"Role Detection in Bicycle-Sharing Networks Using Multilayer Stochastic Block Models"

A new paper of mine was published in final form today. The project started in January 2017 as a group project by students in the first course that I ever taught at UCLA. It's taken awhile, but we're finally done!

Title: Role Detection in Bicycle-Sharing Networks Using Multilayer Stochastic Block Models

Authors: Jane Carlen†, Jaume de Dios Pont, CassidyMentus, Shyr-Shea Chang, Stephanie Wang, and Mason A. Porter

Abstract: In urban systems, there is an interdependency between neighborhood roles and transportation patterns between neighborhoods. In this paper, we classify docking stations in bicycle-sharing networks to gain insight into the human mobility patterns of three major cities in the United States. We propose novel time-dependent stochastic block models, with degree-heterogeneous blocks and either mixed or discrete block membership, which classify nodes based on their time-dependent activity patterns. We apply these models to (1) detect the roles of bicycle-sharing stations and (2) describe the traffic within and between blocks of stations over the course of a day. Ourmodels successfully uncover work blocks, home blocks, and other blocks; they also reveal activity patterns that are specific to each city. Our work gives insights for the design and maintenance of bicycle-sharing systems, and it contributes new methodology for community detection in temporal and multilayer networks with heterogeneous degrees.

RIP Peter Neumann (1940–2020)

This morning, I saw the terrible news that my former Oxford colleague Peter Neumann died today, supposedly due to complications from COVID-19 (although I can't verify if that is the known cause of death). Here is is Peter's Wikipedia entry.

I had the chance to interact with Peter quite a few times at Oxford. When I knew him, he was concentrating on mathematics history, and I contacted him with a query about some mathematical linguistics (concerning, for example, the use of "topological" only versus both "geometric" and "geometrical"). I knew that Peter was the right person to approach when I wanted to dive deeper than what I was able to do via Google. Here is my 2013 blog entry about that.

Peter was one of the people in Oxford who was always so kind and supportive of me (and, from what I can tell, of many others as well). When I got some pointed negative teaching evaluations, Peter invited me to The Queen's College to dinner to chat about things (and to give gentle advice and so on). But if I am getting rewarded with a dinner like that for messing up, it does create strange incentives. My students in my courses now are certainly benefiting from advice Peter gave me over the years. He also supported me in various fights on committees (we were on Teaching Committee together) and particularly in efforts that I made against "We've always done it this way." comments to try to change things in Oxford's Mathematical Institute.

(Tip of the cap to Card Colm Mulcahy.)

Starting Out the Hard Way

I was the TA in the first course that Alex Vladimirsky (now the Director of the PhD program of my graduate alma mater) was ever in charge of.

Two decades later, I am still the most opinionated TA that he's ever had with respect to how to teach a course. People should get the most difficult person out of the way at the beginning, right?

He confirmed this and found out about the ducks at our meeting this morning! It’s perfect bc he tells me that when I need a debugging break, I should talk with a rubber duck, so I think the rubber duck that is living in the tex doc right now has a permanent home 😊 (for now)

— Mallory Gaspard (@mallorygaspard) May 27, 2020

Time has no Meaning.

Time has no meaning.

Also, space has no meaning.

Also, spacetime has no meaning.

(In addition to the fact that now I end up using the same technology to talk to somebody who is 1 mile away as somebody who is on the other side of the world, and that I can be anywhere in the world when I teach my courses online — which is inspiring these "delightful" thoughts — I naturally thought of a line from this sketch. One of my friends has subsequently reminded me of the quote "Time is an illusion. Lunchtime, doubly so.")

My mood is also captured by this video.

Preparing to Teach Classes in Cyberspace

In preparation for online lecturing, I am practicing using Zoom with my cousin.

There appears to be a time lag. pic.twitter.com/GgRI95tku9

— Mason Porter (@masonporter) March 14, 2020

Behind-the-Scenes Pictures of Professors Suddenly Transitioning to Online Teaching

Played to the tune of "March of the Toreadors" or the theme to "The Benny Hill Show", surely?

I am greatly looking forward to behind-the-scenes pix of profs improvising while abruptly transitioning to remote teaching. https://t.co/Lww5ZHzfY5

— Mika McKinnon (@mikamckinnon) March 13, 2020

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.

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

7th Century: Service Obligations Interfering with Research and Teaching

Some things never change...

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.)

"Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction"

A new paper of mine just came out in final form. Here are some details.

Title: Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

Authors: Baichuan Yuan, Hao Li, Andrea L. Bertozzi, P. Jeffrey Brantingham, and Mason A. Porter

Abstract: There is often latent network structure in spatial and temporal data, and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks that we construct from real-world data sets (a location-based social-media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis—such as examinations of community structure and motifs—of the reconstructed networks.

