September 11, 2018 — Jon McLoone, Director, Technical Communication & Strategy

Having a really broad toolset and an open mind on how to approach data can lead to interesting insights that are missed when data is looked at only through the lens of statistics or machine learning. It’s something we at Wolfram Research call multiparadigm data science, which I use here for a small excursion through calculus, graph theory, signal processing, optimization and statistics to gain some interesting insights into the engineering of supersonic cars.

Car gauges

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September 6, 2018 — Brian Wood, Lead Technical Marketing Writer, Document and Media Systems


In my previous post, I demonstrated the first step of a multiparadigm data science workflow: extracting data. Now it’s time to take a closer look at how the Wolfram Language can help make sense of that data by cleaning it, sorting it and structuring it for your workflow. I’ll discuss key Wolfram Language functions for making imported data easier to browse, query and compute with, as well as share some strategies for automating the process of importing and structuring data. Throughout this post, I’ll refer to the US Election Atlas website, which contains tables of US presidential election results for given years:


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August 21, 2018 — Kyle Keane, Director of Summer Programs, Public Relations

The 16th annual Wolfram Summer School was another successful immersive education adventure made possible by the power of the Wolfram Language for rapid scientific exploration and software development. A select group of 62 participants from all around the world (ranging from advanced high-school students to postgraduate students and beyond) worked on a variety of computational projects related to science, technology and innovation and educational innovation. The three-week program was packed with cutting-edge technologies, intellectual discussions, innovation in action and community building.

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August 16, 2018 — Erez Kaminski, Wolfram Technology Specialist, Wolfram Technology Group

For the past two years, FOALE AEROSPACE has been on an exhilarating journey to create an innovative machine learning–based system designed to help prevent airplane crashes, using what might be the most understated machine for the task—the Raspberry Pi. The system is marketed as a DIY kit for aircraft hobbyists, but the ideas it’s based upon can be applied to larger aircraft (and even spacecraft!).

FOALE AEROSPACE is the brainchild of astronaut Dr. Mike Foale and his daughter Jenna Foale. Mike is a man of many talents (pilot, astrophysicist, entrepreneur) and has spent an amazing 374 days in space! Together with Jenna (who is currently finishing her PhD in computational fluid dynamics), he was able to build a complex machine learning system at minimal cost. All their development work was done in-house, mainly using the Wolfram Language running on the desktop and a Raspberry Pi. FOALE AEROSPACE’s system, which it calls the Solar Pilot Guard (SPG), is a solar-charged probe that identifies and helps prevent loss-of-control (LOC) events during airplane flight. Using sensors to detect changes in the acceleration and air pressure, the system calculates the probability of each data point (an instance in time) to be in-family (normal flight) or out-of-family (non-normal flight/possible LOC event), and issues the pilot voice commands over a Bluetooth speaker. The system uses classical functions to interpolate the dynamic pressure changes around the airplane axes; then, through several layers of Wolfram’s automatic machine learning framework, it assesses when LOC is imminent and instructs the user on the proper countermeasures they should take.

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July 26, 2018 — Itai Seggev, Senior Kernel Developer, Algorithms R&D

One of the many beautiful aspects of mathematics is that often, things that look radically different are in fact the same—or at least share a common core. On their faces, algorithm analysis, function approximation and number theory seem radically different. After all, the first is about computer programs, the second is about smooth functions and the third is about whole numbers. However, they share a common toolset: asymptotic relations and the important concept of asymptotic scale.

By comparing the “important parts” of two functions—a common trick in mathematics—asymptotic analysis classifies functions based on the relative size of their absolute values near a particular point. Depending on the application, this comparison provides quantitative answers to questions such as “Which of these algorithms is fastest?” or “Is function a good approximation to function g?”. Version 11.3 of the Wolfram Language introduces six of these relations, summarized in the following table.

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July 19, 2018 — Devendra Kapadia, Kernel Developer, Algorithms R&D

Asymptotic expansions have played a key role in the development of fields such as aerodynamics, quantum physics and mathematical analysis, as they allow us to bridge the gap between intricate theories and practical calculations. Indeed, the leading term in such an expansion often gives more insight into the solution of a problem than a long and complicated exact solution. Version 11.3 of the Wolfram Language introduces two new functions, AsymptoticDSolveValue and AsymptoticIntegrate, which compute asymptotic expansions for differential equations and integrals, respectively. Here, I would like to give you an introduction to asymptotic expansions using these new functions.

