Code packages are provided for:


As used in Russo et al. 2018.


Variance toolbox

This variance toolbox was used for the publication: Churchland MM et al. (2010)  Stimulus onset quenches neural variability: a widespread cortical phenomenon. Nat. Neurosci.

This code has been successfully adapted and used by other laboratories, e.g., Cohen and Maunsell (2009) Attention improves performance primarily by reducing interneuronal correlations. Nat. Neurosci.



The jPCA method was introduced in: Churchland MM et al. (2012)  Structure of neural population dynamics during reaching. Nature. 

jPCA has been used in a number of subsequent publications both by us and by other laboratories, e.g., Michaels et al. (2016) Neural Population Dynamics during Reaching Are Better Explained by a Dynamical System than Representational Tuning.

More recently introduced methods may be preferable to jPCA, depending on the application. In particular, see the HDR method introduced in: Lara AH, Cunningham JP, Churchland MM (2018) Different population dynamics in the supplementary motor area and motor cortex during reaching. Nature Communications

jPCA is a simple and easy-to-use method, but does have some drawbacks that are addressed by the HDR method. jPCA involves removing the time-varying cross-condition mean. In practice this is often acceptable (acceptability can be confirmed via subsequent controls) but for some datasets this may make very asymmetric rotations appear symmetric. The newer HDR method sidesteps this problem, and is more principled in a variety of ways. For motor cortex data. jPCA and HDR produce very similar results. Yet this may not hold in all cases. jPCA may still be the preferred first way to analyze data, but we suggest applying HDR for any scenario where interpretability is a large concern (e.g., if you are concerned that weak rotational structure is exaggerated).

Key optimization code underlying HDR is provided here. However, a specific HDR code package does not exist. Indeed a virtue of HDR is that the cost function can be adapted by the user to embody the hypotheses relevant to the data being analyzed (in contrast, jPCA embodies a single hypothesis: some dimensions may contain rotational dynamical structure).

Columbia Affiliations
Columbia University
Grossman Center for the Statistics of Mind
Zuckerman Mind Brain Behavior Institute