% Algorithm for Revealing Network Interactions (ARNI)
%
% "Model-free inference of direct network interactions from nonlinear collective dynamics"
% Jose Casadiego, Mor Nitzan, Sarah Hallerberg and Marc Timme
% Nature Communications 8, 2192 (2017)
% https://doi.org/10.1038/s41467-017-02288-4
%
% example4.m compares the quality of reconstruction between short and long
% time series with poor temporal resolution on networks of coupled
% chaotic roessler systems. Several short time series are preferable over
% long time series for this type of systems.
%
% Parameters
% ------------------
% MODEL: Dynamical model on network units. Currently, only kuramoto1,
%        kuramoto2, michaelis_menten and roessler are supported. For
%        detailed information about the models, please check methods
%        section in the main manuscript.
% N:     Network size.
% NI:    Number of incoming connections per unit.
% S:     Number of different time series.
% M:     Number of time points per time series.
% NODE:  Unit upon the reconstruction takes place.
% BASIS: Type of basis employed. Currently, polynomial, polynomial_diff,
%        power_series, fourier, fourier_diff and RBF are supported. For
%        more detailed information, please see 'Functions/basis_expansion.m'
%        and Table I in the main manuscript.
% ORDER: Number of bases in the expansion.
%
% Input type
% ------------------
% MODEL: string
% N:     integer
% NI:    integer (NI<N)
% S:     integer
% M:     integer
% NODE:  integer
% BASIS: string
% ORDER: integer
%
% Output
% ------------------
% Figures showing the evolution of fitting costs versus the number of inferred
% interactions using short and long time series on roessler models.
%
% Author: Jose Casadiego
% Date:   June 2018

close all;
addpath('Models/','Functions/')

MODEL={'kuramoto1','kuramoto2','michaelis_menten','roessler'};
BASIS={'polynomial','polynomial_diff','fourier','fourier_diff','power_series','RBF'};
NODE=randperm(25,4);

N=25;
NI=4;
S=50;
M=5;
ORDER=6;

simulate(MODEL{4},N,NI,S,M);

figure('Name','Reconstruction of oscillators using short time series');

% This may take several minutes
t=1;
for node=NODE
    [list,cost,FPR,TPR,AUC]=reconstruct(MODEL{4},node,BASIS{1},ORDER);
    subplot(2,2,t);
    plot(FPR,TPR,'LineWidth',2.5,'Color',[0,0.7,0.9]);
    title(['ROC Curve-Unit: ',num2str(node)]);
    xlabel('FPR');
    ylabel('TPR');
    text(0.4,0.5,['AUC score=',num2str(AUC)])
    t=t+1;
end
set(gcf,'Position',[0 0 1000 500])

S=5;
M=50;

simulate(MODEL{4},N,NI,S,M);

figure('Name','Reconstruction of oscillators using long time series');

% This may take several minutes
t=1;
for node=NODE
    [list,cost,FPR,TPR,AUC]=reconstruct(MODEL{4},node,BASIS{1},ORDER);
    subplot(2,2,t);
    plot(FPR,TPR,'LineWidth',2.5,'Color',[0,0.7,0.9]);
    title(['ROC Curve-Unit: ',num2str(node)]);
    xlabel('FPR');
    ylabel('TPR');
    text(0.4,0.5,['AUC score=',num2str(AUC)])
    t=t+1;
end
set(gcf,'Position',[0 0 1000 500])

'rm' is not recognized as an internal or external command, 
operable program or batch file. 
A subdirectory or file Data already exists. 
Creating network structure...
Simulating time series...
Simulation finished!
Initiating reconstruction...
Reading data...
Estimating time derivatives and constructing input matrices...
Performing ARNI...
Reconstruction has finished!
Quality of reconstruction:
     1

Initiating reconstruction...
Reading data...
Estimating time derivatives and constructing input matrices...
Performing ARNI...
Reconstruction has finished!
Quality of reconstruction:
     1

Initiating reconstruction...
Reading data...
Estimating time derivatives and constructing input matrices...
Performing ARNI...
Reconstruction has finished!
Quality of reconstruction:
     1

Initiating reconstruction...
Reading data...
Estimating time derivatives and constructing input matrices...
Performing ARNI...
Reconstruction has finished!
Quality of reconstruction:
     1

'rm' is not recognized as an internal or external command, 
operable program or batch file. 
A subdirectory or file Data already exists. 
Creating network structure...
Simulating time series...
Simulation finished!
Initiating reconstruction...
Reading data...
Estimating time derivatives and constructing input matrices...
Performing ARNI...
Reconstruction has finished!
Quality of reconstruction:
    0.7150

Initiating reconstruction...
Reading data...
Estimating time derivatives and constructing input matrices...
Performing ARNI...
Reconstruction has finished!
Quality of reconstruction:
    0.6111

Initiating reconstruction...
Reading data...
Estimating time derivatives and constructing input matrices...
Performing ARNI...
Reconstruction has finished!
Quality of reconstruction:
    0.5652

Initiating reconstruction...
Reading data...
Estimating time derivatives and constructing input matrices...
Performing ARNI...
Reconstruction has finished!
Quality of reconstruction:
    0.6884

Published with MATLAB® R2016b