\usepackage{booktabs}
\usepackage[noblocks]{authblk}
\usepackage[hyperfigures,bookmarks,colorlinks,citecolor=black,filecolor=black,linkcolor=black,urlcolor=black]{hyperref}
+\usepackage[capitalise]{cleveref}
\usepackage[sectionbib,sort&compress,numbers]{natbib}
\usepackage[nomargin,inline,draft]{fixme}
\usepackage[x11names,svgnames]{xcolor}
\newcommand{\OM}[1]{\textcolor{red}{\fxnote{OM: #1}}}
-%\SweaveOpts{prefix.string=pub_318_phys_bio_submission_figures_suppl/pub_318_phys_bio_sub_suppl_fig,pdf=TRUE,eps=TRUE}
\oddsidemargin 0.0in
\textwidth 6.5in
\raggedbottom
\begin{document}
\maketitle
-<<results=hide,echo=FALSE>>=
-require(lattice)
-require(grid)
-require(Hmisc)
-require(gridBase)
+<<load.libraries,echo=FALSE,results="hide",warning=FALSE,message=FALSE,error=FALSE,cache=FALSE>>=
+opts_chunk$set(dev="CairoPDF",out.width="\\columnwidth",out.height="0.7\\textheight",out.extra="keepaspectratio")
+opts_chunk$set(cache=TRUE, autodep=TRUE)
+options(scipen = -2, digits = 1)
+library("lattice")
+library("grid")
+library("Hmisc")
+library("gridBase")
to.latex <- function(x){
gsub("\\\\","\\\\\\\\",latexSN(x))
}
\renewcommand{\thetable}{S\@arabic\c@table}
\makeatother
-\section{Competition Implementation}
-\subsection{Implementation changes}
-
-\begin{itemize}
-\item settable maximum number of vesicles to track (default $10^4$)
-\item start with 1~L ($10^{-3}$~m$^3$) cube
-\item if at any point the number of vesicles exceeds the maximum
- number, chop the volume and environment molecule number into tenths,
- randomly select one tenth of the vesicles, and continue tracking.
-\item generations will be counted per vesicle, and each progeny
- vesicle will have a generation number one greater than the parental
- vesicle.
-\item 100 generations can result in as many as $2^{100}$
- ($\Sexpr{to.latex(format(digits=3,2^100))}$) vesicles or as few as
- 101 vesicles.
-\item Environment will use a specific number of each component instead
- of a constant concentration; as the number may be larger than
- \texttt{long long} ($2^{64}$), we use libgmp to handle an arbitrary
- precision number of components
-\end{itemize}
-
-\subsection{Infrastructure changes}
-\begin{itemize}
-\item Rewrite core bits in C
-\item Use libgmp for handling large ints
-\item Use openmpi to split the calculations out over multiple
- machines/processors and allow deploying to larger
- clusters/supercomputers
-\end{itemize}
+% \section{Competition Implementation}
+% \subsection{Implementation changes}
+%
+% \begin{itemize}
+% \item settable maximum number of vesicles to track (default $10^4$)
+% \item start with 1~L ($10^{-3}$~m$^3$) cube
+% \item if at any point the number of vesicles exceeds the maximum
+% number, chop the volume and environment molecule number into tenths,
+% randomly select one tenth of the vesicles, and continue tracking.
+% \item generations will be counted per vesicle, and each progeny
+% vesicle will have a generation number one greater than the parental
+% vesicle.
+% \item 100 generations can result in as many as $2^{100}$
+% ($\Sexpr{2^100}$) vesicles or as few as
+% 101 vesicles.
+% \item Environment will use a specific number of each component instead
+% of a constant concentration; as the number may be larger than
+% \texttt{long long} ($2^{64}$), we use libgmp to handle an arbitrary
+% precision number of components
+% \end{itemize}
+%
+% \subsection{Infrastructure changes}
+% \begin{itemize}
+% \item Rewrite core bits in C
+% \item Use libgmp for handling large ints
+% \item Use openmpi to split the calculations out over multiple
+% machines/processors and allow deploying to larger
+% clusters/supercomputers
+% \end{itemize}
and is dependent on the particular lipid type (PC, PS, SM, etc.). The
forward adjustment parameter, $k_{\mathrm{f}i\mathrm{adj}}$, is based on the
properties of the vesicle and the specific component (type, length,
-unsaturation, etc.) (see Equation~\ref{eq:kf_adj}, and
-Section~\ref{sec:kinetic_adjustments}).