"Why Teachers Should Read John Urschel's Book"

Courtesy of Math with Bad Drawings, here are five (very!) important takeaway messages from John Urschel's new book.

https://t.co/8ut7tFPLte

— Ben Orlin (@benorlin) May 15, 2019

(Tip of the cap to Alex Kontorovich.

Finding Identical Packs of Skittles

One blogger has examined the probability of finding identical packs of skittles and posted their data online.

In my new lower-division mathematical modeling course (Math 42; "Introduction to Data-Driven Mathematical Modeling: Life, The Universe, and Everything"), we started our unit on discrete stochastic modeling today, so this post makes me very happy! I have, of course, e-mailed my students about this.

(Tip of the cap to Jeremy Jay.)

Course Nomenclature in our Imminent Data Theory Major

The UCLA mathematics department has a course called "Math 142: Mathematical Modeling", and my new lower-division mathematical-modeling course for our new Data Theory major was thus given the label "Math 42".

Given such an opportunity, I needed an appropriate name for the course. pic.twitter.com/mUGK1th012

— Mason Porter (@masonporter) March 1, 2019

Advice to Students: "Think for Yourself."

This statement gives excellent advice! In fact, it's the main thing that I try to convey to students.

"We are scholars and teachers at Princeton, Harvard, Yale, and other institutions who have some thoughts to share and advice to offer students across the country. Our advice can be distilled to three words:

Think for yourself."

The full statement, which I signed, is worth reading.

The Perils of Generating Functions (and Submitting a Note from a Parent with an Exam)

When I taught Math 1d, my exam instructions included a joke line that went something along the lines of "You may also use a note from your mother, though you won't need one." One student (and fellow Caltech undergrad) actually got her mother to write this note, which is fantastic (despite the threats against both Lloyd House and the Los Angeles Dodgers).

I had this posted on my door at Georgia Tech when I was a postdoc, and I found the note a year ago today when I was going through an old spiral notebook.

As a @Caltech undergraduate, I taught a probability course (Math 1d) and introduced freshmen to the glories of generating functions.

My exam instructions included a line like: "You may also use a note from your mother, though you won't need one."

One student took me up on it. pic.twitter.com/I2Ocif9ttA

— Mason Porter (@masonporter) March 27, 2018

In Phase Space, No One Can Hear You Scream.

My students have their ODE (ordinary differential equation) final tomorrow morning, and I’ve got the perfect shirt to wear for the occasion: "In phase space, no one can hear you scream." pic.twitter.com/79hoysL80A

— Mason Porter (@masonporter) December 14, 2017

The Importance of Specifying Units

It is extremely important to specify units. :)

Also: very well-played!

(Tip of the cap to Melvin Leok.)

Not The Twilight Zone, but The Brillouin Zone

It occurs to me that one should initially introduce the idea of a Brillouin zone to students as if it were narrated by Rod Serling in the style of The Twilight Zone. It might go something like this:

There is a primitive cell in reciprocal space beyond that which is known to undergraduates. It is a fundamental unit into which that space is divided. It can tile lattices as vast as space and as timeless as infinity. It leads to a sequence of disjoint equal-volume regions at increasing distances from the origin, and it lies between the pit of physicists' fears and the summit of their knowledge. This is the region of imagination. It is an area which we call THE BRILLOUIN ZONE.

Update: Joshua Bodyfelt produced a really nice picture after seeing my quote above on Facebook. Here it is.

"New Textbooks for the New Mathematics"

Here is an article, called "New Textbooks for the New Mathematics", by Richard Feynman that appeared in Caltech's publication Engineering and Science in March 1965.

The article includes a reprint of a cartoon from The New Yorker that reminds me of this song. (The song is relevant to the whole article, actually.)

(Tip of the cap to Ben Rogers.)

Bringing Mathematics to the Traumatized and the Perplexed

As many of you know, Steve Strogatz is one of my mathematical heroes. One of the reasons is that he's a master teacher and expositor. (Whenever I get his seal of approval for one of my articles or other efforts, I always feel like I did a good job on it.) Take a look at this new article.

Quoting Steve from this article: "So many of the things that we do in math education—and maybe more generally in education—are giving students answers to questions that they would never think of asking. By definition, that's what it is to be boring."

Conversely, this also speaks to why so many students find networks exciting from the start. They're already asking many of these questions! They just need the words and concepts to make the questions more precise to be able to answer them in a better way.

Excerpts of an Interview with Steve Strogatz about Math

Here are some excerpts of an interview with Steve Strogatz about what mathematics is, teaching math, learning math, and more.

There's some really good stuff in here!