% 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
%
% example3.m generates different time series for kuramoto2 systems and
% reconstructs them under radial basis functions of different orders.
% Greater orders (number of employed basis functions) lead to better results.
%
% 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 different number of bases.
%
% 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'};

N=25;
NI=4;
S=30;
M=10;
NODE=15;

simulate(MODEL{2},25,4,30,10);

ORDER=[5,10,15,20,25,30];
figure('Name','Reconstruction using different number of RBF');

% This may take several minutes
t=1;
for k=ORDER
    [list,cost,FPR,TPR,AUC]=reconstruct(MODEL{2},NODE,BASIS{6},k);
    subplot(2,3,t);
    plot(cost,'-o','LineWidth',2.5,'Color',[0,0.7,0.9],'MarkerFaceColor',[0,0.7,0.9]);
    title({['Fitting Costs: ',num2str(k),' RBF'],['AUC=',num2str(AUC)]});
    xlabel('# Inferred Interactions');
    ylabel('Cost');
    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:
    0.9643

Initiating reconstruction...
Reading data...
Estimating time derivatives and constructing input matrices...
Performing ARNI...
Reconstruction has finished!
Quality of reconstruction:
    0.9762

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

Published with MATLAB® R2016b