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IAN HUTCHINSON: Let's just finish this off by cleaning up this plot and saving it. In the first case, I don't have any labels on my axes. That's bad. Let me put some labels on my axes. X-label is the way you do this. And in this case I have a very simple label that I want. And the same thing, presumably for Y-label. That will at least put some labels on. Aren't they horribly small? But they are there. Now, I want to improve this plot in general. Let me point out another thing that I want to do. I don't want to have hold on permanently, so let me put hold off after the second plot. And that's going to avoid difficulties in the future. So I'm just going to save that. Now in order to improve the size of the labels and so forth that's involved with this, there are a number of things one can do. And in general, I'm going to do this for many of my plots. And so what I want to do is I want to illustrate the fact that my script-- which is calle...

So, we're going to finish now by just talking more about this amazing immune system we have, the adaptive immune system. As I said on Friday, this is really an astonishing recognition system that just plays a key role in us being able to survive in this world that's full of bacteria, and yeast, and fungi, and viruses, parasites. There are things just all the time trying to do us in, and the reason we don't succumb is because we have this amazing immune system. And there are several features about it which I summarized the other day. One is its diversity. It has this incredible ability to recognize entities, including things that are synthesized in a lab that had never been seen on Earth before. It's amazing in terms of that side of it. Coupled with this is this incredible specificity. As I indicated the other day, for example, if it was seeing a benzene ring with a methyl on it, it might be able to recognize this, but it could tell the difference from havi...

PROFESSOR: Today we finish up chapter 13. I think we are finished, but I'll take questions. We get into chapter 14, which starts to get into coding for bandwidth-limited channels. Here we're coding directly in terms of Euclidean space rather than in terms of Hamming space. And there's this wonderful quote from Neil Sloane. "Euclidean space coding is to Hamming space coding as classical music is to rock'n'roll." Meaning that, in the Euclidean space, things are continuous, whereas we were discrete back in Hamming space. Nonetheless, there are strong connections between the two, which in two lectures I'll basically only have a chance to hint at. You were supposed to hand in problem set nine last Friday, or today if you haven't already. Today, we'll hand out the solutions for nine, and then chapter 14 and its problems, which are problem set 10. These are not due. As always, I recommend you do them. The solutions will be handed out Wed...

We will finish our discussion of classical statistical methods by discussing a general method for estimation, the so-called maximum likelihood method. If an unknown parameter can be expressed as an expectation, we have seen that there's a natural way of estimating it. But what if this is not the case? Suppose there's no apparent way of interpreting theta as an expectation. So we need to do something else. So rather than using this approach, we will use a different approach, which is the following. We will find a value of theta that makes the data that we have seen most likely. That is, we will find the value of theta under which the probability of obtaining the particular x that we have seen-- that probability is as large as possible. And that value of theta is going to be our estimate, the maximum likelihood estimate. Here, I wrote a PMF. That's what you would do if X was a discrete random variable. But the same procedure, of course, applies when X is a conti...

Let's finish up by looking at two extended examples. The scenario for both examples is the control system for the International Space Station, which has to handle three recurring tasks: supply ship guidance (SSG), gyroscope control (G), and cabin pressure (CP). For each device, the table shows us the time between successive requests (the period), the service time for each request, and the service deadline for each request. We'll first analyze the system assuming that it's using a weak priority system. First question: What is the maximum service time for the cabin pressure task that still allows all constraints to be met? Well, the SSG task has a maximum allowable latency of 20 ms, i.e., it's service routine must start execution within 20 ms if it is to meet its 25 ms deadline. The G task has a maximum allowable latency of 10 ms if it's to meet its deadline. So no other handler can take longer than 10 ms to run or the G task will miss its deadline. 2. G...