[00:00.920 --> 00:07.820]  Yes, so they're nocturnal, they're mammals, and they echolocate for the most part.
[00:08.040 --> 00:11.480]  Actually, it's a very large, there are many different species of bats.
[00:12.380 --> 00:18.560]  And this is a member of microchoroptera, which means it's small.
[00:19.300 --> 00:20.860]  And it's insectivorous.
[00:22.000 --> 00:25.140]  I'll save some more for later, but not all bats actually echolocate.
[00:25.300 --> 00:30.340]  There's some that are called whispering bats that just whisper, as in it's very difficult to pick up the echolocation call.
[00:30.360 --> 00:33.280]  And they tend to work by olfaction, that is, smelling.
[00:33.980 --> 00:35.760]  They tend to be fruit-eating bats instead.
[00:37.560 --> 00:40.180]  Anyway, so here's a brief outline of the talk.
[00:40.340 --> 00:44.760]  I'll introduce some words, buzzwords mainly, only three of them in fact.
[00:45.100 --> 00:47.040]  We'll talk some about acoustics and sonar.
[00:47.820 --> 00:49.980]  We will talk some about echolocation.
[00:50.740 --> 00:55.800]  And then, so, I say primer to neuroscience, really I don't go into much depth at all.
[00:56.340 --> 00:58.440]  We can go into more depth if you're interested.
[00:58.720 --> 01:03.180]  And so, and that's in that sense, I want the talk to be such that you can interrupt at any moment.
[01:03.320 --> 01:08.120]  If I say something that's very unclear, or you'd like me to go into more depth.
[01:08.840 --> 01:13.600]  There are questions at the end, but if it waits for that long, and if you don't have pen and paper, you'll probably forget.
[01:13.860 --> 01:16.560]  And so, I think it'd be more meaningful if you interrupt as needed.
[01:18.660 --> 01:20.320]  So, reversing biological systems.
[01:20.520 --> 01:21.340]  That's the theme, actually.
[01:21.440 --> 01:23.040]  I don't have slides to that end.
[01:24.720 --> 01:28.580]  But we'll talk a bit more as I go.
[01:29.040 --> 01:31.460]  It's sort of a pervasive aura of the presentation.
[01:31.860 --> 01:34.680]  And then I'll talk some about studying the sonar beam of bats.
[01:37.780 --> 01:39.020]  Cute words.
[01:39.680 --> 01:43.100]  So, has everyone seen these words before?
[01:44.020 --> 01:44.440]  Yeah?
[01:44.780 --> 01:45.320]  Biomimetic?
[01:45.660 --> 01:49.200]  So, the idea with biomimetic is that there's something that mimics a biological system.
[01:51.220 --> 01:55.660]  Even at the cost of some sub-optimality of the system.
[01:56.180 --> 02:00.200]  So, to be clear, optimality is defined with respect to some criterion.
[02:00.600 --> 02:03.100]  For example, we want to minimize power consumption.
[02:03.100 --> 02:05.300]  We want to minimize weight.
[02:05.560 --> 02:09.660]  Or we want to maximize flight time.
[02:09.960 --> 02:11.140]  A variety of parameters.
[02:11.380 --> 02:12.500]  And so, you optimize with respect to those.
[02:12.680 --> 02:13.700]  Biomimetic doesn't seek to do that.
[02:13.800 --> 02:16.000]  It seeks to mimic the biological system.
[02:16.540 --> 02:18.480]  An example project is a robotic samara.
[02:19.020 --> 02:20.500]  I might not be pronouncing that correctly.
[02:20.680 --> 02:23.200]  It's a type of seed that has a wing on it.
[02:23.240 --> 02:23.900]  A single blade.
[02:24.100 --> 02:25.420]  I'm sure you've seen them outside before.
[02:25.740 --> 02:27.840]  They fall from a tree and spin in land.
[02:27.960 --> 02:28.680]  Does everyone know those?
[02:28.780 --> 02:30.140]  You can pick them up and make them do it again.
[02:30.920 --> 02:35.280]  There's a group at the University of Maryland that found out the physics involved in that.
[02:35.480 --> 02:37.940]  And then made a robotic implementation.
[02:38.320 --> 02:40.900]  So, it's a single blade helicopter.
[02:41.400 --> 02:43.440]  We could look at videos after the talk, if you're interested.
