empirical_dynamic_modelling

Repo for running empirical dynamic modelling techniques on data, using lagged coordinate embedding to perform simplex projection and convergent cross mapping (CCM) - techniques which can account for non-linear dynamics to reconstruct attractors from time series data. This is a work in progress!

See Sugihara et al. CCM - https://www.science.org/doi/abs/10.1126/science.1227079

Simplex projection - https://www.nature.com/articles/344734a0

What is this repo for?

• the implementation of lagged coordinate embedding on time series data
• the implementation of simplex projection
• the implementation of convergent cross mapping (CCM) on time series data
• the analysis and visualisation of CCM results

What does this repo contain?

• Modules contain functions for running convergent cross mapping, lagged coordinate embedding and evaluating CCM results
• Accompanying ipynotebooks demonstrate how to use the modules

Modules

'admin_functions.py' - useful administrative functions

'EDM.py' - functions for performing empirical dynamic modelling

'CCM.py' - functions and classes for implementing convergent cross mapping

'kedm_script.sh' - shell script for batch running kedm on salk system

Notebooks

'LE.ipynb' - estimating the lyapunov exponent using lagged coordinate embedding on spontaneous and seizure time series.

'CCM_run.ipynb' - running and implementing CCM algorithm

'CCM_process.ipynb' - preprocessing activity data for running CCM using kEDM

'CCM_ptz_anat.ipynb' - applying CCM to whole brain single cell PTZ-seizure data to understand role of brain anatomy in driving seizures

'CCM_ptz_nonlinear.ipynb' - applying CCM to whole brain single cell PTZ-seizure data to understand role of non-linear dynamics in driving seizures

'CCM_ptz_predict.ipynb' - applying CCM to whole brain single cell PTZ-seizure data to predict seizures