draw (Lout) -- (outer); \draw (X1) -- (L123); \draw (L123) -- (X2); \draw (X3) -- (L123); \draw (L123) -- (outer); \draw (X2.340) -- (L2); \draw (L2) -- (X2.290); \draw (L2) -- (outer.350); \end{tikzpicture} \end{equation}
% Section % \section{Arbitrary diagrams}
\begin{equation}\label{operad_for_groups}\tag{cartesian operad for groups} \begin{tikzpicture}[unoriented WD, baseline=(base)] \node[pack] (p) {\tiny$\rhd$}; \node[pack, right=of p] (q) {\tiny$\lhd$}; \node[pack, right=of q] (r) {\tiny$\lhd$}; \node[pack, right=of r] (s) {\tiny$\rhd$}; \node[pack, right=of s] (t) {\tiny$\lhd$}; \node[outer pack, inner sep = 2pt, fit={(p) (t)}] (outer) {}; \node at ($(p.center)+(0,-3pt)$) (base) {}; \draw (outer.west) -- (p); \draw (p) -- (q); \draw (q) -- (r); \draw (r) -- (s); \draw (s) -- (t); \draw (t) -- (outer.east); \end{tikzpicture} \end{equation}
\begin{equation}\label{sizes}\tag{sizes?} \begin{tikzpicture}[unoriented WD] \node[pack] (p) {}; \node[link, right=1 of p] (l) {}; \node[pack, right=1 of l] (q) {Eq1}; \node[pack, below=1 of l] (r) {}; \node[outer pack, fit=(p) (q) (l) (r)] (outer) {}; \draw (p) to (l); \draw (q) to (l); \draw (q) -- (r); \draw (q) to[bend left] (outer.south); \draw (outer.north -| l) -- (l); \end{tikzpicture} \end{equation}
\begin{equation}\label{grid}\tag{grid}
\begin{tikzpicture}[unoriented WD, font=\footnotesize, pack size=1em, spacing=8pt]
\foreach \i in {1,...,6} {
\foreach \j in {1,...,3} {
\node[pack] at (5*\i,-5*\j) (pack\i\j) {$\dot{u}_{\i,\j}$};
}
}
\node[outer pack, rectangle, rounded corners, fit={($(pack11)+(-3,3)$) ($(pack63)+(3,-3)$)}] (outer) {};
\foreach \i [remember=\i as \lasti (initially 1)] in {1,...,6} {
\foreach \j [remember=\j as \lastj (initially 1)] in {1,...,3} {
\draw (pack\i\j) -- (pack\lasti\j);
\draw (pack\i\j) -- (pack\i\lastj);
\ifnum \i=1 \draw (pack\i\j) -- (pack\i\j -| outer.west);\fi
\ifnum \i=6 \draw (pack\i\j) -- (pack\i\j -| outer.east);\fi
\ifnum \j=1 \draw (pack\i\j) -- (pack\i\j |- outer.north);\fi
\ifnum \j=3 \draw (pack\i\j) -- (pack\i\j |- outer.south);\fi
}
}
\end{tikzpicture}
\end{equation}
\begin{equation}\label{four_packs}\tag{four packs} \begin{tikzpicture}[unoriented WD, spacing=16pt, every label/.style={font=\small}] \node[pack] (f1) {$f_1$}; \node[pack, below right=1.7 and 1 of f1] (f3) {$f_3$}; \node[pack, above right=1.7 and 1 of f3] (f2) {$f_2$}; \node[pack, below right=1.7 and 1 of f2] (f4) {$f_4$}; \node[outer pack, fit=(f1) (f4)] (outer) {}; % \node[link, label=below:$t$] at ($(f1)!-.4!(outer)$) (t) {}; \node[link, label=left:$u$] at ($(f1)!.5!(f3)$) (u) {}; \node[link, label=below:$v$] at (f3 |-f1) (v){}; \node[link, label=left:$w$] at ($(f3)!.5!(f2)$) (w) {}; \node[link, label=below:$x$] at ($(w)!.3!(f4)$) (x) {}; \node[link, below=.5 of f3, label=below:$y$] (y) {}; \node[link, label=above:$z$] at ($(f4)!-.4!(outer)$) (z) {}; % \draw (f1) -- (outer); \draw (v) -- (outer.north-|v); \draw (f4) -- (outer); \draw (f1) -- (v) -- (f2) -- (f3) -- (y); \draw (f1) -- (f3) to[bend right=10] (x); \draw (x) to [bend right=10] (f2); \draw (x) -- (f4); \end{tikzpicture} \end{equation}