[02:43.780 --> 02:44.940]  And I have links and so on.
[02:46.100 --> 02:52.660]  Bioplausible is something that could, in principle, be implemented in a biological system, but not necessarily.
[02:53.480 --> 02:55.300]  And this word is a bit abused.
[02:55.640 --> 03:04.860]  It's abused because when people think of something being parallel and requiring small computational units, they think that, well, it can be implemented in a biological system.
[03:05.160 --> 03:09.080]  That's not necessarily the case, but still, that's the meaning of this word.
[03:09.240 --> 03:11.740]  Something that might be implemented in some biological system.
[03:12.300 --> 03:19.220]  Usually, this work is modeled by or with or through some existing system.
[03:19.220 --> 03:29.240]  The example I give is visual stabilization for flight, inspired by or guided by vision models of the fruit fly, Drosophila.
[03:29.480 --> 03:30.540]  Does everyone know fruit flies?
[03:31.140 --> 03:31.840]  Very small.
[03:31.920 --> 03:34.220]  They pop up all over the place where there's fruit.
[03:35.760 --> 03:36.720]  And bioinspired.
[03:37.140 --> 03:37.940]  So, it's work.
[03:38.080 --> 03:44.320]  This is similar to biomimetic, as in you're building something that's similar to the system, but you're trying to make it better.
[03:45.820 --> 03:51.200]  So, an example I give here is gecko foot adhesive, which is a project at Berkeley.
[03:52.960 --> 03:56.320]  Geckos can walk on walls and a variety of other places very easily.
[03:56.580 --> 04:04.960]  So, there's a group there that studied that in geckos, but in particular, attempted to extend it and implement it in a synthetic material.
[04:04.960 --> 04:06.380]  And they've had fairly good success.
[04:09.540 --> 04:10.020]  Acoustics.
[04:11.140 --> 04:14.840]  Can I see raise of hands or clap or thumbs up if you know Fourier?
[04:15.260 --> 04:16.780]  Fourier transforms Fourier series.
[04:16.960 --> 04:17.340]  Oh, very good.
[04:17.820 --> 04:17.960]  Okay.
[04:18.500 --> 04:26.980]  So, the basic idea, for those who don't, is you're given some signal or some waveform and you want to express it in terms of sinusoids.
[04:26.980 --> 04:33.100]  A sinusoid, and so I don't have a laser pointer, so I'm going to use the mouse, which doesn't show up.
[04:33.520 --> 04:40.360]  So, the top row, so our reference, the signal that we want to describe is this blue rectangle wave.
[04:41.880 --> 04:48.600]  You can begin by finding a sinusoid of a particular frequency, a low frequency, that's very similar to it.
[04:48.700 --> 04:50.200]  Of course, that's a fairly poor approximation.
[04:50.720 --> 04:55.100]  We can add another sinusoid, which is the next row, and we get a little better.
[04:55.100 --> 05:00.820]  And you can continue to add sinusoids until you get a very good approximation to the signal.
[05:02.200 --> 05:03.440]  Is that clear so far?
[05:04.040 --> 05:04.520]  Okay.
[05:05.200 --> 05:09.760]  And that's significant, because given some arbitrary signal, you can talk about spectral content.
[05:10.340 --> 05:16.200]  That is, I can give you... I could snap, and you can record it and decompose it into these sinusoids.
[05:18.180 --> 05:23.240]  Well, more accurately, the Fourier transform has a continuous definition of frequency, but you...
[05:23.240 --> 05:25.440]  You get a sense of spectral content.
[05:26.860 --> 05:30.420]  Clicks are special, or snaps are special, because they have fairly high frequency content.
[05:30.600 --> 05:32.460]  Even though you might not think so, because it's so sudden.
[05:36.360 --> 05:44.140]  It's because it requires a large number of sinusoids, you can think intuitively, to represent that very sharp peak in intensity.
[05:46.180 --> 05:47.960]  So let's look at some examples.
[05:49.080 --> 05:50.100]  Only two, actually.
[05:50.420 --> 05:53.380]  This is a sinusoid, a tone frequency.
[05:53.620 --> 05:54.360]  It's 100 hertz.
[05:54.980 --> 06:02.260]  The equation at the top, so sine 2 times pi times t, which is time, times 100, which gives us the 100 hertz.
