"The Topology of Data"

Our introduction to a topological data analysis (TDA) for a general physics audience was published today in Physics Today. Here are some details.

Title: The Topology of Data

Authors: Mason A. Porter, Michelle Feng, and Eleni Katifori

Lede: Topological data analysis, which allows systematic investigations of the “shape” of data, has yielded fascinating insights into many physical systems.

"Making Sense of Complexity": A Very Nice Introductory Comic Strip

Sarah Firth's comic strip, Making Sense of Complexity, provides a very nice introduction to complex systems.

How Not to Write a Mathematics Paper: Snarky Edition

Here are some brilliant tips for aspiring mathematics authors!

I don't think I've ever encountered this page before. It's hard to find a favorite. There's also lots of great snark in the explanatory notes.

Here is one bit of snark: "One practical criticism applies to this book as well as a large part of contemporary mathematical production: the various statements are called by different names, such as Lemma, Theorem, Proposition, Corollary; the first three are numbered independently of each other, while the numbers assigned to corollaries are functions of several variables; in addition, numbered formulae have their own separate numeration. The strain placed on the reader by this partial ordering is obvious, but apparently readers seek vengeance on other readers when they turn into authors."

(Tip of the cap to @mathematicsprof.)

Up-Goer Five Text Editor

If any of you want to try explaining an idea using only the ten hundred most common words in the English language, you can try at this page.

(Tip of the cap to Lan Ma.)

A Random Walk Through Public Broadcasting

A few days ago, PBS posted a video introducing random walks to a public audience! Sweet!

Update: This is an episode of a mathematics show called "Infinite Series". The above episode refers to an episode about Markov chains. Take a look at their YouTube channel and Twitter feed.

Fractions of Worms and Singular Limits

Do you know what's worse than taking a bite out of an apple and finding a worm? Taking a bite of an apple and finding half a worm. And do you know what's even worse than that? Taking a bite and finding a quarter of a worm? And even worse than that is taking a bite and finding an eighth of a worm.

I can continue like this, and finding progressively smaller fractions of a worm after the delicious bite is progressively worse --- until we get to the situation in which we take a bite of an apple and don't have any worm. That's the best situation, as we have a normal delicious apple without any worm in it.* In mathematics, we refer to situations like this as a singular limit: the situation of setting a value equal to zero is qualitatively different from the situation of considering a sequence of values that we let approach zero. This is a very important concept in what is called singular perturbation theory, and it shows up all over the place in mathematics and its applications (e.g., in fluid mechanics, quantum mechanics and semiclassical limits, and many other places).

*Unless, of course, one swallows an entire worm with the bite, in which case it's a regular limit and we lose.

(Note: I don't remember seeing this analogy for singular limits before, but if somebody used it and I blocked out where I should be giving credit, please let me know. I could imagine somebody like Steve Strogatz using this type of analogy, for example, but I don't remember seeing him or anyone else use it.)

Update: Dominic Vella reminds me that Michael Berry used this analogy in an article in Physics Today. I definitely read that article, so I assume I got the analogy from there and forgot about it. I did have a nagging feeling that I must have seen it somewhere before even though I wasn't able to place it. And, no, I am not surprised that Michael Berry would use such an analogy. He's very good with analogies (and many other things).

Fractions and Percentages

Alright, this really irks me: When your quantity or label is clearly a fraction, don't bloody call the thing a "percentage". So many people make this mistake. There is a multiplicative factor of 100 that specifically makes these objects different, and this is taught explicitly from an early age. Grrr....

Update: As it turns out, the example that reminded me of this particular one of my pet peeves turned out to correctly be a percentage. Go figure. Anyway, I am obviously fallible. (This is a common mistake, though, and it's annoying.)

Unearthed: A Report I Wrote on the KdV Equation During College

Oh, wow. From some 'random' googling, I just found the rough draft of a report on the KdV equation that I wrote my senior year in college. This apparently got uploaded when various past things from courses that Jerry Marsden taught were collected, scanned, and uploaded.

My exposition (including of the KdV equation!), my citation practices and being very thorough about giving proper credit for results and the exposition of others (right now, I think that my old report should have included specific statements of whose discussions I was following and not just citations to those papers), and my work on nonlinear waves has advanced a lot since that report -- though I think that one can see many hints of my current style in it. Certainly one can see some of my current research interests. I had completely forgotten about this old report. (My handwriting in parts of the report is almost exactly the same as now, though! :P)

If you want to compare my old exposition to my current exposition, see the Scholarpedia entry on solitons that I wrote with Norm Zabusky.

I should perhaps use this as before/after to show my students for certain assignments. I think this could be helpful for some interesting teaching opportunities.

I'm not sure why the rough draft was uploaded, though. Maybe Jerry's copy of the final draft got lost?

