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Welcome to our first guest lecture in Computational Neuroscience.

Â We're honored to have with us today Federiki, my colleague in the department

Â of physiology and biophysics at the University of Washington.

Â Fred was an undergraduate and graduate student at the University of California

Â in Berkeley. His graduate work [UNKNOWN] focused on

Â building theoretical studies of signal processing in the nervous system.

Â Fred then went on to a post-doc with Eric Schwartz at the University of Chicago,

Â working on mechanisms of synoptic transmission in the retina.

Â He then did a second post-doc with Dennis Baylor at Stanford, where he worked on

Â light transduction in photo-receptors. So, Fred is truly remarkable in having

Â made a transition from truly elegant theoretical work.

Â Which led to the publication of what's been a highly influential book, Spikes,

Â to truly elegant experimental work. The creativity and excellence of Fred's

Â work has lead to his recognition as an investigator at the Howard Hughes Medical

Â Institute. In his work, Fred combines a mastery of

Â technique with a beautiful clarity of thought.

Â And we're delighted to give you this opportunity to hear from him a little bit

Â about his research. >> Thanks for the introduction.

Â My lecture today will be about vision and starlight and the mechanisms that let us

Â see under these conditions. We know, from a long history of

Â behavioral measurements, that our ability to see under these conditions is limited

Â more by the division of light into discreet photons.

Â The physical nature of light itself, than it is by biological noise and

Â inefficiencies. As we'll see in a minute, that raises

Â some general computational issues. First, let me introduce the retina

Â itself, which is where the visual process begins.

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So, the situation we're thinking about is a few rods out a of a pool of a thousand

Â absorb photons, all of the rods are generating noise.

Â We want to know how to pool signals across those rods to reliably extract

Â signals from those rods that absorbed photons.

Â Those sparse signals can reject noise from the remaining rods.

Â This is a situation where averaging, you normally think about averaging as being a

Â good strategy to extract weak signals. Under these circumstances, averaging is a

Â disaster. That's because the signal is not

Â uniformly spread across the array of detectors.

Â It's a little bit like a situation where you're in a football stadium.

Â There's a 1000 people yelling of you, you care about a few of them.

Â Under those circumstances, a good strategy for extracting signals from

Â those few people you care about would not be to stick a microphone at the 50 yard

Â line. And average across everybody, all those

Â sources of sound in the stadium. Instead you would need to go seat by seat

Â and make a selection, is this likely to be the person who I care about, based on

Â some prior information about them. Say the, the people you care about gotta

Â be a little bit louder than average. So you go seat by seat, make a selection

Â about which people to retain, which people to reject and then average those

Â resulting signals. So, looking for something analogous here.

Â That is, we're looking for some kind of threshold, which selectively retains

Â signals from those rather likely to be absorbing photons.

Â And rejects noise from the remaining from the remaining rods.

Â The behavioral consequences for getting this right are fairly extreme, that's

Â because the signal is so sparse. If we can reject noise from the 99.9% of

Â rods that are just generating noise and selectively retain signals from the on

Â order of .1% of the rods, that absorb photons.

Â We stand to win considerably. Okay.

Â So, what we're looking for then is some kind of thresholding non linearity, which

Â retains signals from those rods that absorb photons and rejects noise from the

Â remaining rods. They mention this as a general issue,

Â it's one that comes up in many other cases in the nervous system.

Â Cases in which you have convergence of many inputs onto a downstream cell and a

Â small subset of those inputs are active while all of the inputs are generating

Â noise. There are a number of conceptual and

Â technical advantages for studying this issue in the context of photon detection

Â in the retina. One of those is that we have access to

Â the signal and noise properties of the rod photo receptors, so we can measure

Â the responses of the rods to single photons.

Â We can measure the noise and the rod responses and we can summarize those by

Â constructing distributions, that capture the probability that the rod generates a

Â given amplitude response. We can plot that as probability versus

Â amplitude. For those rods in black that failed to

Â absorb a photon and are just generating noise.

Â And those rods in red that absorbed a photon and are generating single photon

Â response. Those give us the basis for making

Â theoretical prediction about how to make a selection between signal and noise.

Â Particularly, we might think that this threshold in non-linearity should come

Â in, and slice out and eliminate responses from those rods that are generating

Â noise. And retain responses from those rods that

Â generate single photon responses. It's nice because we have a theoretical

Â basis for what an appropriate readout might be, for the rod array under these

Â conditions. We also know a great deal from the

Â anatomy about where such a thresholding non-linearity might be implemented.

