From 607d06bef7a238f0ed7f2e72ac3860044827f2cc Mon Sep 17 00:00:00 2001
From: Claus Jonathan Fritzemeier <clausjonathan.fritzemeier@hhu.de>
Date: Wed, 17 Dec 2014 16:00:28 +0100
Subject: [PATCH] tidy up
---
inst/doc/sybil.R | 565 -----------------
inst/doc/sybil.Rnw | 1494 --------------------------------------------
2 files changed, 2059 deletions(-)
delete mode 100644 inst/doc/sybil.R
delete mode 100644 inst/doc/sybil.Rnw
diff --git a/inst/doc/sybil.R b/inst/doc/sybil.R
deleted file mode 100644
index 2b46b6f..0000000
--- a/inst/doc/sybil.R
+++ /dev/null
@@ -1,565 +0,0 @@
-### R code from vignette source 'sybil.Rnw'
-### Encoding: UTF-8
-
-###################################################
-### code chunk number 1: sybil.Rnw:433-434
-###################################################
-library(sybil)
-
-
-###################################################
-### code chunk number 2: sybil.Rnw:443-444
-###################################################
-library(help = "sybil")
-
-
-###################################################
-### code chunk number 3: sybil.Rnw:448-449
-###################################################
-help(doubleGeneDel)
-
-
-###################################################
-### code chunk number 4: sybil.Rnw:453-454
-###################################################
-help.search("flux variability analysis")
-
-
-###################################################
-### code chunk number 5: sybil.Rnw:457-458 (eval = FALSE)
-###################################################
-## vignette("sybil")
-
-
-###################################################
-### code chunk number 6: sybil.Rnw:479-480
-###################################################
-mp <- system.file(package = "sybil", "extdata")
-
-
-###################################################
-### code chunk number 7: sybil.Rnw:483-484
-###################################################
-mod <- readTSVmod(prefix = "Ec_core", fpath = mp, quoteChar = "\"")
-
-
-###################################################
-### code chunk number 8: sybil.Rnw:504-505 (eval = FALSE)
-###################################################
-## modelorg2tsv(mod, prefix = "Ec_core")
-
-
-###################################################
-### code chunk number 9: sybil.Rnw:510-511
-###################################################
-data(Ec_core)
-
-
-###################################################
-### code chunk number 10: sybil.Rnw:524-525
-###################################################
-ex <- findExchReact(Ec_core)
-
-
-###################################################
-### code chunk number 11: sybil.Rnw:528-530
-###################################################
-upt <- uptReact(ex)
-ex[upt]
-
-
-###################################################
-### code chunk number 12: sybil.Rnw:536-538
-###################################################
-mod <- changeBounds(Ec_core, ex[c("EX_glc(e)", "EX_lac_D(e)")], lb = c(0, -10))
-findExchReact(mod)
-
-
-###################################################
-### code chunk number 13: sybil.Rnw:557-558
-###################################################
-optL <- optimizeProb(Ec_core, algorithm = "fba", retOptSol = FALSE)
-
-
-###################################################
-### code chunk number 14: sybil.Rnw:563-564
-###################################################
-opt <- optimizeProb(Ec_core, algorithm = "fba", retOptSol = TRUE)
-
-
-###################################################
-### code chunk number 15: sybil.Rnw:570-571
-###################################################
-lp_obj(opt)
-
-
-###################################################
-### code chunk number 16: sybil.Rnw:575-576
-###################################################
-checkOptSol(opt)
-
-
-###################################################
-### code chunk number 17: sybil.Rnw:590-591
-###################################################
-fba <- optimizeProb(Ec_core, algorithm = "fba")
-
-
-###################################################
-### code chunk number 18: sybil.Rnw:594-595
-###################################################
-mod_obj(fba)
-
-
-###################################################
-### code chunk number 19: sybil.Rnw:599-600
-###################################################
-mtf <- optimizeProb(Ec_core, algorithm = "mtf", wtobj = mod_obj(fba))
-
-
-###################################################
-### code chunk number 20: sybil.Rnw:603-604
-###################################################
-lp_obj(mtf)
-
-
-###################################################
-### code chunk number 21: sybil.Rnw:609-611
-###################################################
-nvar(fluxdist(fba))
-nvar(fluxdist(mtf))
-
-
-###################################################
-### code chunk number 22: sybil.Rnw:616-618
-###################################################
-help("sysBiolAlg_fba-class")
-help("sysBiolAlg_mtf-class")
-
-
-###################################################
-### code chunk number 23: sybil.Rnw:621-623
-###################################################
-?fba
-?mtf
-
-
-###################################################
-### code chunk number 24: sybil.Rnw:628-630
-###################################################
-fl <- getFluxDist(mtf)
-length(fl)
-
-
-###################################################
-### code chunk number 25: sybil.Rnw:635-637
-###################################################
-fd <- getFluxDist(mtf, ex)
-getNetFlux(fd)
-
-
-###################################################
-### code chunk number 26: sybil.Rnw:642-643
-###################################################
-mod_obj(mtf)
-
-
-###################################################
-### code chunk number 27: sybil.Rnw:654-655
-###################################################
-ko <- optimizeProb(Ec_core, gene = "b2276", lb = 0, ub = 0)
-
-
-###################################################
-### code chunk number 28: sybil.Rnw:676-678
-###################################################
-ko <- optimizeProb(Ec_core, gene = "b2276", lb = 0, ub = 0,
- algorithm = "lmoma", wtflux = getFluxDist(mtf))
-
-
-###################################################
-### code chunk number 29: sybil.Rnw:694-697 (eval = FALSE)
-###################################################
-## ko <- optimizeProb(Ec_core, gene = "b2276", lb = 0, ub = 0,
-## algorithm = "room", wtflux = getFluxDist(mtf),
-## solverParm = list(PRESOLVE = GLP_ON))
-
-
-###################################################
-### code chunk number 30: sybil.Rnw:729-730
-###################################################
-opt <- oneGeneDel(Ec_core)
-
-
-###################################################
-### code chunk number 31: sybil.Rnw:744-745
-###################################################
-checkOptSol(opt)
-
-
-###################################################
-### code chunk number 32: sybil.Rnw:749-750
-###################################################
-plot(opt, nint = 20)
-
-
-###################################################
-### code chunk number 33: sybil.Rnw:756-759
-###################################################
-opt <- oneGeneDel(Ec_core, algorithm = "lmoma", wtflux = getFluxDist(mtf))
-checkOptSol(opt)
-plot(opt, nint = 20)
-
-
-###################################################
-### code chunk number 34: sybil.Rnw:765-766
-###################################################
-opt <- geneDeletion(Ec_core)
-
-
-###################################################
-### code chunk number 35: sybil.Rnw:769-771 (eval = FALSE)
-###################################################
-## opt2 <- geneDeletion(Ec_core, combinations = 2)
-## opt3 <- geneDeletion(Ec_core, combinations = 3)
-
-
-###################################################
-### code chunk number 36: sybil.Rnw:787-789
-###################################################
-opt <- fluxVar(Ec_core, percentage = 80, verboseMode = 0)
-plot(opt)
-
-
-###################################################
-### code chunk number 37: sybil.Rnw:817-819
-###################################################
-opt <- robAna(Ec_core, ctrlreact = "EX_o2(e)", verboseMode = 0)
-plot(opt)
-
-
-###################################################
-### code chunk number 38: sybil.Rnw:836-843
-###################################################
-Ec_core_wo_glc <- changeUptake(Ec_core, off = "glc_D[e]")
-opt <- phpp(Ec_core_wo_glc,
- ctrlreact = c("EX_succ(e)", "EX_o2(e)"),
- redCosts = TRUE,
- numP = 25,
- verboseMode = 0)
-plot(opt)
-
-
-###################################################
-### code chunk number 39: phpp_rf
-###################################################
-plot(opt, "EX_succ(e)")
-
-
-###################################################
-### code chunk number 40: phpp_rs
-###################################################
-plot(opt, "EX_o2(e)")
-
-
-###################################################
-### code chunk number 41: sybil.Rnw:877-878
-###################################################
-opt <- oneGeneDel(Ec_core, algorithm = "fba", fld = "all")
-
-
-###################################################
-### code chunk number 42: sybil.Rnw:881-882
-###################################################
-sum <- summaryOptsol(opt, Ec_core)
-
-
-###################################################
-### code chunk number 43: sybil.Rnw:896-897
-###################################################
-printExchange(sum, j = c(1:50), dense = TRUE)
-
-
-###################################################
-### code chunk number 44: sybil.Rnw:912-916
-###################################################
-ref <- optimizeProb(Ec_core)
-opt <- oneGeneDel(Ec_core)
-let <- lethal(opt, wt = mod_obj(ref))
-nletid <- c(1:length(allGenes(Ec_core)))[! let]
-
-
-###################################################
-### code chunk number 45: sybil.Rnw:925-926 (eval = FALSE)
-###################################################
-## gmat <- combn(nletid, 3)
-
-
-###################################################
-### code chunk number 46: sybil.Rnw:931-932 (eval = FALSE)
-###################################################
-## opt <- multiDel(Ec_core, nProc = 4, todo = "geneDeletion", del1 = gmat)
-
-
