March 7, 2019 — Ed Pegg Jr, Editor, Wolfram Demonstrations Project

## Similar Triangle Dissections

Version 12 of the Wolfram Language introduces solvers for geometry problems. The documentation for the new function `GeometricScene` has a neat example showing the following piece of code, with `GeometricAssertion` calling for seven similar triangles:

✕
o=Sequence[Opacity[.9],EdgeForm[Black]];plasticDissection=RandomInstance[GeometricScene[{a,b,c,d,e,f,g},{ a=={1,0},e=={0,0},Line[{a,e,d,c}], p0==Polygon[{a,b,c}], p1==Style[Polygon[{b,d,c}],Orange,o], p2==Style[Polygon[{d,f,e}],Yellow,o], p3==Style[Polygon[{b,f,d}],Blue,o], p4==Style[Polygon[{g,f,b}],Green,o], p5==Style[Polygon[{e,g,f}],Magenta,o], p6==Style[Polygon[{a,e,g}],Purple,o], GeometricAssertion[{p0,p1,p2,p3,p4,p5,p6},"Similar"]}],RandomSeeding->28] |

February 1, 2019 — Andrew Steinacher, Lead Developer, Wolfram|Alpha Scientific Content

## New Archive Conversion Utility in Version 12

Soon there will be 100,000 questions on MathOverflow.net, a question-and-answer site for professional mathematicians! To celebrate this event, I have been working on a Wolfram Language utility package to convert archives of Stack Exchange network websites into Wolfram Language entity stores.

The archives are hosted on the Internet Archive and are updated every few months. The package, although not yet publicly available, will be released in the coming weeks as part of Version 12 of the Wolfram Language—so keep watching this space for more news about the release!

January 10, 2019 — Brian Wood, Lead Technical Writer, Document and Media Systems

So far in this series, I’ve covered the process of extracting, cleaning and structuring data from a website. So what does one do with a structured dataset? Continuing with the Election Atlas data from the previous post, this final entry will talk about how to store your scraped data permanently and deploy results to the web for universal access and sharing.

September 6, 2018 — Brian Wood, Lead Technical 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:

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.

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.

May 31, 2018 — Sjoerd Smit, Technical Consultant, European Sales

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.

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!

March 21, 2018

Patrik Ekenberg, Applications Engineer, Wolfram MathCore

Jan Brugård, CEO, Wolfram MathCore

Explore the contents of this article with a **free Wolfram SystemModeler trial**. We are excited to announce the latest installment in the Wolfram SystemModeler series, Version 5.1, where our primary focus has been on pushing the scope of use for models of systems beyond the initial stages of development.

Since 2012, SystemModeler has been used in a wide variety of fields with an even larger number of goals—such as optimizing the fuel consumption of a car, finding the optimal dosage of a drug for liver disease and maximizing the lifetime of a battery system. The Version 5.1 update expands SystemModeler beyond its previous usage horizons to include a whole host of options, such as:

- Exporting models in a form that includes a full simulation engine, which makes them usable in a wide variety of tools
- Providing the right interface for your models so that they are easy for others to explore and analyze
- Sharing models with millions of users with the simulation core now included in the Wolfram Language

March 2, 2018 — Brian Wood, Lead Technical Writer, Document and Media Systems

Do you want to do more with data available on the web? Meaningful data exploration requires computation—and the Wolfram Language is well suited to the tasks of acquiring and organizing data. I’ll walk through the process of importing information from a webpage into a Wolfram Notebook and extracting specific parts for basic computation. Throughout this post, I’ll be referring to this website hosted by the National Weather Service, which gives 7-day forecasts for locations in the western US: