From b516f2ac4f64344789ce248cd1fcff85b87b2e49 Mon Sep 17 00:00:00 2001
From: m-iancu <mihnea.iancu88@gmail.com>
Date: Mon, 27 Apr 2015 04:56:46 +0200
Subject: [PATCH] more

---
 adoptions/conc.tex      |   2 +-
 adoptions/intro.tex     |   6 +-
 adoptions/paper-blx.bib |  11 --
 adoptions/paper.pdf     | Bin 433298 -> 430265 bytes
 adoptions/paper.tex     |   5 +-
 adoptions/patterns.tex  | 325 +++++++++++++++++++++++-----------------
 adoptions/phenomena.tex |  30 ++--
 7 files changed, 204 insertions(+), 175 deletions(-)
 delete mode 100644 adoptions/paper-blx.bib

diff --git a/adoptions/conc.tex b/adoptions/conc.tex
index 8d5ae94..d9c48a2 100644
--- a/adoptions/conc.tex
+++ b/adoptions/conc.tex
@@ -11,7 +11,7 @@ contribution in the commons. It is the realms structure with its equivalent pill
 abstraction capabilities that gives the recaps the necessary flexibility to adequately
 model the variety of anchors we see in mathematical documents.
 
-We have validated our model by identifying the recaps and their types in 15 recent papers
+We have validated our model by identifying the recaps and their types in 30 recent papers
 randomly selected from a preprint archive. To obtain a more scientific evaluation of the
 model, we need a much larger and more varied sample. We are currently developing an
 annotation ontology for realms and recaps for the KAT annotator~\cite{DumGinKoh:katsd14}
diff --git a/adoptions/intro.tex b/adoptions/intro.tex
index 8f41711..a2a21a3 100644
--- a/adoptions/intro.tex
+++ b/adoptions/intro.tex
@@ -44,17 +44,17 @@ checker.
 On the other hand, libraries of formalized mathematics directly represent the structure
 of a mathematical knowledge commons, usually in graph of files and file inclusions or a
 graph of theories and theory morphisms (see ~\cite{RabKoh:WSMSML13} for a survey). The
-respective graphs supply identifiers for knowledge items detail their relations to each
+respective graphs supply identifiers for knowledge items and detail their relations to each
 other.
 
 It stands to reason that the two dissemination and aggregation approaches can profit from
 each other. The scientific publication process can profit from a more explicitly
 represented knowledge commons, which enables added-value services for finding,
 understanding, and applying relevant knowledge items -- after all the document/knowledge
-space even in mathematics is much to large and complex for a single human to process. Of
+space even in mathematics is much too large and complex for a single human to process. Of
 course a prerequisite for this is computer support in the aggregation of the knowledge
 space. Conversely, formal libraries can profit from a dissemination process based on the
-publication self-contained documents to scale the secondary aspects (quality control,
+publication of self-contained documents to scale the secondary aspects (quality control,
 checkpointing, citation stability, persistence, attention management) of assembling large
 bodies of knowledge. Even though formal developments are machine-checkable, their
 authoring, maintenance, refactoring, \ldots are processes that need at least some human
diff --git a/adoptions/paper-blx.bib b/adoptions/paper-blx.bib
deleted file mode 100644
index a2ce9cd..0000000
--- a/adoptions/paper-blx.bib
+++ /dev/null
@@ -1,11 +0,0 @@
-@Comment{$ biblatex control file $}
-@Comment{$ biblatex version 2.3 $}
-Do not modify this file!
-
-This is an auxiliary file used by the 'biblatex' package.
-This file may safely be deleted. It will be recreated as
-required.
-
-@Control{biblatex-control,
-  options = {2.3:0:0:1:0:0:1:1:0:1:0:0:12:1:3:1:79:+},
-}
diff --git a/adoptions/paper.pdf b/adoptions/paper.pdf
index d6f4b6b7d726ef83dd1e27393eacfe5d4ac38cda..246ff5b58f872ecb4e3d075ab78051175dfef72d 100644
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diff --git a/adoptions/paper.tex b/adoptions/paper.tex
index f2d7b71..35ce3c6 100644
--- a/adoptions/paper.tex
+++ b/adoptions/paper.tex
@@ -9,6 +9,7 @@
 \usepackage[show]{ed}
 \usepackage{paralist}
 \usepackage{listings}
+\usepackage{caption,subcaption}
 
 \usepackage[linkcolor=black]{hyperref}
 
@@ -71,10 +72,6 @@
 \end{abstract}
 %\setcounter{tocdepth}{3}\tableofcontents\newpage
 
-\ednote{MK@MI: capitalize all captions}
-\ednote{MK@MI: I have xscaled all figures, that should make them more amenable to
-  side-by-side treatment, but they need to be tweaked a bit still}
-
 \section{Introduction}\label{sec:intro}
 \input{intro}
 
diff --git a/adoptions/patterns.tex b/adoptions/patterns.tex
index e912d54..b30f93d 100644
--- a/adoptions/patterns.tex
+++ b/adoptions/patterns.tex
@@ -87,7 +87,7 @@ below.
   \draw[view, bend left = 10] (bot2) to (bot3);
   \draw[view, bend left = 10] (bot3) to (bot2);
  \end{tikzpicture}
- \caption{The architecture of a realm}\label{fig:realm}\vspace*{-1em}
+ \caption{The Architecture of a Realm}\label{fig:realm}\vspace*{-1em}
 \end{wrapfigure}
 Figure \ref{fig:realm} shows a prototypical realm with $F$ as its interface theory (also
 called a \emph{face}) and $n$ pillars each representing a different (yet equivalent)
@@ -111,32 +111,31 @@ contribution in a single theory is a simplification for presentational simplicit
 does not lead to a loss of generality. The view $v$ ensures that the paper can make use of
 concepts and theorems from the realm, as they can be accessed via $v$.
 