-###################################################
-### code chunk number 47: sybil.Rnw:943-944 (eval = FALSE)
-###################################################
-## mapply(checkOptSol, opt)
-
-
-###################################################
-### code chunk number 48: sybil.Rnw:955-957
-###################################################
-opt <- optimizeProb(Ec_core, poCmd = list("getRedCosts"))
-postProc(opt)
-
-
-###################################################
-### code chunk number 49: sybil.Rnw:993-994 (eval = FALSE)
-###################################################
-## optimizeProb(Ec_core, method = "exact")
-
-
-###################################################
-### code chunk number 50: sybil.Rnw:997-998 (eval = FALSE)
-###################################################
-## optimizeProb(Ec_core, solver = "cplexAPI", method = "dualopt")
-
-
-###################################################
-### code chunk number 51: sybil.Rnw:1021-1024 (eval = FALSE)
-###################################################
-## opt <- oneGeneDel(Ec_core,
-## solverParm = list(TM_LIM = 1000,
-## PRESOLVE = GLP_ON))
-
-
-###################################################
-### code chunk number 52: sybil.Rnw:1037-1041 (eval = FALSE)
-###################################################
-## opt <- optimizeProb(Ec_core,
-## solverParm = list(CPX_PARAM_SCRIND = CPX_ON,
-## CPX_PARAM_EPRHS = 1E-09),
-## solver = "cplexAPI")
-
-
-###################################################
-### code chunk number 53: sybil.Rnw:1060-1064 (eval = FALSE)
-###################################################
-## opt <- optimizeProb(Ec_core,
-## solverParm = list(verbose = "full",
-## timeout = 10),
-## solver = "lpSolveAPI")
-
-
-###################################################
-### code chunk number 54: sybil.Rnw:1078-1079
-###################################################
-help(SYBIL_SETTINGS)
-
-
-###################################################
-### code chunk number 55: sybil.Rnw:1101-1102 (eval = FALSE)
-###################################################
-## SYBIL_SETTINGS("parameter name", value)
-
-
-###################################################
-### code chunk number 56: sybil.Rnw:1107-1108 (eval = FALSE)
-###################################################
-## SYBIL_SETTINGS("parameter name")
-
-
-###################################################
-### code chunk number 57: sybil.Rnw:1113-1114 (eval = FALSE)
-###################################################
-## SYBIL_SETTINGS()
-
-
-###################################################
-### code chunk number 58: sybil.Rnw:1129-1130
-###################################################
-SYBIL_SETTINGS("SOLVER", "cplexAPI", loadPackage = FALSE)
-
-
-###################################################
-### code chunk number 59: sybil.Rnw:1136-1137
-###################################################
-SYBIL_SETTINGS("METHOD")
-
-
-###################################################
-### code chunk number 60: sybil.Rnw:1140-1141
-###################################################
-SYBIL_SETTINGS("SOLVER", "glpkAPI")
-
-
-###################################################
-### code chunk number 61: sybil.Rnw:1144-1145
-###################################################
-SYBIL_SETTINGS("METHOD")
-
-
-###################################################
-### code chunk number 62: sybil.Rnw:1180-1182
-###################################################
-data(Ec_core)
-Ec_core
-
-
-###################################################
-### code chunk number 63: sybil.Rnw:1186-1187
-###################################################
-help("modelorg")
-
-
-###################################################
-### code chunk number 64: sybil.Rnw:1194-1195
-###################################################
-react_num(Ec_core)
-
-
-###################################################
-### code chunk number 65: sybil.Rnw:1198-1199
-###################################################
-id <- react_id(Ec_core)
-
-
-###################################################
-### code chunk number 66: sybil.Rnw:1202-1203
-###################################################
-react_id(Ec_core)[13] <- "biomass"
-
-
-###################################################
-### code chunk number 67: sybil.Rnw:1207-1209
-###################################################
-cg <- gray(0:8/8)
-image(S(Ec_core), col.regions = c(cg, rev(cg)))
-
-
-###################################################
-### code chunk number 68: sybil.Rnw:1222-1223 (eval = FALSE)
-###################################################
-## mod <- readTSVmod(reactList = "reactionList.txt")
-
-
-###################################################
-### code chunk number 69: sybil.Rnw:1247-1248
-###################################################
-help("optsol")
-
-
-###################################################
-### code chunk number 70: sybil.Rnw:1252-1254
-###################################################
-os <- optimizeProb(Ec_core)
-is(os)
-
-
-###################################################
-### code chunk number 71: sybil.Rnw:1257-1258
-###################################################
-lp_obj(os)
-
-
-###################################################
-### code chunk number 72: sybil.Rnw:1261-1262
-###################################################
-getFluxDist(os)
-
-
-###################################################
-### code chunk number 73: sybil.Rnw:1307-1308
-###################################################
-lp <- optObj(solver = "glpkAPI", method = "exact")
-
-
-###################################################
-### code chunk number 74: sybil.Rnw:1332-1333
-###################################################
-lp <- initProb(lp)
-
-
-###################################################
-### code chunk number 75: sybil.Rnw:1337-1342
-###################################################
-cm <- Matrix(c(0.5, 2, 1, 1), nrow = 2)
-loadLPprob(lp, nCols = 2, nRows = 2, mat = cm,
- lb = c(0, 0), ub = rep(1000, 2), obj = c(1, 1),
- rlb = c(0, 0), rub = c(4.5, 9), rtype = c("U", "U"),
- lpdir = "max")
-
-
-###################################################
-### code chunk number 76: sybil.Rnw:1347-1348
-###################################################
-lp
-
-
-###################################################
-### code chunk number 77: sybil.Rnw:1351-1352
-###################################################
-status <- solveLp(lp)
-
-
-###################################################
-### code chunk number 78: sybil.Rnw:1355-1356
-###################################################
-getMeanReturn(code = status, solver = solver(lp))
-
-
-###################################################
-### code chunk number 79: sybil.Rnw:1359-1361
-###################################################
-status <- getSolStat(lp)
-getMeanStatus(code = status, solver = solver(lp))
-
-
-###################################################
-### code chunk number 80: sybil.Rnw:1365-1367
-###################################################
-getObjVal(lp)
-getFluxDist(lp)
-
-
-###################################################
-### code chunk number 81: sybil.Rnw:1370-1371
-###################################################
-getRedCosts(lp)
-
-
-###################################################
-### code chunk number 82: sybil.Rnw:1374-1376
-###################################################
-delProb(lp)
-lp
-
-
-###################################################
-### code chunk number 83: sybil.Rnw:1407-1409
-###################################################
-ec <- sysBiolAlg(Ec_core, algorithm = "fba")
-is(ec)
-
-
-###################################################
-### code chunk number 84: sybil.Rnw:1414-1415
-###################################################
-opt <- optimizeProb(ec)
-
-
-###################################################
-### code chunk number 85: sybil.Rnw:1422-1425
-###################################################
-ecr <- sysBiolAlg(Ec_core, algorithm = "room", wtflux = opt$fluxes)
-is(ecr)
-ecr
-
-
-###################################################
-### code chunk number 86: sybil.Rnw:1474-1475 (eval = FALSE)
-###################################################
-## promptSysBiolAlg(algorithm = "foo")
-
-
diff --git a/inst/doc/sybil.Rnw b/inst/doc/sybil.Rnw
deleted file mode 100644
index a054974..0000000
--- a/inst/doc/sybil.Rnw
+++ /dev/null
@@ -1,1494 +0,0 @@
-\documentclass[a4paper,headings=small,captions=tableheading]{scrartcl}
-\usepackage[english]{babel}
-\usepackage[T1]{fontenc}
-\usepackage[utf8]{inputenc}
-\usepackage{textcomp,lmodern}
-\typearea[current]{last}
-\usepackage{fixltx2e,mparhack,mathdots}
-
-
-\usepackage{xspace}
-\usepackage{paralist}
-\usepackage{footmisc}
-\usepackage{booktabs}
-\usepackage{natbib}
-\usepackage{hyperref}
-
-\usepackage{microtype}
-
-\newcommand{\Comp}[1]{\texttt{#1}}
-
-\addtolength{\skip\footins}{0.5\baselineskip}
-\usepackage{fnpos}
-
-
-\hypersetup{
- pdftitle = {sybil -- Efficient Constrained Based Modelling in R},
- pdfauthor = {Gabriel Gelius-Dietrich},
- pdfsubject = {constrained based modelling},
- pdfkeywords = {Optimization, FBA, MOMA, ROOM},
- pdfborder = {0 0 0},
- pdfhighlight = {/N}
-}
-
-
-% glyphs in pdf figures
-\pdfinclusioncopyfonts=1
-
-\newcommand{\pkg}[1]{\emph{#1}}
-\newcommand{\pkgname}{\pkg{sybil}\xspace}
-\newcommand{\prgname}[1]{\textsc{#1}}
-
-%\newcommand{\cplex}{IBM\textregistered{} %
-% ILOG\textregistered{} CPLEX\textregistered{}%
-%}
-\newcommand{\cplex}{IBM ILOG CPLEX}
-
-\title{sybil -- Efficient Constrained Based Modelling in R}
-%\VignetteIndexEntry{sybil -- Efficient Constrained Based Modelling in R}
-%\VignettePackage{sybil}
-\author{Gabriel Gelius-Dietrich}
-
-
-% ---------------------------------------------------------------------------- %
-% entire document
-% ---------------------------------------------------------------------------- %
-
-\begin{document}
-
-
-\maketitle
-
-\tableofcontents
-
-% ---------------------------------------------------------------------------- %
-
-\section{Introduction}
-
-The R-package \pkgname{} is a Systems Biology Library for R, implementing
-algorithms for constraint based analysis of metabolic networks.
