From a86962cbfd0321387c920a04188512d0de2f3036 Mon Sep 17 00:00:00 2001 From: KatolaZ Date: Mon, 19 Oct 2015 16:30:12 +0100 Subject: First commit of MAMMULT documentation --- doc/latex/mammult_doc.tex | 265 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 265 insertions(+) create mode 100644 doc/latex/mammult_doc.tex (limited to 'doc/latex/mammult_doc.tex') diff --git a/doc/latex/mammult_doc.tex b/doc/latex/mammult_doc.tex new file mode 100644 index 0000000..4d93d88 --- /dev/null +++ b/doc/latex/mammult_doc.tex @@ -0,0 +1,265 @@ +\documentclass[a4paper,11pt]{book} + +\usepackage[british]{babel} +\usepackage[latin1]{inputenc} +\usepackage{hyperref} +\usepackage{amsmath, amssymb} + +\newcommand{\lay}[1]{^{[#1]}} +\newcommand{\avg}[1]{\langle #1 \rangle} + + +\newcommand{\myprogram}[3]{\subsubsection{\texttt{#1}} + \textbf{NAME} + + {\textbf{#1} - #2} + + \vspace{0.5cm} + \noindent + \textbf{SYNOPSYS} + + {\textbf{#1} { }\texttt{\textit{#3} } } +} + +\newcommand{\mydescription}[1]{ + \vspace{0.5cm} + \noindent + \textbf{DESCRIPTION} + + {#1} +} + +\newcommand{\myreturn}[1]{ + \vspace{0.5cm} + \noindent + \textbf{OUTPUT} + + {#1} +} + + +\newcommand{\myreference}[1]{ + \vspace{0.5cm} + \noindent + \textbf{REFERENCE} + + {#1} +} + +%% +%% REFERENCES +%% + +\newcommand{\refgrowth}{V. Nicosia, G. Bianconi, V. Latora, + M. Barthelemy, ``Growing multiplex networks'', + \textit{Phys. Rev. Lett.} {\bf 111}, 058701 (2013). + + Link to paper: \url{http://prl.aps.org/abstract/PRL/v111/i5/e058701} +} +\newcommand{\refnonlinear}{V. Nicosia, G. Bianconi, V. Latora, + M. Barthelemy, ``Non-linear growth and condensation in multiplex + networks'', \textit{Phys. Rev. E} {\bf 90}, 042807 (2014). + + Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807} +} +\newcommand{\refmetrics}{F. Battiston, V. Nicosia, V. Latora, + ``Structural measures for multiplex networks'', + \textit{Phys. Rev. E} {\bf 89}, 032804 (2014). + + Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804} +} +\newcommand{\refcorrelations}{V. Nicosia, V. Latora, ``Measuring and + modeling correlations in multiplex networks'', \textit{Phys. Rev. E} + {\bf 92}, 032805 (2015). + + Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805}} + +\newcommand{\refreducibility}{M. De Domenico, V. Nicosia, A. Arenas, + V. Latora, \textit{``Structural reducibility of multilayer + networks''}, Nat. Commun. {\bf 6}, 6864 (2015). + + Link to paper: \url{http://www.nature.com/ncomms/2015/150423/ncomms7864/full/ncomms7864.html} +} +\newcommand{\refvisibility}{L. Lacasa, V. Nicosia, V. Latora, + \textit{``Network structure of multivariate time series''}, accepted + for publication in Scientific Reports, arxiv:1408.0925 (2015). + + Link to paper: \url{http://arxiv.org/abs/1408.0925} +} + +\newcommand{\refbiased}{F. Battiston, V. Nicosia, V. Latora, + \textit{``Biased random walks on multiplex networks''}, arxiv:1505.01378 (2015). + + Link to paper: \url{http://arxiv.org/abs/1505.01378} +} +\newcommand{\refising}{F. Battiston, A. Cairoli, V. Nicosia, A. Baule, V. Latora, + \textit{``Interplay between consensus and coherence in a model of interacting opinions''}, accepted + for publication in Physica D, arxiv:1506.04544 (2015). + + Link to paper: \url{http://arxiv.org/abs/1506.04544} +} +\newcommand{\refcommunity}{F. Battiston, J. Iacovacci, V. Nicosia, G. Bianconi, V. Latora, + \textit{``Emergence of multiplex communities in collaboration networks''}, arxiv:1506.01280 (2015). + + Link to paper: \url{http://arxiv.org/abs/1506.01280} +} + +\newcommand{\refaxelrod}{F. Battiston, V. Nicosia, V. Latora, M. San Miguel, + \textit{``Layered social influence promotes multiculturality''}, in preparation (2015). + + %Link to paper: \url{http://arxiv.org/abs/inpreparation} +} +\newcommand{\refmotifs}{F. Battiston, M. Chavez, V. Nicosia, V. Latora, + \textit{``Multilayer motifs in brain networks''}, in preparation (2015). + + %Link to paper: \url{http://arxiv.org/abs/inpreparation} +} + +\title{MAMMULT: Metrics And Models for MULTilayer networks} + + +\begin{document} + +\maketitle + +\chapter{Structural descriptors} + +\section{Basic node, edge, and layer properties} + +\subsection{Node and layer activity} + +This section includes programs related to the computation of node and +layer activity, activity vectors, pairwise multiplexity, pairwise +normalised Hamming distance, node degree