Hitting All the Marks: Exploring New Bounds for Sparse Rulers and a Wolfram Language Proof

February 12, 2020 — Ed Pegg Jr, Editor, Wolfram Demonstrations Project

The sparse ruler problem has been famously worked on by Paul Erdős, Marcel J. E. Golay, John Leech, Alfréd Rényi, László Rédei and Solomon W. Golomb, among many others. The problem is this: what is the smallest subset of so that the unsigned pairwise differences of give all values from 1 to ? One way to look at this is to imagine a blank yardstick. At what positions on the yardstick would you add 10 marks, so that you can measure any number of inches up to 36?

Another simple example is of size 3, which has differences , and . The sets of size 2 have only one difference. The minimal subset is not unique; the differences of also give .

Part of what makes the sparse ruler problem so compelling is its embodiment in an object inside every schoolchild’s desk—and its enduring appeal lies in its deceptive simplicity. Read on to see precisely just how complicated rulers, marks and recipes can be.

Invasion of the Stink Bugs: 20 Years of Marmorated Mayhem in One Map

January 23, 2020 — Jofre Espigule-Pons, Document & Media Systems

Who has not encountered a stink bug? Perhaps the better question is not if, but when. I remember well my first interactions with stink bugs—partly because of their pungent, cilantro-like odor, but also because in my native Catalan language they are called Bernat pudent (“stinky Bernat”) and Bernat is my twin brother’s name.

So when I encountered the stink bug again when visiting Champaign, Illinois, for the 2019 Wolfram Technology Conference, it brought up a lot of fond childhood memories. This time, however, two things had changed: the frequency of encounters with the stink bug seemed exponentially greater, and I now had the Wolfram Language to more fully (and computationally) satisfy my curiosity about this reviled insect and its growing impact on our ecosystem. So to get a better picture of the arrival and spread of this invasive bug across the US, I used available observation data and the Wolfram Language to make a map of sightings over the past two decades.

From an Hour of Code to a Lifetime of Coding with the Wolfram Language

December 12, 2019 — Ishwarya Vardhani, Education Partnerships Manager, Partnerships

Happy Hour of Code! There’s no better reason to start learning or continue honing your programming skills than the Hour of Code, an annual celebration of computer science during Computer Science Education Week. While we like to think that every hour is a great hour to code, we look forward to the Hour of Code event as an opportunity to come together and share some of our best Wolfram Language resources for students. Since its 2013 launch, the Hour of Code has been an immense success, introducing valuable programming skills to millions of students. So with this year’s Hour already underway, let’s take a look at the ways you can get started!

Duking It Out in the Wolfram Language: A Breakdown of the 2019 Livecoding Championship

November 13, 2019 — Jesse Friedman, Software Engineer, Engine Connectivity Engineering

Two weeks ago, I had the pleasure of returning as a commentator for the fourth annual Livecoding Championship, a special event held during the 2019 Wolfram Technology Conference. We had such an incredible turnout this year, with 27 total participants and 14 earning at least one point! Conference attendees and Wolfram staff competed for the title of Livecoding Champion, with seven questions (plus one tiebreaker!) challenging their speed, agility and knowledge of the Wolfram Language. It was a high-spirited battle for first place, and while I had prepared “answer key” solutions in advance, I always look forward to the creativity and cleverness that competitors demonstrate in their wide range of approaches to each question.

By popular request, in addition to revisiting the questions, I’ll walk you through how competitors reached their solutions and earned their points, as a kind of “study guide” for next year’s aspiring champions. So hold on to your keyboards—we’re going in!

Building a Lattice Boltzmann–Based Wind Tunnel with the Wolfram Language

November 7, 2019 — Paritosh Mokhasi, Kernel Developer, Algorithms R&D

My student days learning fluid dynamics were all about studying complicated equations and various methods of simplifying and manipulating these equations to get some kind of a result. Unfortunately, this left very little to the imagination when it came to getting an intuitive feel for how a fluid would behave in different situations. When I took my first experimental fluid dynamics course, I got to see how one would use different visualization techniques to understand qualitatively the behavior of the flow. These visualizations gave me a way of creatively looking at a flow, and, as an added bonus, they looked stunning. All these experiments and visualizations were being carried out inside a wind tunnel.