-Among other functions, \pkgname currently provides efficient methods for
-flux-balance analysis (FBA), minimization of metabolic adjustment (MOMA),
-regulatory on/off minimization (ROOM), flux variability Analysis and robustness
-Analysis.
-The package \pkgname{} makes use of the sparse matrix implementation in the
-R-package \pkg{Matrix}.
-
-
-% ---------------------------------------------------------------------------- %
-
-\section{Installation}
-
-The package \pkgname{} itself depends on an existing installation of the
-package \pkg{Matrix}. In order to run optimizations, at least one of the
-following additional R-packages and the corresponding libraries are required:
-\pkg{glpkAPI}, \pkg{cplexAPI}, \pkg{clpAPI} or \pkg{lpSolveAPI}.
-These packages are available from
-CRAN\footnote{\url{http://cran.r-project.org/}\label{cranfoot}}.
-Additionally, \pkg{sybilGUROBI}---supporting the Gurobi
-optimizer\footnote{\url{http://www.gurobi.com}}---is available on request.
-
-
-% ---------------------------------------------------------------------------- %
-
-\section{Input files}
-\label{inputformats}
-
-Input files for \pkgname are text files containing a description of the
-metabolic model to analyze. These descriptions are basically lists of
-reactions.
-Two fundamentally different types of text files are supported:
-\begin{inparaenum}[i)]
-\item in tabular form (section~\ref{tabmod}), or
-\item in SBML format (section~\ref{sbmlmod}).
-\end{inparaenum}
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Tabular form} \label{tabmod}
-
-Models in tabular form can be read using the function \Comp{readTSVmod()} and
-written using the function \Comp{modelorg2tsv()}.
-Each metabolic model description consists of three tables:
-\begin{enumerate}
-\item A model description, containing a model name, the compartments of the
- model and so on (section~\ref{moddesc}).
-\item A list of all metabolites (section~\ref{metlist}).
-\item A list of all reactions (section~\ref{reactlist}).
-\end{enumerate}
-A model must contain at least a list of all reactions. All other tables are
-optional. The tables contain columns storing the required data. Some of these
-columns are optional, but if a certain table exists, there must be a minimal set
-of columns. The column names (the first line in each file) are used as keywords
-and cannot be changed.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{Field and entry delimiter} \label{delim}
-
-There are two important variables in connection with text based tables: The
-fields (columns) of the tables are separated by the value stored in the variable
-\Comp{fielddelim}. If a single entry of a field contains a list of entries,
-they are separated by the value of the variable \Comp{entrydelim}.
-The default values are given table~\ref{delimtab}.
-\begin{table}
-\centering
-\caption{Field and entry delimiters and their default values.}
-\label{delimtab}
-\begin{tabular}{cc}
-\toprule
-variable & default value \\
-\midrule
-\Comp{fielddelim} & \Comp{\textbackslash t} \\
-\Comp{entrydelim} & \Comp{,\textvisiblespace} \\
-\bottomrule
-\end{tabular}
-\end{table}
-The default behavior is, that the columns of each table are separated by a
-single \Comp{tab} character. If a column entry holds more than one entry, they
-are separated by a comma followed by a single
-whitespace \Comp{\textvisiblespace} (not a tab!).
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{Model description} \label{moddesc}
-Every column in this table can have at most one entry, meaning each entry will
-be a single character string. If a model description file is used, there should
-be at least the two columns \Comp{name} and \Comp{id}. If they are
-missing---or if no model description file is used---they will be set to the file
-name of the reaction list, which must be there (any file name extension and the
-string \Comp{\_react} at the end of the file name, will be removed). The model
-description file contains the following fields:
-\begin{description}
-
-\item[name]
-A single character string giving the model name. If this field is empty, the
-filename of the reaction list is used.
-
-\item[id]
-A single character string giving the model id. If this field is empty, the
-filename of the reaction list is used.
-
-\item[description]
-A single character string giving a model description (optional).
-
-\item[compartment]
-A single character string containing the compartment names. The names must be
-separated by the value of \Comp{fielddelim} (optional, see section~\ref{delim}).
-
-\item[abbreviation]
-A single character string containing the compartment abbreviations. The
-abbreviations must be in square brackets and separated by the value of
-\Comp{fielddelim} as mentioned above (optional).
-
-\item[Nmetabolites]
-A single integer value giving the number of metabolites in the model (optional).
-
-\item[Nreactions]
-A single integer value giving the number of reactions in the model (optional).
-
-\item[Ngenes]
-A single integer value giving the number of unique, independent genes in the
-model (optional).
-
-\item[Nnnz]
-A single integer value giving the number of non-zero elements in the
-stoichiometric matrix of the model (optional).
-
-\end{description}
-The file \Comp{Ec\_core\_desc.tsv} (in \Comp{extdata/}) contains an exemplarily
-table for the core energy metabolism of \emph{E.~coli}
-\citep{Palsson:2006fk,Orth:2010fk}.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{Metabolite list} \label{metlist}
-
-This table is used in order to match metabolite id's given in the list of
-reactions to long metabolite names. This table is optional, but if it is used,
-the columns \Comp{abbreviation} and \Comp{name} should not be empty.
-\begin{description}
-
-\item[abbreviation]
-A list of single character strings containing the metabolite abbreviations.
-
-\item[name]
-A list of single character strings containing the metabolite names.
-
-\item[compartment]
-A list of character strings containing the metabolite compartment names. Each
-entry can contain more than one compartment name, separated by \Comp{fielddelim}
-(optional, currently unused).
-
-\end{description}
-The file \Comp{Ec\_core\_met.tsv} (in \Comp{extdata/}) contains an exemplarily
-table for the core energy metabolism of \emph{E.~coli}
-\citep{Palsson:2006fk,Orth:2010fk}.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{Reaction list} \label{reactlist}
-
-This table contains the reaction equations used in the metabolic network.
-\begin{description}
-
-\item[abbreviation]
-A list of single character strings containing the reaction abbreviations
-(optional, if empty, a warning will be produced). Entries in the field
-abbreviation are used as reaction id's, so they must be unique. If they are
-missing, they will be set to $v_i,\ i \in \{1, \dots, n\}\ \forall i$ with
-$n$ being the total number of reactions.
-
-\item[name]
-A list of single character strings containing the reaction names (optional, if
-empty, the reaction id's (abbreviations) are used as reaction names.
-
-\item[equation]
-A list of single character strings containing the reaction equation. See
-section~\ref{writeEQ} for a description of reaction equation strings.
-
-\item[reversible]
-A list of single character strings indicating if a particular reaction is
-reversible or not. If the entry is set to \Comp{Reversible} or \Comp{TRUE}, the
-reaction is considered as reversible, otherwise not. If this column is not used,
-the arrow symbol of the reaction string is used (optional, see
-section~\ref{writeEQ}).
-
-\item[compartment]
-A list of character strings containing the compartment names in which the
-current reaction takes place. Each entry can contain more than one name,
-separated by \Comp{fielddelim} (optional, currently unused).
-
-\item[lowbnd]
-A list of numeric values containing the lower bounds of the reaction rates.
-If not set, zero is used for an irreversible reaction and the value of
-\Comp{def\_bnd * -1} for a reversible reaction. See documentation of the
-function \Comp{readTSVmod} for the argument \Comp{def\_bnd} (optional).
-
-\item[uppbnd]
-A list of numeric values containing the upper bounds of the reaction rates.
-If not set, the value of \Comp{def\_bnd} is used. See documentation of the
-function \Comp{readTSVmod} for the argument \Comp{def\_bnd} (optional).
-
-\item[obj\_coef]
-A list of numeric values containing objective values for each reaction
-(optional, if missing, zero is used).
-
-\item[rule]
-A list of single character strings containing the gene to reaction associations
-(optional).
-
-\item[subsystem]
-A list of character strings containing the reaction subsystems. Each reaction
-can belong to more than one subsystem. The entries are separated by
-\Comp{fielddelim} (optional).
-
-\end{description}
-The file \Comp{Ec\_core\_react.tsv} (in \Comp{extdata/}) contains an exemplarily
-table for the core energy metabolism of \emph{E.~coli}
-\citep{Palsson:2006fk,Orth:2010fk}.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{How to write a reaction equation string} \label{writeEQ}
-
-\begin{figure}[t]
-\centering
-\includegraphics{net-crop}
-\caption{Simple example network. A) showing a closed network, B) an open
- network. Capital letters are used as metabolite id's, lower case
- letters are used as compartment id's: b: boundary metabolite,
- c:~cytosol and e: external metabolite. Internal reactions are named
- $v_{1:7}$, transport reactions $b_{1:3}$. Reactions $v_3$ and $v_4$ are
- reversible, all others are irreversible.