-In our analysis we restrict ourselves to the case where there is a single recap for
-simplicity and expositional clarity. The approach can be extended to multiple recaps from
-the same realm with minimal effort -- but the diagrams become messy. This already covers
-the majority of research papers we have analyzed; they build on an earlier paper and
+In our analysis we first restrict ourselves to the case where there is a single recap for
+simplicity and expositional clarity.  This already covers
+the majority of research papers we have analyzed; they mainly build on one earlier paper and
 extend it. Indeed, all three examples from Section~\ref{sec:cg-preprints} fall into this
 category, they import the definitions and terminology from a central cited paper, but call
-on others from the same realm for results, context, and support.
+on others from the same realm for results, context, and support. 
+
+
 
-%Mathematical papers re-introduce concepts with the implied assumption of semantic equivalence in the context of the paper.
-%I.e. every statement in the paper holds for the original definition too, but not necessarily the converse.
 
 \begin{figure}[ht]\centering
  \begin{tikzpicture}[xscale=.7]
   %realm
-  \draw[realm] (-1,-1.7) rectangle (5,2.8) {};
+  \draw[realm] (-1,-2.3) rectangle (5,2.6) {};
   %p-paper
-  \draw[pillar] (-4.2,-0.5) rectangle (-1.8,2.8) {};
+  \draw[pillar] (-4.2,-0.8) rectangle (-1.8,2.3) {};
   %p1
-  \draw[pillar] (-0.5,-1.5) rectangle (1.5,1.8) {};
+  \draw[pillar] (-0.5,-1.8) rectangle (1.5,1.8) {};
   %p2
-  \draw[pillar] (2.5,-1.5) rectangle (4.5,1.8) {};
+  \draw[pillar] (2.5,-1.8) rectangle (4.5,1.8) {};
   
-  \node (r-name)  at (4.5,2.6) {$\mathit{Realm}$};
-  \node (p-name)  at (-1.7,2.6) {$\mathit{Paper}$};
-  \node (p1-name)  at (0,1.6) {$\mathit{Pillar_1}$};
-  \node (p2-name)  at (4.0,1.6) {$\mathit{Pillar_n}$};
+  \node (r-name)  at (2,-2.1) {$\mathit{Realm}$};
+  \node (p-name)  at (-3,-0.6) {$\mathit{Paper}$};
+  \node (p1-name)  at (0.5,-1.6) {$\mathit{Pillar_1}$};
+  \node (p2-name)  at (3.5,-1.6) {$\mathit{Pillar_n}$};
   
 
   \node[thy] (recap) at (-3,0) {Recap};
@@ -170,15 +169,16 @@ on others from the same realm for results, context, and support.
  \caption{General Case for Recaps}\label{fig:rec-gen}
 \end{figure}
 
-We recognize four special cases for recaps based on the nature of $r$ and discuss each
+We recognize four special cases for (single) recaps based on the nature of $r$ and discuss each
 individually below.  First we have to decide the home theory of the symbols that the recap
 introduces.  If the home is the cited theory then $r$ is an import and we have a
-\emph{plain recap} (\ref{rc:pl}) .  Otherwise, we have new symbols in the recap theory
+\emph{plain recap} (\ref{rc:pl}). Otherwise, we have new symbols in the recap theory
 that are somehow related with the ones in the cited one.  In that situation we have three
 sub-cases depending on the relation between the recap and cited theory: \emph{equivalence
   recap} (\ref{rc:eq}), \emph{specialization recap} (\ref{rc:sp}) and, in the informal case, \emph{postulated
   recap} (\ref{rc:ge}).
-
+  
+Finally, we have the case where the paper builds on several others and has \emph{multiple recaps} (\ref{rc:mr}).
 
 \subsection{Special case: Plain Recaps}\label{rc:pl}
 One situation is that of plain recaps where the relation $r$ is an inclusion into the
@@ -193,34 +193,37 @@ realm's literature (see Figure \ref{fig:agg-covers}). It also makes $v$ exist as
 by $v_1$ modulo conservativity.
 
 \begin{figure}[ht]\centering
- \begin{tikzpicture}[xscale=.7]
+\begin{center}
+\begin{subfigure}[b]{0.5\textwidth}
+\begin{center}
+\begin{tikzpicture}[xscale=.8]
   %realm
-  \draw[realm] (-1,-1.7) rectangle (5,2.8) {};
+  \draw[realm] (-0.7,-2.2) rectangle (3.7,2.6) {};
   %p-paper
-  \draw[pillar] (-4.5,-0.5) rectangle (-1.5,2.8) {};
+  \draw[pillar] (-3.7,-0.7) rectangle (-1.1,2.3) {};
   %p1
-  \draw[pillar] (-0.5,-1.5) rectangle (1.5,1.8) {};
+  \draw[pillar] (-0.5,-1.7) rectangle (1.5,1.8) {};
   %p2
-  \draw[pillar] (2.5,-1.5) rectangle (4.5,1.8) {};
+  \draw[pillar] (2.0,-1.7) rectangle (3.5,1.8) {};
   
