News, Views & Insights
Today we celebrate the arrival of the 36th (x.x) version of the Wolfram Language and Mathematica: Version 14.1. We’ve been doing this since 1986: continually inventing new ideas and implementing them in our larger and larger tower of technology. And it’s always very satisfying to be able to deliver our latest achievements to the world.
Today we celebrate a new waypoint on our journey of nearly four decades with the release of Version 14.0 of Wolfram Language and Mathematica. Over the two years since we released Version 13.0 we’ve been steadily delivering the fruits of our research and development in .1 releases every six months. Today we’re aggregating these—and more—into Version 14.0.
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.
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.
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 […]
|
✕
net = NetModel["ResNet-101 Trained on ImageNet Competition Data"]
|
|
✕
net[]
|
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.
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!
One of the Holy Grails of mathematics is the Riemann zeta function, especially its zeros. One representation of is the infinite sum . In the last few years, the interest in partial sums of such infinite sums and their zeros has grown. A single cosine or sine function is periodic, and the distribution of its zeros is straightforward to describe. A sum of two cosine functions can be written as a product of two cosines, . Similarly, a sum of two sine functions can be written as a product of . This reduces the zero-finding of a sum of two cosines or sines to the case of a single one. A sum of three cosine or sine functions, , is already much more interesting.
Fifteen years ago, in the notes to chapter 4 of Stephen Wolfram’s A New Kind of Science, a log plot of the distribution of the zero distances... ... of the zero distribution of ---showing characteristic peaks---was shown.