- Metabolites A\textsubscript{b}, C\textsubscript{b} and
- E\textsubscript{b} are boundary metabolites and will be removed in
- order to obtain an open network.}
-\label{netex}
-\end{figure}
-
-Any reaction string can be written without space. They are not required
-but showed here, in order to make the string more human readable.
-
-\paragraph{Compartment Flag} Each reaction string may start with a compartment
-flag in square brackets followed by a colon. The compartment flag here gives the
-location of all metabolites appearing in the reaction.
-\begin{verbatim}
-[c] :
-\end{verbatim}
-The compartment flag can consist of more than one letter and---if used---must be
-an element of the field \Comp{abbreviation} in the model description. The letter
-\Comp{b} is reserved for boundary metabolites (argument \Comp{extMetFlag} in
-function \Comp{readTSVmod()}), which can be transported inside the system (those
-metabolites are only used in closed systems and will be removed during file
-parsing).
-
-If the reaction string does not start with a compartment flag, the flag may be
-appended (without whitespace) to each metabolite id (e.\,g. for transport
-reactions):
-\begin{verbatim}
-h2o[e] <==> h2o[c]
-\end{verbatim}
-If no compartment flag is found, it is set to \Comp{[unknown]}.
-
-\paragraph{Reaction Arrow}
-All reactions must be written in the direction educt to product, so that all
-metabolites left of the reaction arrow are considered as educts, all metabolites
-on the right of the reaction arrow are products.
-
-The reaction arrow itself consists of one or more \Comp{=} or \Comp{-} symbols.
-The last symbol must be a \Comp{>}. If a reaction arrow starts with \Comp{<}, it
-is taken as reversible, if the field \Comp{reversible} in the reaction list is
-empty. If the field \Comp{reversible} is set to \Comp{TRUE} or
-\Comp{Reversible}, the reactions will be treated as a reversible reaction,
-independent of the reaction arrow. Each reaction must contain exactly one
-reaction arrow.
-
-\paragraph{Stoichiometric Coefficients}
-Stoichiometric coefficients must be in round brackets in front of the
-corresponding metabolite:
-\begin{verbatim}
-(2) h[c] + (0.5) o2[c] + q8h2[c] --> h2o[c] + (2) h[e] + q8[c]
-\end{verbatim}
-Setting the stoichiometric coefficient in brackets makes it possible for the
-metabolite id to start with a number.
-
-\paragraph{Metabolite Id's}
-The abbreviation of a metabolite name (a metabolite id) must be unique for the model and
-must not contain \Comp{+}, \Comp{(} or \Comp{)} characters.
-
-\paragraph{Examples}
-
-A minimal reaction list without compartment flags for figure~\ref{netex}B
-(open network):
-\begin{verbatim}
-equation
-A --> B
-B <==> D
-D <==> E
-B --> C
- --> A
-C -->
-E -->
-\end{verbatim}
-The same as above including compartment flags and external metabolites and all
-transport reactions for figure~\ref{netex}A (closed network). The reactions
-which take place in only one compartment (do not include a transport of
-metabolites across membranes) have their compartment flag at the beginning
-of the line (\Comp{[c]} in this example). For transport reactions all
-metabolites have their own compartment flag, e.\,g. in line 5 metabolite
-\Comp{A} is transported from compartment \Comp{[e]} (external) to compartment
-\Comp{[c]} (cytosol):
-\begin{verbatim}
-equation
-[c]: A --> B
-[c]: B <==> D
-[c]: D <==> E
-[c]: B --> C
-A[e] --> A[c]
-C[c] --> C[e]
-E[c] --> E[e]
-A[b] --> A[e]
-C[e] --> C[b]
-E[e] --> E[b]
-\end{verbatim}
-The same as above including reaction id's for figure~\ref{netex} (fields are
-separated by tabulators):
-\begin{verbatim}
-abbreviation equation
-v2 [c]: A --> B
-v3 [c]: B <==> D
-v4 [c]: D <==> E
-v6 [c]: B --> C
-v1 A[e] --> A[c]
-v7 C[c] --> C[e]
-v5 E[c] --> E[e]
-b1 A[b] --> A[e]
-b3 C[e] --> C[b]
-b2 E[e] --> E[b]
-\end{verbatim}
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{SBML} \label{sbmlmod}
-
-In order to read model files written in systems biology markup language (SBML),
-the package \pkg{sybilSBML} is required, which is available from
-CRAN\footnote{\url{http://CRAN.R-project.org/package=sybilSBML}\label{sybilhome}}.
-
-
-% ---------------------------------------------------------------------------- %
-
-\section{Usage}
-
-In the following sections, it is assumed, that package \pkg{glpkAPI} is
-installed additionally to \pkgname, thus GLPK is used as optimization software.
-Load \pkgname{} in a running R session:
-<<>>=
-library(sybil)
-@
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Documentation}
-
-Get a list of all functions provided with \pkgname:
-<<>>=
-library(help = "sybil")
-@
-Get details of the usage of a particular function in \pkgname
-(e.\,g. \Comp{doubleGeneDel()}):
-<<>>=
-help(doubleGeneDel)
-@
-Search through help files for a specific topic
-(e.\,g. ``flux variability analysis''):
-<<>>=
-help.search("flux variability analysis")
-@
-Open this vignette:
-<<eval=FALSE>>=
-vignette("sybil")
-@
-% Demo??
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Reading a model in tabular form}
-
-The package \pkgname can read metabolic network models written in tabular form
-as described in section~\ref{tabmod}. A reconstruction of the central metabolism
-of \emph{E. coli} \citep{Orth:2010fk,Palsson:2006fk} is included as an example
-dataset. The example dataset consists of three files:
-\begin{enumerate}
-\item \Comp{Ec\_core\_desc.tsv} containing the model description,
-\item \Comp{Ec\_core\_met.tsv} containing the metabolite list and
-\item \Comp{Ec\_core\_react.tsv} containing the reaction list.
-\end{enumerate}
-These files are located in the directory \Comp{extdata/} in the package
-\pkgname{}. The exact location of the files can be retrieved with the
-\Comp{system.file()} command:
-<<>>=
-mp <- system.file(package = "sybil", "extdata")
-@
-Now the model files can be read in by using the command \Comp{readTSVmod()}:
-<<print=true>>=
-mod <- readTSVmod(prefix = "Ec_core", fpath = mp, quoteChar = "\"")
-@
-If the fields in the input files for function \Comp{readTSVmod()} are quoted,
-argument \Comp{quoteChar} must be used. The value of \Comp{quoteChar} is passed
-to the argument \Comp{quote} of the R~function \Comp{read.table()}. Argument
-\Comp{fpath} gets the path to the directory containing the model files. Argument
-\Comp{prefix} can be used, if the file names of the model files end like the
-file names used in the above example. All have the same base name
-\Comp{"Ec\_core"} which is used for argument \Comp{prefix}. Function
-\Comp{readTSVmod()} now assumes, that the model files are named as follows:
-\begin{itemize}
-\item the model description file (if exists): \Comp{<prefix>\_desc}\,,
-\item the list of metabolites (if exists): \Comp{<prefix>\_met} and
-\item the list of reactions (must be there): \Comp{<prefix>\_react}\,.
-\end{itemize}
-The file name suffix depends on the field delimiter. If the fields are
-tab-delimited, the default is \Comp{.tsv}\,. Function \Comp{readTSVmod()}
-returns an object of class \Comp{modelorg}.
-Models (instances of class \Comp{modelorg}, see section~\ref{classmod}) can be
-converted to files in tabular form with the command \Comp{modelorg2tsv}:
-<<eval=FALSE>>=
-modelorg2tsv(mod, prefix = "Ec_core")
-@
-This will generate the three files shown in the list above (see also
-section~\ref{tabmod}).
-Load the example dataset included in \pkgname.
-<<>>=
-data(Ec_core)
-@
-The example model is a `ready to use' model, it contains a biomass objective
-function and an uptake of glucose \citep{Orth:2010fk,Palsson:2006fk}. It is the
-same model as used in the text files before.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Media conditions} \label{envir}
-
-The current set of exchange reactions in the model can be accessed with the
-function \Comp{findExchReact()}.
-<<print=true>>=
-ex <- findExchReact(Ec_core)
-@
-The subset of uptake reactions can be retrieved by method \Comp{uptReact}.
-<<print=true>>=
-upt <- uptReact(ex)
-ex[upt]
-@
-Function \Comp{findExchReact()} returns an object of class \Comp{reactId\_Exch}
-(extending class \Comp{reactId}) which can be used to alter reaction bounds
-with function \Comp{changeBounds()}. Make lactate the main carbon source instead
-of glucose:
-<<>>=
-mod <- changeBounds(Ec_core, ex[c("EX_glc(e)", "EX_lac_D(e)")], lb = c(0, -10))
-findExchReact(mod)
-@
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Flux-balance analysis} \label{fba}
-
-Perform flux-balance analysis (FBA) by using method \Comp{optimizeProb} of class
-\Comp{modelorg}.
