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