+unsaturation, etc.) (see \cref{eq:kf_adj,sec:kinetic_adjustments}).
$\left[C_{i_\mathrm{monomer}}\right]$ is the molar concentration of
monomer of the $i$th component. $\left[S_\mathrm{vesicle}\right]$ is the surface
area of the vesicle per volume. The base backwards kinetic parameter
for the $i$th component is $k_{\mathrm{b}i}$ and its adjustment parameter
-$k_{\mathrm{b}i\mathrm{adj}}$ (see Equation~\ref{eq:kb_adj}, and
-Section~\ref{sec:kinetic_adjustments}).
+$k_{\mathrm{b}i\mathrm{adj}}$ (see \cref{eq:kb_adj,sec:kinetic_adjustments}).
$\left[C_{i_\mathrm{vesicle}}\right]$ is the molar concentration of
the $i$th component in the vesicle.
\subsection{Per-Lipid Kinetic Parameters}
-<<echo=FALSE,results=hide>>=
+<<kf_prime,echo=FALSE,results='hide'>>=
kf.prime <- c(3.7e6,3.7e6,5.1e7,3.7e6,2.3e6)
kf <- (as.numeric(kf.prime)*10^-3)/(63e-20*6.022e23)
@
% \centering
% \begin{tabular}{c c c c c c c c}
% \toprule
-% Type & $k_\mathrm{f}$ $\left(\frac{\mathrm{m}}{\mathrm{s}}\right)$ & $k'_\mathrm{f}$ $\left(\frac{1}{\mathrm{M} \mathrm{s}}\right)$ & $k_\mathrm{b}$ $\left(\mathrm{s}^{-1}\right)$ & Area $\left({\AA}^2\right)$ & Charge & $\mathrm{CF}1$ & Curvature \\
+% Type & $k_\mathrm{f}$ $\left(\frac{\mathrm{m}}{\mathrm{s}}\right)$ & $k'_\mathrm{f}$ $\left(\frac{1}{\mathrm{M} \mathrm{s}}\right)$ & $k_\mathrm{b}$ $\left(\mathrm{s}^{-1}\right)$ & Area $\left({Å}^2\right)$ & Charge & $\mathrm{CF}1$ & Curvature \\
% \midrule
% PC & $\Sexpr{to.latex(format(digits=3,scientific=TRUE,kf[1]))}$ & $3.7 \times 10^6$ & $2 \times 10^{-5}$ & 63 & 0 & 2 & 0.8 \\
% PS & $\Sexpr{to.latex(format(digits=3,scientific=TRUE,kf[2]))}$ & $3.7 \times 10^6$ & $1.25\times 10^{-5}$ & 54 & -1 & 0 & 1 \\
% \end{table}
%%% \DLA{I think we may just reduce these three sections; area, $k_\mathrm{f}$
-%%% and $k_\mathrm{b}$ to Table~\ref{tab:kinetic_parameters_lipid_types} with
+%%% and $k_\mathrm{b}$ to \cref{tab:kinetic_parameters_lipid_types} with
%%% references.}
%%%
%%% \RZ{Yes, but we also have to have then as comments the numbers that
to be 9.6 hr. As this is a first order reaction, and the primary
limiting step in exchange is lipid desorption, $k_\mathrm{b}$ for DMPC is
$k_{\mathrm{b}_\mathrm{PC}}=\frac{\log 2}{9.6 \times 60 \times 60} \approx
-\Sexpr{to.latex(format(log(2)/(9.6*60*60),digits=2))}
+\Sexpr{log(2)/(9.6*60*60)}
\mathrm{s}^{-1}$. We assume that $k_\mathrm{b}$ for SM is the same as for PC.