-Method \Comp{optimizeProb} performs flux-balance analysis
-\citep{Edwards:2002kx,Orth:2010vn}. It returns a list containing the return
-value of the optimization process (\Comp{"ok"}), the solution status
-(\Comp{"stat"}), the value of the objective function after optimization
-(\Comp{"obj"}), the resulting flux distribution---the phenotype of the metabolic
-network---(\Comp{"fluxes"}) and results of pre- and post processing commands, if
-given (\Comp{"preP"} and \Comp{"postP"}). Also, a vector of integers will be
-returned (\Comp{"fldind"}). The flux value \Comp{fluxes[fldind[i]]} is the flux
-value of reaction \Comp{i} in the model (see section~\ref{mtf}).
-<<print=true>>=
-optL <- optimizeProb(Ec_core, algorithm = "fba", retOptSol = FALSE)
-@
-Perform FBA, return an object of class \Comp{optsol\_optimizeProb}
-(extends class \Comp{optsol}, see section~\ref{classopt}, this is the default
-behavior).
-<<print=true>>=
-opt <- optimizeProb(Ec_core, algorithm = "fba", retOptSol = TRUE)
-@
-The variable \Comp{opt} contains an object of class \Comp{optsol\_optimizeProb},
-a data structure storing all results of the optimization and providing methods
-to access the data (see section~\ref{classopt}).
-Retrieve the value of the objective function after optimization.
-<<>>=
-lp_obj(opt)
-@
-Translate the return and status codes of the optimization software into human
-readable strings.
-<<>>=
-checkOptSol(opt)
-@
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Minimize total flux} \label{mtf}
-
-Usually, an FBA solution is not unique. There can be many equivalent flux
-distributions supporting the same objective value. A method to decide for one
-out of these solutions is to compute the flux distribution minimizing the total
-absolute flux (MTF) but still supporting the objective value of the FBA
-solution. At first, an objective value, for example calculated via FBA, is
-required:
-<<>>=
-fba <- optimizeProb(Ec_core, algorithm = "fba")
-@
-Get the optimized value of the objective function:
-<<>>=
-mod_obj(fba)
-@
-Now, the objective value of the solution in \Comp{fba} is used to compute a
-flux distribution with a minimized total absolute flux:
-<<>>=
-mtf <- optimizeProb(Ec_core, algorithm = "mtf", wtobj = mod_obj(fba))
-@
-The value of the objective function for the MTF algorithm now is
-<<>>=
-lp_obj(mtf)
-@
-which is the minimized sum of all absolute flux values. The number of variables
-of the MTF problem is three times the number of the variables of the FBA
-solution
-<<>>=
-nvar(fluxdist(fba))
-nvar(fluxdist(mtf))
-@
-which is due to the different formulations of the two optimization problems.
-Consult the documentation of class \Comp{sysBiolAlg} (section~\ref{classsba})
-for more detailed information on the algorithms.
-<<>>=
-help("sysBiolAlg_fba-class")
-help("sysBiolAlg_mtf-class")
-@
-There are also shortcuts available:
-<<>>=
-?fba
-?mtf
-@
-Method \Comp{getFluxDist} can be used to get the flux distribution of the MTF
-solution; the values of the variables corresponding to the reactions in the
-metabolic network.
-<<>>=
-fl <- getFluxDist(mtf)
-length(fl)
-@
-The flux distribution of the exchange reactions can be retrieved in a similar
-way (variable \Comp{ex} contains the exchange reactions of the \emph{E. coli}
-model, see section~\ref{envir}).
-<<print=true>>=
-fd <- getFluxDist(mtf, ex)
-getNetFlux(fd)
-@
-Function \Comp{getNetFlux()} the absolute flux values of the exchange reactions
-grouped by flux direction. The value of the objective function given in the
-model (here: biomass production) can be accessed by method \Comp{mod\_obj}:
-<<>>=
-mod_obj(mtf)
-@
-which is of course the same value as for the FBA algorithm.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Genetic perturbations} \label{komut}
-
-To compute the metabolic phenotypes of \emph{in silico} knock-out mutants,
-argument \Comp{gene} of method \Comp{optimizeProb} can be used.
-<<print=true>>=
-ko <- optimizeProb(Ec_core, gene = "b2276", lb = 0, ub = 0)
-@
-Argument \Comp{gene} gets a character vector of gene locus tags present in the
-used model. The flux boundaries of reactions affected by the genes given in
-argument \Comp{gene} will be set to the values of arguments \Comp{lb} and
-\Comp{ub}. If both arguments are set to zero, no flux through the affected
-reactions is allowed.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{Minimization of metabolic adjustment (MOMA)} \label{MOMA}
-
-The default algorithm used by method \Comp{optimizeProb} is
-FBA \citep{Edwards:2002kx,Orth:2010vn}, implying the assumption, that the
-phenotype of the mutant metabolic network is independent of the wild-type
-phenotype. An alternative is the MOMA algorithm described in
-\citet{Segre:2002fk} minimizing the hamiltonian distance of the wild-type
-phenotype and the mutant phenotype (argument \Comp{algorithm = "lmoma"} computes
-a linearized version of the MOMA algorithm; \Comp{algorithm = "moma"} runs the
-quadratic formulation).
-<<print=true>>=
-ko <- optimizeProb(Ec_core, gene = "b2276", lb = 0, ub = 0,
- algorithm = "lmoma", wtflux = getFluxDist(mtf))
-@
-The variable \Comp{ko} contains the solution of the linearized version of the
-MOMA algorithm. A wild-type flux distribution can be set via argument
-\Comp{wtflux}, here, the flux distribution computed through the MTF algorithm
-was used. If argument \Comp{wtflux} is not set, a flux distribution based on
-FBA will be used.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{Regulatory on/off minimization (ROOM)} \label{ROOM}
-
-Another alternative is the ROOM algorithm (regulatory on/off minimization)
-described in \citet{Shlomi:2005fk}. Set argument \Comp{algorithm} to \Comp{room}
-in order to run ROOM.
-<<eval=FALSE>>=
-ko <- optimizeProb(Ec_core, gene = "b2276", lb = 0, ub = 0,
- algorithm = "room", wtflux = getFluxDist(mtf),
- solverParm = list(PRESOLVE = GLP_ON))
-@
-ROOM is a mixed integer programming problem which requires for GLPK to switch
-on the pre-solver. See section \ref{optparm} for more information on setting
-parameters to the mathematical programming software.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{Multiple knock-outs} \label{multknockout}
-
-Method \Comp{optimizeProb} can be used to study the metabolic phenotype of one
-knock-out mutant. The purpose of functions \Comp{oneGeneDel()},
-\Comp{doubleGeneDel()} and \Comp{geneDeletion()} is the simulation of multiple
-\emph{in silico} knock-outs (see table~\ref{tabmultko}).
-\begin{table}
-\centering
-\caption{Functions used to simulate multiple
- \emph{in silico} knock-out mutants.}
-\label{tabmultko}
-\begin{tabular}{ll}
-\toprule
-function & purpose \\
-\midrule
-\Comp{oneGeneDel()} & single gene knock-outs \\
-\Comp{doubleGeneDel()} & pairwise gene knock-outs \\
-\Comp{geneDeletion()} & simultaneous deletion of $n$ genes \\
-\bottomrule
-\end{tabular}
-\end{table}
-Function \Comp{oneGeneDel()} simulates all possible single gene knock-out
-mutants in a metabolic model (default algorithm is FBA).
-<<print=true>>=
-opt <- oneGeneDel(Ec_core)
-@
-The function \Comp{oneGeneDel} gets an argument \Comp{geneList}, a character
-vector containing the gene id's to knock out. If \Comp{geneList} is missing,
-all genes are taken into account. The example model contains 137 independent
-genes, so 137 optimizations will be performed.
-
-The result stored in the variable \Comp{opt} is an object of class
-\Comp{optsol\_geneDel}, extending class \Comp{optsol\_optimizeProb}
-(see section~\ref{fba}). Method \Comp{checkOptSol} gives an overview about the
-results and status of the optimizations. Additionally, class \Comp{optsol}
-contains a method \Comp{plot}, plotting a histogram of the values of the
-objective function given in the model after optimization
-(section~\ref{classopt}).
-<<>>=
-checkOptSol(opt)
-@
-Plot the histogram:
-\begin{center}
-<<fig=TRUE>>=
-plot(opt, nint = 20)
-@
-\end{center}
-Argument \Comp{algorithm} can be used here to use MOMA to compute the mutant
-flux distributions. Additionally, a wild-type solution can be provided.
-\begin{center}
-<<fig=TRUE>>=
-opt <- oneGeneDel(Ec_core, algorithm = "lmoma", wtflux = getFluxDist(mtf))
-checkOptSol(opt)
-plot(opt, nint = 20)
-@
-\end{center}
-In order to perform all possible double-knock-out mutants, or $n$-knock-out
-mutants, the function \Comp{geneDeletion} can be used. Perform single gene
-deletions (in principle the same as before with \Comp{oneGeneDel}).
-<<>>=
-opt <- geneDeletion(Ec_core)
-@
-Compute all double-knock-out mutants and all triple-knock-out mutants
-<<eval=FALSE>>=
-opt2 <- geneDeletion(Ec_core, combinations = 2)
-opt3 <- geneDeletion(Ec_core, combinations = 3)
-@
-which will result in 9317 optimizations for double-knock-outs and
-419\,221~Optimizations for triple-knock-outs using the metabolic model of the
-core energy metabolism of \emph{E.\,coli}. This model contains 137 genes.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Flux variability analysis}
-
-The function \Comp{fluxVar} performs a flux variability analysis with a given
-model \citep{Mahadevan:2003fk}. The minimum and maximum flux values for each
-reaction in the model are calculated, which still support a certain percentage
-of a given optimal functional state $Z_{\mathrm{opt}}$.