-  \node (r-name)  at (4.5,2.6) {$\mathit{Realm}$};
-  \node (p-name)  at (-2,2.6) {$\mathit{Paper}$};
-  \node (p1-name)  at (0,1.6) {$\mathit{Pillar_1}$};
-  \node (p2-name)  at (4.0,1.6) {$\mathit{Pillar_n}$};
+  \node (r-name)  at (1.5,-2.0) {$\mathit{Realm}$};
+  \node (p-name)  at (-2.4, -0.5) {$\mathit{Paper}$};
+  \node (p1-name)  at (0.5,-1.5) {$\mathit{Pillar_1}$};
+  \node (p2-name)  at (2.75,-1.5) {$\mathit{Pillar_n}$};
   
 
-  \node[thy] (recap) at (-3,0) {\cn{CACF}};
-  \node[thy] (pcont) at (-3,2) {\cn{MToCACF}};
+  \node[thy] (recap) at (-2.4,0) {\cn{CACF}};
+  \node[thy] (pcont) at (-2.4,2) {\cn{MToCACF}};
   
   \node[thy] (top1) at (0.5,1) {$\top$};
   \node[thy] (citp) at (0.5,0) {CPaper};
   \node[thy] (bot1) at (0.5,-1) {$\bot$};  
   
-  \node[thy] (top2) at (3.5,1) {$\top$};
-  \node[thy] (bot2) at (3.5,-1) {$\bot$};
+  \node[thy] (top2) at (2.75,1) {$\top$};
+  \node[thy] (bot2) at (2.75,-1) {$\bot$};
   
   
-  \node[thy] (r) at (2,2.3) {Realm Face};
+  \node[thy] (r) at (1.5,2.3) {Realm Face};
   
   \draw[view] (r) to node[above] {$\cn{v}$} (pcont);
   \draw[view] (r) to node[left] {$\cn{v_1}$} (top1);
@@ -236,37 +239,39 @@ by $v_1$ modulo conservativity.
   \draw[view, bend left = 10] (bot2) to (bot1);
   \draw[view, bend left = 10] (bot1) to (bot2);
  \end{tikzpicture}
- \caption{Publication graph for plain recaps (Example \ref{ex:covers})}\label{fig:rec-covers}
-\end{figure}
-
-
-\begin{figure}[ht]\centering
- \begin{tikzpicture}[xscale=.7]
+ \caption{Publication Graph}\label{fig:rec-covers}
+ \end{center}
+
+\end{subfigure}
+\hfill
+\begin{subfigure}[b]{0.45\textwidth}
+\begin{center}
+ \begin{tikzpicture}[xscale=.8]
   %realm
-  \draw[realm] (-3,-3.7) rectangle (5,2.8) {};
+  \draw[realm] (-2.7,-4.2) rectangle (3.7,2.6) {};
   %p1
-  \draw[pillar] (-2.5,-3.5) rectangle (1.5,1.8) {};
+  \draw[pillar] (-2.5,-3.7) rectangle (1.5,1.8) {};
   %p2
-  \draw[pillar] (2.5,-3.5) rectangle (4.5,1.8) {};
+  \draw[pillar] (2.0,-3.7) rectangle (3.5,1.8) {};
   
-  \node (r-name)  at (4.5,2.6) {$\mathit{Realm}$};
-  \node (p1-name)  at (-2,1.6) {$\mathit{Pillar_1}$};
-  \node (p2-name)  at (4.0,1.6) {$\mathit{Pillar_n}$};
+  \node (r-name)  at (0.7,-4.0) {$\mathit{Realm}$};
+  \node (p1-name)  at (-0.5,-3.5) {$\mathit{Pillar_1}$};
+  \node (p2-name)  at (2.75,-3.5) {$\mathit{Pillar_n}$};
   
 
-  \node[thy] (recap) at (-1.5,-1) {\cn{CACF}};
-  \node[thy] (pcont) at (-1.5,0) {\cn{MToCACF}};
+  \node[thy] (recap) at (-1.3,-1) {\cn{CACF}};
+  \node[thy] (pcont) at (-1.3,0) {\cn{MToCACF}};
   
   \node[thy] (top1) at (-0.5,1) {$\top$};
-  \node[thy] (tcdots1) at (0.5,-0.5) {$\cdots$};  
+  \node[thy] (tcdots1) at (1.0,-0.5) {$\cdots$};  
   \node[thy] (citp) at (-0.5,-2) {CPaper};
   \node[thy] (bot1) at (-0.5,-3) {$\bot$};  
   
-  \node[thy] (top2) at (3.5,1) {$\top$};
-  \node[thy] (bot2) at (3.5,-3) {$\bot$};
+  \node[thy] (top2) at (2.75,1) {$\top$};
+  \node[thy] (bot2) at (2.75,-3) {$\bot$};
   
   
-  \node[thy] (r) at (1.5,2.3) {Realm Face};
+  \node[thy] (r) at (0.7,2.3) {Realm Face};
   
   \draw[view] (r) to node[left] {$\cn{v_1}$} (top1);
   \draw[view] (r) to node[right] {$\cn{v_2}$} (top2);
@@ -283,9 +288,15 @@ by $v_1$ modulo conservativity.
   \draw[view, bend left = 10] (bot2) to (bot1);
   \draw[view, bend left = 10] (bot1) to (bot2);
  \end{tikzpicture}
- \caption{Aggregation graph for plain recaps (Example \ref{ex:covers})}\label{fig:agg-covers}
+ \caption{Aggregation Graph}\label{fig:agg-covers}
+ \end{center}
+\end{subfigure}
+\caption{Plain Recaps (Example \ref{ex:covers})}
+
+\end{center}
 \end{figure}
 
+
 Plain recaps can also model the formal examples (e.g. Example \ref{ex:mizar}) but in that 
 situation it is not too interesting as we have the degenerate case for the realm itself.
 
