"Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains"

A paper of mine was just published in final form. Here are some details.

Title: Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains

Authors: Guo Deng, Christopher J. Lustri, and Mason A. Porter

Abstract: We study ``nanoptera," which are nonlocalized solitary waves with exponentially small but nondecaying oscillations, in two singularly perturbed Hertzian chains with precompression. These two systems are woodpile chains (which we model as systems of Hertzian particles and springs) and diatomic Hertzian chains with alternating masses. We demonstrate that nanoptera arise from the Stokes phenomenon and appear as special curves (called Stokes curves) are crossed in the complex plane. We use techniques from exponential asymptotics to obtain approximations of the oscillation amplitudes. Our analysis demonstrates that traveling-wave solutions in a singularly perturbed woodpile chain have a single Stokes curve, which generates oscillations behind the wave front. Comparing these asymptotic predictions with numerical simulations reveals that our asymptotic approximation accurately describes the nondecaying oscillatory behavior in a woodpile chain. We perform a similar analysis of a diatomic Hertzian chain, and we show that each nanopteron solution has two distinct exponentially small oscillatory contributions. We demonstrate that there exists a set of mass ratios for which these two contributions cancel to produce localized solitary waves. This result builds on prior experimental and numerical observations that there exist mass ratios that support localized solitary waves in diatomic Hertzian chains without precompression. Comparing our asymptotic and numerical results for a diatomic Hertzian chain with precompression reveals that our exponential asymptotic approach accurately predicts the oscillation amplitude for a wide range of system parameters, but it fails to identify several values of the mass ratio that correspond to localized solitary-wave solutions.

2021 Baseball Comeback Players of the Year

Baseball's comeback players of the year for 2021 have been announced. The American League winner is Trey Mancini of the Baltimore Orioles, and the National League winner is now-retired Buster Posey of the San Francisco Giants.

2021 Baseball Most Valuable Player Awards

Baseball announced its 2021 Most Valueable Player Awards today as the culmination of this year's awards. Once again, the results are unsurprising. Shohei Ohtani of the Los Angeles Angels was a unanimous winner in the American League (duh), and Bryce Harper of the Philadelphia Phillies won in the National League.

2021 Cy Young Awards

Major League Baseball has announced its 2021 Cy Young Awards for pitching excellence. Robbie Ray of the Toronto Blue Jays won the award in the American League, and Corbin Burnes of the Milwaukee Brewers won in the National League.

The National League race was very close; Burnes narrowly beat out Zack Wheeler of the Philadelphia Phillies and the Los Angeles Dodgers' Max Scherzer wasn't horribly far away either. Walker Buehler of the Dodgers finished 4th in the balloting.

2021 Baseball Managers of the Year

Major League Baseball has announced its 2021 Managers of the Year. The Americal League Manager of the Year is Kevin Cash of the Tampa Bay Rays, and the National League Manager of the year is Gabe Kapler of the San Fransisco Giants.

As with the Rookies of the Year, neither winner is surprising.

2021 Baseball Rookies of the Year

The 2021 Rookies of the Year were announced today. Jonathan India of the Cincinnati Reds won in the National League, and Randy Arozarena of the Tampa Bay Rays won in the American League.

Neither choice is surprising.

Some More Trips

I have had a few more short academic trips in the last couple of weeks. I spent a day at Harvey Mudd to talk to the students in Heather Zinn Brooks's class on mathematics and democracy. Then I took a trip to Michigan state to give an applied-mathematics colloquium, and now I am in San Diego State to give a mathematics colloquium.

Major League Relievers of the Year

The Mariano Rivera Award and Trevor Hoffmann Award have been awarded to the top relievers in the American League and National League, respectively. Liam Hendricks of the Chicago White Sox won the former, and Josh Hader of the Milwakuee Brewers won the latter.

"Pull Out All the Stops: Textual Analysis via Punctuation Sequences"

One of my papers, which has been available publicly for more than a year, is finally out in final form, with its coordinates (its page numbers and so on). Here are the details.

Title: Pull Out All the Stops: Textual Analysis via Punctuation Sequences

Authors: Alexandra N. M. Darmon, Marya Bazzi, Sam D. Howison, and Mason A. Porter

Abstract: Whether enjoying the lucid prose of a favourite author or slogging through some other writer's cumbersome, heavy-set prattle (full of parentheses, em dashes, compound adjectives, and Oxford commas), readers will notice stylistic signatures not only in word choice and grammar but also in punctuation itself. Indeed, visual sequences of punctuation from different authors produce marvellously different (and visually striking) sequences. Punctuation is a largely overlooked stylistic feature in stylometry, the quantitative analysis of written text. In this paper, we examine punctuation sequences in a corpus of literary documents and ask the following questions: Are the properties of such sequences a distinctive feature of different authors? Is it possible to distinguish literary genres based on their punctuation sequences? Do the punctuation styles of authors evolve over time? Are we on to something interesting in trying to do stylometry without words, or are we full of sound and fury (signifying nothing)?