-\begin{center}
-<<fig=TRUE>>=
-opt <- fluxVar(Ec_core, percentage = 80, verboseMode = 0)
-plot(opt)
-@
-\end{center}
-% The example below is based upon the metabolic model of the human red blood cell
-% by \citet{Palsson:2006fk} and \citet{Price:2004fk}.
-% <<>>=
-% rbc <- readTSVmod(reactList = "rbc.tsv", fpath = mp, quoteChar = "\"")
-% @
-% Perform flux variability analysis.
-% \begin{center}
-% <<fig=TRUE>>=
-% opt <- fluxVar(Ec_core, percentage = 1, verboseMode = 0)
-% plot(opt)
-% @
-% \end{center}
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Robustness analysis}
-
-The function \Comp{robAna} performs a robustness analysis with a given model.
-The flux of a control reaction will be varied stepwise between the maximum and
-minimum value the flux of the control reaction can reach \citep{Palsson:2006fk}.
-The example below shows a flux variability analysis based upon the metabolic
-model of the core energy metabolism of \emph{E.\,coli} using the exchange flux
-of oxygen as control reaction.
-\begin{center}
-<<fig=TRUE>>=
-opt <- robAna(Ec_core, ctrlreact = "EX_o2(e)", verboseMode = 0)
-plot(opt)
-@
-\end{center}
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Phenotypic phase plane analysis}
-
-The function \Comp{phpp} performs a phenotypic phase plane
-analysis \citep{Edwards:2001fk,Edwards:2002uq} with a given model. The flux of
-two control reactions will be varied stepwise between a given maximum and
-minimum value. The example below shows a phenotypic phase plane analysis based
-upon the metabolic model of the core energy metabolism of \emph{E.\,coli} using
-the exchange fluxes of oxygen and succinate as control reactions. First, the
-uptake of glucose is switched off.
-\begin{center}
-<<fig=TRUE>>=
-Ec_core_wo_glc <- changeUptake(Ec_core, off = "glc_D[e]")
-opt <- phpp(Ec_core_wo_glc,
- ctrlreact = c("EX_succ(e)", "EX_o2(e)"),
- redCosts = TRUE,
- numP = 25,
- verboseMode = 0)
-plot(opt)
-@
-\end{center}
-Plot reduced costs of succinate import flux and oxygen import flux.
-
-<<fig=TRUE, label=phpp_rf, include=FALSE>>=
-plot(opt, "EX_succ(e)")
-@
-<<fig=TRUE,label=phpp_rs, include=FALSE>>=
-plot(opt, "EX_o2(e)")
-@
-
-\begin{minipage}{0.45\textwidth}
-\begin{center}
-\includegraphics[width=\textwidth]{sybil-phpp_rf}
-\end{center}
-\end{minipage}
-\hfill
-\begin{minipage}{0.45\textwidth}
-\begin{center}
-\includegraphics[width=\textwidth]{sybil-phpp_rs}
-\end{center}
-\end{minipage}
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Summarizing simulation results}
-
-Each simulation generates an object of class \Comp{optsol} containing all
-the results of the optimizations. In order to get a quick overview of the
-results, the function \Comp{summaryOptsol()} can be used. At first, let's
-compute all single gene knock-outs of the metabolic model of the core energy
-metabolism of \emph{E.\,coli}:
-<<>>=
-opt <- oneGeneDel(Ec_core, algorithm = "fba", fld = "all")
-@
-Generate a summary:
-<<print=true>>=
-sum <- summaryOptsol(opt, Ec_core)
-@
-The function \Comp{summaryOptsol()} returns an object of class
-\Comp{optsolSummary} and needs the object of class \Comp{optsol} (results of
-simulations) and the corresponding object of class \Comp{modelorg} (the entire
-metabolic network). The generated object of class \Comp{summaryOptsol} contains
-some information about the flux distribution, substrates, products and limiting
-reactions.
-
-The method \Comp{printExchange()} prints a subset of the flux distribution for
-the exchange reactions in the model. Each column represents the environment of
-one optimization. The symbol \Comp{"-"} indicates that the corresponding
-metabolite is imported (is a substrate); the symbol \Comp{"+"} indicates, that
-the corresponding metabolite excreted (is a product).
-<<>>=
-printExchange(sum, j = c(1:50), dense = TRUE)
-@
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Parallel computing}
-
-The package \pkgname{} provides basic support for the R-package \pkg{parallel}
-in function \Comp{multidel()}. The following example shows the computation of
-all possible triple-knock-out mutants using the model of the core energy
-metabolism of \emph{E.\,coli}. The set of genes included in the analysis will
-be reduced to genes, which are not lethal. A gene $i$ is considered as
-``lethal'', if in a single-gene-knockout the deletion of gene $i$ results in a
-maximum growth ratio of zero.
-<<>>=
-ref <- optimizeProb(Ec_core)
-opt <- oneGeneDel(Ec_core)
-let <- lethal(opt, wt = mod_obj(ref))
-nletid <- c(1:length(allGenes(Ec_core)))[! let]
-@
-
-\noindent
-At first, a wild-type maximum growth rate is computed and stored in the variable
-\Comp{ref}. Then, all single-gene knock-outs are computed. The variable
-\Comp{let} contains pointers to the gene id's of genes, who's deletion is
-lethal. The variable \Comp{nletid} contains pointers to the gene id's of all
-genes, except for the lethal ones.
-<<eval=FALSE>>=
-gmat <- combn(nletid, 3)
-@
-The variable \Comp{gmat} now contains a matrix with three rows, each column is
-one combination of three values in \Comp{nletid}; one set of genes to knock-out
-in one step.
-<<eval=FALSE>>=
-opt <- multiDel(Ec_core, nProc = 4, todo = "geneDeletion", del1 = gmat)
-@
-The function \Comp{multiDel} performs a \Comp{geneDeletion} with the model
-\Comp{Ec\_core} on four CPU's (argument \Comp{nProc}) on a shared memory
-machine. Argument \Comp{del1} is the matrix containing the sets of genes to
-delete. This matrix will be split up in smaller sub-matrices all having about the
-same number of columns and three rows. The sub-matrices are passed to
-\Comp{geneDeletion} and are processed on separate cores in parallel. The
-resulting variable \Comp{opt} now contains a list of four objects of class
-\Comp{optsol\_genedel}. Use \Comp{mapply} to access the values stored in the
-\Comp{optsol} objects.
-<<eval=FALSE>>=
-mapply(checkOptSol, opt)
-@
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Interacting with the optimization process}
-
-Method \Comp{optimizeProb} provides a basic mechanism to run commands before
-and or after solving the optimization problem. In order to retrieve the reduced
-costs after the optimization, use argument \Comp{poCmd}.
-<<>>=
-opt <- optimizeProb(Ec_core, poCmd = list("getRedCosts"))
-postProc(opt)
-@
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Optimization software}
-
-To solve optimization problems,
-GLPK\footnote{Andrew Makhorin: GNU Linear Programming Kit, version~4.42 or
-higher
-
-\url{http://www.gnu.org/software/glpk/glpk.html}},
-\cplex\footnote{\cplex{} version 12.2 (or higher) from the IBM Academic
-Ini\-tia\-tive
-
-\url{https://www.ibm.com/developerworks/university/academicinitiative/}},
-COIN-OR Clp\footnote{COIN-OR linear programming version 1.12.0 or higher
-\url{https://projects.coin-or.org/Clp}}
-or lp\_solve\footnote{lp\_solve via R-package \pkg{lpSolveAPI} version 5.5.2.0-5
-or higher
-
-\url{http://lpsolve.sourceforge.net/5.5/index.htm}}
-can be used (package \pkg{sybilGUROBI} providing support for Gurobi
-optimization\footnote{\url{http://www.gurobi.com}} is available on request).
-All functions performing optimizations, get the arguments
-\Comp{solver} and \Comp{method}. The first setting the desired solver and the
-latter setting the desired optimization algorithm.
-Possible values for the argument \Comp{solver} are:
-\begin{itemize}
-\item \Comp{"glpkAPI"}, which is the default,
-\item \Comp{"cplexAPI"},
-\item \Comp{"clpAPI"} or
-\item \Comp{"lpSolveAPI"}.
-\end{itemize}
-Perform FBA, using GLPK as solver and ``simplex exact'' as algorithm.
-<<eval=FALSE>>=
-optimizeProb(Ec_core, method = "exact")
-@
-Perform FBA, using \cplex{} as solver and ``dualopt'' as algorithm.
-<<eval=FALSE>>=
-optimizeProb(Ec_core, solver = "cplexAPI", method = "dualopt")
-@
-The R-packages \pkg{glpkAPI}, \pkg{clpAPI} and \pkg{cplexAPI}
-provide access to the C-API of the corresponding optimization software.
