Thursday, November 28, 2019

My TDA (Topological Data Analysis) Origin Story

Based on what I saw as an undergraduate, I thought that algebraic topology was hopelessly abstract, and then I encountered Konstantin Mischaikow's work when I was a postdoc at Georgia Tech. He was using these ideas to analyze experimental data from areas like fluid mechanics. This stuck in my head, but I didn't work on these topics for many years. However, it stuck in the back of my head for about a decade, as this had made an impression on me. (I was aware of work of some others as well, but this is the one that made an impression, because of the close collaboration with experimentalists.) I was spending a bunch of time on granular networks as well as on generalizing network analysis from graphs to various more complicated structures (and I also had the desire to look more at "higher-order" interactions more generally).

During one of my daily arXiv routines, I noticed a paper by Konstantin and collaborators that used topological data analysis (TDA), so I saw that we were looking at the same systems, but in different ways. I contacted him, visited him early in 2013, and we started a joint TDA project --- but it turned out to be on spreading dynamics on networks, rather than on granular networks. Our first paper (which was led by Dane Taylor and coauthored with many other excellent people, including my Oxford colleague Heather Harrington) was published in final form in Nature Communications in 2015. I viewed this as just one paper; I never intended to start a large new direction in my research program. Back at Oxford, one student saw that I was part of that and wanted to work with Heather and me on applications of TDA. Then more students saw the 2015 paper and what this student was doing, and they wanted to work with us on TDA.

After I moved to UCLA, more students (starting with Michelle Feng) saw that I had some papers on TDA and wanted to work with me on those topics, partly because they wanted to do things with applications but also wanted to continue pursuing more theoretical mathematical subjects as well. I also really like the idea of taking "traditionally pure" areas of mathematics and bringing more and more of them into applications. It's a really exciting thing to do. And the work on applications also yields really great insights into the mathematical theory. (Because it does go in both directions, after all.)

Most recently, at least among people who have officially joined my group, Abby Hickok saw the work that Michelle and I have been doing, and she has ideas for building further on that work. And now TDA (along with work involving the intersection of dynamics, networks, and simplicial complexes) has become an important part of my research program,

Anyway, it was an all an accident.

Wednesday, November 27, 2019

Facial Recognition Software for Sheep

This is classical improbable research. This is extremely useful for many things, so first it may make you laugh, but then it makes you think.

(Tip of the cap to Richard Parker.)

A Golden Age of Mathematics: Happening Right Now!

Monday, November 25, 2019

Tales from the ArXiv: Mathematics Paper or Science-Fiction Novel?

A new paper, which looks very fascinating, that just appeared on arXiv is called Tropical Principal Component Analysis on the Space of Ultrametrics.

Tropical PCA sounds very promising and fascinating. Additionally, I think the title of this paper would make a great title for a science-fiction novel.

Saturday, November 23, 2019

Data Analysis of Exuberant and Uncouth College Fight Songs did some data analysis of college fight songs.

UCLA's fight song is apparently called "Sons of Westwood" (ugh).

How can they write such an article without mentioning Tom Lehrer?

Friday, November 22, 2019

Tetris with Gelatin

This is so awesome!

Wednesday, November 20, 2019

Some of my Past Materials Related to Academic Job Applications and Related Things

I've gotten an e-mail from someone indicating that the job-related materials that I have posted have been helpful to them, so this is a good impetus for me to broadcast them again in case others find them useful.

It's Applied-Mathematician Season

Or possibly duck season?

Tuesday, November 19, 2019

AirBnB Rental of a Pirate Ship on the Mississippi River

If I ever find myself with a conference or other event in the Minneapolis–St. Paul area of Minnesota, I may well partake of staying in a pirate ship. Yarrrrr!

Monday, November 18, 2019

LaTeX Without Hats

Technically, with hats.

Note: I think that the official lyrics have "We can..." in the first line that I show, but when Men Without Hats sing it, it does sound somewhat like they include an extra de facto syllable.

Update (11/19/19): I did a copy-and-paste and clearly should have looked a bit more for a better website. I didn't even notice the "They're are" until I saw Ernie Barreto's comment on Facebook. Here is a better site.