\begin{equation}\label{no penetration}\tag{no penetration} \begin{tikzpicture}[penetration=0, unoriented WD, spacing=16pt, every label/.style={font=\small}] \node[pack] (f1) {$f_1$}; \node[pack, below right=1.7 and 1 of f1] (f3) {$f_3$}; \node[pack, above right=1.7 and 1 of f3] (f2) {$f_2$}; \node[pack, below right=1.7 and 1 of f2] (f4) {$f_4$}; \node[outer pack, fit=(f1) (f4)] (outer) {}; % \node[link, label=below:$t$] at ($(f1)!-.4!(outer)$) (t) {}; \node[link, label=left:$u$] at ($(f1)!.5!(f3)$) (u) {}; \node[link, label=below:$v$] at (f3 |-f1) (v){}; \node[link, label=left:$w$] at ($(f3)!.5!(f2)$) (w) {}; \node[link, label=below:$x$] at ($(w)!.3!(f4)$) (x) {}; \node[link, below=.5 of f3, label=below:$y$] (y) {}; \node[link, label=above:$z$] at ($(f4)!-.4!(outer)$) (z) {}; % \draw (f1) -- (outer); \draw (v) -- (outer.110-|v); \draw (f4) -- (outer); \draw (f1) -- (v) -- (f2) -- (f3) -- (y); \draw (f1) -- (f3) to[bend right=10] (x); \draw (x) to [bend right=10] (f2); \draw (x) -- (f4); \end{tikzpicture} \end{equation}
\begin{equation}\label{beamer, no labels}\tag{beamer, no labels} \begin{tikzpicture}[unoriented WD, spacing=8pt, font=\tiny] \node[pack] (f1) {$f_1$}; \node[pack, below right=1.7 and 1 of f1] (f3) {$f_3$}; \node[pack, above right=1.7 and 1 of f3] (f2) {$f_2$}; \node[pack, below right=1.7 and 1 of f2] (f4) {$f_4$}; \node[outer pack, fit=(f1) (f4)] (outer) {}; % \node[link] at ($(f1)!-.4!(outer)$) (t) {}; \node[link] at ($(f1)!.5!(f3)$) (u) {}; \node[link] at (f3 |-f1) (v){}; \node[link] at ($(f3)!.5!(f2)$) (w) {}; \node[link] at ($(w)!.3!(f4)$) (x) {}; \node[link, below=.5 of f3] (y) {}; \node[link] at ($(f4)!-.4!(outer)$) (z) {}; % \draw (f1) -- (outer); \draw (v) -- (outer.north-|v); \draw (f4) -- (outer); \draw (f1) -- (v) -- (f2) -- (f3) -- (y); \draw (f1) -- (f3) to[bend right=10] (x); \draw (x) to [bend right=10] (f2); \draw (x) -- (f4); \end{tikzpicture} \end{equation}
\begin{equation}\label{eqn.cospan}\tag{cospan} \begin{tikzpicture}[penetration=0, unoriented WD, spacing=20pt, pack size=25pt]
\begin{scope}[font=\small]
\node[pack] (a) {$a$};
\node[pack, right=4 of a] (b) {$b$};
\node[pack] at ($(a)!.5!(b)+(0,-2)$) (c) {$c$};
\node[outer pack, fit=(a) (b) (c)] (outer) {};
\end{scope}
% \begin{scope}[font=\fontsize{5pt}{0}\selectfont] \draw[shorten >= -3pt, shorten <=-3pt] (outer.200) to[bend left=50pt] node[pos=-.1] {$2$} node[pos=.5, link, label={[above right, font=\footnotesize]:$t$}] {} node[pos=1.1] {$1$} (outer.240); \draw[shorten >= -3pt] (a) to[bend left=20pt] node[pos=-.1] {$1$} node[pos=.5, link, label={[above, font=\footnotesize]:$u$}] {} node[pos=1.15] {$3$} (outer.170); \draw[shorten >= -3pt] (a) to[bend right=20pt] node[pos=-.15] {$2$} node[pos=.5, link, label={[right, font=\footnotesize]:$v$}] {} node[pos=1.25] {$4$} (outer.130);
\draw (a) to
