Tales from the ArXiv: "Calculating Spherical Harmonics Without Derivatives"

There is a new paper on the arXiv that apparently includes a new way of calculating spherical harmonics.

A part that some of you may find interesting is the pedagogical discussion at the beginning of Section 5, which starts: "Historically, there are five ways that spherical harmonics can be derived."

The one that is easiest (by far) for me to understand is the oldest method, which is by solving the differential equation. But I am mathematically inclined, and people with more physical intuition may prefer other methods.

(People who are more comfortable than I am with Lie manipulations may also prefer other approaches.)

Anyway, I appreciate the discussion in this paper.

"Can Multilayer Networks Advance Animal Behavior Research?"

The final version of a new paper of mine now has its final coordinates in a journal. Here are some details.

Title: Can Multilayer Networks Advance Animal Behavior Research?

Authors: Matthew J. Silk, Kelly R. Finn, Mason A. Porter, and Noa Pinter-Wollman

Abstract: Interactions among individual animals — and between these individuals and their environment — yield complex, multifaceted systems. The development of multilayer network analysis offers a promising new approach for studying animal social behavior and its relation to eco-evolutionary dynamics.

Innovative Pitching Usage: Micro-Starts by Relievers

The Rays started playing around with an interesting innovation in their pitcher usage in a recent series against the Angels: They started a reliever for one inning to face the tough top of their lineup, and then they brought in their scheduled "starter" for the second inning.

The Rays are doing this again in their upcoming series against the Orioles.

I think there is a lot of traction for more of this, though it will depend on a team's rotation (e.g., if you have one like the Astros, this is probably not as helpful as for the Rays), player, player egos, and so on.

What Happens at Caltech Stays at Caltech

Well, obviously.

"The Pole Arm of Archaeology" and Other Epic Scholar Visualizations

Dan Hicks posted some epically bad scholar visualizations as a Twitter thread. My favorite one is The Pole Arm of Archaeology, which is about as epic as it sounds. ;)

"The Pole Arm of Archaeology" (1977) #WorstAcademicDiagrams pic.twitter.com/l8pwq6XYdF

— Dan Hicks (@ProfDanHicks) May 16, 2018

(Tip of the cap to Brian Cox.)

'Working Paper' in Collaboration with International Monetary Fund: "Evolution of the Global Financial Network and Contagion: A New Approach"

A 'working paper' from a collaboration with folks from the International Monetary Fund (IMF) came out today. You can download it from this website. We also hope to submit a version of this work to a journal for publication. Here are some details.

Title: Evolution of the Global Financial Network and Contagion: A New Approach

Authors: Yevgeniya Korniyenko, Manasa Patnam, Rita Maria del Rio-Chanon, and Mason A. Porter

Abstract: This paper studies the interconnectedness of the global financial system and its susceptibility to shocks. A novel multilayer network framework is applied to link debt and equity exposures across countries. Use of this approach—that examines simultaneously multiple channels of transmission and their important higher order effects—shows that ignoring the heterogeneity of financial exposures, and simply aggregating all claims, as often done in other studies, can underestimate the extent and effects of financial contagion.The structure of the global financial network has changed since the global financial crisis, impacted by European bank’s deleveraging and higher corporate debt issuance. Still, we find that the structure of the system and contagion remain similar in that network is highly susceptible to shocks from central countries and those with large financial systems (e.g., the USA and the UK). While, individual European countries (excluding the UK) have relatively low impact on shock propagation, the network is highly susceptible to the shocks from the entire euro area. Another important development is the rising role of the Asian countries and the noticeable increase in network susceptibility to shocks from China and Hong Kong SAR economies.

Compilation of "Awesome" #BadStockPhotosOfMyJob

These stock photos of jobs (with much focus on scientific ones) are indeed hilariously bad.

Mathematics and physics get the familiar, cheesy writing-in-the-mirror treatment in some of these.

(Tip of the cap to Justin Howell.)

Fun Fact: My First Publication was a Dungeons & Dragons Character!

My first publication (except items in @Caltech's newspaper) was not mathematical or scientific in any way. It was a Dungeons & Dragons character!

I won a contest to design the thief on a cover of Polyhedron.