-They are also available from CRAN\footref{cranfoot}.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Setting parameters to the optimization software}
-\label{optparm}
-
-All functions performing optimizations can handle the argument
-\Comp{solverParm} getting a list or data frame containing parameters used by the
-optimization software.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{GLPK}
-
-For available parameters used by GLPK, see the GLPK and the \pkg{glpkAPI}
-documentation.
-<<eval=FALSE>>=
-opt <- oneGeneDel(Ec_core,
- solverParm = list(TM_LIM = 1000,
- PRESOLVE = GLP_ON))
-@
-The above command performs a single gene deletion experiment
-(see section~\ref{multknockout}), sets the time limit for each optimization to
-one second and does pre-solving in each optimization.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{\cplex}
-
-For available parameters used by \cplex{}, see the \cplex{} and the
-\pkg{cplexAPI} documentation.
-<<eval=FALSE>>=
-opt <- optimizeProb(Ec_core,
- solverParm = list(CPX_PARAM_SCRIND = CPX_ON,
- CPX_PARAM_EPRHS = 1E-09),
- solver = "cplexAPI")
-@
-The above command performs FBA, sets the messages to screen switch to ``on''
-and sets the feasibility tolerance to $10^{-9}$.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{COIN-OR Clp}
-
-At the time of writing, it is not possible to set any parameters when using
-COIN-OR Clp.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{lpSolveAPI}
-
-See the \pkg{lpSolveAPI} documentation for parameters for \Comp{lp\_solve}.
-<<eval=FALSE>>=
-opt <- optimizeProb(Ec_core,
- solverParm = list(verbose = "full",
- timeout = 10),
- solver = "lpSolveAPI")
-@
-The above command performs FBA, sets the verbose mode to ``full''
-and sets the timeout to ten seconds.
-
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Setting parameters in sybil}
-
-Parameters to \pkgname{} can be set using the function \Comp{SYBIL\_SETTINGS}.
-Parameter names and their default values are shown in table~\ref{sybilparm},
-all possible values are described in the \Comp{SYBIL\_SETTINGS} documentation.
-<<>>=
-help(SYBIL_SETTINGS)
-@
-\begin{table}
-\centering
-\caption{Available parameters in \pkgname{} and their default values.}
-\label{sybilparm}
-\begin{tabular}{ll}
-\toprule
-parameter name & default value \\
-\midrule
-\Comp{SOLVER} & \Comp{glpkAPI} \\
-\Comp{METHOD} & \Comp{simplex} \\
-\Comp{SOLVER\_CTRL\_PARM} & \Comp{as.data.frame(NA)} \\
-\Comp{ALGORITHM} & \Comp{fba} \\
-\Comp{TOLERANCE} & \Comp{1E-6} \\
-\Comp{MAXIMUM} & \Comp{1000} \\
-\Comp{OPT\_DIRECTION} & \Comp{max} \\
-\Comp{PATH\_TO\_MODEL} & \Comp{.} \\
-\bottomrule
-\end{tabular}
-\end{table}
-The function \Comp{SYBIL\_SETTINGS} gets at most two arguments:
-<<eval=FALSE>>=
-SYBIL_SETTINGS("parameter name", value)
-@
-the first one giving the name of the parameter to set (as character string) and
-the second one giving the desired value. If \Comp{SYBIL\_SETTINGS} is called
-with only one argument
-<<eval=FALSE>>=
-SYBIL_SETTINGS("parameter name")
-@
-the current setting of \Comp{"parameter name"} will be returned. All parameters
-and their values can be achieved by calling \Comp{SYBIL\_SETTINGS} without
-any argument.
-<<eval=FALSE>>=
-SYBIL_SETTINGS()
-@
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{Solver software specific}
-
-The two parameters \Comp{SOLVER} and \Comp{METHOD} depend on each other, e.\,g.
-the method called \Comp{simplex} is only available when \Comp{glpkAPI} is used
-as solver software. Each solver has its own specific set of methods available in
-order to solve optimization problems. If one changes the parameter \Comp{SOLVER}
-to, let's say \Comp{cplexAPI}, the parameter \Comp{METHOD} will automatically
-be adjusted to the default method used by \Comp{cplexAPI}.
-Set parameter solver to \cplex{} for every optimization:
-<<>>=
-SYBIL_SETTINGS("SOLVER", "cplexAPI", loadPackage = FALSE)
-@
-Now, \cplex{} is used as default solver e.\,g. in \Comp{optimizeProb} or
-\Comp{oneGeneDel}, and parameter \Comp{METHOD} has changed to the default method
-in \pkg{cplexAPI}. Setting argument \Comp{loadPackage} to \Comp{FALSE} prevents
-loading the API package. Get the current setting for \Comp{Method}:
-<<>>=
-SYBIL_SETTINGS("METHOD")
-@
-Reset the solver to \Comp{glpkAPI}:
-<<>>=
-SYBIL_SETTINGS("SOLVER", "glpkAPI")
-@
-Now, the default method again is \Comp{simplex}
-<<>>=
-SYBIL_SETTINGS("METHOD")
-@
-It is not possible to set a wrong method for a given solver. If the desired
-method is not available, always the default method is used.
-Parameters to the solver software (parameter \Comp{SOLVER\_CTRL\_PARM}) must be
-set as \Comp{list} or \Comp{data.frame} as described in section~\ref{optparm}.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{Analysis specific}
-
-The parameter \Comp{ALGORITHM} controls the way gene deletion analysis will be
-performed. The default setting \Comp{"fba"} will use flux-balance analysis (FBA)
-as described in \citet{Edwards:2002kx} and \citet{Orth:2010vn}. Setting this
-parameter to \Comp{"lmoma"}, results in a linearized version of the MOMA
-algorithm described in \citet{Segre:2002fk} ("moma" will run the original
-version). The linearized version of MOMA, like it is implemented in the COBRA
-Toolbox \citep{Becker:2007uq,Schellenberger:2011fk}, can be used in functions
-like \Comp{oneGeneDel()} via the Boolean argument \Comp{COBRAflag}.
-Setting the parameter \Comp{"ALGORITHM"} to \Comp{"room"} will run a regulatory
-on/off minimization as described in \citet{Shlomi:2005fk}.
-See also section~\ref{komut} for details on gene deletion analysis.
-
-
-% ---------------------------------------------------------------------------- %
-
-\section{Central data structures}
-
-\subsection{Class modelorg} \label{classmod}
-
-The class \Comp{modelorg} is the core datastructure to represent a metabolic
-network, in particular the stoichiometric matrix $S$.
-An example (E.\,coli core flux by \citep{Palsson:2006fk}) is shipped within
-\pkgname and can be loaded this way:
-<<>>=
-data(Ec_core)
-Ec_core
-@
-The generic method \Comp{show} displays a short summary of the parameters of the
-metabolic network. See
-<<>>=
-help("modelorg")
-@
-for the list of available methods. All slots of an object of class
-\Comp{modelorg} are accessible via setter and getter methods having the same
-name as the slot. For example, slot \Comp{react\_num} contains the number of
-reactions in the model (equals the number of columns in $S$). Access the
-number of reactions in the \emph{E.\,coli} model.
-<<>>=
-react_num(Ec_core)
-@
-Get all reaction is's:
-<<>>=
-id <- react_id(Ec_core)
-@
-Change a reaction id:
-<<>>=
-react_id(Ec_core)[13] <- "biomass"
-@
-Plot an image of the stoichiometric matrix $S$:
-\begin{center}
-<<fig=TRUE>>=
-cg <- gray(0:8/8)
-image(S(Ec_core), col.regions = c(cg, rev(cg)))
-@
-\end{center}
-Matrices in objects of class \Comp{modelorg} are stored in formats provided by
-the \pkg{Matrix}-package\footnote{http://CRAN.R-project.org/package=Matrix}.
-
-Objects of class \Comp{modelorg} can easily be created. Sources are common file
-formats like tab delimited files from the
-BiGG database \citep{Schellenberger:2010fk}\footnote{\url{http://bigg.ucsd.edu}}
-or SBML files (with package \pkg{sybilSBML}\footref{sybilhome}).
-See section~\ref{inputformats} on
-page \pageref{inputformats} about supported file formats and their description.
-Read a reaction list generated from the BiGG database:
-<<eval=FALSE>>=
-mod <- readTSVmod(reactList = "reactionList.txt")
-@
-Here, \Comp{"reactionList.txt"} is an from BiGG database exported reaction
-list. Usually, these files do neither contain an objective function, nor upper
-and lower bounds on the reaction rates. They need to be added to the returned
-object of class \Comp{modelorg} using the methods \Comp{obj\_coef<-},
-\Comp{lowbnd<-} and \Comp{uppbnd<-}, or by adding the columns \Comp{obj\_coef},
-\Comp{lowbnd} and \Comp{uppbnd} to the input file.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Class optsol} \label{classopt}
-
-\begin{figure}
- \centering
- \includegraphics{optsol-class}
- \caption{UML representation of class \Comp{optsol}.}
- \label{optsol-class}
-\end{figure}
-
-The derived classes of class \Comp{optsol} (optimization solution) are used to
-store information and results from various optimization problems and their
-biological relation. See
-<<>>=
-help("optsol")
-@
-for the list of available methods to access the
-data (figure~\ref{optsol-class}). A simple demonstration would be:
-<<print=true>>=
-os <- optimizeProb(Ec_core)
-is(os)
-@
-Retrieve objective value.