node[pos=-.05] {$3$} node[pos=.5, link, label={[above, font=\footnotesize]:$w$}] {} node[pos=1.05] {$1$} (b); \draw (a) to[bend right] node[pos=-.1] {$4$} node[pos=.5, link, label={[above, font=\footnotesize]:$x$}] {} node[pos=1.1] {$1$} (c); \draw (b) to[bend left] node[pos=-.1] {$2$} node[pos=.5, link, label={[above, font=\footnotesize]:$y$}] (y) {} node[pos=1.1] {$2$} (c); \node[link, label={[above, font=\footnotesize]:$s$}] at ($(y)!.5!(outer.0)$) {}; \draw[shorten >= -3pt] (c) to node[pos=-.15] {$3$} node[pos=.5, link, label={[left, font=\footnotesize]:$z$}] {} node[pos=1.25] {$6$} (outer); \draw[shorten >= -3pt] (y) to node[pos=1.15] {$5$} (outer.-30); \end{scope} \begin{scope}[font=\scriptsize,x=1em, decoration={brace, amplitude=4pt},y=3ex] \node[link, label=$1$, below right=0 and 10 of b.90] (a1) {}; \node[link, label=$2$, right=1 of a1] (a2) {}; \node[link, label=$3$, right=1 of a2] (a3) {}; \node[link, label=$4$, right=1 of a3] (a4) {}; \node[link, label=$1$, right=1 of a4] (b1) {}; \node[link, label=$2$, right=1 of b1] (b2) {}; \node[link, label=$1$, right=1 of b2] (c1) {}; \node[link, label=$2$, right=1 of c1] (c2) {}; \node[link, label=$3$, right=1 of c2] (c3) {}; \draw[decorate] ($(a1.north)+(-2pt,10pt)$) to node[above=6pt] {$a$} ($(a4.north)+(2pt,10pt)$); \draw[decorate] ($(b1.north)+(-2pt,10pt)$) to node[above=6pt] {$b$} ($(b2.north)+(2pt,10pt)$); \draw[decorate] ($(c1.north)+(-2pt,10pt)$) to node[above=6pt] {$c$} ($(c3.north)+(2pt,10pt)$); \node[link, label=$s$] at ($(a1)!.5!(a2)+(0,-2.5)$) (s) {}; \node[link, label=$t$, right=1 of s] (t) {}; \node[link, label=$u$, right=1 of t] (u) {}; \node[link, label=$v$, right=1 of u] (v) {}; \node[link, label=$w$, right=1 of v] (w) {}; \node[link, label=$x$, right=1 of w] (x) {}; \node[link, label=$y$, right=1 of x] (y) {}; \node[link, label=$z$, right=1 of y] (z) {}; \node[link, label={[below]:$1$}] at ($(t)+(0,-2)$) (outer1) {}; \node[link, label={[below]:$2$}, right=1 of outer1] (outer2) {}; \node[link, label={[below]:$3$}, right=1 of outer2] (outer3) {}; \node[link, label={[below]:$4$}, right=1 of outer3] (outer4) {}; \node[link, label={[below]:$5$}, right=1 of outer4] (outer5) {}; \node[link, label={[below]:$6$}, right=1 of outer5] (outer6) {}; \draw[decorate] ($(outer6.south)+(2pt,-12pt)$) to node[below=6pt] {outer} ($(outer1.south)+(-2pt,-12pt)$); \end{scope} \begin{scope}[->, shorten >=8pt, thin, in=90, out=-90]
\draw (a1) to (u); \draw (a2) to (v); \draw (a3) to (w); \draw (a4) to (x); \draw (b1) to (w); \draw (b2) to (y); \draw (c1) to (x); \draw (c2) to (y); \draw (c3) to (z);
\end{scope} \begin{scope}[->, shorten >=2pt, thin, in=-90, out=90] \draw (outer1) to (t); \draw (outer2) to (t); \draw (outer3) to (u); \draw (outer4) to (v); \draw (outer5) to (y); \draw (outer6) to (z); \end{scope} \end{tikzpicture} \end{equation}
