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Computation & Analysis

Embracing Uncertainty: Better Model Selection with Bayesian Linear Regression

Readers who follow the Mathematica Stack Exchange (which I highly recommend to any Wolfram Language user) may have seen this post recently, in which I showed a function I wrote to make Bayesian linear regression easy to do. After finishing that function, I have been playing around with it to get a better feel of what it can do, and how it compares against regular fitting algorithms such as those used by Fit. In this blog post, I don’t want to focus too much on the underlying technicalities (check out my previous blog post to learn more about Bayesian neural network regression); rather, I will show you some of the practical applications and interpretations of Bayesian regression, and share some of the surprising results you can get from it.

Sjoerd Smit, Wolfram Europe
Current Events & History

Spherical Aberration Optics Problem Finally Solved Using the Wolfram Language

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.

Swede White, Public Relations Manager
Computation & Analysis

Taking the Cerne Abbas Walk: From Conceptual Art to Computational Art

Cerne Abbas Walk is an artwork by Richard Long, in the collection of the Tate Modern in London and on display at the time of this writing. Several of Long’s works involve geographic representations of his walks, some abstract and some concrete. Cerne Abbas Walk is described by the artist as “a six-day walk over all roads, lanes and double tracks inside a six-mile-wide circle centred on the Giant of Cerne Abbas.” The Tate catalog notes that “the map shows his route, retracing and re-crossing many roads to stay within a predetermined circle.”

The Giant in question is a 180-foot-high chalk figure carved into a hill near the village of Cerne Abbas in South West England. Some archaeologists believe it to be of Iron Age pedigree, some think it to date from the Roman or subsequent Saxon periods and yet others find the bulk of evidence to indicate a 17th-century origin as a political satire. (I find the last theory to be both the most amusing and the most convincing.)

I found the geographic premise of Cerne Abbas Walk intriguing, so I decided to replicate it computationally.

Jesse Friedman, Software Engineer, Engine Connectivity Engineering
Computation & Analysis

The Ultimate Team Generator with the Wolfram Language

Every summer, I play in a recreational Ultimate Frisbee league—just “Ultimate” to those who play. It’s a fun, relaxed, coed league where I tend to win more friends than games.

The league is organized by volunteers, and one year, my friend and teammate Nate was volunteered to coordinate it. A couple weeks before the start of the season, Nate came to me with some desperation in his voice over making the teams. The league allows each player to request to play with up to eight other players—disparagingly referred to as their “baggage.” And Nate discovered that with over 100 players in a league, each one requesting a different combination of teammates, creating teams that would please everyone seemed to become more complicated by the minute.

Luckily for him, the Wolfram Language has a suite of graph and network tools for things like social media. I recognized that this seemingly overwhelming problem was actually a fairly simple graph problem. I asked Nate for the data, spent an evening working in a notebook and sent him the teams that night.

Bob Sandheinrich, Development Manager, Document & Media Systems
Education & Academic

Building Uniform Polyhedra for Version 12

Since I started working at Wolfram, I’ve been a part of several different projects. For Version 12, my main focus was replicating models of the uniform polyhedra with the Wolfram Language to ensure that the data fulfilled certain criteria to make our models precise, including exact coordinates, consistent face orientation and a closed region in order to create a proper mesh model of each solid.

Working with visual models of polyhedra is one thing, but analyzing them mathematically proved to be much more challenging. Starting with reference models of the polyhedra, I found that the Wolfram Language made mathematical analysis of uniform polyhedra particularly efficient and easy.

But first, what really are polyhedra, and why should we care? With Version 12, we can explore what polyhedra are and how they’ve earned their continued place in our imaginations.

Keren Garcia, Algorithms R&D
Best of Blog

Mathematica 12 Available on the New Raspberry Pi 4

With the recent announcement of the all-new Raspberry Pi 4, we are proud to announce that our latest development, Version 12 of Mathematica and the Wolfram Language, is available for you to use when you get your hands on the Raspberry Pi 4.

Mathematica 12 is a major milestone in our journey that has spanned 30 years, significantly extending the reach of Mathematica and introducing a whole array of new features, including significant expansion of numerical, mathematic and geometric computation, audio and signal processing, text and language processing, machine learning, neural networks and much more. Version 12 gives Mathematica users new levels of power and effectiveness. With thousands of different updates across the system, and 278 new functions in 103 areas, there is so much to explore.

Jacob Wells, Technical Specialist, European Sales
Education & Academic

How I Used Last-Mover Advantage to Make Money: An Exploration of Yahtzee and Coin Flipping

This week, I won some money applying a mathematical strategy to a completely unpredictable gambling game. But before I explain how, I need to give some background on last-mover advantage.

Some time ago, I briefly considered doing some analysis of the dice game Yahtzee. But I was put off by the discovery that several papers (including this one) had already enumerated the entire game state graph to create a strategy for maximizing the expected value of the score (which is 254.59).

However, maximizing the expected value of the score only solves the solo Yahtzee game. In a competitive game, and in many other games, we are not actually trying to maximize our score—we are trying to win, and these are not always the same thing.

Jon McLoone, Director, Technical Communication & Strategy
Education & Academic

Easter Eggs in Plain Sight, Climate Change Challenges and Knitted Images: Wolfram Community Highlights

Wolfram Community is our favorite, continually growing forum to share and show support for projects using the Wolfram Language, connect with other Mathematica aficionados and find solutions for coding questions. It's also a great platform for sharing computational innovations that can benefit your local community—or beyond. We've collected some of the exciting ways Wolfram Community members have been giving back through Wolfram technology—check them out!

Chapin Langenheim, Editor & Web Project Coordinator, Project Management
Announcements & Events

The Wolfram Function Repository: Launching an Open Platform for Extending the Wolfram Language

We’re on an exciting path these days with the Wolfram Language. Just three weeks ago we launched the Free Wolfram Engine for Developers to help people integrate the Wolfram Language into large-scale software projects. Now, today, we’re launching the Wolfram Function Repository to provide an organized platform for functions that are built to extend the […]

Stephen Wolfram
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