% 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
%
% example1.m generates different time series of networks of dynamical
% systems starting from different intial conditions and reconstructs the
% connectivity for a selected unit. Increasing the number of different time
% series leads 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
% ------------------
% Figure showing: (1) evolution of fitting costs versus the number of inferred
% interactions with actual inferred interactions; and, (2) Receiver-Operating
% -Characteristic Curve.
%
%
% Author: Jose Casadiego
% Date:   June 2018

clc;
clear;
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=50;
M=5;
ORDER=6;

simulate(MODEL{2},N,NI,S,M);

NODE=21;

tic();
[list,cost,FPR,TPR,AUC]=reconstruct(MODEL{2},NODE,BASIS{2},ORDER);
toc();

figure('Name',['Reconstruction for unit ',num2str(NODE)]);
ax1=subplot(2,1,1);
plot(cost,'-o','LineWidth',2.5,'Color',[0,0.7,0.9],'MarkerFaceColor',[0,0.7,0.9]);
title({'Evolution of Fitting Costs';'(Actual connections shown above)'});
xlabel('# Inferred Interactions');
ylabel('Cost');

for i=1:length(cost)
    text(1.01*i,1.03*cost(i),num2str(list(i)))
end

ax2=subplot(2,1,2);
plot(FPR,TPR,'LineWidth',2.5,'Color',[0,0.7,0.9])
title('Receiver-Operating-Characteristic Curve');
xlabel('False Positives Rate');
ylabel('True Positives Rate');
text(0.4,0.5,['AUC score=',num2str(AUC)])

'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

Elapsed time is 1.095521 seconds.

Published with MATLAB® R2016b