\begin{equation}\label{side by side}\tag{side by side} \begin{tikzpicture}[oriented WD, bb min width =.5cm, bbx=.5cm, bb port sep =1,bb port length=.08cm, bby=.15cm] \node[bb={2}{2},green!25!black,bb name = {\tiny$X_1$}] (X11) {}; \node[bb={3}{3},green!25!black,below right=of X11,bb name = {\tiny$X_2$}] (X12) {}; \node[bb={2}{1}, green!25!black,above right=of X12,bb name = {\tiny$X_3$}] (X13) {}; \draw (X11_out1) to (X13_in1); \draw (X11_out2) to (X12_in1); \draw (X12_out1) to (X13_in2);
\node[bb={2}{2}, green!25!black, below right = -1 and 1.5 of X12, bb name = {\tiny$X_4$}] (X21) {}; \node[bb={1}{2}, green!25!black, above right=-1 and 1 of X21,bb name = {\tiny$X_5$}] (X22) {}; \draw (X21_out1) to (X22_in1); \draw let \p1=(X22.north east), \p2=(X21.north west), \n1={\y1+\bby}, \n2=\bbportlen in
(X22_out1) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X21_in1);
\node[bb={2}{2}, fit = {($(X11.north east)+(-1,3)$) (X12) (X13) ($(X21.south)$) ($(X22.east)+(.5,0)$)}, bb name ={\scriptsize $Y$}] (Z) {};
\draw (Z_in1') to (X11_in2); \draw (Z_in2') to (X12_in2); \draw (X12_out2) to (X21_in2); \draw let \p1=(X22.south east),\n1={\y1-\bby}, \n2=\bbportlen in (X21_out2) to (\x1+\n2,\n1) to (Z_out2'); \draw let \p1=(X12.south east), \p2=(X12.south west), \n1={\y1-\bby}, \n2=\bbportlen in (X12_out3) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X12_in3); \draw let \p1=(X22.north east), \p2=(X11.north west), \n1={\y2+\bby}, \n2=\bbportlen in
(X22_out2) to[in=0] (\x1+\n2,\n1) -- (\x2-\n2,\n1) to[out=180] (X11_in1);
\draw let \p1=(X13_out1), \p2=(X22.north east), \n2=\bbportlen in (X13_out1) to (\x1+\n2,\y1) -- (\x2+\n2,\y1) to (Z_out1'); \end{tikzpicture} \hspace{.5in} \begin{tikzpicture}[unoriented WD, surround sep=1pt, font=\tiny] \node[pack] (p1) {$X_1$}; \node[pack, below right = 1 and 1 of p1] (p2) {$X_2$}; \node[pack, above right = 2 and 1 of p2] (p3) {$X_3$}; \node[pack, below right = 2 and 1 of p3] (p4) {$X_4$}; \node[pack, above right = 0 and 2 of p4] (p5) {$X_5$}; \node[outer pack, fit=(p1) (p2) (p3) (p4) (p5)] (outer) {}; \draw (outer) to (p1.170); \draw (outer) to (p2.210); \draw (outer) to (p4.300); \draw (outer.20) to (p3.10); \draw (p1) to (p3); \draw (p1) to (p2); \draw (p2) to (p4); \draw (p4) to (p5); \draw (p2) to (p3); \draw (p5.100) to[bend right=60pt] (p4.110); \draw (p5.80) to[bend right=50pt] (p1.90); \end{tikzpicture} \end{equation}
\begin{equation}\label{clustering}\tag{clustering} \begin{tikzpicture}[unoriented WD, spacing=6pt, font=\tiny, baseline=(outer.center)] \node[pack] (f1) {$f_1$}; \node[pack, below right=1.7 and 1 of f1] (f3) {$f_3$}; \node[pack, above right=1.7 and 1 of f3] (f2) {$f_2$}; \node[pack, below right=1.7 and 1 of f2] (f4) {$f_4$}; \node[outer pack, fit=(f1) (f4)] (outer) {}; % \node[link] at ($(f1)!-.4!(outer)$) (t) {}; \node[link] at ($(f1)!.5!(f3)$) (u) {}; \node[link] at (f3 |-f1) (v){}; \node[link] at ($(f3)!.5!(f2)$) (w) {}; \node[link] at ($(w)!.3!(f4)$) (x) {}; \node[link, below left=.3 and .3 of f3] (y) {}; \node[link] at ($(f4)!-.4!(outer)$) (z) {}; % \draw (f1) -- (outer); \draw (v) -- (outer.north-|v); \draw (f4) -- (outer); \draw (f1) -- (v); \draw (v) -- (f2); \draw (f2) -- (w); \draw (w) -- (f3); \draw (f3) -- (y); \draw (f1) -- (f3); \draw (f3) to[bend right=10] (x); \draw (x) to [bend right=10] (f2); \draw (x) -- (f4); \node[intermediate pack, dotted, inner sep=0, fit=(f3) (y)] {}; \pgfmathanglebetweenpoints{\pgfpointanchor{f2}{center}}{\pgfpointanchor{f3}{center}}
