Wolfram Computation Meets Knowledge

Date Archive: 2012 December

Education & Academic

Hunting for Turing Machines at the Wolfram Science Summer School

This year is the 100th birthday of Alan Turing, so at the 2012 Wolfram Science Summer School we decided to turn a group of 40 unassuming nerds into ferocious hunters. No, we didn't teach our geeks to take down big game. These are laptop warriors. And their prey? Turing machines! In this blog post, I'm going to teach you to be a fellow hunter-gatherer in the computational universe. Your mission, should you choose to accept it, is to FIND YOUR FAVORITE TURING MACHINE. First, I'll show you how a Turing machine works, using pretty pictures that even my grandmother could understand. Then I'll show you some of the awesome Turing machines that our summer school students found using Mathematica. And I'll describe how I did an über-search through 373 million Turing machines using my Linux server back home, and had it send me email whenever it found an interesting one, for two weeks straight. I'll keep the code to a minimum here, but you can find it all in the attached Mathematica notebook. Excited? Primed for the hunt? Let me break it down for you. The rules of Turing machines are actually super simple. There's a row of cells called the tape:
Announcements & Events

Welcome, National Museum of Mathematics

I was just in New York City for the grand opening of the National Museum of Mathematics. Yes, there is now a National Museum of Mathematics, right in downtown Manhattan. And it's really good---a unique and wonderful place. Which I’m pleased to say I’ve been able to help in various ways in bringing into existence over the past 3 years. Of all companies, ours is probably the one that has been most involved in bringing math to the world (Mathematica, Wolfram|Alpha, Wolfram Demonstrations Project, MathWorld, Computer-Based Math, Wolfram Foundation, …). And for a long time I've thought how nice it would be if there were a substantial, physical, "museum of mathematics" somewhere. But until recently I'd sort of assumed that if such a thing were going to exist, I'd have to be the one to make it happen. A little more than 3 years ago, though, my older daughter picked out of my mail a curious folding geometrical object---which turned out to be an invitation to an event about the creation of a museum of mathematics. At first, it wasn't clear what kind of museum this was supposed to be. But as soon as we arrived at the event, it started to be much clearer: this was "math as physical experience". With the centerpiece of the event, for example, being a square-wheeled tricycle that one could ride on a cycloidal "road"---a mathematical possibility that, as it happens, was the subject of some early Mathematica demonstrations.

Modeling in the Search for New Drugs—G-Protein-Coupled Receptors (GPCRs)

Explore the contents of this article with a free Wolfram SystemModeler trial. Yesterday, the Nobel Prize in Chemistry was awarded to Robert J. Lefkowitz and Brian K. Kobilka for having mapped how a family of cellular receptors called G-protein-coupled receptors (GPCRs) work. The Nobel Prize winners' research has proven to be very important in the development of novel therapeutic drugs—about 40–50% of all therapeutic drugs in use today are centered on GPCRs. The real beauty of GPCR-based response systems is that they include components that are used over and over again for the response to external signals in many kinds of cellular functions throughout our bodies. Sight, smell, and the adrenaline response are examples of these GPCR-mediated responses with physiologically important functions. Identifying new targets for therapeutic drug intervention includes analysis of the complex webs of signaling pathways and feedback systems in our cells, extending beyond the first event of a signal connecting with the GPCR on the cell surface, which is non-trivial. Lately the cost-effective practice of using mathematical models as an initial step for finding those elusive new targets, and also as a tool for understanding how other reactions of a cell might be affected by a new drug, has been growing. In this blog post we are going to use modeling and simulation in order to illustrate how the GPCR-based cellular response to an external signal can be modified. And by performing this analysis, I thought we should also see how we can find promising targets for therapeutic drug design, which are then aimed at either increasing or decreasing the response. Since the first two steps in the pathways are identical in most of the GPCR-based signal responses in a cell, we can freely choose a representative model. One such well understood signal response pathway that uses GPCR is the mating pheromone response in yeast, which we are here going to explore using Mathematica and Wolfram SystemModeler.
Announcements & Events

“What Are You Going to Do Next?”
Introducing the Predictive Interface

There aren't very many qualitatively different types of computer interfaces in use in the world today. But with the release of Mathematica 9 I think we have the first truly practical example of a new kind---the computed predictive interface. If one's dealing with a system that has a small fixed set of possible actions or inputs, one can typically build an interface out of elements like menus or forms. But if one has a more open-ended system, one typically has to define some kind of language. Usually this will be basically textual (as it is for the most part for Mathematica); sometimes it may be visual (as for Wolfram SystemModeler). The challenge is then to make the language broad and powerful, while keeping it as easy as possible for humans to write and understand. And as a committed computer language designer for the past 30+ years, I have devoted an immense amount of effort to this. But with Wolfram|Alpha I had a different idea. Don't try to define the best possible artificial computer language, that humans then have to learn. Instead, use natural language, just like humans do among themselves, and then have the computer do its best to understand this. At first, it was not at all clear that such an approach was going to work. But one of the big things we've learned from Wolfram|Alpha is with enough effort (and enough built-in knowledge), it can. And indeed two years ago in Mathematica 8 we used what we'd done with Wolfram|Alpha to add to Mathematica the capability of taking free-form natural language input, and automatically generating from it precise Mathematica language code. But let's say one's just got some output from Mathematica. What should one do next? One may know the appropriate Mathematica language input to give. Or at least one may be able to express what one wants to do in free-form natural language. But in both cases there's a kind of creative act required: starting from nothing one has figure out what to say. So can we make this easier? The answer, I think, is yes. And that's what we've now done with the Predictive Interface in Mathematica 9. The concept of the Predictive Interface is to take what you've done so far, and from it predict a few possibilities for what you're likely to want to do next.
Announcements & Events

Mathematica Experts Live: New in Mathematica 9

Curious about Mathematica 9? You can see it in action in three free online events. Our experts will introduce you to new features in usability, computation, data manipulation, and visualization. Live Q&A sessions during each event will give you a chance to ask questions. Topics covered: Predictive Interface and Units: December 10, 1–2pm EST Get a look at the new interface paradigm and systemwide units support. Our experts will demonstrate the next-computation Suggestions Bar, context-sensitive Input Assistant, and units features, from unit conversion to dimensional analysis.   Social Networks and Data Science: December 12, 1–2:30pm EST Learn about Mathematica 9's new social network analysis capabilities with built-in access to social media data, plus other graphs and networks enhancements and new computational features in data science, such as reliability, survival analysis, and random processes.   Data Manipulation and Visualization: December 14, 1–2:30pm EST Get the scoop on new features for image and signal processing, interactive gauges, legends for plots and charts, and integrating with R directly from our experts.