-<<>>=
-lp_obj(os)
-@
-Retrieve flux distribution.
-<<>>=
-getFluxDist(os)
-@
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Class optObj} \label{classoo}
-
-\begin{figure}
- \centering
- \includegraphics{optObj-class}
- \caption{UML representation of class \Comp{optObj}.}
- \label{optObj-class}
-\end{figure}
-
-The class \Comp{optObj} is \pkgname's internal representation of an optimization
-problem (figure~\ref{optObj-class}). Objects of this class harbor four slots:
-\begin{inparaenum}[i)]
-\item \Comp{oobj}: a pointer to the C-structure of the problem object (depending
- on the solver software),
-\item \Comp{solver}: the name of the solver,
-\item \Comp{method}: the name of the optimization method used by the solver and
-\item \Comp{probType}: single character string, describing the problem type
- (e.\,g. \Comp{lp}: linear programming, or \Comp{mip}: mixed integer
- programming).
-\end{inparaenum}
-
-The package \pkgname provides several functions to alter the problem object.
-Each function takes care of the special needs of every supported solver. The
-following example should illustrate the purpose of class \Comp{optObj}.
-Consider a linear programming problem, here written in lp formatted file
-format:
-\begin{verbatim}
-Maximize
- obj: + x_1 + x_2
-Subject To
- r_1: + 0.5 x_1 + x_2 <= 4.5
- r_2: + 2 x_1 + x_2 <= 9
-Bounds
- 0 <= x_1 <= 1000
- 0 <= x_2 <= 1000
-\end{verbatim}
-In order to solve this lp problem with \pkgname{}, an object of class
-\Comp{optObj} has to be created. The constructor function has the same name as
-the class it builds.
-<<print=true>>=
-lp <- optObj(solver = "glpkAPI", method = "exact")
-@
-The first argument is the used solver software, in this case it is GLPK. The
-second optional argument gives the method, how the solver software has to solve
-the problem. Here, it is the simplex exact algorithm of GLPK. The constructor
-function \Comp{optObj()} (figure~\ref{optObj-const}) returns an object of class
-\Comp{optObj\_glpkAPI} in this case. This class enables \pkgname to communicate
-with the GLPK software. The constructor function \Comp{optObj()} calls the
-function \Comp{checkDefaultMethod()} which tries to load the specified solver
-package and also checks if all other arguments (\Comp{method} and \Comp{pType})
-are valid arguments. Each solver package has its own set of methods for specific
-types of optimization (e.\,g. linear programming or quadratic programming) and
-is thus available maybe not for all problem types.
-
-\begin{figure}
- \centering
- \includegraphics{optObj-const}
- \caption{Work flow of the constructor function \Comp{optObj()}.}
- \label{optObj-const}
-\end{figure}
-
-
-Initialize the new problem object. Each solver software needs to create
-specific data structures to hold the problem and solution data.
-<<print=true>>=
-lp <- initProb(lp)
-@
-Slot \Comp{oobj} holds a pointer to the problem object of GLPK. Now, we need to
-allocate space for the problem data and load the data into the problem object.
-<<>>=
-cm <- Matrix(c(0.5, 2, 1, 1), nrow = 2)
-loadLPprob(lp, nCols = 2, nRows = 2, mat = cm,
- lb = c(0, 0), ub = rep(1000, 2), obj = c(1, 1),
- rlb = c(0, 0), rub = c(4.5, 9), rtype = c("U", "U"),
- lpdir = "max")
-@
-The first command generates the constraint matrix in sparse format (see also
-documentation in package \pkg{Matrix}). The second command loads the problem
-data into the problem object.
-<<>>=
-lp
-@
-All data are now set in the problem object, so it can be solved.
-<<print=true>>=
-status <- solveLp(lp)
-@
-Translate the status code in a text string.
-<<>>=
-getMeanReturn(code = status, solver = solver(lp))
-@
-Check the solution status.
-<<>>=
-status <- getSolStat(lp)
-getMeanStatus(code = status, solver = solver(lp))
-@
-Retrieve the value of the objective function and the values of the variables
-after optimization.
-<<>>=
-getObjVal(lp)
-getFluxDist(lp)
-@
-Get the reduced costs.
-<<>>=
-getRedCosts(lp)
-@
-Delete problem object and free all memory allocated by the solver software.
-<<>>=
-delProb(lp)
-lp
-@
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsection{Class sysBiolAlg} \label{classsba}
-
-\begin{figure}
- \centering
- \includegraphics{sysBiolAlg-class}
- \caption{UML representation of class \Comp{sysBiolAlg}.}
- \label{sysBiolAlg-class}
-\end{figure}
-
-The class \Comp{sysBiolAlg} holds objects of class \Comp{optObj} which are
-prepared for a particular kind of algorithm, e.\,g. FBA, MOMA or ROOM
-(figure~\ref{sysBiolAlg-class}). Class \Comp{optObj} takes care of the
-communication between \pkgname and the solver software. Class \Comp{sysBiolAlg}
-instead is responsible for the algorithm used to analyze a metabolic network.
-The constructor function \Comp{sysBiolalg()} (figure~\ref{sysBiolAlg-const})
-gets at least two arguments:
-\begin{inparaenum}[1.]
-\item an object of class \Comp{modelorg} (section~\ref{classmod}) and
-\item a single character string indicating the name of the desired algorithm.
-\end{inparaenum}
-Further arguments are passed through argument \Comp{\dots} to the corresponding
-constructor of the class extending class \Comp{sysBiolAlg}. The base class
-\Comp{sysBiolAlg} is virtual, no objects can be created from that class
-directly. The constructor function builds an instance of a class extending the
-base class:
-<<>>=
-ec <- sysBiolAlg(Ec_core, algorithm = "fba")
-is(ec)
-@
-Now, the variable \Comp{ec} contains an object of class \Comp{sysBiolAlg\_fba}.
-Slot \Comp{problem} of that object is of class \Comp{optObj} and is prepared
-for FBA. The optimization can be performed with method \Comp{optimizeProb}:
-<<>>=
-opt <- optimizeProb(ec)
-@
-The return value of \Comp{optimizeProb} is discussed in section~\ref{fba}.
-Method \Comp{optimizeProb} of class \Comp{sysBiolAlg} always returns a list,
-not an object of class \Comp{optsol}.
-In order to run a ROOM analysis create an object of class
-\Comp{sysBiolAlg\_room}:
-<<>>=
-ecr <- sysBiolAlg(Ec_core, algorithm = "room", wtflux = opt$fluxes)
-is(ecr)
-ecr
-@
-Argument \Comp{wtflux} gets the optimal flux distribution computed via FBA
-earlier. It is used by the constructor method of class \Comp{sysBiolAlg\_room}.
-
-\begin{figure}
- \centering
- \includegraphics{sysBiolAlg-const}
- \caption{Work flow of the constructor function \Comp{sysBiolAlg()}.}
- \label{sysBiolAlg-const}
-\end{figure}
-
-\begin{figure}[ht]
- \centering
- \includegraphics{sysBiolAlg-init}
- \caption{Work flow of the constructor methods of classes extending
- class \Comp{sysBiolAlg}. The gray shaded part is done by the
- constructor method or the base class.}
- \label{sysBiolAlg-init}
-\end{figure}
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{Constructor methods}
-
-The base class \Comp{sysBiolAlg} contains a constructor method \Comp{initialize}
-which is called by the constructor methods of the subclasses via
-\Comp{callNextMethod()} (figure~\ref{sysBiolAlg-init}). Every subclass has its
-own constructor method preparing all necessary data structures in order to call
-the constructor of the base class. For example, for the ROOM algorithm, a
-``wild type'' flux distribution is required (argument \Comp{wtflux} in the
-example above). The constructor of class \Comp{sysBiolAlg\_room} generates all
-data structures to build the optimization problem, e.\,g. the constraint matrix,
-objective coefficients, right hand side, \dots{} It passes all these data to
-the constructor of \Comp{sysBiolAlg} via a call to \Comp{callNextMethod()}.
-This constructor generates the object of class \Comp{optObj} while taking care
-on solver software specific details.
-
-
-% ---------------------------------------------------------------------------- %
-
-\subsubsection{New algorithms}
-
-In order to extend the functionality of \pkgname with new algorithms, a new
-class describing that algorithm is required. The function
-\Comp{promptSysBiolAlg()} generates a skeletal structure of a new class definition
-and a corresponding constructor method. To implement an algorithm named ``foo'',
-run
-<<eval=FALSE>>=
-promptSysBiolAlg(algorithm = "foo")
-@
-which generates a file \Comp{sysBiolAlg\_fooClass.R} containing the new class
-definition. The class \Comp{sysBiolAlg\_foo} will extend class \Comp{sysBiolAlg}
-directly and will not add any slots to the class. Additionally, an unfinished
-method \Comp{initialize} is included. Here it is necessary to generate the data
-structures required by the new algorithm. There are comments in the skeletal
-structure guiding through the process.
-
-
-%% maybe next chapter: how to extend sybil, example fluxVar or robAna
-
-% ---------------------------------------------------------------------------- %
-
-\newpage
-
-\bibliographystyle{abbrvnat}
-\bibliography{sybil}
-
-\end{document}
--
GitLab