Devendra Kapadia

Getting to the Point: Asymptotic Expansions in the Wolfram Language

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.

CONTINUE READING »


Patrik Ekenberg
Anna Palmer

Why Is Sickle Cell Anemia Common in Areas with Malaria? Teaching Life Science with Modeling

July 12, 2018
Patrik Ekenberg, Applications Engineer, Wolfram MathCore
Anna Palmer, Intern, Wolfram MathCore

Life science teaches us to answer everything from “How can vaccines be used to indirectly protect people who haven’t been immunized?” to “Why are variations in eye color almost exclusively present among humans and domesticated animals?” You can now learn to answer these questions by using modeling with Wolfram’s virtual labs. Virtual labs are interactive course materials that are used to make teaching come alive, provide an easy way to study different concepts and promote student curiosity.

Cat with different eye colors

CONTINUE READING »


Jon McLoone

Programming Minecraft on the Raspberry Pi

July 5, 2018 — Jon McLoone, Director, Technical Communication & Strategy

The standard Raspbian software on the Raspberry Pi comes with a basic implementation of Minecraft and a full implementation of the Wolfram Language. Combining the two provides a fun playground for learning coding. If you are a gamer, you can use the richness of the Wolfram Language to programmatically generate all kinds of interesting structures in the game world, or to add new capabilities to the game. If you are a coder, then you can consider Minecraft just as a fun 3D rendering engine for the output of your code.

Minecraft

CONTINUE READING »


Brian Wood

The Shape of the Vote: Exploring Congressional Districts with Computation

June 26, 2018 — Brian Wood, Lead Technical Marketing Writer, Technical Communications and Strategy Group

In the past few decades, the process of redistricting has moved squarely into the computational realm, and with it the political practice of gerrymandering. But how can one solve the problem of equal representation mathematically? And what can be done to test the fairness of districts? In this post I’ll take a deeper dive with the Wolfram Language—using data exploration with Import and Association, built-in knowledge through the Entity framework and various GeoGraphics visualizations to better understand how redistricting works, where issues can arise and how to identify the effects of gerrymandering.

CONTINUE READING »


Stephen Wolfram

We’ve Come a Long Way in 30 Years (But You Haven’t Seen Anything Yet!)

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

CONTINUE READING »


Sebastian Bodenstein
Matteo Salvarezza
Meghan Rieu-Werden
Taliesin Beynon

Launching the Wolfram Neural Net Repository

June 14, 2018
Sebastian Bodenstein, Senior Developer, Advanced Research Group
Matteo Salvarezza, Developer, Advanced Research Group
Meghan Rieu-Werden, Data Manager, Advanced Research Group
Taliesin Beynon, Lead Developer, Advanced Research Group

Hero

Today, we are excited to announce the official launch of the Wolfram Neural Net Repository! A huge amount of work has gone into training or converting around 70 neural net models that now live in the repository, and can be accessed programmatically in the Wolfram Language via NetModel:

net = NetModel

net = NetModel["ResNet-101 Trained on ImageNet Competition Data"]

Peacock Input

net[]

Peacock Output

Neural nets have generated a lot of interest recently, and rightly so: they form the basis for state-of-the-art solutions to a dizzying array of problems, from speech recognition to machine translation, from autonomous driving to playing Go. Fortunately, the Wolfram Language now has a state-of-the-art neural net framework (and a growing tutorial collection). This has made possible a whole new set of Wolfram Language functions, such as FindTextualAnswer, ImageIdentify, ImageRestyle and FacialFeatures. And deep learning will no doubt play an important role in our continuing mission to make human knowledge computable.

CONTINUE READING »


Sjoerd Smit

How Optimistic Do You Want to Be? Bayesian Neural Network Regression with Prediction Errors

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

CONTINUE READING »


Carlo Giacometti

Learning to Listen: Neural Networks Application for Recognizing Speech

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

Introduction

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

CONTINUE READING »


Michael Trott

Strange Circles in the Complex Plane—More Experimental Mathematics Results

May 10, 2018 — Michael Trott, Chief Scientist

The Shape of the Differences of the Complex Zeros of Three-Term Exponential Polynomials

In my last blog, I looked at the distribution of the distances of the real zeros of functions of the form with incommensurate , . And after analyzing the real case, I now want to have a look at the differences of the zeros of three-term exponential polynomials of the form for real , , . (While we could rescale to set and for the zero set , keeping and will make the resulting formulas look more symmetric.) Looking at the zeros in the complex plane, one does not see any obvious pattern. But by forming differences of pairs of zeros, regularities and patterns emerge, which often give some deeper insight into a problem. We do not make any special assumptions about the incommensurability of , , .

The differences of the zeros of this type of function are all located on oval-shaped curves. We will find a closed form for these ovals. Using experimental mathematics techniques, we will show that ovals are described by the solutions of the following equation:


… where:

CONTINUE READING »

Posted in: Mathematics

Melanie Moore

Experience Innovation and Insight at the 2018 Wolfram Technology Conference

May 3, 2018 — Melanie Moore, Communications Project Manager

Join us October 16–19, 2018, for four days of hands-on training, workshops, talks and networking with creators, experts and enthusiasts of Wolfram technology. We’ll kick off on Tuesday, October 16, with a keynote address by Wolfram founder and CEO Stephen Wolfram.

CONTINUE READING »

Posted in: Events