The Information Theory of Developmental Pruning: Optimizing Global Network Architecture Using Local Synaptic Rules

Another paper from the Hennig lab is out, this one is from Carolin Scholl's master's thesis. Once again, we used an artificial neural network to get intuition about biology. The paper is on BioRiv, and you can also get the PDF here. 

Brain–Machine Interfaces: Closed-Loop Control in an Adaptive System

Edit: I'm pleased to announce that the in-press preprint is now available from Annual Reviews [pdf].

During the first pandemic lockdown in 2020, I had the pleasure of preparing an introductory review on brain-machine interfaces with Ethan Sorrell. It will be published in the 2021 Annual Review of Control, Robotics, and Autonomous Systems. The review is in press now, but I thought I'd share a little sneak peak by way of some figures.

More figures and clip-art are on github. The clip art and figure components are free to reuse (CC NY-NC 4), but Annual Reviews owns the copyright to composed figures and sub-figures.

Convolution with the Hartley transform

The Hartley transform can be computed by summing the real and imaginary parts of the Fourier transform.

\begin{equation}\begin{aligned} \mathcal F \mathbf a &= \mathbf x + i\mathbf y \\ \mathcal H \mathbf a &= \mathbf x + \mathbf y, \end{aligned}\end{equation}

where $\mathbf a$, $\mathbf x$, and $\mathbf y$ are real-valued vectors, $\mathcal F$ is the Fourier transform, and $\mathcal H$ is the Hartley transform. It has several useful properties.

• It is unitary, and also an involution: it is its own inverse.
• Its output is real-valued, so it can be used with numerical routines that cannot handle complex numbers.
• It can be computed in $\mathcal O (n \log(n))$ time using standard Fast Fourier Transform (FFT) libraries.

Gaussian process models for hippocampal grid cells

These notes are structured as an iPython/Jupyter notebook tutorial written in python 3, and depend only on the numpy and scipy libraries. [download as: .ipynb , .html , .pdf ]

Gaussian Processes (GPs) generalize the idea of multivariate Gaussian distributions to distributions over functions. In neuroscience, they can be used to estimate how the firing rate of a neuron varies as a function of other variables (e.g. to track retinal waves ). Lately, we've been using Gaussian processes to describe the firing rate map of hippocampal grid cells .

We review Bayesian inference and Gaussian processes, explore applications of Gaussian Processes to analyzing grid cell data, and finally construct a GP model of the log-rate that accounts for the Poisson noise in spike count data. Along the way, we discuss fast approximations for these methods, like kernel density estimation , or approximating GP inference using convolutions.

Edit: There is a bug in the "covariance_crosshairs" function, there should be a square-root around "chi2.isf(1-p,df=2)".