@@ -303,32 +314,45 @@ written down in the paper as ``\textsf{There are several equivalent ways to defi
 sample papers we studied.
 % Moreover, examples \ref{ex:quant} and \ref{ex:calculi} also fit in this category. 
 
+Note that adding an equivalent definition corresponds to a \textbf{realm extension}, where
+the face is fixed, and the view from the face to the current theory can be
+postulated. Therefore, in Figure \ref{fig:rec-mnets} the paper effectively extends the
+realm (or the current pillar) as introduced in Section \ref{sec:prel-realms}.  This
+corresponds to the mathematical practice of ``contributing to'' a field (or mathematical
+theory). This resulting realm after knowledge aggregation is shown in Figure
+\ref{fig:rec-mnets-aggr}, where the new paper contributes a new pillar to the realm. The
+equivalence is ensured by $v_{from}$ and $v_{to}$ as we take into account conservativity
+to reduce them to the $\bot$ theory.
+
 \begin{figure}[ht]\centering
- \begin{tikzpicture}[xscale=.7]
+\begin{center}
+\begin{subfigure}[b]{0.45\textwidth}
+\begin{center}
+ \begin{tikzpicture}[xscale=.8]
   %realm
-  \draw[realm] (-1,-1.7) rectangle (5,2.8) {};
+  \draw[realm] (-0.7,-2.3) rectangle (3.7,2.6) {};
   %p-paper
-  \draw[pillar] (-4.5,-0.5) rectangle (-1.5,2.8) {};
+  \draw[pillar] (-3.5,-0.8) rectangle (-1.5,2.3) {};
   %p1
-  \draw[pillar] (-0.5,-1.5) rectangle (1.5,1.8) {};
+  \draw[pillar] (-0.5,-1.8) rectangle (1.5,1.8) {};
   %p2
-  \draw[pillar] (2.5,-1.5) rectangle (4.5,1.8) {};
+  \draw[pillar] (2.0,-1.8) rectangle (3.5,1.8) {};
   
-  \node (r-name)  at (4.5,2.6) {$\mathit{Realm}$};
-  \node (p-name)  at (-2,2.6) {$\mathit{Paper}$};
-  \node (p1-name)  at (0,1.6) {$\mathit{Pillar_1}$};
-  \node (p2-name)  at (4.0,1.6) {$\mathit{Pillar_n}$};
+  \node (r-name)  at (1.5,-2.1) {$\mathit{Realm}$};
+  \node (p-name)  at (-2.5,-0.6) {$\mathit{Paper}$};
+  \node (p1-name)  at (0.5,-1.6) {$\mathit{Pillar_1}$};
+  \node (p2-name)  at (2.75,-1.6) {$\mathit{Pillar_n}$};
   
 
-  \node[thy] (recap) at (-3,0) {\cn{MNets}};
-  \node[thy] (pcont) at (-3,2) {\cn{ICMnets}};
+  \node[thy] (recap) at (-2.5,0) {\cn{MNets}};
+  \node[thy] (pcont) at (-2.5,2) {\cn{ICMnets}};
   
   \node[thy] (top1) at (0.5,1) {$\top$};
   \node[thy] (citp) at (0.5,0) {CPaper};
   \node[thy] (bot1) at (0.5,-1) {$\bot$};  
   
-  \node[thy] (top2) at (3.5,1) {$\top$};
-  \node[thy] (bot2) at (3.5,-1) {$\bot$};
+  \node[thy] (top2) at (2.75,1) {$\top$};
+  \node[thy] (bot2) at (2.75,-1) {$\bot$};
   