In our investigation, we examine a large corpus of documents from Project Gutenberg (a digital library with many possible editorial influences). We extract punctuation sequences from each document in our corpus and record the number of words that separate punctuation marks. Using such information about punctuation-usage patterns, we attempt both author and genre recognition, and we also examine the evolution of punctuation usage over time. Our efforts at author recognition are particularly successful. Among the features that we consider, the one that seems to carry the most explanatory power is an empirical approximation of the joint probability of the successive occurrence of two punctuation marks. In our conclusions, we suggest several directions for future work, including the application of similar analyses for investigating translations and other types of categorical time series.

"Detection of Functional Communities in Networks of Randomly Coupled Oscillators Using the Dynamic-Mode Decomposition"

One of my papers just came out in final form last week. Here are some details.

Title: Detection of Functional Communities in Networks of Randomly Coupled Oscillators Using the Dynamic-Mode Decomposition

Abstract: Dynamic-mode decomposition (DMD) is a versatile framework for model-free analysis of time series that are generated by dynamical systems. We develop a DMD-based algorithm to investigate the formation of functional communities in networks of coupled, heterogeneous Kuramoto oscillators. In these functional communities, the oscillators in a network have similar dynamics. We consider two common random-graph models (Watts–Strogatz networks and Barabási–Albert networks) with different amounts of heterogeneities among the oscillators. In our computations, we find that membership in a functional community reflects the extent to which there is establishment and sustainment of locking between oscillators. We construct forest graphs that illustrate the complex ways in which the heterogeneous oscillators associate and disassociate with each other.

Dodgers Advance to the National League Championship Series!

The Dodgers beat the Giants 2–1 in the elimination game of the NLDS to advance to the National League Championship Series against the Braves!!!

Today was game 5 of the National League Division Series. We were tied 1–1 entering the 9th inning and scored one run in the top of the inning. Max Scherzer entered the game in the bottom of the 9th and earned a save.

The called strike on the check swing to end the game was a really bad call.

Dodgers Win Wild Card Elimination Game on a Walk-Off Homerun!

The Dodgers have just beaten the Cardinals in the Wild Card elimination game!

We'll be going to face the Giants (in our first ever postseason series against them) in the National League Division Series!

The Dodgers and Giants had the two best records during the regular season.

Some Baseball Musings on the Last Day of the 2021 Regular Season

Despite some possibilities for drama, there won't be any Game 163 for any teams. (There was late-inning drama in two of the relevant AL games today, and that is why there won't be any of these extra games.)

We (i.e., the Dodgers) have a win-or-go-home Wild Card 'playoff' against the Cardinals on Wednesday. I'll have it on silent at first while I am participating as a panelist in the UCLA math department job-application panel (which I suggested to our department head that we should do, and thankfully we're doing it), and then I'll have sound on for most of the game once the panel is over.

Trea Turner ended up winning the NL battle title handily. I have trouble picking an MVP, because I think the Padres going into the tank will hurt Tatis Jr.'s chances. That said, I still think he merits it, although if we're going to do pure performance after the Padres fall, maybe Juan Soto ultimately was somewhat better overall? The NL Cy Young award is hard to predict, as a lot of votes will get split. Right now, I think it will be Walker Buehler by a nose over Scherzer, Burnes, and Zack Wheeler. Urías will get some down-ballot votes, but despite the gaudy win totals, the other pitchers I mentioned (and some I have not) have been better them him. Jonathan India will when the NL ROY.

In the AL, Ohtani is the MVP. I think Gerrit Cole is a slightly better Cy Young choice than Robbie Ray, who many announcers seem to think is the heavy favorite. He's a good choice, but I think that Cole has been slightly better. Randy Arozarena is technically still a rookie, but I think I need to look more closely at some of the other viable options as well.

Finally, reports of Joey Votto's demise appear to have been greatly exaggerated (although he has changed his hitting style).

"Math Prof" (a parody of “Dentist” from Little Shop of Horrors)

“Math Prof”

(a parody of “Dentist” from Little Shop of Horrors)

[MATHEMATICS PROFESSOR]
When I was younger, just a small geeky kid,
My mama noticed nerdy things I did,
Like countin' all the lights in the ceilings
I'd find their patterns, and after these things
I'd create a small maze and see where it led
That's when my mama said

[POSTDOCS]
What did she say?