[06:03.600 --> 06:08.700]  The axes are... the axi labels are small, so I'll tell you about them.
[06:10.280 --> 06:16.300]  That's peak to peak of 2, and the time range you see is from 0 to 30 milliseconds.
[06:16.940 --> 06:20.120]  So 100 hertz, that means every cycle completes in 10 milliseconds.
[06:22.880 --> 06:26.000]  So, when we are given some signal, we want to visualize it.
[06:26.140 --> 06:27.220]  And there are a variety of ways to do it.
[06:27.300 --> 06:30.260]  This is... you could say this is a general problem with studying data.
[06:30.260 --> 06:31.320]  How do we look at it?
[06:31.780 --> 06:39.080]  And one way to look at acoustic data is something called a spectrogram, which shows frequency content with respect to time.
[06:39.900 --> 06:42.040]  That is, on the x-axis, we have time.
[06:42.220 --> 06:44.460]  On the y-axis, we have frequency.
[06:44.780 --> 06:46.620]  And the colors indicate intensity.
[06:47.460 --> 06:49.020]  So red would be more intense.
[06:49.180 --> 06:51.000]  Blue is zero, or very low.
[06:51.620 --> 06:58.160]  And so, from that tone frequency that we just looked at, which is 100 hertz, we get this spectrogram, which is a solid bar at 100.
[06:59.800 --> 07:02.780]  So, over time, it's always 100 hertz.
[07:03.080 --> 07:04.060]  A constant frequency.
[07:06.380 --> 07:16.120]  With a more complicated function like this one, where we are decreasing the frequency at an exponentially increasing rate, it's not obvious what we are looking at.
[07:16.320 --> 07:17.460]  So it's a constant amplitude.
[07:17.680 --> 07:19.040]  And we can see that from this plot.
[07:19.540 --> 07:28.260]  But when you look at it here, and some of the shape here is an artifact of the rendering program, GNUplot.
[07:29.620 --> 07:33.740]  But when you look at it, it's not obvious what the content is.
[07:34.620 --> 07:46.200]  And this is a good example because when you're recording something, some sound, or it doesn't have to be sound, but anything we're interested in, the frequency content, you might not be able to understand it just by looking at the time wave form.
[07:46.200 --> 07:51.420]  By the time wave form, I mean the horizontal axis is time, vertical axis is intensity.
[07:53.420 --> 07:56.100]  But if we look at the spectrogram, it becomes much more clear what's happening.
[07:57.840 --> 08:00.720]  So, x-axis is time, y-axis is frequency again.
[08:01.060 --> 08:05.200]  And now we can see the peak frequency content is decreasing exponentially.
[08:08.140 --> 08:09.640]  Does everyone feel good about that?
[08:11.040 --> 08:16.260]  If you look at plots of voices, human speech, which I don't have any slides on that.
[08:16.380 --> 08:17.980]  If you're interested, we can do it after the talk together.
[08:19.080 --> 08:19.820]  Or otherwise.
[08:20.780 --> 08:22.280]  There are harmonics.
[08:22.400 --> 08:24.960]  We'll get to see a harmonic when we look at a bat vocalization.
[08:25.220 --> 08:27.200]  But there's much more rich structure than this.
[08:27.280 --> 08:29.200]  These are contrived examples to make the point.
[08:30.320 --> 08:35.320]  And just as a side note, another way you'll see these represented often is with the logarithmic axis.
[08:35.680 --> 08:39.860]  That means for every step on the y-axis, there's a change in order of magnitude.
[08:40.560 --> 08:48.800]  That's done because in the cochlea, the human cochlea and most mammalian cochlea, the frequency distribution is logarithmic.
[08:50.300 --> 08:51.500]  So, fun fact.
[08:53.300 --> 08:53.740]  Okay.
[08:54.240 --> 08:54.860]  So, sonar.
[08:55.560 --> 08:58.340]  Well, how does everyone feel about acoustics so far?
[08:58.500 --> 08:59.640]  We just barely touched on it.
[09:00.260 --> 09:00.940]  I didn't mention this.
[09:01.020 --> 09:03.000]  Something very fundamental that I assumed you would know.
[09:03.320 --> 09:04.780]  Sound is a pressure wave.