Â In particular, the rod signals traverse the retina through a specialized circuit.

Â The first cell in that circuit is known as a rod bipolar cell.

Â And rod bipolar cells receive input from multiple rods.

Â So, that means that they have already combined signals from multiple rods.

Â If they do so in a linear fashion, in other words they equally weight inputs

Â from rods that are generating noise and signal.

Â You've already begun to average the rod responses and you've begun to

Â inextricably mix signal and noise. So, the last opportunity, where we have

Â access to the responsive individual rod photoreceptors.

Â We have the full capability of making a selection of those rods that are

Â absorbing photon, and generating single proton response.

Â Versus signals or noise from those rods that fail to absorb a photon.

Â Is here at the synap between the rods and the rod bipolar cell.

Â So, anatomically we have a good prediction about where such a

Â thresholding non-linearity might occur. It should occur at the synapse between

Â rods and rod bipolar cells. Indeed if we record from rod bipolar

Â cells, we see evidence for such a thresholding non-linearity.

Â We can now take the measured distribution of rod signal and noise, and ask what the

Â appropriate non-linearity is to predict the bipolar responses.

Â I summarize that here. So, again these, this is plotting

Â probability versus the amplitude, the distribution of rods that are generating

Â noise responses. And the distribution of responses from

Â rods that absorbed the protons. On the same scale, I plotted the

Â estimated non-linearity at the synapse between the rods and the rod bipolar

Â cells. That's here in blue.

Â I plotted gain of the non-linearity versus the amplitude.

Â So, you think of this non-linearity as everything to the left get's eliminated.

Â So, all this noise and a good chunk of the single proton response distribution

Â gets eliminated. And only those responses that are to the

Â right of this transition from the non-linearity between the gain of 0 and 1

Â are retrained. So, we see evidence for non linear

Â threshold between rod and rod-bipolar cells, it's kind of what predicted.

Â Interesting thing here is, that we not have predicted the location of this non

Â linearity. In particular, it is located well up into

Â the single photon response distribution. Naively we might look at these and say,

Â well I should really put a line here, right at the crossing point between the

Â noise distribution and the signal distribution.

Â That would be choosing a location for this threshold in non-linearity, which

Â makes a decision based on the likelihood of the given amplitude response.

Â If the amplitude of the response is, is if a given amplitude response is more

Â likely to have arisen from this distribution of single photon responses,

Â we would retain it. If it's more likely to have risen, arisen

Â from the noise distribution, we would eliminate it.

Â Instead this thresholding non-linearity seems to be pushed off to the right.

Â In other words, we're eliminating many single photon responses, which seems like

Â exactly the opposite of what we'd like to do, to build a system that operates on

Â low light levels. However, this particular way of plotting

Â the data, is somewhat misleading. An what we've not accounted for here, is

Â the prior probability that the rod absorbs a photon.

Â You can think about that as there is some area under this curve, the noise curve

Â which represents the likelihood if the rod is generating noise.

Â There is some area here under the single proton response distribution curve, which

Â is the likelihood of probability the rod absorbs a photo.

Â 11:39

However we really want to think about these distributions as what would happen

Â near visual threshold, when something like one in ten thousand rods absorb a

Â photon. And that's what I've plotted over here.

Â So, now the area underneath the noise distribution and the signal distribution

Â had been scaled to represent this prior probability that something like 1 in

Â 10,000 robs absorbs a photon. So, the area under the signal

Â distribution here is 10,000 times smaller than the area under the noise

Â distribution. That shifts this crossing point of the

Â signal and noise distribution far out to the right.

Â And it shifts it to a point that's very close to the location of the transition

Â of the non-linearity between a gain of 0 and a gain of 1.

Â In other words, if you're simply applying a rule like maximum likelihood, you get a

Â given amplitude response from the rod. And you're going to associate that with

Â noise, if that amplitude is more likely to have originated from the noise

Â distribution. You're going to associate it with signal

Â if that amplitude is more likely to have originated from the signal distribution.

Â That simple rule can predict the position of this nonlinearity and predict in

Â particular that you should throw away many single photon responses.

Â You should do that because the cost of accepting those amplitudes, down in here,

Â is to allow lots of noise to come through the system.

Â Much more noise than you would like to allow to come through.

Â So, the basic bottom line here is the nice example in which the prior

Â probability has an important impact on how we think about signal detection

Â theory working. Now we think about appropriate strategies

Â for extracting sparse signals from many noisy inputs.

Â