To estimate the $k_\mathrm{b}$ of PE and PS, we used the data from
\citet{Nichols1982:ret_amphiphile_transfer} who measured the rate of
\frac{k_{\mathrm{b}_\mathrm{PC}}\times\mathrm{PE}}{\mathrm{PC}} \approx
\frac{2\times 10^{-5}\,\mathrm{s}^{-1} \times
0.45\,\mathrm{min}^{-1}}{0.89\,\mathrm{min}^{-1}} \approx
-\Sexpr{to.latex(format(log(2)/(9.6*60*60)*0.45/0.89,digits=2))}$~$\mathrm{s}^{-1}$
+\Sexpr{log(2)/(9.6*60*60)*0.45/0.89}$~$\mathrm{s}^{-1}$
and likewise, $k_{\mathrm{b}_\mathrm{PS}}\approx
-\Sexpr{to.latex(format(log(2)/(9.6*60*60)*0.55/0.89,digits=3))}$~$\mathrm{s}^{-1}$.
+\Sexpr{log(2)/(9.6*60*60)*0.55/0.89}$~$\mathrm{s}^{-1}$.
The $k_\mathrm{b}$ of SM was determined using the work of
\citet{Bai1997:lipid_movementbodipy}, who measured spontaneous
transfer of C$_5$-DMB-SM and C$_5$-DMB-PC from donor and acceptor
$2.2\times10^{-3}$~$\mathrm{s}^{-1}$ respectively; using the ratio of
$k_\mathrm{b}$ of C$_5$-DMB-SM to the $k_\mathrm{b}$ of C$_5$-DMB-PC times the $k_\mathrm{b}$ of
PC ($\frac{3.4 \times 10^{-2}\mathrm{s}^{-1}}{2.2 \times
- 10^{-3}\mathrm{s}^{-1}}
-\Sexpr{to.latex(format(log(2)/(9.6*60*60),digits=2))}\mathrm{s}^{-1}$,
+ 10^{-3}\mathrm{s}^{-1}}\approx
+\Sexpr{log(2)/(9.6*60*60)}\mathrm{s}^{-1}$),
we obtain $k_{\mathrm{b}_\mathrm{SM}} \approx
-\Sexpr{to.latex(format(log(2)/(9.6*60*60)*3.4e-2/2.2e-3,digits=2,scientific=TRUE))}$.
+\Sexpr{log(2)/(9.6*60*60)*3.4e-2/2.2e-3}$.
In the case of CHOL, \citet{Jones1990:lipid_transfer} measured the
$t_{1/2}$ of [$^3$H] transfer from POPC vesicles and found it to be 41
minutes, leading to a $k_{\mathrm{b}_\mathrm{CHOL}} = \frac{\log 2}{41\times
60} \approx
-\Sexpr{to.latex(format(log(2)/(41*60),digits=2,scientific=TRUE))}$~$\mathrm{s}^{-1}$.
+\Sexpr{log(2)/(41*60)}$~$\mathrm{s}^{-1}$.
\subsubsection{Headgroup Surface Area for lipid types}
Different lipids have different headgroup surface areas, which contributes to
$\left[S_\mathrm{vesicle}\right]$. \citet{Smaby1997:pc_area_with_chol}
measured the surface area of POPC with a Langmuir film balance, and
-found it to be 63~$\AA^2$ at $30$~$\frac{\mathrm{mN}}{\mathrm{m}}$.
-Molecular dynamic simulations found an area of 54 $\AA^2$ for
+found it to be 63~Å$^2$ at $30$~$\frac{\mathrm{mN}}{\mathrm{m}}$.
+Molecular dynamic simulations found an area of 54 Å$^2$ for
DPPS\citep{Cascales1996:mds_dpps_area,Pandit2002:mds_dpps}, which is
-in agreement with the experimental value of 56~$\AA^2$ found using a
+in agreement with the experimental value of 56~Å$^2$ found using a
Langmuir balance by \citet{Demel1987:ps_area}.