   
   \node[thy] (r) at (2,2.3) {Realm Face};
@@ -350,45 +374,37 @@ sample papers we studied.
   \draw[view, bend left = 10] (bot2) to (bot1);
   \draw[view, bend left = 10] (bot1) to (bot2);
  \end{tikzpicture}
- \caption{Publication graph for equivalence recaps (Example \ref{ex:mnets})}\label{fig:rec-mnets}
-\end{figure}
-
-Note that adding an equivalent definition corresponds to a \textbf{realm extension}, where
-the face is fixed, and the view from the face to the current theory can be
-postulated. Therefore, in Figure \ref{fig:rec-mnets} the paper effectively extends the
-realm (or the current pillar) as introduced in Section \ref{sec:prel-realms}.  This
-corresponds to the mathematical practice of ``contributing to'' a field (or mathematical
-theory). This resulting realm after knowledge aggregation is shown in Figure
-\ref{fig:rec-mnets-aggr}, where the new paper contributes a new pillar to the realm. The
-equivalence is ensured by $v_{from}$ and $v_{to}$ as we take into account conservativity
-to reduce them to the $\bot$ theory.
-
-\begin{figure}[ht]\centering
- \begin{tikzpicture}[xscale=.7]
+ \caption{Publication Graph}\label{fig:rec-mnets}
+\end{center}
+ \end{subfigure}
+\hfill
+\begin{subfigure}[b]{0.45\textwidth}
+\begin{center}
+ \begin{tikzpicture}[xscale=.8]
   %realm
-  \draw[realm] (-4,-1.7) rectangle (5,2.8) {};
+  \draw[realm] (-3.2,-2.3) rectangle (3.7,2.6) {};
   %p0
-  \draw[pillar] (-3.5,-1.5) rectangle (-1.5,1.8) {};
+  \draw[pillar] (-3.0,-1.8) rectangle (-1.0,1.8) {};
   %p1
-  \draw[pillar] (-0.5,-1.5) rectangle (1.5,1.8) {};
+  \draw[pillar] (-0.5,-1.8) rectangle (1.5,1.8) {};
   %p2
-  \draw[pillar] (2.5,-1.5) rectangle (4.5,1.8) {};
+  \draw[pillar] (2.0,-1.8) rectangle (3.5,1.8) {};
   
-  \node (r-name)  at (4.5,2.6) {$\mathit{Realm}$};
-  \node (p3-name)  at (-2.8,1.6) {$\mathit{Pillar_{n+1}}$};
-  \node (p1-name)  at (0,1.6) {$\mathit{Pillar_1}$};
-  \node (p2-name)  at (4.0,1.6) {$\mathit{Pillar_n}$};
+  \node (r-name)  at (0.25,-2.1) {$\mathit{Realm}$};
+  \node (p3-name)  at (-2.0,-1.6) {$\mathit{Pillar_{n+1}}$};
+  \node (p1-name)  at (0.5,-1.6) {$\mathit{Pillar_1}$};
+  \node (p2-name)  at (2.75,-1.6) {$\mathit{Pillar_n}$};
 
-  \node[thy] (recap) at (-2.5,-1) {\cn{MNets}};
-  \node[thy] (pcont) at (-2.5,1) {\cn{ICMnets}};
+  \node[thy] (recap) at (-2.0,-1) {\cn{MNets}};
+  \node[thy] (pcont) at (-2.0,1) {\cn{ICMnets}};
   
   \node[thy] (top1) at (0.5,1) {$\top$};
   \node[thy] (citp) at (0.5,0) {CPaper};
   \node[thy] (bot1) at (0.5,-1) {$\bot$};
     
   
-  \node[thy] (top2) at (3.5,1) {$\top$};
-  \node[thy] (bot2) at (3.5,-1) {$\bot$};
+  \node[thy] (top2) at (2.75,1) {$\top$};
+  \node[thy] (bot2) at (2.75,-1) {$\bot$};
   
   
   \node[thy] (r) at (0.5,2.3) {Realm Face};
@@ -410,7 +426,11 @@ to reduce them to the $\bot$ theory.
   \draw[view, bend left = 10] (bot2) to (bot1);
   \draw[view, bend left = 10] (bot1) to (bot2);
  \end{tikzpicture}
- \caption{Aggregation graph for equivalence recaps (Example \ref{ex:mnets})}\label{fig:rec-mnets-aggr}
+ \caption{Aggregation Graph}\label{fig:rec-mnets-aggr}
+\end{center}
+\end{subfigure}
+\caption{Equivalence Recaps (Example \ref{ex:mnets})}
+\end{center}
 \end{figure}
 
 
@@ -436,29 +456,29 @@ for simplicity -- the aggregation is similar as for equivalence recaps, except w
 realm.
 
 \begin{figure}[ht]\centering
- \begin{tikzpicture}[xscale=.7]
+ \begin{tikzpicture}[xscale=.8]
   %realm
-  \draw[realm] (-1,-1.7) rectangle (5,2.8) {};
+  \draw[realm] (-0.8,-2.3) rectangle (4.8,2.6) {};
   %p-paper
-  \draw[pillar] (-6,-0.5) rectangle (-4,2.8) {};
+  \draw[pillar] (-6.2,-0.8) rectangle (-4.2,2.3) {};
   %p1
-  \draw[pillar] (-0.5,-1.5) rectangle (1.5,1.8) {};
+  \draw[pillar] (-0.5,-1.8) rectangle (1.5,1.8) {};
   %p2
-  \draw[pillar] (2.5,-1.5) rectangle (4.5,1.8) {};
+  \draw[pillar] (2.5,-1.8) rectangle (4.5,1.8) {};
   %realm2
   \draw[realm] (-3.5,-1.8) rectangle (-1.5,-.5) {};
   
   
-  \node (r-name)  at (4.5,2.6) {$\mathit{Realm}$};
-  \node (r2-name)  at (-2.1,-1.6) {$\mathit{Realm_2}$};
+  \node (r-name)  at (2,-2.1) {$\mathit{Realm_1}$};
+  \node (r2-name)  at (-2.5,-1.6) {$\mathit{Realm_2}$};
 
