Dynamical differential covariance (DDC)
Reference: https://www.pnas.org/doi/abs/10.1073/pnas.2117234119
All scripts were carefully annotated. Below is a quick summary.
Connectivity estimation:
- estimators.m: Common estimators including covariance <x,x>, Precision matrix, nonlinear averaging matrix <R(x),x>, dCov computed by symmetric difference quotient
- dCov_numerical.m: dCov calculated by different numerical estimations of the time derivative
- derivative_123.m: Supporting file for dCov_numerical.m
- DDC calculation: matrix product of dCov and <x,x>^{-1} or <R(x),x>^{-1}
- L2 regularized DDC calculation: dCov_linear_Reg.m
PSD Bootstrapping (evaluate significance of connections)
- PSDBootstrap_example.m: generate null timeseries under the null hypothesis that each time series is independent; calculate the null FC matrices
- PSDBootstrap_Getmdl.m: fit the best AR model to the order of q for each time series
Network simulations:
- Linear_simulation.m: simulation of linear stochastic systems
- Nonlinear_simulation.m: simulation of nonlinear stochastic systems
- LIF_network_YC.m: Leaky-integrate-and-Fire network simulation
- simulate_reduced_wong_wang.ipynb: Reduced Wong-Wang simulation
Performance evaluation:
- FC_GT_ROC.m: classification sensitivity for LIF network recovery
- c_sensitivity_YC.m: c-sensitivity calculation
HCP dataset
- rs-fMRI time series data available through https://www.humanconnectome.org
- dMRI dataset available through https://www.eneuro.org/content/8/1/ENEURO.0416-20.2020/tab-article-info
- ATLAS_HCP_dMRIparcel_to_IC100node_connectivity.m: convert parcel-level dMRI strength to IC-level dMRI strength
Demo (MATLAB syntax):
For HCP ICA preprocessed time series:
TR = 0.72;
[T, N] = size(V); % number of timepoints x number of nodes
V_obs = zscore(V)
[dCov1, dCov2,~,~] = dCov_numerical(V_obs,TR);
[Cov,Precision,B,~] = estimators(V_obs,prctile(V_obs(:),50),TR);
Delta_L = dCov2*Precision
Delta_ReLU = dCov2*B