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June 21, 2018 — Stephen Wolfram

30 years of Mathematica

Technology for the Long Term

On June 23 we celebrate the 30th anniversary of the launch of Mathematica. Most software from 30 years ago is now long gone. But not Mathematica. In fact, it feels in many ways like even after 30 years, we’re really just getting started. Our mission has always been a big one: to make the world as computable as possible, and to add a layer of computational intelligence to everything.

Our first big application area was math (hence the name “Mathematica”). And we’ve kept pushing the frontiers of what’s possible with math. But over the past 30 years, we’ve been able to build on the framework that we defined in Mathematica 1.0 to create the whole edifice of computational capabilities that we now call the Wolfram Language—and that corresponds to Mathematica as it is today.

From when I first began to design Mathematica, my goal was to create a system that would stand the test of time, and would provide the foundation to fill out my vision for the future of computation. It’s exciting to see how well it’s all worked out. My original core concepts of language design continue to infuse everything we do. And over the years we’ve been able to just keep building and building on what’s already there, to create a taller and taller tower of carefully integrated capabilities.

It’s fun today to launch Mathematica 1.0 on an old computer, and compare it with today:

Older Mac versus iPhone

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May 31, 2018 — Sjoerd Smit, Technical Consultant

Neural networks are very well known for their uses in machine learning, but can be used as well in other, more specialized topics, like regression. Many people would probably first associate regression with statistics, but let me show you the ways in which neural networks can be helpful in this field. They are especially useful if the data you’re interested in doesn’t follow an obvious underlying trend you can exploit, like in polynomial regression.

In a sense, you can view neural network regression as a kind of intermediary solution between true regression (where you have a fixed probabilistic model with some underlying parameters you need to find) and interpolation (where your goal is mostly to draw an eye-pleasing line between your data points). Neural networks can get you something from both worlds: the flexibility of interpolation and the ability to produce predictions with error bars like when you do regression.

Bayesian Neural Nets

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May 24, 2018 — Carlo Giacometti, Kernel Developer, Algorithms R&D


Recognizing words is one of the simplest tasks a human can do, yet it has proven extremely difficult for machines to achieve similar levels of performance. Things have changed dramatically with the ubiquity of machine learning and neural networks, though: the performance achieved by modern techniques is dramatically higher compared with the results from just a few years ago. In this post, I’m excited to show a reduced but practical and educational version of the speech recognition problem—the assumption is that we’ll consider only a limited set of words. This has two main advantages: first of all, we have easy access to a dataset through the Wolfram Data Repository (the Spoken Digit Commands dataset), and, maybe most importantly, all of the classifiers/networks I’ll present can be trained in a reasonable time on a laptop.

It’s been about two years since the initial introduction of the Audio object into the Wolfram Language, and we are thrilled to see so many interesting applications of it. One of the main additions to Version 11.3 of the Wolfram Language was tight integration of Audio objects into our machine learning and neural net framework, and this will be a cornerstone in all of the examples I’ll be showing today.

Without further ado, let’s squeeze out as much information as possible from the Spoken Digit Commands dataset!

Spoken Digit Commands dataset

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April 12, 2018 — Stephen Wolfram

Wolfram Challenges

The more one does computational thinking, the better one gets at it. And today we’re launching the Wolfram Challenges site to give everyone a source of bite-sized computational thinking challenges based on the Wolfram Language. Use them to learn. Use them to stay sharp. Use them to prove how great you are.

The Challenges typically have the form: “Write a function to do X”. But because we’re using the Wolfram Language—with all its built-in computational intelligence—it’s easy to make the X be remarkably sophisticated.

The site has a range of levels of Challenges. Some are good for beginners, while others will require serious effort even for experienced programmers and computational thinkers. Typically each Challenge has at least some known solution that’s at most a few lines of Wolfram Language code. But what are those lines of code?

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