\let\angle\pgfmathresult
\node[intermediate pack, inner sep=\psize/1.5, rotate fit=\angle, fit=(f2) (f3)] {}; \end{tikzpicture} \end{equation}
\begin{equation}\label{post-clustering}\tag{post-clustering} \begin{tikzpicture}[unoriented WD, spacing=14pt, font=\small, every label/.style={font=\footnotesize}] \node[pack] (f1) {$f_1$}; \node[pack, right=of f1] (f23) {$f_{23}$}; \node[pack, right=of f23] (f4) {$f_4$}; \node[outer pack, fit=(f1) (f4)] (outer) {}; \node[link, left=of f1] (link 0) {}; \node[link] at ($(f1)!.5!(f23)+(0,.5)$) (link 1) {}; \node[link] at ($(f1)!.5!(f23)+(0,-.5)$) (link 2) {}; \node[link] at ($(f23)!.5!(f4)$) (link 3) {}; \node[link, right=of f4] (link 4) {}; \draw (outer) -- (link 0); \draw (link 0) -- (f1); \draw (f1) to[bend left=5] (link 1); \draw (f1) to[bend right=5] (link 2); \draw[shorten >=0] (link 1) -- (link 1 |- outer.north); \draw (f23) to[bend right=5] (link 1); \draw (f23) to[bend left=5] (link 2); \draw (f23) -- (link 3); \draw (link 3) -- (f4); \draw (f4) -- (link 4); \draw (link 4) -- (outer); \end{tikzpicture} \end{equation}
\begin{equation}\label{interfaces}\tag{interfaces} \begin{tikzpicture} [unoriented WD, spacing=10pt, link size=1pt, pack size=12pt, surround sep=3pt, font=\tiny] \node[pack] (f) {}; \node[pack,right=of f] (g) {}; \draw (g) -- +(.5,0); \node[pack, right=of g] (h) {}; \draw (h) -- +(.5,0); \draw (h) -- +(-.5,0); \node[pack, right=of h] (i) {}; \draw (i) -- +(-.2,.4); \draw (i) -- +(-.2,-.4); \draw (i) -- +(.5,0); \end{tikzpicture} \end{equation}
\begin{equation}\label{objects_morphisms}\tag{objects and morphisms} \begin{tikzpicture} [unoriented WD, spacing=10pt, link size=1pt, pack size=12pt, surround sep=3pt, font=\tiny] \node[font=\normalsize] (objects) {objects:}; \node[pack,right=of objects] (f) {}; \node[pack,right=of f] (g) {}; \node[pack, right=of g] (h) {}; \node[pack, right=of h] (i) {}; \draw (g) -- +(.5,0); \draw (h) -- +(.5,0); \draw (h) -- +(-.5,0); \draw (i) -- +(-.2,.4); \draw (i) -- +(-.2,-.4); \draw (i) -- +(.5,0); \node[right=of i, font=\normalsize] (etc) {etc.}; %% \node[below=4 of objects, font=\normalsize] (morphisms) {morphisms:}; \node[pack, above right=0 and 3 of morphisms] (f1) {$f_1$}; \node[pack, below right=1.7 and 1 of f1] (f3) {$f_3$}; \node[pack, above right=1.7 and 1 of f3] (f2) {$f_2$}; \node[pack, below right=1.7 and 1 of f2] (f4) {$f_4$}; \node[outer pack, fit=(f1) (f4)] (outer) {}; % \node[link] at ($(f1)!-.4!(outer)$) (t) {}; \node[link] at ($(f1)!.5!(f3)$) (u) {}; \node[link] at (f3 |-f1) (v){}; \node[link] at ($(f3)!.5!(f2)$) (w) {}; \node[link] at ($(w)!.3!(f4)$) (x) {}; \node[link, below=.5 of f3] (y) {}; \node[link] at ($(f4)!-.4!(outer)$) (z) {}; % \draw[shorten >=-2pt, shorten >=-2pt] (f1) -- (outer); \draw (v) -- (outer.north-|v); \draw[shorten >=-2pt, shorten >=-2pt] (f4) -- (outer); \draw (f1) -- (v) -- (f2) -- (f3) -- (y); \draw (f1) -- (f3) to[bend right=10] (x); \draw (x) to [bend right=10] (f2); \draw (x) -- (f4); \end{tikzpicture} \end{equation}
