Thursday, November 28, 2019
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
Okay... pic.twitter.com/Qbsm6yptuH— Thomas Lumley (@tslumley) November 27, 2019
(Tip of the cap to Richard Parker.)
My opinion is that we are, right now, in a golden age of mathematics.— Mason Porter (@masonporter) November 27, 2019
I really like the quote below, and that's what I try to convey to my students and postdocs. https://t.co/EDt196FML9 pic.twitter.com/MmkbY28HN6
Monday, November 25, 2019
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
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
Wednesday, November 20, 2019
In case it's of interest to those of you on the academic job market (or people with mentees on the market), I have posted some of my materials: (1) a research statement; (2) a teaching statement; and (3) two equity, diversity, and inclusion statements: https://t.co/HDMKUPNTvF— Mason Porter (@masonporter) November 20, 2019
Tuesday, November 19, 2019
Monday, November 18, 2019
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
Friday, November 15, 2019
Thursday, November 14, 2019
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.
Wednesday, November 13, 2019
You can read ESPN's summary of this week's Major Baseball Awards on this page.
Tuesday, November 12, 2019
ESPN is tabulate this week's award winners on this page.
Monday, November 11, 2019
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
The sort of paper title that one ultimately regrets, I think. pic.twitter.com/g19H4yTdn7— Stuart Ritchie (@StuartJRitchie) November 10, 2019
(Tip of the cap to Chris Marcum.)
Saturday, November 09, 2019
In case you ever wanted to see the Karate Club network visualized using a capuccino embedding.— Mason Porter (@masonporter) November 10, 2019
(Thanks to University of Michigan postdoc Sofia Piltz for trying this out for me at BeanBerry Cafe in Ann Arbor. She'll try it with a higher-contrast and more circular picture later.) pic.twitter.com/nqLpcJrfmY
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
Monday, November 04, 2019
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 ℂ(𝜔), where ω 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 ℂ(𝜔) 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 ω.
Sunday, November 03, 2019
Academics complaining that departmental service obligations interfere with their research and teaching. Assyria, mid 7th century BC: pic.twitter.com/SCkmgFk8by— Christopher Jones (@cwjones89) November 2, 2019
(Tip of the cap to multiple people.)