This package contains the codes for the simulated results in: 
Dynamic Analysis of Higher-Order Coordination in Neuronal Assemblies via De-Sparsified Orthogonal Matching Pursuit

Data files:
	SimData.mat:					Simulated spiking data of 5 neurons
	SimResults_HistoryDependent.mat:		Saved results of history-dependent analysis, generated by HistoryDependentAnalysis_script.m

The following scripts can be run in MATLAB to generate the simulated result figure	
Script files:
	HistoryDependentAnalysis_script.m:		Perform history-dependent analysis of rth-order coordinated spiking in simulated data
	HistoryIndependentAnalysis_script.m:		Perform history-independent analysis of rth-order coordinated spiking in simulated data
	SingleTrialAnalyses_script.m:			Analyze simulated data with Pearson correlation, coefficient of variation, and avg. CIF difference

Functions:
	adomp_mGLM.m:					Implementation of AdOMP for dynamic history-dependent discretized MkPP model
	omp_mGLM_cv.m:					Cross-validate for sparsity level using static log-likelihood for discretized MkPP model
	getDesMat.m:					Construct set of history covariates for history-dependent analysis
	
	SynchHistTest_dynamic.m:			Statistical inference of rth-order coordinated spiking in history-dependent model
	SynchTest_dynamic.m:				Statistical inference of rth-order coordinated spiking in history-independent model
	NoncentChi2FiltSmooth.m:			State-space dynamic estimation of non-centrality parameter for characterizing limiting distribution of alt. hypothesis
	
	SynchCorrelation.m:				Avg. Pearson correlation as a single-trial measure of coordinated spiking
	SpikeRegularity.m:				Avg. Coefficient of variation in interspike intervals as a single-trial measure of higher-order coordinated spiking
	SynchCIF.m:					Avg. difference between rth-order mark CIFs and rate of independent rth-order interactions as a single-trial measure 
							of coordinated spiking

Codes were developed and tested using MATLAB R2017b.