Sunday, November 17, 2019

Thursday, November 14, 2019

2019 Most Valuable Player Awards

Major League Baseball has announced the 2019 Most Valuable Player awards, and it's a southern California affair: Cody Bellinger of the Los Angeles Dodgers won in the National League (damn right!), and Mike Trout of the Los Angeles Angeles (of Anaheim) won in the American League (good!).

You can find the vote tallies of all players who received MVP votes on this page, and you can take a look at ESPN's summary of this season's awards in Major League Baseball on this page.

A New Paper (and a Great Meta-Acknowledgement) on the Cost of Formatting in Scientific Papers

I am very amused. :)

Wednesday, November 13, 2019

2019 Cy Young Awards

The 2019 Cy Young Awards, for the best pitching performances in the American and National League, were announced today by Major League Baseball. In the American League, Justin Verlander of the Houston Astros edged out teammate Gerrit Cole. (It would have been really cool if they had tied, but I agree that Verlander is a slightly better choice as the winner.) In the National League, Jacob DeGrom won in a landslide over Hyun-Jin Ryu and Max Scherzer (who were tied for 2nd place), who were barely ahead of Jack Flaherty. Stephen Strasburg finished in 5th place, and he was within striking distance of Flaherty.

You can read ESPN's summary of this week's Major Baseball Awards on this page.

Tuesday, November 12, 2019

2019 Managers of the Year

The 2019 Managers of the Year in Major League Baseball are Mike Shildt (of the St. Louis Cardinals) in the National League and Rocco Baldelli (of the Minnesota Twins) in the American League.

ESPN is tabulate this week's award winners on this page.

Monday, November 11, 2019

Tales from the ArXiv: "Tautological Algebra"

I feel like tautological algebra is what we get from many of our students.

2019 Rookies of the Year

Unsurprisingly, Pete Alonso of the New York Mets and Yordan รlvarez of the Houston Astros were runaway winners of Rookie of the Year in the National League and American League, respectively.

Take a look at this page for a tabulation of Major League Baseball's 2019 awards. Today's announcement of the Rookies of the Year kicks off a week of pronouncements. The three finalists for each award were announced previously.

Update: The vote tallies are available at this page.

Sunday, November 10, 2019

Paper Title of the Day: "p-ing Everywhere"

(Tip of the cap to Chris Marcum.)

Saturday, November 09, 2019

Visualization of the Zachary Karate Club Network Using a Cappuccino Embedding

Sofia found this picture in one of Petter Holme's presentations, although it reminds me of one of them from old papers and t-shirt designs.

Wednesday, November 06, 2019

Tales from the ArXiv: An Epic 1-Panel Figure

Chris Lustri just pointed me to Figure 1 (see below) in this paper. Although it doesn't have 81 panels, it is awesome in its own way.

Monday, November 04, 2019

"Supracentrality Analysis of Temporal Networks with Directed Interlayer Coupling"

A new book chapter in the edited book Temporal Network Theory was just published in final form. Here are some details.

Titles: Supracentrality Analysis of Temporal Networks with Directed Interlayer Coupling

Authors: Dane Taylor, Mason A. Porter, and Peter J. Mucha

Abstract: We describe centralities in temporal networks using a supracentrality framework to study centrality trajectories, which characterize how the importances of nodes change in time. We study supracentrality generalizations of eigenvector-based centralities, a family of centrality measures for time-independent networks that includes PageRank, hub and authority scores, and eigenvector centrality. We start with a sequence of adjacency matrices, each of which represents a time layer of a network at a different point or interval of time. Coupling centrality matrices across time layers with weighted interlayer edges yields a supracentrality matrix โ„‚(๐œ”), where ฯ‰ controls the extent to which centrality trajectories change over time. We can flexibly tune the weight and topology of the interlayer coupling to cater to different scientific applications. The entries of the dominant eigenvector of โ„‚(๐œ”) represent joint centralities, which simultaneously quantify the importance of every node in every time layer. Inspired by probability theory, we also compute marginal and conditional centralities. We illustrate how to adjust the coupling between time layers to tune the extent to which nodes’ centrality trajectories are influenced by the oldest and newest time layers. We support our findings by analysis in the limits of small and large ฯ‰.

Sunday, November 03, 2019

7th Century: Service Obligations Interfering with Research and Teaching

Some things never change...

(Tip of the cap to multiple people.)

Friday, November 01, 2019

"Challenge Accepted"

(Tip of the cap to Card Colm Mulcahy.)