January 15, 2015 — Oleksandr Pavlyk, Kernel Technology

January 16, 2015, marks the 360th birthday anniversary of Jacob Bernoulli (also James, or Jacques).

Input 1 through Output 4

Jacob Bernoulli was the first mathematician in the Bernoulli family, which produced many notable mathematicians of the seventeenth and eighteenth centuries.

Jacob Bernoulli’s mathematical legacy is rich. He introduced Bernoulli numbers, solved the Bernoulli differential equation, studied the Bernoulli trials process, proved the Bernoulli inequality, discovered the number e, and demonstrated the weak law of large numbers (Bernoulli’s theorem).

Jacob Bernoulli's mathematical achievements

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January 6, 2015 — Mikael Forsgren, Wolfram MathCore

Mathematical modeling is not just used for understanding and designing new products and drugs; modeling can also be used in health care, and in the future, your doctor might examine your liver with a mathematical model just like the one researchers at AstraZeneca have developed.

Liver

The liver is a vital organ, and currently there isn’t really a way to compensate for loss of liver function in the long term. The liver performs a wide range of functions, including detoxification, protein synthesis, and secretion of compounds necessary for digestion, just to mention a few. In the US and Europe, up to 15 % of all acute liver failure cases are due to drug-induced liver injury, and the risk of injuring the liver is of major concern in testing new drug candidates. So in order to safely monitor the impact of a new drug candidate on the liver, researchers at the pharmaceutical company AstraZeneca have recently published a method for evaluating liver function that combines magnetic resonance imaging (MRI) and mathematical modeling—potentially allowing for early identification of any reduced liver function in humans.

Last year, Wolfram MathCore and AstraZeneca worked together on a project where we investigated some modifications of AstraZeneca’s modeling framework. We presented the promising results at the ISMRM-ESMRMB Joint Annual Meeting, which is the major international magnetic resonance conference. In this blog post, I’ll show how the Wolfram Language was used to calculate liver function and how more complex models of liver function can be implemented in Wolfram SystemModeler.

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December 29, 2014 — Tom Sherlock, User Interface Group

As an amateur astronomer, I’m always interested in ways to use Mathematica in my hobby. In earlier blog posts, I’ve written about how Mathematica can be used to process and improve images taken of planets and nebulae. However, I’d like to be able to control my astronomical hardware directly with the Wolfram Language.

In particular, I’ve been curious about using the Wolfram Language as a way to drive my telescope mount, for the purpose of automating an observing session. There is precedent for this because some amateurs use their computerized telescopes to hunt down transient phenomena like supernovas. Software already exists for performing many of the tasks that astronomers engage in—locating objects, managing data, and performing image processing. However, it would be quite cool to automate all the different tasks associated with an observing session from one notebook.

Mathematica is highly useful because it can perform many of these operations in a unified manner. For example, Mathematica incorporates a vast amount of useful astronomical data, including the celestial coordinates of hundreds of thousands of stars, nebula, galaxies, asteroids, and planets. In addition to this, Mathematica‘s image processing and data handling functionality are extremely useful when processing astronomical data.

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December 15, 2014 — Wolfram Blog Team

It’s the holiday season, and Wolfram is gearing up for bright lights and winter weather by holding a new Tweet-a-Program challenge. To help us celebrate the holidays, tweet your best holiday ornament-themed lines of Wolfram Language code. As with our other challenges, we’ll use the Wolfram Language to randomly select winning tweets (along with a few of our favorites) to pin, retweet, and share with our followers. If you’re a lucky winner, we’ll send you a free Wolfram T-shirt!

If you need some help getting into the holiday spirit, check out these examples:

Snowflake

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December 3, 2014 — Adriana O'Brien, Business Development, Partnerships

Get ready, get set… code! It’s the time of year to get thinking about programming with the Hour of Code.

For many years, Wolfram Research has promoted and supported initiatives that encourage computation, programming, and STEM education, and we are always thrilled when efforts are taken by others to do the same. Code.org, in conjunction with Computer Science Education Week, is sponsoring an event to encourage educators and organizations across the country to dedicate a single hour to coding. This hour gives kids (and adults, too!) a taste of what it means to study computer science—and how it can actually be a creative, fun, and fulfilling process. Millions of students participated in the Hour of Code in past years, and instructors are looking for more engaging activities for their students to try. Enter the Wolfram Language.

Built into the Wolfram Language is the technology from Wolfram|Alpha that enables natural language input—and lets students create code just by writing English.

W|A using natural language

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November 26, 2014 — Rita Crook, Marketing Projects Manager

The Imitation Game, a movie portraying Alan Turing’s life (who would have celebrated his 100th birthday on Mathematica‘s 23rd birthday—read our blog post), was released this week, which we’ve been looking forward to. Turing machines were one of the focal points of the movie, and we launched a prize in 2007 to determine whether the 2,3 Turing machine was universal.

