% 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
%
% example2.m generates different time series for two different dynamical
% systems under different types of coupling functions, ($$h(x_j)$$ and $$h(x_i,x_j)$$)
% starting from different intial conditions and reconstructs the connectivity
% for a selected unit. Increasing the number of different time series leads
% to better results. Bivariate coupling functions are only correctly
% represented by bivariate coupling functions. Analogously, univariate
% functions are only correctly represented by univariate basis functions.
%
% 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 bases for models kuramoto2 and
% michaelis_menten.
%
% 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'};
NAMES={'Polynomial','Polynomial Diff','Fourier','Fourier Diff','Power Series','Radial Basis Function'};

N=25;
NI=4;
S=30;
M=10;
NODE=15;
ORDER=6;

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

% This make take several minutes
figure('Name',['Reconstruction with different basis for ', MODEL{2}]);
for i=1:length(BASIS)
    [list,cost,FPR,TPR,AUC]=reconstruct(MODEL{2},NODE,BASIS{i},ORDER);
    subplot(2,3,i);
    plot(cost,'-o','LineWidth',2.5,'Color',[0,0.7,0.9],'MarkerFaceColor',[0,0.7,0.9]);
    title({['Fitting Costs: ',NAMES{i}],['AUC=',num2str(AUC)]});
    xlabel('# Inferred Interaction');
    ylabel('Cost');
end
set(gcf,'Position',[0 0 1000 500])

simulate(MODEL{3},N,NI,S,M);

% This make take several minutes
figure('Name',['Reconstruction with different basis for ', MODEL{3}]);
for i=1:length(BASIS)
    [list,cost,FPR,TPR,AUC]=reconstruct(MODEL{3},NODE,BASIS{i},ORDER);
    subplot(2,3,i);
    plot(cost,'-o','LineWidth',2.5,'Color',[0,0.7,0.9],'MarkerFaceColor',[0,0.7,0.9]);
    title({['Fitting Costs: ',NAMES{i}],['AUC=',num2str(AUC)]});
    xlabel('# Inferred Interactions');
    ylabel('Cost');
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:
    0.3095

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:
    0.2262

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:
    0.9881

'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:
    0.3550

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:
    0.3850

Initiating reconstruction...
Reading data...
Estimating time derivatives and constructing input matrices...
Performing ARNI...
Reconstruction has finished!
Quality of reconstruction:
    0.8000

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

Published with MATLAB® R2016b