-  \node (p-name)  at (-4.5,2.6) {$\mathit{Paper}$};
-  \node (p1-name)  at (0,1.6) {$\mathit{Pillar_1}$};
-  \node (p2-name)  at (4.0,1.6) {$\mathit{Pillar_n}$};
+  \node (p-name)  at (-5.2,-0.6) {$\mathit{Paper}$};
+  \node (p1-name)  at (0.5,-1.6) {$\mathit{Pillar_1}$};
+  \node (p2-name)  at (3.5,-1.6) {$\mathit{Pillar_n}$};
   
 
-  \node[thy] (recap) at (-5,0) {\cn{ATM}};
-  \node[thy] (pcont) at (-5,2) {\cn{ATMhalt}};
+  \node[thy] (recap) at (-5.2,0) {\cn{ATM}};
+  \node[thy] (pcont) at (-5.2,2) {\cn{ATMhalt}};
   
   \node[thy] (citpex) at (-2.5,-1) {$\cn{atm}(2^{-n})$};
   \draw[view] (recap) to node[above] {$\cn{v_{to}}$} (citpex);
@@ -489,7 +509,7 @@ realm.
   \draw[view, bend left = 10] (bot2) to (bot1);
   \draw[view, bend left = 10] (bot1) to (bot2);
  \end{tikzpicture}
- \caption{Publication graph for specialization recaps (Example \ref{ex:atm})}\label{fig:rec-atm}
+ \caption{Publication Graph for Specialization Recaps (Example \ref{ex:atm})}\label{fig:rec-atm}
 \end{figure}
 
 \subsection{Postulated Recap/Adoption}\label{rc:ge}
@@ -500,7 +520,7 @@ in the case where a more formal development is used we could represent it as an
 However, the home theory of the new symbols must be the current development in order for it to be self-contained, so we cannot use an include. 
 Instead we envision a special kind of import that \emph{adopts} the included symbols effectively changing their home theory to the current one.
 But, then the view $v$ is not justified so we must also assert its existence.
-In that case we call $v$ a \emph{postulated} view and the the relation $r$ an \emph{adoption} (see Figure \ref{fig:rec-slides}). 
+In that case we call $v$ a \emph{postulated} view and the the relation $r$ is an \emph{adoption} (see Figure \ref{fig:rec-slides}). 
 We leave working out the precise details of postulated views and adoptions in flexiformal theory graphs for future work.
 
 This is the situation in Example \ref{ex:course} where the recap theory \cn{SET} includes only
@@ -511,20 +531,20 @@ implying that the semantics of the two symbols is compatible with that given in
 literature (which we represent as a realm).
 
 \begin{figure}[ht]\centering
- \begin{tikzpicture}[xscale=.7]
+ \begin{tikzpicture}[xscale=.8]
   %realm
-  \draw[realm] (-1,-1.7) rectangle (5,2.8) {};
+  \draw[realm] (-0.8,-2.3) rectangle (4.8,2.6) {};
   %p-paper
-  \draw[pillar] (-4.5,-0.5) rectangle (-1.5,2.8) {};
+  \draw[pillar] (-4.3,-0.8) rectangle (-1.7,2.3) {};
   %p1
-  \draw[pillar] (-0.5,-1.5) rectangle (1.5,1.8) {};
+  \draw[pillar] (-0.5,-1.8) rectangle (1.5,1.8) {};
   %p2
-  \draw[pillar] (2.5,-1.5) rectangle (4.5,1.8) {};
+  \draw[pillar] (2.5,-1.8) rectangle (4.5,1.8) {};
   
-  \node (r-name)  at (4.5,2.6) {$\mathit{Realm}$};
-  \node (p-name)  at (-2,2.6) {$\mathit{Paper}$};
-  \node (p1-name)  at (0,1.6) {$\mathit{Pillar_1}$};
-  \node (p2-name)  at (4.0,1.6) {$\mathit{Pillar_n}$};
+  \node (r-name)  at (2,-2.1) {$\mathit{Realm}$};
+  \node (p-name)  at (-3,-0.6) {$\mathit{Paper}$};
+  \node (p1-name)  at (0.5,-1.6) {$\mathit{Pillar_1}$};
+  \node (p2-name)  at (3.5,-1.6) {$\mathit{Pillar_n}$};
   
 
   \node[thy] (recap) at (-3,0) {\cn{SET}};
@@ -555,7 +575,7 @@ literature (which we represent as a realm).
   \draw[view, bend left = 10] (bot2) to (bot1);
   \draw[view, bend left = 10] (bot1) to (bot2);
  \end{tikzpicture}
- \caption{Publication graph for generalization/unspecified recaps (Example \ref{ex:course})}\label{fig:rec-slides}
+ \caption{Publication Graph for Generalization/Unspecified Recaps (Example \ref{ex:course})}\label{fig:rec-slides}
 \end{figure}
 
 Note that we omit the aggregation part for this case as the purpose of such educational or
@@ -584,45 +604,69 @@ contribute to it.
 %   distinguish several cases below.
 % \end{oldpart}
 
-\begin{newpart}{MK: this must be reread and better cross-reference}
-\subsection{Multiple Recaps}
+\subsection{Multiple Recaps}\label{rc:mr}
 Up to now we have only treated cases with single recaps to ease the exposition. But papers
 and especially textbooks often recap from different realms and base the rest of the
 exposition on them.
 