(For it, I corresponded with editor @erikmona.) #myfirstpublication pic.twitter.com/tTfFHVFdPk

— Mason Porter (@masonporter) May 15, 2018

You Wouldn't Like These Functions When They're Angry

There is a family of special functions called Anger functions. You wouldn't like them when they're angry.

Here is the context: Physics Today has agreed to publish an obituary for Norman Zabusky, so I needed to find some information that they require to be part of it. This led me to Norman's PhD thesis, which I found online. It briefly mentions something called Lommel polynomials, with which I wasn't familiar. The definition in a thesis appendix was terse — it's not exactly an important part of the thesis — so I looked at Wikipedia, and I kept seeing links to special functions that weren't familiar to me, and I have followed a couple of them. Anger functions are one family.

These various special functions are closely related to Bessel functions.

Meaningless Connections and Empty Entities

And I spend lots and lots of time studying these things, including in the context of applications like social media. ;)

pic.twitter.com/fPtP3XTUUG

— Ben Orlin (@benorlin) May 10, 2018

(Tip of the cap to Jane Shevtsov.)

The Pulse of Manhattan

Seriously.

The population of #Manhattan, hour-by-hour. #NYC #datavizhttps://t.co/KATB4uq9va pic.twitter.com/ov3xTQlVm0

— Randy Olson (@randal_olson) May 9, 2018

Taking the First Stab at "Taking the First Stab"

I couldn't find this with a simple Google search, but if you think about it, the origin of the phrase "take the first stab" has to be rather violent.

Maybe a nice piece of art to go with somebody starting to write the initial draft of an academic paper would be a picture of a scientist quite literally taking an initial stab through a pile or papers or perhaps through a laptop.

(If anybody has a favored website for etymology and similar matters, please let me know. I was hoping my global search would turn up a good answer on one of those pages.)

And, by all means, somebody should take the first stab at answering my query.

Video of my Tutorial in Paper-Writing in Applied Mathematics

Here is a video of my recent (4/20) tutorial on paper-writing in applied mathematics.

Here is the video of my tutorial on paper-writing in applied mathematics: https://t.co/uAbUatOpnS

For reasons unbenownst to me, YouTube decided to classify it as a "comedy".

Maybe that's a feature, rather than a bug?

— Mason Porter (@masonporter) May 9, 2018

You can also download the slides.

I hope that people find it helpful!

Important Paper on Seussian Configurations of Random-Graph Models

In network science, it is with very good reason that one should speak of "a" configuration model rather than "the" configuration model. To see an excellent discussion of this and related issues, be sure to go through this paper by Bailey Fosdick, Daniel Larremore, Joel Nishimura, and Johan Ugander.

Title: Configuring Random Graph Models with Fixed Degree Sequences

Authors: Bailey K. Fosdick, Daniel B. Larremore, Joel Nishimura, and Johan Ugander


In 2014, Aaron Clauset, David Kempe, and I (with help from Dan Larremore) organized a Mathematics Research Community in Network Science.

In addition to creating a network of network scientists from diverse backgrounds, some work was started there, and today the published version of what is in my opinion an extremely important paper has come out in final form in SIAM Review's 'Research Spotlights' section. I am, of course, talking about the aforementioned paper.

I'm very happy indeed for such excellent work to arise from this.

Congratulations to authors Bailey Fosdick, Daniel Larremore, Joel Nishimura, and Johan Ugander for creating this awesome paper!

I am posting this with an absolutely lovely Seussian picture from an arXiv version of the paper. This picture doesn't appear to have made the cut for the published piece. In addition to its wit and whimsy, a really great thing about the picture and its accompanying verse is that it also encodes the main message of the paper.

Note: I am on the editorial board of the Research Spotlights section of SIAM Review, but I had nothing whatsoever to do with the handling of this paper.

Albert Pujols gets his 3000th Career Hit!

Albert Pujols collected his 3000th career hit tonight, becoming the 32nd member of the club. He is one of four Major Leaguers with at least 600 homeruns and at least 3000 hits.

Awesome Google Doodle

The new Google Doodle, which celebrates Georges Méliès, is really, really cool. Go interact with it!

Our Memorial Article for Norman J. Zabusky (1929–2018)

Along with David Campbell and Alan Newell, I have written a memorial article for my collaborator Norman Zabusky, who died in February. It was posted online earlier today.