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PROFESSOR: OK. Today I'll use this trinity-- the science, engineering, technology trinity-- as sort of a theme that we're going to develop through the whole term. And we'll just briefly refresh ourselves, or remind ourselves, what Professor Lauffenburger talked about on Tuesday. And then I'm going to go a little bit into some detail about how information is used in biology, in cells. It's a way of gaining a broad perspective of a facet of the biological basis for bioengineering. but it's also a way to introduce to you how we can use that information in developing technology. OK. Now just a few odds and ends. We do have a course website. On that course website will be articles that I may or may not download from newspapers or magazines. Generally, if you want to be in the biospace, read the newspapers, you know. Today the concern is the occurrence of the flu virus in Africa now. So it's now spread from China to Turkey from the Middle East down t...

PROFESSOR: OK, Let's use the last 10 minutes to discuss an application. So that's our Fermi golden rule there. Let's leave it in the blackboard. So the example I will discuss qualitatively will not compute the rate for this example is auto ionization, or also called Auger transitions. So we imagine of-- I think the reason this example is interesting is that there is continuum states, sometimes in cases that you would not think about it, or you wouldn't have thought about them. So let's assume we have a helium atom. So you have two electrons, z equals 2, two protons and two electrons. And I will assume that we have a hydrogenic state. So you see the Hamiltonian of this whole , atom there's a P1 squared over 2n plus a P2 squared over 2n, roughly for each electron, plus or minus e squared over r1 minus e squared over r2, and then plus e squared over r1 minus r2, which is the Coulomb repulsion. So that's roughly the Hamiltonian you need to consider...

We will now use the Bayes rule in an important application that involves a discrete unknown random variable and a continuous measurement. Our discrete unknown random variable will be one that takes the values plus or minus 1 with equal probability. And the measurement will be another random variable, Y, which is equal to the discrete random variable, but corrupted by additive noise that we denote by W. So what we get to observe is the sum of K and W. This is a common situation in digital communications. We're trying to send one bit of information whether K is plus 1 or minus 1, but the observation that we're making is corrupted by a communication channel, by some noise that is present in the channel, and on the basis of the value of Y that we will observe, we will try to guess what was sent. The assumption that we will make about the noise is that it is a standard normal random variable. So suppose that we observed a specific value for the random variable Y. We wa...

PROFESSOR: I want to use this applet, Amplitude and Phase: First Order, to show you some of the functionalities that are common to the MIT mathlets. First of all, if your browser window looks like this, so that the label at the top is too large, or like this, so that it's missing some of the window, it's because you have the zoom on your browser set wrong. And you can adjust it with command or control plus or minus keys, so that it looks correct. So let's see what we have in this applet. At the top, you can see the differential equation that this applet deals with. This differential equation models many different physical phenomena, and the story I want to tell you involves the ocean, measured by this blue level here, connected to a bay by this channel. And here's a measure of the water level in the bay. As time goes on, the level of water in the ocean changes because of tides, and the water level in the bay follows suit mediated by a slanting level in the...

In this video we'll use hierarchical clustering to cluster the movies in the movie lens data set by genre. After we make our clusters, we'll see how they can be used to make recommendations. There are two steps to hierarchical clustering. First we have to compute the distances between all data points. And then we need to cluster the points. To compute the distances we can use the dist function. We only want a cluster movies on the genre variable, not on the title variable, so we'll cluster on columns two through 20. So let's call the output distances, and we'll use the dist function, where the first argument is moviesmovies[2:20], this is what we want to cluster on. And the second argument is method="euclidean", meaning that we want to use euclidean distance. Now let's cluster our movies using the hclust function for hierarchical clustering. We'll call the output clusterMovies, and use hclust where the first argument is distances, the...

In this lecture, we'll use a technique called Bag of Words to build text analytics models. Fully understanding text is difficult, but Bag of Words provides a very simple approach. It just counts the number of times each word appears in the text and uses these counts as the independent variables. For example, in the sentence, "This course is great. I would recommend this course my friends," the word this is seen twice, the word course is seen twice, the word great is seen once, et cetera. In Bag of Words, there's one feature for each word. This is a very simple approach, but is often very effective, too. It's used as a baseline in text analytics projects and for natural language processing. This isn't the whole story, though. Preprocessing the text can dramatically improve the performance of the Bag of Words method. One part of preprocessing the text is to clean up irregularities. Text data often as many inconsistencies that will cause algorithms ...

We can use a 2-to-1 multiplexer to build a settable storage element. Recall that a MUX selects as its output value the value of one of its two data inputs. The output of the MUX serves as the state output of the memory component. Internally to the memory component we'll also connect the output of the MUX to its D0 data input. The MUX's D1 data input will become the data input of the memory component. And the select line of the MUX will become the memory component's load signal, here called the gate. When the gate input is LOW, the MUX's output is looped back through MUX through the D0 data input, forming the bi-stable positive feedback loop discussed in the last section. Note our circuit now has a cycle, so it no longer qualifies as a combinational circuit. When the gate input is HIGH, the MUX's output is determined by the value of the D1 input, i.e., the data input of the memory component. To load new data into the memory component, we set the gate in...

We'll use the stack to hold a procedure's activation record. That includes the values of the arguments to the procedure call. We'll allocate words on the stack to hold the values of the procedure's local variables, assuming we don't keep them in registers. And we'll use the stack to save the return address (passed in LP) so the procedure can make nested procedure calls without overwriting its return address. The responsibility for allocating and deallocating the activation record will be shared between the calling procedure (the "caller") and the called procedure (the "callee"). The caller is responsible for evaluating the argument expressions and saving their values in the activation record being built on the stack. We'll adopt the convention that the arguments are pushed in reverse order, i.e., the first argument will be the last to be pushed on the stack. We'll explain why we made this choice in a couple of slides… ...