The Neuroscientist's tale

I've been reading Brad Voytek's blog since my second year of undergraduate, and his writing has certainly had an influence in my interest to pursue Computational Neuroscience. Recently he acquired a tenure track position at UCSD, and has written about his journey there. It ends with some pretty decent advice that I'll try not to forget over the next few years.

http://blog.ketyov.com/2013/07/the-neuroscience-tenure-track.html

LIUF 2013 Semi-Final

This was semi-final of a fencing competition I took part in recently. I was 12-8 up at one point, somehow managed to concede 7 hits in a row without even scoring a double hit.



Hopefully I'll learn from the experience...

Spike Triggered Average

A spike triggered average is a method used in Neuroscience to determine the stimulus that a cell is selective for, by averaging over stimuli presented over a given time window before each spike. An efficient representation of this is the Wiener kernel formulation, which works when the stimulus can be characterised as Gaussian white noise, and works even better when it is possible to get synchronised noisy spike trains across many trials so as to smooth out some of the responses with the intrinsic noise. This basically cross-correlates the average spiking activity over many trials (not necessarily averaged across time, but some smoothing can be useful), and normalises by the variance of the stimulus to extract a filter that describes the system that relates stimulus to response. In other words, it's a model of a neuron that says the neuron is just a filter for the stimulus to output a spiking response.

One of the properties of Gaussian white noise is that all frequencies are present in the data, i.e., that samples are uncorrelated in time. However, as with any random sample it's likely there is some spurious autocorrelation present, so it's worth accounting for. In this case, a correction is quite easy to implement. It also reduces some of the need for regularisation

Again, in MATLAB:

function g = STA(r, s, window, lambda)

% Finds the first-order Wiener kernel g that corresponsds to the spike-triggered average of a neuron. Assume neural response r and stimulus s are row vectors. Lambda is regularisation constant. Window is the length of the filter to be extracted.

% Cross-correlate and extract filter.

xrs = xcorr(r - mean(r),s,window, 'unbiased');

xrs = xrs(1:window+1);

% Correct for autocorrelation

xss = xcorr(s, 2*window, 'unbiased');

xss = circshift(xss, [0, -2*window]);

xss = xss(1:window+1);

XSS = toeplitz(xss);

% Regularise

S = XSS + lambda*eye(size(XSS));

% Extract filter

g = S\xrs'; 

Modular Robotics

I showed this to my family a few months ago...


They didn't get it. I was unbelievably excited when I saw this video. All ten minutes of it. They just sat there looking a little bored and started complaining very quickly. If anything I thought my younger brothers might be impressed by the implications for real life Transformers.

To me this is what the future of robotics will be: small uniform cell-like components that rearrange to perform a task. Of course, these modules are still fairly large and will need a few re-designs to get them on the same scale as biological cells. But as far as I can tell this is the right direction to be going in. A lot of people will possibly disagree, but I think the major advances that will be seen in robotics will be biologically inspired.

The main argument I see for this is that the process of robotics research has been slowly developing over the last century or so, with some great stumbling blocks in terms of creating any naturalistic movement e.g. walking. However the process of evolution has been tackling these problems waaaay longer, and so we are likely to see some 'designs' already optimised for these problems in Biology. This does of course require actually understanding the biophysics of each solution, but implementing these solutions in robots could actually be used to validate understanding. In the case of the above robot, it isn't really addressing anything like biophysically plausible motion (it's more an exercise in logic programming as far as I can tell) but I can see something like being used as a model of skeletal cells, which can be applied to motion.

One argument against this I've heard, is that by studying Biophysics we are only studying one implementation of the problem, rather than creating an appropriate solution, e.g., we didn't need to study birds to build the aeroplane. However I would argue that the computational constraints we see in robotics controllers are in many cases the same as in neural controllers, so by studying the optimal solution found in neural controllers and implementing in a robotic controller would actually solve the problem at hand.

So far, I've seen some of the work in Edinburgh looking at insect motion (I turned down the opportunity to work with these- a slight hint of regret), which isn't using anything modular like this. So it may even be the case that it is unnecessary to use modular components at all to create decent biologically inspired designs. Ignoring issues of complexity (I can hear the dismissal of my argument already), tackling these issues with more modular designs seems like a worthy pursuit.

Manipulating spike count variance

Using a leaky integrate and fire neuron to generate spiking from fluctuating stimuli, but I wanted to generate data with different spike count variance. The problem came when two sources of variance worked to change other aspects of spike counts I didn't want. Increasing trial-by-trial noise promoted noise-driven activity, i.e., the rate went up, but the variance didn't increase that much. Increasing stimulus noise (which in truth shouldn't really be called noise, since it is these fluctuations that drive spiking), rapidly increased the firing rate and actually decreased spike variance.

These two forces needed to be balanced then. For future reference, muck about by decreasing stimulus noise, and increasing trial-by-trial noise.

Time-Correlated Gaussian Noise

Short Matlab script for generated time-correlated gaussian noise thanks to my supervisor. It takes the previous sample and generated a new sample with sampling rate dt based on a gaussian with time constant tau, mean mu and sd sig.

function y = tcorr_randn(y_prev,mu, sig, tau, dt)

y = mu + (y_prev - mu)*exp(-dt/tau) + sig*sqrt(1-exp(-2*dt/tau))*randn;

end

Interspike intervals: The fast way?

A reminder for myself more than anything

For a set of spike data distributed across time, i.e., a N x T matrix, where N is number of cells, T is total time steps dt:

function [ints, spt] = isi(spikes, dt)

% Uses spike data to output interspike intervals and accompanying spike times.

[N, T] = size(spikes);

ints = []; % intervals

spt = []; % spiketimes

% Find isi for each cell

for n = 1:N

    spiketime = find(spikes(n,:) == 1);

    ints = [ints,spiketime(1),diff(spiketime)];

    spt = [spt,spiketime];

end

if isempty(ints)

    ints = inf;

end

ints = ints/(dt*T);

[spt col] = sort(spt, 'ascend'); spiketimes in ascending order

ints = ints(col); intervals sorted by spiketime

end

I would very much like to know if there is a faster way, particularly if it means I could find for all cells at once. Currently it isn't completely matlab efficient.