\citet{Shaikh2002:pe_phase_sm_area} measured the area of SM using a
-Langmuir film balance, and found it to be 61~$\AA^2$. Using $^2$H NMR,
+Langmuir film balance, and found it to be 61~Å$^2$. Using $^2$H NMR,
\citet{Thurmond1991:area_of_pc_pe_2hnmr} found the area of
-DPPE-d$_{62}$ to be 55.4 $\AA^2$. \citet{Robinson1995:mds_chol_area}
-found an area for CHOL of 38~$\AA^2$ using molecular dynamic
+DPPE-d$_{62}$ to be 55.4 Å$^2$. \citet{Robinson1995:mds_chol_area}
+found an area for CHOL of 38~Å$^2$ using molecular dynamic
simulations.
% robinson's chol area is kind of crappy; they did it using MDS, but
simulations is around $1.5$, which leads to a $\Delta \Delta
G^\ddagger$ of $\Sexpr{to.latex(format(digits=3,to.kcal(2^1.5)))}
\frac{\mathrm{kcal}}{\mathrm{mol}}$, and a total range of possible
-values depicted in Figure~\ref{fig:unf_graph}.
+values depicted in \cref{fig:unf_graph}.
% \RZ{Explain here, or even earlier that the formulas were ad hoc
% adjusted to correspond to ``reasonable'' changes in the Eyring
% not include a term for it in this formalism.
-\setkeys{Gin}{width=6.4in}
\begin{figure}
-<<fig=TRUE,echo=FALSE,results=hide,width=10,height=5>>=
+<<unf_graph,echo=FALSE,results='hide',fig.width=10,fig.height=5,cache=FALSE>>=
layout(matrix(1:2,nrow=1,ncol=2))
curve(2^x,from=0,to=sd(c(0,4)),
xlab=expression(paste(stdev,group("(",italic(un[vesicle]),")"))),
$\Sexpr{format(digits=3,to.kcal(60^(-.165*-1)))}
\frac{\mathrm{kcal}}{\mathrm{mol}}$ to
$0\frac{\mathrm{kcal}}{\mathrm{mol}}$, and the total range of possible
-values seen in Figure~\ref{fig:chf_graph}.
+values seen in \cref{fig:chf_graph}.
\begin{figure}
-<<fig=TRUE,echo=FALSE,results=hide,width=14,height=7>>=
+<<chf_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
of $\Sexpr{format(digits=3,to.kcal(10^(0.13*0.213)))}
\frac{\mathrm{kcal}}{\mathrm{mol}}$. This is a consequence of the
relatively matched curvatures in our environment. The full range of
-$cu_\mathrm{f}$ values possible are shown in Figure~\ref{fig:cuf_graph}.
+$cu_\mathrm{f}$ values possible are shown in \cref{fig:cuf_graph}.
% 1.5 to 0.75 3 to 0.33
\begin{figure}
-<<fig=TRUE,echo=FALSE,results=hide,width=14,height=7>>=
+<<cuf_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
\begin{figure}
-<<fig=TRUE,echo=FALSE,results=hide,width=14,height=5>>=
+<<lf_graph,echo=FALSE,results='hide',fig.width=14,fig.height=5>>=
layout(matrix(1:2,nrow=1,ncol=2))
curve(2^x,from=0,to=sd(c(12,24)),
xlab=expression(paste(stdev,group("(",italic(l[vesicle]),")"))),
\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with 0 unsaturation
to
$\Sexpr{format(digits=3,to.kcal(7^(1-1/(5*(2^-1.7-2^-4)^2+1))))}\frac{\mathrm{kcal}}{\mathrm{mol}}$
-for monomers with 4 unsaturations. See Figure~\ref{fig:unb_graph} for
+for monomers with 4 unsaturations. See \cref{fig:unb_graph} for
the full range of possible values.
\begin{figure}
-<<fig=TRUE,echo=FALSE,results=hide,width=14,height=7>>=
+<<unb_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
$\Sexpr{format(digits=3,to.kcal(20^(-.164*-1)))}
\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with charge $-1$ to
$0\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with charge $0$.