The New World of Notebook Publishing

October 24, 2019 — Stephen Wolfram

Wolfram Notebooks on the Web

We’ve been working towards it for many years, but now it’s finally here: an incredibly smooth workflow for publishing Wolfram Notebooks to the web—that makes possible a new level of interactive publishing and computation-enabled communication.

You create a Wolfram Notebook—using all the power of the Wolfram Language and the Wolfram Notebook system—on the desktop or in the cloud. Then you just press a button to publish it to the Wolfram Cloud—and immediately anyone anywhere can both read and interact with it on the web.

It’s an unprecedentedly easy way to get rich, interactive, computational content onto the web. And—together with the power of the Wolfram Language as a computational language—it promises to usher in a new era of computational communication, and to be a crucial driver for the development of “computational X” fields.

From Data to Insights: An Online Course for Learning the Multiparadigm Workflow

September 17, 2019 — Brian Wood, Lead Technical Writer, Document and Media Systems

Our interactive Multiparadigm Data Science (MPDS) course has been up at Wolfram U for over a month now, and we’re pretty satisfied with the results so far. Hundreds of people have started the course—including students from our first Data Science Boot Camp, who joined us at Wolfram headquarters for a three-week training camp. Thanks to the success of the boot camp, we have also had several projects submitted for advanced MPDS certification, which will soon be available within the interactive course.

But what exactly does it mean to be a practitioner of MPDS? And how might the multiparadigm approach improve my computational projects? To find out, I decided to try this free course for myself.

September 5, 2019 — Daniel Lichtblau, Symbolic Algorithms Developer, Algorithms R&D

A Year Ago Today

The code from that blog was in a language/script in which I am not fluent. My coauthor on two authorship attribution papers (and other work), Catalin Stoean, was able to download the data successfully. I first did some quick validation (to be seen) and got solid results. Upon setting the software loose on the op-ed in question, a clear winner emerged. So for a short time I “knew” who wrote that piece. Except. I decided more serious testing was required.

Designing the Wolfram U Data Science Course for Learning the Multiparadigm Workflow

August 15, 2019 — Abrita Chakravarty, Training and Development Specialist, Wolfram U

A few weeks back, we announced Wolfram U’s latest open online course: Multiparadigm Data Science (MPDS). This course gives a hands-on introduction to basic concepts of data science through a multiparadigm approach—using various types of data, modern analytical techniques, automated machine learning and a range of interfaces for communicating your data science results. Our goal is to increase your understanding of data science while allowing you to take advantage of multiparadigm insights—whether you’re a newcomer working on a simple problem or an expert using well-established methods.

As the content creator and instructor, I’d like to provide some background on myself and my approach to the MPDS course. Beyond doing data science, I’ve found that multiparadigm principles make both teaching and learning more effective. In this post, I’ll give insight to the design of the course—the main goals, what topics are included and how to use the built-in interactivity to get the most out of your experience.

Spherical Aberration Optics Problem Finally Solved Using the Wolfram Language

August 13, 2019 — Swede White, Public Relations Manager

Solving a 2,000-Year-Old Mystery

It’s not every day that a 2,000-year-old optics problem is solved. However, Rafael G. González-Acuña, a doctoral student at Tecnológico de Monterrey, set his sights on solving such a problem—spherical aberration in lenses. How can light rays focus on a single point, taking into account differing refraction? It was a problem that, according to Christiaan Huygens back in 1690, even Isaac Newton and Gottfried Leibniz couldn’t sort out, and was formulated two millennia ago in Greek mathematician Diocles’s work, On Burning Mirrors.

But González-Acuña and his colleagues realized that today, they had the use of the Wolfram Language and its computational tools to solve this age-old problem. The result? A breakthrough publication that outlines an analytical solution to why and how lensed images are sharper in the center than at the edges, with 99.999999999% accuracy simulating 500 light beams.

As it happens, González-Acuña was recently at the Wolfram Summer School, and we had the opportunity to ask him a little bit about his work.