[MATHEMATICS PROFESSOR]
She said, "My boy, I think someday
You'll find a way
To make your natural tendencies pay
You'll be a math prof
You have a talent for countin’ things up
Son, be a math prof
People will pay you to be all stuck-up
Your temperament's wrong for the priesthood
And business would suit you still less
Son, be a math prof
You'll be a success

[POSTDOCS]
Here he is, folks, the leader of the proof!
Watch him be oh so aloof!
Oh, my god!
He's a math prof and he'll never ever be any good
Who wants a thesis defense with someone in that mood?

[STUDENT]
Oh that hurts! I don’t know!

[MATHEMATICS PROFESSOR]
Oh, shut up. Think faster. Now go!
I am your math prof

[STUDENT]
Goodness gracious!

[MATHEMATICS PROFESSOR]
And I enjoy the career that I picked

[POSTDOCS]
Really love it

[MATHEMATICS PROFESSOR]
I am your math prof

[STUDENT]
Proving theorems

[MATHEMATICS PROFESSOR]
And I get off on the pain I inflict

[POSTDOCS]
Really love it

[MATHEMATICS PROFESSOR]
I thrill when I ask a tough question

[POSTDOCS]
Tough question
[MATHEMATICS PROFESSOR]
It's swell though they tell me I'm maladjusted
And though it may cause my students distress,
Somewhere, somewhere in Heaven above me
I know, I know, that my mama's proud of me
Oh, mama
'Cause I'm a math prof and a success
Say pi!

[STUDENT]
Pi!

[MATHEMATICS PROFESSOR]
Say mu!

[STUDENT]
Mu!

[MATHEMATICS PROFESSOR]
Say nu!

[STUDENT]
Nu!

[MATHEMATICS PROFESSOR]
Now prove it!

2021 Ig Nobel Prizes!

The 2021 Ig Nobel laureates have been announced!

I think my favorite one this year is the prize in chemistry, but I of course have fondness for the winners in complex systems (especially with one of them published in Physical Review E).

What Happens in Boulder Stays in Boulder

I am taking my first trip since January 2020!

I'll be visiting CU Boulder to give an applied-mathematics colloquium. This will also be only my second in-person presentation (I gave one at IPAM a couple of weeks ago) since the start of the pandemic.

I haven't been to Boulder since around 2003 or 2004. I am looking forward to my trip, although traveling is even more nerve-wracking than before.

"Social Network Analysis for Social Neuroscientists"

A paper of mine that was posted in advanced access more than a year ago has now finally been posted in final form. It is a survey and perspective article on social network analysis for social neuroscientists. Here are some details.

Title: Social Network Analysis for Social Neuroscientists

Authors: Elisa C. Baek, Mason A. Porter, and Carolyn Parkinson

Abstract: Although social neuroscience is concerned with understanding how the brain interacts with its social environment, prevailing research in the field has primarily considered the human brain in isolation, deprived of its rich social context. Emerging work in social neuroscience that leverages tools from network analysis has begun to advance knowledge of how the human brain influences and is influenced by the structures of its social environment. In this paper, we provide an overview of key theory and methods in network analysis (especially for social systems) as an introduction for social neuroscientists who are interested in relating individual cognition to the structures of an individual’s social environments. We also highlight some exciting new work as examples of how to productively use these tools to investigate questions of relevance to social neuroscientists. We include tutorials to help with practical implementations of the concepts that we discuss. We conclude by highlighting a broad range of exciting research opportunities for social neuroscientists who are interested in using network analysis to study social systems.

Dodgers Acquire Max Scherzer and Trea Turner!

The Dodgers have made a huge splash in the trade market: they have acquired Max Scherzer and Trea Turner from the Washington Nationals for a load of prospects. This is exactly the trade that we needed. Scherzer, who will eventually be a Hall of Famer, is still an excellent and durable starter; and Turner is an outstanding infielder (who is also rather underrated, in my view, even amidst the wide recognition of his excellence), and I wouldn't be surprised if he eventually also makes the Hall of Fame. Just before then, the Dodgers also acquired pitcher Danny Duffy from the Royals.

Note: I didn't post this yesterday because I wanted to wait until the deal with the Nationals was done, rather than being something that the Dodgers were "finalizing".

XKCD and Flawed Data

XKCD nailed it yet again, especially with the mouseover text.

My Current Mathematics Genealogy

Here is my current mathematics genealogy.

My current Mathematics Genealogy (with doctoral students only): https://t.co/EAOiY0tasi

My MGP page (24 doctoral students): https://t.co/p35XlLXjoA

Current doctoral students: Abby Hickok, Grace Li, Jerry Luo, Kaiyan Peng, Mina Shahi

Also: I can't wait to have grandstudents! pic.twitter.com/dOU2wviu1V

— Mason Porter (@masonporter) July 16, 2021