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:

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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.

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Posted in: Events

Michael Trott

A Tale of Three Cosines—An Experimental Mathematics Adventure

April 24, 2018 — Michael Trott, Chief Scientist

Identifying Peaks in Distributions of Zeros and Extrema of Almost-Periodic Functions: Inspired by Answering a MathOverflow Question

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…

A New Kind of Science, notes from Chapter 4

… of the zero distribution of —showing characteristic peaks—was shown.

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Posted in: Mathematics

Joanna Crown

Five Ways to Make Your Technical Presentations Awesome

April 19, 2018 — Joanna Crown, Strategic Projects

“Tell me and I forget. Teach me and I remember. Involve me and I learn.” — Benjamin Franklin

I can count on one hand the best presentations I have ever experienced, the most recent being my university dynamics lecturer bringing out his electric guitar at the end of term to demonstrate sound waves; a pharmaceutical CEO giving an impassioned after-dinner oration about how his love of music influenced his business decisions; and last but not least, my award-winning attempt at explaining quantum entanglement using a marble run and a cardboard box (I won a bottle of wine).

It’s perhaps equally easy to recall all the worst presentations I’ve experienced as well—for example, too many PowerPoint presentations crammed full of more bullet points than a shooting target; infinitesimally small text that only Superman’s telescopic vision could handle; presenters intent on slowly reading every word that they’ve squeezed onto a screen and thoroughly missing the point of a presentation: that of succinctly communicating interesting ideas to an audience.

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Cat Frazier

Announcing Wolfram Presenter Tools

April 17, 2018 — Cat Frazier, Project Manager, Wolfram Blog

Introducing the Ultimate Technical Presentation Environment with Live Interactivity

We are delighted to announce that Wolfram’s latest comprehensive notebook technology extension is here. Released with Version 11.3 of Wolfram desktop products, Wolfram Presenter Tools is the world’s first fully computational presentation environment, seamlessly extending the notebook workflow for easy creation and delivery of dynamic presentations and slide shows, automatically scaled to fit any screen size. Our unique presentation features include rapid stylesheet updating and automatic slide breaking based on cell style.

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Stephen Wolfram

Launching the Wolfram Challenges Site

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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Sandra Sarac

European Wolfram Technology Conference 2018

April 12, 2018 — Sandra Sarac, Marketing Coordinator, European Sales

This year, we’ll be in Oxford for the European Wolfram Technology Conference. Join us June 14–15 for two days of expert talks showcasing the latest releases in Wolfram technologies, in-depth explorations of key features and practical use cases for integrating Wolfram technologies in your ecosystem.

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Posted in: Events

Patrik Ekenberg
Jan Brugård

Unleash Your Models with SystemModeler 5.1

March 21, 2018
Patrik Ekenberg, Applications Engineer, Wolfram MathCore
Jan Brugård, CEO, Wolfram MathCore

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

Wolfram SystemModeler 5.1

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Swede White

User Research: Deep Learning for Gravitational Wave Detection with the Wolfram Language

March 14, 2018 — Swede White, Media & Communications Specialist

Daniel George is a graduate student at the University of Illinois at Urbana-Champaign, Wolfram Summer School alum and Wolfram intern whose award-winning research on deep learning for gravitational wave detection recently landed in the prestigious pages of Physics Letters B in a special issue commemorating the Nobel Prize in 2017.

We sat down with Daniel to learn more about his research and how the Wolfram Language plays a part in it.

DanielGeorgeAward

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Stephen Wolfram

Roaring into 2018 with Another Big Release: Launching Version 11.3 of the Wolfram Language & Mathematica

March 8, 2018 — Stephen Wolfram

The Release Pipeline

Last September we released Version 11.2 of the Wolfram Language and Mathematica—with all sorts of new functionality, including 100+ completely new functions. Version 11.2 was a big release. But today we’ve got a still bigger release: Version 11.3 that, among other things, includes nearly 120 completely new functions.

This June 23rd it’ll be 30 years since we released Version 1.0, and I’m very proud of the fact that we’ve now been able to maintain an accelerating rate of innovation and development for no less than three decades. Critical to this, of course, has been the fact that we use the Wolfram Language to develop the Wolfram Language—and indeed most of the things that we can now add in Version 11.3 are only possible because we’re making use of the huge stack of technology that we’ve been systematically building for more than 30 years.

11.3We’ve always got a large pipeline of R&D underway, and our strategy for .1 versions is to use them to release everything that’s ready at a particular moment in time. Sometimes what’s in a .1 version may not completely fill out a new area, and some of the functions may be tagged as “experimental”. But our goal with .1 versions is to be able to deliver the latest fruits of our R&D efforts on as timely a basis as possible. Integer (.0) versions aim to be more systematic, and to provide full coverage of new areas, rounding out what has been delivered incrementally in .1 versions.

In addition to all the new functionality in 11.3, there’s a new element to our process. Starting a couple of months ago, we began livestreaming internal design review meetings that I held as we brought Version 11.3 to completion. So for those interested in “how the sausage is made”, there are now almost 122 hours of recorded meetings, from which you can find out exactly how some of the things you can now see released in Version 11.3 were originally invented. And in this post, I’m going to be linking to specific recorded livestreams relevant to features I’m discussing.

What’s New?

OK, so what’s new in Version 11.3? Well, a lot of things. And, by the way, Version 11.3 is available today on both desktop (Mac, Windows, Linux) and the Wolfram Cloud. (And yes, it takes extremely nontrivial software engineering, management and quality assurance to achieve simultaneous releases of this kind.)

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