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Some of you might want to present what happens over time with your photographs. Other than creating a video, it's usually quite compelling when watching a dynamic phenomena that's true. And if you think about it, all of science is ultimately dynamic, right? Things change over time. We generally assume one has to watch a moving image to see that change. So here, for example, you are seeing something called the Belousov-Zhabotinsky reaction. It's a complicated oscillating reaction that we're observing within a Petri dish. But it's not a video, in the sense that it wasn't taken with a video camera. You're seeing a series of still images that I made and I was privileged to make in professor Zhabotinsky's lab at Brandeis. I took the images 11 seconds apart over a period of five minutes. By the way, I made the images in film, which became slide formats, as you might remember-- or then again, maybe you don't! And you're seeing digital scan...

There were some other questions sort of running along this general idea of the fact that the information in DNA doesn't go, even though it encodes the information for proteins goes via this rRNA intermediate. Someone asked what was the M. The M is for messenger. The idea being that since the DNA, at least in eukaryotes the DNA was in the nucleus and proteins were made out of the cytoplasm, somehow that information had to be carried from the nucleus where the DNA was out to the cytoplasm. And that's where the term messenger was because the RNA was seen as something that would carry the information out. Now, a point here, it's really critical because we're going to continue to talk about gene regulation. And that is when a cell is making one of these mRNAs, it doesn't make one single copy of all of the genes that are in the genome on one RNA. Instead it does it either one gene at a time, which is the usual case, or occasionally as we see in the lac opero...

I just recalling some of the notation we are going to need for today, and a couple of the facts that we're going to use, plus trying to clear up a couple of confusions that the recitations report. This can be thought of two ways. It's a formal polynomial in D, in the letter D. It just has the shape of the polynomial, D squared plus AD plus B. A and B are constant coefficients. But, it's also, at the same time, if you think what it does, it's a linear operator on functions. It's a linear operator on functions like y of t. You think of it both ways: formal polynomial because we want to do things like factoring it, substituting two for D and things like that. Those are things you do with polynomials. You do them algebraically. You can take the formal derivative of the polynomial because it's just sums of powers. On the other hand, as a linear operator, it does something to functions. It differentiates them, multiplies them by constants or something li...

Some content in this video is not covered under our Creative Commons license. See the closing credits for more information. SARA JAMES: Hello my name is Sara James. I've been working the past seven years at MIT Lincoln Laboratory, doing radar signal processing. Today, I'm here to tell you about the image processing workshop of the girls who build. So the image processing section of this workshop is actually done with a software called Processing. Processing is open source, free, and it's available at Processing.org to download, for just about any sort of operating system that you can think of. This software is actually developed for people that are not doing coding, day to day. During this section of the workshop we're trying to expose participants to image processing concepts, within the context of real world applications. Furthermore, we're trying to demystify coding, and show participants that they can do this too. You'll be doing four exercises...

Let's talk about some of the great innovations that are happening at local levels in our workplaces across the country. If you're like me, I'm sure you're frustrated with the gridlock that is blocking any progress in public policy in Washington. I've seen this go on for 30 years in our field where Congress and the President can't pass anything because there's an impasse between business and labor on employment and labor policy. So we need to look to other places for innovations today. The good news is that there's a lot going on at the local level in established companies, in startups, in state and local governments, in non-profits. And so that's where historically, most of our major innovations at work have occurred. So let's look at a few of these. You've heard of companies such as Southwest Airlines started, in 1970. It's the most profitable airline in the United States. It has consistently been rated as one of the best p...

PROFESSOR: So some of the standard questions that we've examined already about random graphs are the probability of getting from one place to another, or the expected time to get from one place to another. But a different kind of question that comes up in a fundamental way is the probability of being someplace. So let's examine that. Here is the graph with states blue, orange, and green that we've seen before. And suppose that I start at state B. And I ask, what's the probability of being at each of these states after one step? So to start with, I'm interested in p B, p O, and p G-- which is the probability of being at state B, the probability of being at state O, and the probability of being at state G. The sum of the probabilities is going to be 1. And initially when I tell you that I'm at state B, it means the probability of being at B is 1, and the other two is 0. And I'm interested in the way that these probabilities update after one step....

PROFESSOR: We just saw some random variables come up in the bigger number game. And we're going to be talking now about random variables, just formally what they are and their definition of independence for random variables. But let's begin by looking at the informal idea. Again, a random variable is a number that's produced by a random process. So a typical example that comes up where you get a random variable is you've got some system that you're watching and you're going to time it to see when the next crash comes, if it crashes. So assuming that this is unpredictable that it happens in some random way, then the number of hours from the present until the next time the system crashes is a number that's produced by this random process of whether the system works or not. Number of faulty pixels in a monitor. When you're building the monitors and delivering them to the actual computer manufacturers, there's a certain probability that som...