-See Figure~\ref{fig:chb_graph} for the full range of possible values
+See \cref{fig:chb_graph} for the full range of possible values
of $ch_\mathrm{b}$.
\begin{figure}
-<<fig=TRUE,echo=FALSE,results=hide,width=14,height=7>>=
+<<chb_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
for monomers with curvature 1.3 to
$0\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with curvature near
1. The full range of values possible for $cu_\mathrm{b}$ are shown in
-Figure~\ref{fig:cub_graph}
+\cref{fig:cub_graph}
% \RZ{What about the opposite curvatures that actually do fit to each
% other?}
\begin{figure}
-<<fig=TRUE,echo=FALSE,results=hide,width=14,height=7>>=
+<<cub_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
$\Sexpr{format(digits=3,to.kcal(3.2^abs(24-17.75)))}\frac{\mathrm{kcal}}{\mathrm{mol}}$
for monomers with length 24 to $0\frac{\mathrm{kcal}}{\mathrm{mol}}$
for monomers with length near 18. The full range of possible values of
-$l_\mathrm{b}$ are shown in Figure~\ref{fig:lb_graph}
+$l_\mathrm{b}$ are shown in \cref{fig:lb_graph}
% (for methods? From McLean84LIB: The activation free energies and free
% energies of transfer from self-micelles to water increase by 2.2 and
\begin{figure}
-<<fig=TRUE,echo=FALSE,results=hide,width=14,height=7>>=
+<<lb_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
for monomers with complex formation $2$ to
$0\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with complex
formation $0$. The full range of possible values for $CF1_\mathrm{b}$ are
-depicted in Figure~\ref{fig:cf1b_graph}.
+depicted in \cref{fig:cf1b_graph}.
\begin{figure}
-<<fig=TRUE,echo=FALSE,results=hide,width=14,height=7>>=
+<<cf1b_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
Determining the number of molecules to add to the lipid membrane
($n_i$) requires knowing $k_{\mathrm{f}i_\mathrm{adj}}$, the surface area of the
-vesicle $S_\mathrm{vesicle}$ (see Section \ref{sec:ves_prop}), the time interval
+vesicle $S_\mathrm{vesicle}$ (see \cref{sec:ves_prop}), the time interval
$dt$ during which lipids are added, the base $k_{\mathrm{f}i}$, and the
concentration of the monomer in the environment
-$\left[C_{i\mathrm{vesicle}}\right]$ (see Equation~\ref{eq:state}).
-$k_{\mathrm{f}i\mathrm{adj}}$ is calculated (see Equation~\ref{eq:kf_adj}) based on the
+$\left[C_{i\mathrm{vesicle}}\right]$ (see \cref{eq:state}).
+$k_{\mathrm{f}i\mathrm{adj}}$ is calculated (see \cref{eq:kf_adj}) based on the
vesicle properties and their hypothesized effect on the rate (in as
many cases as possible, experimentally based)
-(see Section~\ref{sec:kinetic_adjustments} for details). $dt$ can be varied
-(see Section~\ref{sec:step_duration}), but for a given step is constant. This
+(see \cref{sec:kinetic_adjustments} for details). $dt$ can be varied
+(see \cref{sec:step_duration}), but for a given step is constant. This
leads to the following:
$n_i = k_{\mathrm{f}i}k_{\mathrm{f}i_\mathrm{adj}}\left[C_{i_\mathrm{monomer}}\right]S_\mathrm{vesicle}\mathrm{N_A}dt$
immediately before and immediately after splitting are stored
to produce later output.
-\section{Analyzing output}
-
-The analysis of output is handled by a separate perl program which
-shares many common modules with the simulation program. Current output
-includes simulation progress, summary tables, summary statistics, and
-various graphs.
-
-\subsection{PCA plots}
-
-Two major groups of axes that contribute to vesicle variation between
-subsequent generations are the components and properties of vesicles.
-Each component in a vesicle is an axis on its own; it can be measured
-either as an absolute number of molecules in each component, or the
-fraction of molecules of that component over the total number of
-molecules; the second approach is often more convenient, as it allows
-vesicles with different number of molecules to be directly compared
-(though it hides any effect of vesicle size).