-\begin{figure}[ht]\centering
+% The approach can be extended to multiple recaps from
+% the same realm with minimal effort -- but the diagrams become messy. We discuss multiple recaps from different realms
+% in Section \ref{rc:mr}.
+
+\begin{figure}[ht]
+\begin{center}
+\begin{subfigure}[b]{0.45\textwidth}
+\begin{center}
 \begin{tikzpicture}
-  \draw[pillar] (-.5,-.3) rectangle (1.5,1.3);
-  \node at (1,1.5) {\it Paper};
+  \draw[pillar] (-.5,-.8) rectangle (1.5,1.3);
+  \node at (0.5,-.6) {\it Paper};
   \node[thy] (r1) at (0,0) {$R_1$};
   \node[thy] (r2) at (1,0) {$R_2$};
-  \node[thy] (c) at (.5,1) {$C$};
+  \node[thy] (c) at (.5,1) {Contrib.};
   \draw[conservative] (r1) to (c);
   \draw[conservative] (r2) to (c);
 
-  \draw[realm] (-1.5,-.5) rectangle (-1,1.5);
-  \draw[realm] (2,-.5) rectangle (2.5,1.5);
-  \node[thy] (f1) at (-1.25,0) {$F_1$};
-  \node[thy] (f2) at (2.25,0) {$F_2$};
-  \draw[struct] (f1) -- node[below]{$\tau_1$} (r1);
-  \draw[struct] (f2) -- node[below]{$\tau_2$} (r2);
+  \draw[realm] (-2.1,-.8) rectangle (-0.9,0.3);
+  \draw[realm] (1.9,-0.8) rectangle (3.1,0.3);
+  \node (r1-name)  at (-1.5,-0.6) {$\mathit{Realm_1}$};
+  \node (r2-name)  at (2.5,-0.6) {$\mathit{Realm_2}$};
+
+  
+  \node[thy] (f1) at (-1.5,0.0) {$\mathrm{Face_1}$};
+  \node[thy] (f2) at (2.5,0.0) {$\mathrm{Face_2}$};
+  \draw[struct] (f1) -- node[below]{$v_1$} (r1);
+  \draw[struct] (f2) -- node[below]{$v_2$} (r2);
 \end{tikzpicture}
+\caption{Publication Graph}
+\end{center}
+\end{subfigure}
 \qquad
+\begin{subfigure}[b]{0.45\textwidth}
+\begin{center}
 \begin{tikzpicture}
-  \draw[realm] (-.5,1) rectangle (1.5,3);
-  \node at (.5,3.3) {\it Union Realm};
-  \node[thy] (t) at (.5,1.5) {$R_1\cup R_2$};
-  \node[thy] (c) at (.5,2.5) {$C$};
+  \draw[realm] (-.5,0.2) rectangle (1.5,3.3);
+  \node at (0.5,.4) {\it Union Realm};
+  \node[thy] (t) at (.5,1.0) {$R_1\cup R_2$};
+  \node[thy] (c) at (.5,2.0) {Contrib.};
+  \node[thy] (fu) at (.5,3.0) {$\mathrm{Face_\textit{u}}$};
+  \draw[struct] (fu) -- node[left]{$v$} (c);
+
   \draw[conservative] (t) to (c);
 
-  \draw[realm] (-1.5,0) rectangle (-1,2);
-  \draw[realm] (2,0) rectangle (2.5,2);
-  \node[thy] (f1) at (-1.25,.5) {$F_1$};
-  \node[thy] (f2) at (2.25,.5) {$F_2$};
-  \draw[struct] (f1) -- node[below]{$\tau_1$} (t);
-  \draw[struct] (f2) -- node[below]{$\tau_2$} (t);
+  \draw[realm] (-2.1,0.2) rectangle (-0.9,1.3);
+  \draw[realm] (1.9,0.2) rectangle (3.1,1.3);
+  \node (r1-name)  at (-1.5,0.4) {$\mathit{Realm_1}$};
+  \node (r2-name)  at (2.5,0.4) {$\mathit{Realm_2}$};
+  \node[thy] (f1) at (-1.5,1.0) {$\mathrm{Face_1}$};
+  \node[thy] (f2) at (2.5,1.0) {$\mathrm{Face_2}$};
+  \draw[struct] (f1) -- node[below]{$v_1$} (t);
+  \draw[struct] (f2) -- node[below]{$v_2$} (t);
 \end{tikzpicture}
-\caption{Multiple Recaps}\label{fig:multiple}
+\caption{Aggregation Graph}
+\end{center}
+\end{subfigure}
+\caption{Multiple Recaps (Example \ref{ex:rudin})}\label{fig:multiple}
+\end{center}
 \end{figure}
 
 This is a the situation on the left of Figure~\ref{fig:multiple}; for the aggregation
@@ -638,7 +682,6 @@ will usually add some conditions -- like conditions (a) and (b) in (\ref{q:topvs
 use that for the base theories of the realms. This does not invalidate our claim that
 there is always a natural realm -- which may have to be created -- for the contribution of
 the ``paper''.
-\end{newpart}
 
