Thursday, May 31, 2018
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.
Sunday, May 27, 2018
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.
Thursday, May 24, 2018
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.
Tuesday, May 22, 2018
Thursday, May 17, 2018
(Tip of the cap to Brian Cox.)
Tuesday, May 15, 2018
'Working Paper' in Collaboration with International Monetary Fund: "Evolution of the Global Financial Network and Contagion: A New Approach"
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.
Mathematics and physics get the familiar, cheesy writing-in-the-mirror treatment in some of these.
(Tip of the cap to Justin Howell.)
My first publication (except items in @Caltech's newspaper) was not mathematical or scientific in any way. It was a Dungeons & Dragons character!— Mason Porter (@masonporter) May 15, 2018
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
Saturday, May 12, 2018
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.
Thursday, May 10, 2018
(Tip of the cap to Jane Shevtsov.)
Wednesday, May 09, 2018
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.
Here is the video of my tutorial on paper-writing in applied mathematics: https://t.co/uAbUatOpnS— Mason Porter (@masonporter) May 9, 2018
For reasons unbenownst to me, YouTube decided to classify it as a "comedy".
Maybe that's a feature, rather than a bug?
You can also download the slides.
I hope that people find it helpful!
Tuesday, May 08, 2018
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.