-
-In order to visualize the variation between and transition of
-subsequent generations of vesicles from their initial state in the
-simulation, to their final state at the termination of the simulation,
-we plot the projection of the generations onto the two principle PCA
-axes (and alternatively, any pairing of the axes).
-
-\subsection{Carpet plots}
-
-Carpet plots show the distance/similarity between the composition or
-properties of all generations in a single run. The difference between
-each group of vesicle can be calculated using Euclidean distance
-(properties and compositions) or H similarity (composition only). We
-must use Euclidean distance for properties because the H distance
-metric is invalid when comparing negative vector elements to positive
-vector elements.
-
-In addition to showing distance or similarity, carpet plots also
-depict propersomes and composomes as square boxes on the diagonals and
-propertypes and compotypes as rectangles off the diagonals, each
-propertype or compotype with a distinct color.
-
-\subsection{Propersomes, propertypes, composomes and compotypes}
-
-A generation is considered to be a propersome if it is less than $0.6$
-units (by Euclidean distance of normalized properties) away from the
-generation immediately following and preceding. Likewise, a generation
-is in a composome if its H similarity is more than $0.9$ (by the
-normalized H metric) from the preceding and following generations.
-Propersomes and composomes are then assigned to propertypes and
-compotypes using Paritioning Around Medioids
-(PAM). All values of $k$ between 2 and 15
-(or the number of propersomes and composomes, if that is less than 15)
-are tried, and the clustering with the smallest
-silhouette~\citep{Rousseeuw1987:silhouettes} is chosen as the ideal
-clustering~\citep{Shenhav2005:pgard}.
+% \section{Analyzing output}
+%
+% The analysis of output is handled by a separate perl program which
+% shares many common modules with the simulation program. Current output
+% includes simulation progress, summary tables, summary statistics, and
+% various graphs.
+%
+% \subsection{PCA plots}
+%
+% Two major groups of axes that contribute to vesicle variation between
+% subsequent generations are the components and properties of vesicles.
+% Each component in a vesicle is an axis on its own; it can be measured
+% either as an absolute number of molecules in each component, or the
+% fraction of molecules of that component over the total number of
+% molecules; the second approach is often more convenient, as it allows
+% vesicles with different number of molecules to be directly compared
+% (though it hides any effect of vesicle size).
+%
+% In order to visualize the variation between and transition of
+% subsequent generations of vesicles from their initial state in the
+% simulation, to their final state at the termination of the simulation,
+% we plot the projection of the generations onto the two principle PCA
+% axes (and alternatively, any pairing of the axes).
+%
+% \subsection{Carpet plots}
+%
+% Carpet plots show the distance/similarity between the composition or
+% properties of all generations in a single run. The difference between
+% each group of vesicle can be calculated using Euclidean distance
+% (properties and compositions) or H similarity (composition only). We
+% must use Euclidean distance for properties because the H distance
+% metric is invalid when comparing negative vector elements to positive
+% vector elements.
+%
+% In addition to showing distance or similarity, carpet plots also
+% depict propersomes and composomes as square boxes on the diagonals and
+% propertypes and compotypes as rectangles off the diagonals, each
+% propertype or compotype with a distinct color.
+%
+% \subsection{Propersomes, propertypes, composomes and compotypes}
+%
+% A generation is considered to be a propersome if it is less than $0.6$
+% units (by Euclidean distance of normalized properties) away from the
+% generation immediately following and preceding. Likewise, a generation
+% is in a composome if its H similarity is more than $0.9$ (by the
+% normalized H metric) from the preceding and following generations.
+% Propersomes and composomes are then assigned to propertypes and
+% compotypes using Paritioning Around Medioids
+% (PAM). All values of $k$ between 2 and 15
+% (or the number of propersomes and composomes, if that is less than 15)
+% are tried, and the clustering with the smallest
+% silhouette~\citep{Rousseeuw1987:silhouettes} is chosen as the ideal
+% clustering~\citep{Shenhav2005:pgard}.
\bibliographystyle{unsrtnat}
projects / ool / lipid_simulation_formalism.git / blobdiff