 %%% Local Variables:
 %%% mode: latex
diff --git a/adoptions/phenomena.tex b/adoptions/phenomena.tex
index ebf24e2..bbfa9ee 100644
--- a/adoptions/phenomena.tex
+++ b/adoptions/phenomena.tex
@@ -33,8 +33,8 @@ Mathematical documents traditionally have:
   \begin{inparaenum}[\em i\rm)]
   \item recapitulates or surveys concepts and results from the documents/knowledge commons
     to make the document self-contained (for its intended audience)
-  \item identifies any assumptions and give the ensuing contributions a sound
-    terminological basis
+  \item identifies any assumptions and gives the ensuing contributions a sound
+    terminological basis.
   \end{inparaenum}
 \item\label{md:contri} The \defemph{contributions} part, which contains the development of
   new knowledge in form of e.g. new insights, new interpretations of known concepts, new
@@ -42,7 +42,7 @@ Mathematical documents traditionally have:
 \item\label{md:eval} An \defemph{evaluation} of the contributions in terms of
   applicability or usability.
 \item\label{md:relwork} A discussion of \defemph{related work} which reviews the
-  contributions and their relation to existing approaches and results from the literature
+  contributions and their relation to existing approaches and results from the literature.
 \item\label{md:concl} A \defemph{conclusion} which summarizes the contribution with the
   benefit of hindsight and relates it to the claims made in the introduction.
 \item\label{md:aux} Literature references, an index, a glossary, etc. and possibly
@@ -50,7 +50,7 @@ Mathematical documents traditionally have:
 \end{compactenum}
 Even though the form or order of the structural elements may vary over publication venues,
 and certain elements may be implicit or even missing altogether, the overall structure is
-surprisingly stable.
+generally stable.
 
 It may be surprising that only one in eleven parts of a mathematical document -- the
 ``contributions'' -- arguably the largest -- is fully dedicated to transporting the
@@ -65,7 +65,7 @@ analyze in more detail next.
 
 \subsection{Common Ground/Recapitulation in Mathematical Research}\label{sec:cg-preprints}
 
-To get an overview over recaps in the literature, we randomly selected 15 papers from the
+To get an overview over recaps in the literature, we randomly selected 30 papers from the
 new submissions to \url{http://arxiv.org/archive/math} and analyzed their structure. All
 had a significant common ground section that recapitulates the central notions and fixes
 notations. We show two examples where the mathematics involved is relatively elementary.
@@ -114,7 +114,7 @@ terminology and definitions is not direct, but involves a choice.
     define multinets. Here we present them using pencils of plane curves.}''
 \end{example}
 
-The next example is not from our 15 examples, since we want to show an even more complex
+The next example is not from our 30 examples, since we want to show an even more complex
 situation.
 
 \begin{example}\label{ex:atm}
@@ -211,17 +211,17 @@ the courses become insular; how are students going to communicate with mathemati
 have learned their maths from other courses? This is where alluding to the literature
 comes in, by connecting the course notes with it.
 
-\begin{newpart}{MK: re-read}
-  The situation in mathematical textbooks is similar in structure to that in research
-  papers --perhaps more pronounced. Consider the following passage from Rudin's classical
-  introductory textbook to Functional Analysis~\cite[p. 6f]{Rudin:fa73}.
-
+\begin{example}\label{ex:rudin}
+The situation in mathematical textbooks is similar in structure to that in research
+papers --perhaps more pronounced. Consider the following passage from Rudin's classical
+introductory textbook to Functional Analysis~\cite[p. 6f]{Rudin:fa73}.
 \begin{labeledquote}\label{q:topspace}\sf
   \textbf{1.5 Topological spaces} A \emph{topological space} is a set $S$ in which a
   collection $\tau$ of subsets (called \emph{open sets}) has been specified, with the
   following properties: $S$ is open, $\emptyset$ is open, [\ldots] Such a collection is
   called a \emph{topology} on $S$. [\ldots]
 \end{labeledquote}
+\ednote{@MK: this looks like something is missing}
 and later -- vector spaces have been recapped earlier in section 1.4: 
 \begin{labeledquote}\sf\label{q:topvs}
 \textbf{1.6 Topological vector spaces} Suppose $\tau$ is a topology on a vector space $X$
@@ -241,16 +241,16 @@ do not add new knowledge or new results, but aggregate and organize the already
 ones, possibly reformulating them for a more uniform exposition. But still, one can
 distinguish recap parts -- as the ones above -- which are much more telegraphic in nature
 from the primary material presented in the textbook.
-\end{newpart}
+\end{example}
 
 
 \subsection{Common Ground in Formal Mathematics}
-Where applicable, common ground in formal mathematics is typical established via direct
+Where applicable, common ground in formal mathematics is typically established via direct
 imports of symbols, theorems, notations, etc.  Formal documents emphasize correctness and
 do not focus on human readability so they do not re-introduce concepts or provide,
 verbalizations of definitions.
 
-For instance, In Isabelle and Coq knowledge is organized \emph{Theories} and
+For instance, In Isabelle and Coq knowledge is organized in \emph{Theories} and
 \emph{Modules} which are effectively named sets of declarations.  The incremental
 development process is enabled via the \textsc{imports} and, respectively, \textsc{Require
   Import} statements that effectively opens a library module by name and enables its
@@ -267,7 +267,7 @@ ground section.
  The notation and terminology used in this paper have been introduced in the
 following papers: [4], [11], [12], [19], [9], [3], [5], [6], [21], [22], [1], [2], [7], [18],
 [20], [24], [25], [23], [16], [13], [14], [10], [15], and [8].
-[\ldots]2
+[\ldots]
 In this paper $T$ , $U$ are non empty topological spaces, $t$ is a point of $T$ , and
 $n$ is a natural number.
 \end{labeledquote}
-- 
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