\begin{equation}\label{famous_operations1}\tag{famous operations1} \begin{tikzpicture}[unoriented WD, pack size=4pt, font=\small, spacing=10pt] \node[pack] (mult M) {$M$}; \node[pack, right=of mult M] (mult N) {$N$}; \node[outer pack, fit=(mult M) (mult N)] (mult outer) {}; \draw (mult M) -- (mult outer); \draw (mult M) -- (mult N); \draw (mult N) -- (mult outer); \node[anchor=south] at (mult outer.north) (mult text) {Multiplication $MN$}; % \node[pack, right=6 of mult outer] (khat M) {$M$}; \node[pack, right= of khat M] (khat N) {$N$}; \node[outer pack, fit=(khat M) (khat N)] (khat outer) {}; \node[link] at ($(khat M)!.5!(khat N)$) (khat link) {}; \draw (khat M) -- (khat outer); \draw (khat M) -- (khat link) -- (khat outer.north); \draw (khat N) -- (khat link); \draw (khat N) -- (khat outer); \node at (khat outer|-mult text) {Khatri-Rao: $M\odot N$}; % \node[pack, right=6 of khat outer] (trace M) {$M$}; \node[outer pack, fit=(trace M)] (trace outer) {}; \node[link, above=.25 of trace M.north] (trace link) {}; \draw (trace M.30) to[out=0, in=0] (trace link); \draw (trace M.150) to[out=180, in=180] (trace link); \node at (trace outer|-mult text) {Trace: $\mathrm{Tr}(M)$}; % \node[pack, below=5 of mult outer] (hada M) {$M$}; \node[pack, below=of hada M] (hada N) {$N$}; \node[outer pack, fit=(hada M) (hada N)] (hada outer) {}; \node[link, left=-.6 of hada outer] (hada link 1) {}; \node[link, right=-.6 of hada outer] (hada link 2) {}; \draw (hada M) to [bend right] (hada link 1); \draw (hada N) to [bend left] (hada link 1); \draw (hada M) to [bend left] (hada link 2); \draw (hada N) to [bend right] (hada link 2); \draw (hada link 1) -- (hada outer); \draw (hada link 2) -- (hada outer); \node[anchor=south] at (hada outer.north) (hada text) {Hadamard: $M\circ N$}; % \node[pack] at (hada M-|khat outer) (kron M) {$M$}; \node[pack, below=of kron M] (kron N) {$N$}; \node[outer pack, fit=(kron M) (kron N)] (kron outer) {}; \draw[shorten >=0] (kron M) -- (kron M -| kron outer.west); \draw[shorten >=0] (kron M) -- (kron M -| kron outer.east); \draw[shorten >=0] (kron N) -- (kron N -| kron outer.west); \draw[shorten >=0] (kron N) -- (kron N -| kron outer.east); \node at (kron outer |- hada text) {Kronecker: $M\otimes N$}; % \node[pack] at (kron outer-|trace outer) (ptrace M) {$M$}; \node[outer pack, fit=(ptrace M)] (ptrace outer) {}; \node[link, above=.25 of ptrace M.north] (ptrace link) {}; \draw (ptrace M.30) to[out=0, in=0] (ptrace link); \draw (ptrace M.150) to[out=180, in=180] (ptrace link); \draw (ptrace M.270) -- (ptrace outer); \node at (ptrace outer |- hada text) {Partial trace: $\mathrm{Tr}^m_n(M)$}; \end{tikzpicture} \end{equation}
\end{document} </tex>