vectors. + +\input{./latex/structure/activity/node_activity.tex} +\input{./latex/structure/activity/layer_activity.tex} +\input{./latex/structure/activity/node_activity_vectors.tex} +\input{./latex/structure/activity/layer_activity_vectors.tex} +\input{./latex/structure/activity/multiplexity.tex} +\input{./latex/structure/activity/hamming_dist.tex} +\input{./latex/structure/activity/node_degree_vectors.tex} +\input{./latex/structure/activity/degs_to_binary.tex} +\input{./latex/structure/activity/degs_to_activity_overlap.tex} + +\subsection{Layer aggregation} + +This section includes programs to obtain various single-layer +aggregated graphs associated to a multiplex network. + +\input{./latex/structure/metrics/aggregate_layers_w.tex} +\input{./latex/structure/metrics/intersect_layers.tex} + +\subsection{Node degree, participation coefficient, cartography} + +This section includes programs to compute the total degree and +participation coefficient of each node, and to draw the cartography +diagram of a multiplex. + +\input{./latex/structure/metrics/overlap_degree.tex} +\input{./latex/structure/metrics/cartography_from_layers.tex} +\input{./latex/structure/metrics/cartography_from_deg_vectors.tex} +\input{./latex/structure/metrics/cartography_from_columns.tex} + +\subsection{Edge overlap, reinforcement} +This section includes programs to compute the egde overlap and to +evaulate the edge reinforcement effect. + +\input{./latex/structure/metrics/edge_overlap.tex} +\input{./latex/structure/metrics/avg_edge_overlap.tex} +\input{./latex/structure/reinforcement/reinforcement.tex} + +\section{Inter-layer degree correlations} + +\subsection{Node ranking} + +This section includes various utilities to compute and compare node +rankings induced by any generic structural node property, including +degree at different layers. + +\input{./latex/structure/correlations/rank_nodes.tex} +\input{./latex/structure/correlations/rank_nodes_thresh.tex} +\input{./latex/structure/correlations/rank_occurrence.tex} + +\subsection{Interlayer degree correlation coefficients} + +This section includes programs for the computation of various +inter-layer degree correlation coefficients. + +\input{./latex/structure/correlations/compute_pearson.tex} +\input{./latex/structure/correlations/compute_rho.tex} +\input{./latex/structure/correlations/compute_tau.tex} + + +\subsection{Interlayer degree correlation functions} + +This section includes programs to compute intra-layer and inter-layer +degree correlation functions, and to fit those functions with a +power-law. + + +\input{./latex/structure/correlations/dump_k_q.tex} +\input{./latex/structure/correlations/knn_q_from_layers.tex} +%% \input{./latex/structure/correlations/knn_q_from_layers_log.tex} +\input{./latex/structure/correlations/knn_q_from_degrees.tex} +%% \input{./latex/structure/correlations/knn_q_from_degrees_log.tex} +\input{./latex/structure/correlations/fit_knn.tex} + +\chapter{Models of multi-layer networks} + +\section{Null models} + +\subsection{Null-models of node and layer activity} + +\input{./latex/models/nullmodels/model_hypergeometric.tex} +\input{./latex/models/nullmodels/model_MDM.tex} +\input{./latex/models/nullmodels/model_MSM.tex} +\input{./latex/models/nullmodels/model_layer_growth.tex} + + +\section{Growing multiplex networks} + +\subsection{Linear preferential attachment} + +\input{./latex/models/growth/nibilab_linear_delta.tex} +\input{./latex/models/growth/nibilab_linear_delay.tex} +\input{./latex/models/growth/nibilab_linear_delay_mix.tex} +\input{./latex/models/growth/nibilab_linear_random_times.tex} +%%\input{./latex/models/growth/nibilab_semilinear.tex} + +\subsection{Non-linear preferential attachment} + +\input{./latex/models/growth/nibilab_nonlinear.tex} + + +\subsection{Utilities} + +\input{./latex/models/growth/node_deg_over_time.tex} + +\section{Multiplex networks with inter-layer degree correlations} + +\subsection{Models based on simulated annealing} + +\input{./latex/models/correlations/tune_rho.tex} +\input{./latex/models/correlations/tune_qnn_adaptive.tex} + + +\chapter{Dynamics on multi-layer networks} + +\section{Interacting opinions - Multilayer ising model} + +\input{./latex/dynamics/Ising/multiplex_ising.tex} + +\section{Biased random walks} + +\subsection{Stationary distribution} + +\input{./latex/dynamics/randomwalks/statdistr2.tex} + +\subsection{Entropy rate} + +\input{./latex/dynamics/randomwalks/entropyrate2add.tex} +\input{./latex/dynamics/randomwalks/entropyrate2mult.tex} +\input{./latex/dynamics/randomwalks/entropyrate2int.tex} + +\end{document} -- cgit v1.2.3