Wolfram Computation Meets Knowledge

Date Archive: 2013 February

Computation & Analysis

Behind the Scenes at the National Museum of Mathematics Meta-Logo

The National Museum of Mathematics, which opened in Manhattan in December, doesn't have a logo. It has an infinite family of logos. And the logos the museum uses for official business are not created by design professionals. They're designed by the museum's visitors. The logo is itself an exhibit in the museum. The museum's unique meta-logo was conceived and implemented at Wolfram Research. When I say "implemented," I don't mean just "calculated" or "rendered," but actually "programmed." This is a logo that requires an implementation.
Announcements & Events

Studying Wolfram Science in the Summertime

Last year was the 10th anniversary of the publication of A New Kind of Science and the 10th installment of the Wolfram Science Summer School (formerly the NKS Summer School). To read more about the anniversary, check out the series of blog posts by Stephen Wolfram, starting here. The Wolfram Science Summer School is a three-week research school focused on advancing student projects in the field of complex systems. Students tend to be undergraduates, graduates, post-docs, professionals, and professors. Summer school students have historically represented a wide array of topical areas, including (but not limited to): computer science, mathematics, physics, biology, ecology, architecture, music, philosophy, political science, and economics. I've been helping out with the summer school since 2008. That first year up in beautiful Burlington, Vermont, I was lucky enough to be a student while I helped coordinate the event. Since then I've published a paper based on my 2008 project, and have worked on NKS methods as applied to music, social networks, and epidemic spread.
Design & Visualization

Image Effects in Mathematica

Mathematica 9 has just been released with many new or enhanced capabilities for image processing. You can perform morphological operations, color manipulation, segmentation analysis, feature detection, and more, most of which can be applied to the new Image3D object as well. A byproduct of this whole ecosystem is that now it is easier than ever to use Mathematica to create and apply effects to your images. Two Mathematica super functions that can be used to apply transformations directly to an image are ImageApply, which is a pixel operator, and ImageFilter, which considers the pixel as well as a neighborhood of pixels around it and works as a local filter. For example, you can remove the blue channel and perform a gamma correction only on the green channel by doing the following:
Announcements & Events

Explore Mathematica’s Visualization Capabilities: Free Virtual Workshop

Mathematica 9 added a slew of powerful visualization functions to its already long list of capabilities when it was released last November. To help highlight some of these and other visualization features, Wolfram Research is presenting a free virtual workshop. At the virtual workshop you can attend talks on a variety of topics, including 3D geometric modeling, data visualization, and interactive applications, and learn how to get started with your own projects. The workshop will also feature a panel discussion and Q&A sessions with Wolfram experts.
Education & Academic

Announcement: Our First CBM Country

I'm very excited to announce that computerbasedmath.org has found the first country ready for our completely new kind of math education: it's Estonia. (...and here’s the press release). I thought Estonia could be first. They are very active on using technology (first to publish cabinet decisions immediately online, first to include programming in their mainstream curriculum), have ambition to improve their (already well respected) STEM aptitude and lack the dogma and resistance to change of many larger countries. There aren't so many countries with all those characteristics. In our first Estonia project we will work with them to rewrite key years of school probability and statistics from scratch. This is an area that's just crazy to do without a computer, even harmful. It's an area that's only come to the fore since computers because it only makes sense with lots of data. No-one in real life does these hand analyses or works with only 5 data points, so why do we make our students? Why get students emulating what computers do so much better (computing) rather than concentrate on imaginative thinking, analysis and problem-solving that students ought to be able to do so much better even than today's computers?
Education & Academic

Centennial of Markov Chains

On January 23, 1913 of the Julian calendar, Andrey A. Markov presented for the Royal Academy of Sciences in St. Petersburg his analysis of Pushkin's Eugene Onegin. He found that the sequence of consonants and vowels in the text could be well described as a random sequence, where the likely category of a letter depended only on the category of the previous or previous two letters. At the time, the Russian Empire was using the Julian calendar. The 100th anniversary of the celebrated presentation is actually February 5, 2013, in the now used Gregorian calendar. To perform his analysis, Markov invented what are now known as "Markov chains," which can be represented as probabilistic state diagrams where the transitions between states are labeled with the probabilities of their occurrences.
Education & Academic

The Ultimate Univariate Probability Distribution Explorer

In this blog post, we want to report some work in progress that might interest users of probability and statistics and also those who wonder how we add new knowledge every day to Wolfram|Alpha. Since the beginning in 1988, Mathematica knew not only elementary functions (sqrt, exp, log, etc.) but many special functions of mathematical physics (such as the Bessel function K and the Riemann Zeta function) and number theoretical functions. All together, Mathematica knows now more than 300 such functions. The Wolfram Functions Site lists 300,000+ formulas and identities for these functions. And, based on Mathematica's algorithmic computation capabilities and the Functions Site's identities, most of this knowledge is now easily accessible in Wolfram|Alpha. For example, relation between sin(x) and cos(x), series representations of the Beta function, relation between BesselJ(n, x) and AiryAi(x), differential equation for ellipticF(phi, m), and examples of complicated indefinite integrals containing erf. But Wolfram|Alpha also knows about many special functions that are not in Mathematica because they are less common or less general. For instance, haversine(x), double factorial binomial(2n, n), Dickman rho(10/3), BesselPolynomialY[6, x], Conway's base 13 function(4003/371293), and Goldbach function(1000). Mathematica 7 knew 42 probability distributions; Mathematica 9 knows over 130 (parametric) probability distributions. Based on Mathematica, Wolfram|Alpha can answer a lot of queries about these distributions, such as characteristic function of the hyperbolic distribution or variance of the binomial distribution with p = 1/3, and give general overview pages for queries such as Student's t distribution or Gumbel distribution.