These two analyses are from Raposo*, Kaufman*, and Churchland 2014, and are implemented in Matlab code. PAIRS stands for "Projection Angle Index of Response Similarity", and is a method for determining whether recorded neurons' responses are more clustered than expected by chance. Variance Alignment is a method for determining whether two sets of data from the same neurons share similar covariance patterns. For example, you might be interested in whether neurons exhibit similar covariance patterns during stimulus presentation and movement, or during presentation of a visual stimulus versus during presentation of an auditory one. See the paper or the comments in the code for further explanation. Variance Alignment requires the Statistics Toolbox.

Demixing Principal Component Analysis (dPCA) is a really useful technique invented by Wieland Brendel and Christian Machens. It is much like PCA, but tries to rotate your axes so that each component contains signals from only one source. For example, some components might contain only untuned activity that ramps with time, while others might contain the tuning you're interested in. All credit for this technique goes to Wieland and Christian; it's listed here because I really like the technique (and made a very small contribution to the Matlab code).

This isn't exactly software, but TeX is almost programming. Wondering how to write an academic document (especially a dissertation) in TeX but don't know how? Check out the guide I wrote.