Words of Wisdom from Bill James

"To use academic jargon is rude, lazy, elitist, and counter-productive. It diminishes the influence of the academic world; it diminishes the influence of thinking people on the general debate. If you want people to accept your ideas, you have to speak in language that others can understand. This is common sense, and it is common courtesy."

Amen.

(Of course, one needs to be precise in journal articles, but that doesn't mean that certain things can't be made understandable or that we can't speak and write things in other venues to help facilitate understanding. Anyway, the point is: Know thy audience!)

Scholarpedia Entry: "Soliton"

My scholarpedia entry on solitons is now officially live.

Hopefully, this will become the first port of call for information about solitary waves and solitons---that is certainly the intent of the article.

"Communities in Networks"

My survey/review article on community structure in networks finally came out today! I poured what was left of my soul into this one. (Among other things, I devoted a very large fraction of my winter "break" to work on this article.) This paper might well be my best chance in a long time to make a name for myself.


Title: Communities in Networks

Authors: Mason A. Porter, Jukka-Pekka Onnela, Peter J. Mucha

Abstract (arXiv only; The Notices doesn't use abstracts): We survey some of the concepts, methods, and applications of community detection, which has become an increasingly important area of network science. To help ease newcomers into the field, we provide a guide to available methodology and open problems, and discuss why scientists from diverse backgrounds are interested in these problems. As a running theme, we emphasize the connections of community detection to problems in statistical physics and computational optimization.

50 Years of Anderson Localization!

Do you know why I'm excited today? (Actually, this is very recent news, as I only found out about this a few minutes ago.)

Here's why: The August 2009 issue of Physics Today includes a 50 year retrospective on Anderson localization. I won't read it until my hard copy arrives, but I am very much looking forward to reading these articles.

As described in the wikipedia entry, Anderson localization is "the absence of diffusion of waves in a random medium". (Imagine a crystal with defects that do their damnedest to curtail wave transmission. Admittedly, I'm not trying to score major points for accuracy with this description.)

I think I want this on my tombstone.

Today I'd like to blog about the editorial by American Scientist Editor-in-Chief David Schoonmaker in the May-June issue of that magazine. This is the issue in which my article on the origin of the FPU problem appears, and David spent a lot of his editorial writing about our memorable in-person editing incident when I was visiting Peter Mucha, a collaborator at University of North Carolina at Chapel Hill. I had spent the entire day working on network science research with Peter and then we started our marathon meeting at 6pm. As David writes:

... Still, as someone who has lived through the advent of television and dial phones and the invention of fax and the Internet, I recognize that there also have been losses. A recent evening spent with the first author of "Fermi, Pasta, Ulam and the Birth of Experimental Mathematics" (pages 214--221) really brought that home (he visited here, much as I would have enjoyed visiting him in Oxford, England).

Mason Porter, contributing editor David Schneider and I sat for almost four hours fussing over the details of the text, captions and figures for the article. Refreshingly, Mason is a young scientists---indeed the recipient of the 2008 Sigma Xi Young Investigator Award---who cares deeply about language. He felt no compunction about challenging our choices in wording, yet was perfectly willing to be reasoned out of his own preferences. (Thank goodness there were two of us editors!)

The result could not have happened in an e-mail exchange. Together, the three of us found solutions that wouldn't have arisen without the spontaneity of human contact. It was not lost on me that Enrico Fermi, John Pasta and Stanislaw Ulam made their "little discovery" at a time (1955) when personal communications were rarely more electronically enhanced than the telephone. Would they have found what they did using e-mail?

In the aftermath of that stimulating but exhausting evening, I have reflected on my working relationship with other American Scientist authors. ...

After we were done, it was too late to get dinner and I had some other urgent work to do (and a talk to prepare from scratch for the next day). I spent about 3 more hours on various bits of urgent work that night before I needed to crash because my body was starting to shake somewhat uncontrollably. I didn't even have time to start preparing my slides, so I did that the next morning. (I somehow managed to give a really good talk on some results that I had never presented before, so I guess I am able to do a reasonable job under that kind of time crunch---though I don't want to do it again!)

In some ways, David's editorial would be appropriate for my tombstone---though there are other things I would actually prefer there; for example, I really like the one that says, "I told you I was sick."---though it's perhaps more accurate to say that I want to be remembered as someone who is really, really anal. Since this article came out, I have received a small number of compliments by e-mail both from people I know and from those I don't, and one of the ones I know even mentioned especially enjoying the editorial comments about that incident. I won't be surprised if others who know me bring it up as will, because I think it will ring rather familiar to them.

In closing, I must admit that I am pondering at the moment whether I should e-mail David to let him know that his editorial doesn't have any Oxford commas. Sadly, however, it is American Scientist policy not to include them.