[09:05.660 --> 09:09.860]  So, when I'm talking right now, I'm causing compressions and rarefactions in the air.
[09:10.060 --> 09:15.820]  That's picked up by a microphone, which is actually, depending on the construction, moving with the pressures.
[09:16.460 --> 09:17.520]  The pressure changes.
[09:17.980 --> 09:18.300]  Okay.
[09:18.420 --> 09:19.640]  That's picked up by a coil.
[09:20.480 --> 09:21.720]  Again, depending on the construction.
[09:23.240 --> 09:23.900]  So, sonar.
[09:25.120 --> 09:27.200]  What we want to do is detect something in the field.
[09:27.480 --> 09:30.060]  In the field being in space.
[09:31.860 --> 09:34.340]  And this is a basic construction of it.
[09:34.640 --> 09:38.360]  I emit some sound, I wait for some time, and I get something back.
[09:39.680 --> 09:41.240]  Now, it's important to note this is continuous.
[09:41.400 --> 09:45.960]  As in, as I'm talking now, my sounds that I'm generating are coming out of my mouth.
[09:46.520 --> 09:49.080]  If you were to visualize it, it's like this string that's coming out.
[09:49.080 --> 09:52.380]  And when I stop, it propagates through space.
[09:53.160 --> 09:53.560]  Okay.
[09:54.040 --> 09:58.800]  And when it comes back, I get the front of it, the so-called wave front, and then the rest follows in.
[09:58.980 --> 09:59.800]  Like spaghetti.
[10:00.240 --> 10:01.480]  If we're saying it's a string analogy.
[10:03.680 --> 10:06.840]  So, let T be time, S is the emitted signal, R is what's received.
[10:07.260 --> 10:12.180]  A simplification, usually, is to assume that what you're getting back is a delayed copy of what you sent out.
[10:13.060 --> 10:17.980]  That's not true, because the visual scene is much more rich than this.
[10:17.980 --> 10:21.460]  But, to a fair approximation, we let that be the case.
[10:22.900 --> 10:25.200]  So, we know the speed of sound, roughly.
[10:26.340 --> 10:30.300]  And, a decent approximation to getting distance is to see this delay.
[10:31.760 --> 10:36.480]  So, I wrote the equation a bit strange here.
[10:37.160 --> 10:38.100]  So, K is this time delay.
[10:38.260 --> 10:38.880]  K is the time delay.
[10:38.980 --> 10:41.900]  It's the flight time from when I emitted to when something came back.
[10:42.540 --> 10:47.100]  And, K is related to distance and speed of sound by K equals 2D over C.
[10:48.300 --> 10:52.880]  Distance, D, is the distance between me and the thing that I am vocalizing on.
[10:53.620 --> 10:56.880]  So, 2D, because there's trip there, trip back.
[10:57.820 --> 10:57.940]  Okay.
[11:02.410 --> 11:04.370]  So, how do we detect it when it's coming back?
[11:06.810 --> 11:07.810]  Not so simple.
[11:08.210 --> 11:10.390]  A general approach is something called cross-correlation.
[11:10.670 --> 11:12.630]  Does everyone or anyone know cross-correlation?
[11:13.590 --> 11:13.990]  Yep.
[11:14.470 --> 11:15.350]  So, you're given some signal.
[11:17.730 --> 11:19.750]  And, so I don't have many graphs for this.
[11:19.830 --> 11:23.710]  I avoided writing equations as much as possible just to try to get some intuition.
[11:24.870 --> 11:27.010]  And, we'll look at a plot soon.
[11:27.250 --> 11:29.990]  But, the basic idea of cross-correlation is you're given some function.
[11:30.430 --> 11:32.350]  You can think of my hand as that function.
[11:32.690 --> 11:35.430]  And, we're given some other function which looks different.
[11:36.090 --> 11:40.650]  Cross-correlation is when you look at them together and multiply them by each other.
[11:40.650 --> 11:45.330]  So, for example, the cross-correlation function is a function of time.
[11:45.710 --> 11:52.650]  If we begin at zero time, which means zero time difference, we align these two and integrate them.
[11:52.810 --> 11:54.530]  We multiply them and integrate over that.
[11:55.330 --> 11:58.050]  The result is something, some particular value.
[11:58.050 --> 12:03.170]  And, you can repeat this at different delays, which means you're effectively sliding one function across another.