So of course, Cumberbatch’s promotional video where he impersonates other beloved actors reached us as well, which got me wondering, could Mathematica‘s machine learning capabilities recognize his voice, or could he fool a computer too?

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November 21, 2014
Matthias Odisio, Mathematica Algorithm R&D
Giulio Alessandrini, Mathematica Algorithm R&D

For most of us, taking bad pictures is incredibly easy. Band-Aid or remedy, digital post-processing can involve altering the photographed scene itself. Say you’re trekking through the mountains taking photos of the horizon, or you’re walking down the street and catch a beautiful perspective of the city, or it’s finally the right time to put the new, expensive phone camera to good use and capture the magic of this riverside… Just why do all the pictures look so bad? They’re all foggy! It’s not that you’re a bad photographer—OK, maybe you are—but that you’ve stumbled on a characteristic problem in outdoor photography: haze.

What is haze? Technically, haze is scattered light, photons bumped around by the molecules in the air and deprived of their original color, which they got by bouncing off the objects you are trying to see. The problem gets worse with distance: the more the light has to travel, the more it gets scattered around, and the more the scene takes that foggy appearance.

What can we do? What can possibly help our poor photographer? Science, of course.

Wolfram recently attended and sponsored the 2014 IEEE International Conference on Image Processing (ICIP), which ended October 30 in Paris. It was a good occasion to review the previous years’ best papers at the conference, and we noticed an interesting take on the haze problem proposed by Chen Feng, Shaojie Zhuo, Xiaopeng Zhang, Liang Shen, and Sabine Süsstrunk [1]. Let’s give their method a try and implement their “dehazing” algorithm.

The core idea behind the paper is to leverage the different susceptibilities of the light being scattered, which depend on the wavelength of the light. Light with a larger wavelength, such as red light, is more likely to travel around the dust, the smog, and all the other particles present in the air than shorter wavelength colors, like green or blue. Therefore, the red channel in an image carries better information about the non-hazy content of the scene.

But what if we could go even further? What prevents us from using the part of the spectrum slightly beyond the visible light? Nothing really—save for the fact we need an infrared camera.

Provided we are well equipped, we can then use the four channels of data (near infrared, red, green, and blue) to estimate the haze color and distribution and proceed to remove it from our image.

RGB, IR removal

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November 17, 2014 — Wolfram Blog Team

This week Wolfram will be celebrating Benoit Mandelbrot‘s birthday and his contributions to mathematics by holding a Tweet-a-Program challenge. In honor of Mandelbrot, tweet us your favorite fractal-themed lines of Wolfram Language code. Then, as with our other challenges, we’ll use the Wolfram Language to randomly select winning tweets (along with a few of our favorites) to pin, retweet, and share with our followers. If you win, we’ll send you a free Wolfram T-shirt!

In Tweet-a-Program’s first few exciting months, we’ve already seen a number of awesome fractal examples like these:

First fractal image

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November 10, 2014 — Christopher Carlson, Senior User Interface Developer, User Interfaces

This year’s Wolfram Technology Conference once again included the One-Liner Competition, an opportunity for some of the world’s most talented Wolfram Language developers to show us the amazing things you can do with tiny pieces of Wolfram Language code.

In previous years, One-Liner submissions were allowed 140 characters and 2D typesetting constructs. This year, in the spirit of Tweet-a-Program, we limited entries to 128-character, tweetable Wolfram Language programs. That’s right: we challenged them to write a useful or entertaining program that fits in a single tweet.

And the participants rose to the occasion. Entries were blind-judged by a panel of Wolfram Research developers, who awarded two honorable mentions and first, second, and third prizes.

One honorable mention went to Michael Sollami for his “Mariner Valley Flyby,” which takes you on a flight through the terrain of the Mariner Valley on Mars. The judges were greatly impressed by the idea and the effect. Unfortunately, a small glitch in the program is visible at the start of the output, due to an error in the code. Since Michael’s submission is right up against the 128-character limit, it would have taken some clever tweaking to fix it.

Mariner Valley Flyby

Mariner Valley Flyby

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November 4, 2014 — Vitaliy Kaurov, Technical Communication & Strategy

Data is critical for an objective outlook, but bare data is not a forecast. Scientific models are necessary to predict pandemics, terrorist attacks, natural disasters, market crashes, and other complex aspects of our world. One of the tools for combating the ongoing and tragic Ebola outbreak is to make computer models of the virus’s possible spread. By understanding where and how quickly the outbreak is likely to appear, policy makers can put into place effective measures to slow transmissions and ultimately bring the epidemic to a halt. Our goal here is to show how to set up a mathematical model that depicts a global spread of a pandemic, using real-world data. The model would apply to any pandemic, but we will sometimes mention and use current Ebola outbreak data to put the simulation into perspective. The results should not be taken as a realistic quantitative projection of current Ebola pandemic.

Ebola animation

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