[12:03.750 --> 12:06.490]  And, you're getting these values out.
[12:07.650 --> 12:11.050]  So, intuitively, when they're aligned, if they were the same...
[12:11.810 --> 12:21.070]  Well, so if this was the other shape, when we get to a perfect alignment and then multiply them, in effect, and then integrate, we get a fairly large value.
[12:21.070 --> 12:26.510]  So, the idea, then, intuitively, is cross-correlation is a way to pick out similarness, given two functions.
[12:28.950 --> 12:29.970]  So, here's an example.
[12:31.570 --> 12:32.690]  X-axis is time.
[12:33.430 --> 12:36.270]  On the left, we see time waveforms.
[12:36.330 --> 12:41.850]  That is, some energy, intensity, whatever you'd like to call the y-axis, with respect to time.
[12:41.850 --> 12:44.650]  On the right, is the cross-correlation.
[12:45.670 --> 12:49.810]  So, first, we have this tone frequency that's on at two seconds.
[12:49.910 --> 12:51.150]  It ends a little after three seconds.
[12:51.910 --> 12:53.770]  In the top left, there's zero noise.
[12:53.950 --> 12:58.390]  And you can tell that because the line is flat, aside from that rectangle burst.
[12:58.630 --> 12:59.030]  Is that clear?
[13:00.870 --> 13:02.150]  And then, the next...
[13:02.150 --> 13:04.390]  So, on the right, then, we see this cross-correlation function.
[13:04.690 --> 13:05.790]  It has a triangular shape.
[13:05.790 --> 13:08.790]  That's because of this shifting that's happening.
[13:08.790 --> 13:13.850]  As we're getting more and more aligned, there's a linear increase in the sum.
[13:14.130 --> 13:16.950]  Don't worry about that so much as the fact that there's a peak, and it's fairly obvious.
[13:17.690 --> 13:21.670]  The peak happens to be at two seconds, or fairly close to it.
[13:21.990 --> 13:27.030]  Which means that we know, using a reference signal, this is...
[13:27.030 --> 13:28.950]  Two seconds is when that sound occurred.
[13:29.310 --> 13:36.110]  I didn't show it here, but I used as a reference signal an exact copy of the rectangle wave at time zero.
[13:37.550 --> 13:42.130]  So, in the context of a sonar system, that means I emit something, and I know what it should look like.
[13:42.250 --> 13:42.790]  I have a copy.
[13:43.030 --> 13:44.070]  After all, I emitted it.
[13:44.990 --> 13:52.530]  And so, when I'm receiving something back, as I'm receiving it, I can cross-correlate what's coming in with this original signal that I emitted.
[13:53.150 --> 13:55.190]  We should get a peak if there's a very good match.
[13:56.750 --> 13:59.030]  The second row has a little bit more noise.
[14:01.210 --> 14:04.070]  So, the top row has a peak amplitude of five.
[14:05.130 --> 14:07.290]  The original signal, rather, has a peak amplitude of five.
[14:07.550 --> 14:09.630]  The second row has noise of one.
[14:09.930 --> 14:10.490]  Variance one.
[14:10.630 --> 14:11.230]  It's Gaussian noise.
[14:11.570 --> 14:13.770]  This is what you might see if you actually had an electrical system.
[14:14.170 --> 14:17.010]  If you look at the wire, there's background noise, it might be called.
[14:18.130 --> 14:21.550]  So, you can still just visually see the rectangle.
[14:22.930 --> 14:28.030]  And if we look on the right, the cross-correlation shows the result, and we see the peak again.
[14:28.610 --> 14:34.790]  However, for the last example, there's variance of ten in the noise, which means it's very difficult.
[14:35.010 --> 14:39.670]  As in, when you look at this visually, I suspect you cannot see the rectangle wave itself.
[14:40.130 --> 14:41.450]  If you can, you should interrupt me.
[14:43.690 --> 14:46.230]  But on the right, the cross-correlation is fairly clear.
[14:47.050 --> 14:52.370]  This is a contrived example, because we're assuming Gaussian noise, which means it's zero mean.
[14:52.830 --> 14:55.790]  It's fairly straightforward to get rid of when you're averaging.
[14:57.270 --> 14:59.070]  But, I think the point still stands.
[14:59.190 --> 14:59.890]  You can pull out a...