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Willie Wong
Works at Michigan State University
Attended Princeton University
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Willie Wong

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Signal boost, also, a reminder to self.
 
Mathematical Reviews and zbMATH ask for your feedback to revise the MSC classification scheme. More info at http://msc2020.org.
Mathematical Reviews (MR) and zbMATH cooperate in maintaining the Mathematics Subject Classification (MSC), which is used by these reviewing services, publishers, and others to categorize items in the mathematical sciences literature. The current version, MSC2010, consists of 63 areas classified ...
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Shared with no comment, beside that there are some rather interesting anecdotes buried in the discussions. 
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That was one of my first thoughts too. 
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Dear NRA: how the fuck is a good guy with a gun supposed to help in this scenario?
Gunmen kill five police officers during a protest in Dallas against police shootings of black men, with three suspects in custody and one dead, media say.
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Random observation: margin of leave versus remain is just under 1.3 million votes. That is about the same number as British expats living in Europe. 
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I've been reading that a lot of science in the UK is funded from EU sources. Supposed to be reason to expect an exodus of British scientists, when those sources dry up. Thoughts?
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Why MathOverflow is great. 
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Continuing on my previous post: I've retrofitted one of my recent papers (http://arxiv.org/abs/1601.01303v1 to be exact) to show how a cross reference visualization would look "in the wild".

... and it is a lot wilder than I expected.

Because of that, I added some code to, whenever possible, do some automatic compression/collation of nodes. It is of limited effectiveness since the writing of the original paper was not done with this software in mind. I am also not sure whether this is a useful feature, since it reduced the number of nodes, but at the expense of increasing a bit the density of the graph (the reduction in the number of edges is not proportional to the reduction of number of nodes). It is not clear whether the condensed graph is more readable. (You can see that version http://users.math.msu.edu/users/wongwwy/testd3/shocks-demo-condensed.html).

Also, +Ian Agol, this paper is only 1/5 of the length of a Christodoulou opus. I don't know how big a screen would be required to actually visualize those.

(I am now somewhat curious about the typical complexity of cross references within a paper, especially how it scales with length; one expect nodes to grow more or less linearly, but what about edges? This is probably something that can be experimentally found by analyzing TeX sources from arXiv.)
Cross-reference graph for Speck, Holzegel, Luk, and Wong (2016). Search Double click on node to show entry details. (None selected) • TeX label.
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+Ian Agol I am pretty sure in what I posted there are closed directed loops. (I'll explain below why.) But to answer your question: yes, I can. I am not sure I want it in the Javascript visualizer: for analytics like that I would prefer to just put it in a Python or Julia script that would be faster and easier to run (without haven't to start a web server).

Technically speaking what the code does is that a LaTeX package outputs two files in comma-separated format, one of them storing all the edges, the other storing all the metadata for the vertices, the first file by itself of course already give the complete representation of the graph. And the data can easily be analyzed using most scientific programming languages (Julia and Python both have great graph theory packages so I don't have to reinvent the wheel).

However, whether there are closed directed loops depend a bit on how the proof is written/typed. And closed directed loops does not necessarily mean circular argument in the proofs!

1. Trivial example: suppose I have a complicated theorem with a lot of hypotheses. And I pulled out one step of the proof as a Lemma. If in the proof of the Lemma one writes: "From the hypothesis 3 of \ref{thm1} we see..." and in the proof of the Theorem one writes "Thus it follows from \ref{lem1}..." then the graph will have a cycle!

This is largely a problem of how we write proofs! If we do it in a more structured way (closer to what Knuth proposed in his recent articles) then for example all the hypotheses can be separately pulled out of the theorem statement and referred to separately, and this will break the cycle. Another way to solve this problem would be to include different semantic versions of '\ref', where references to "hypotheses" and references to "conclusions" are distinguished.

2. Less trivial example: analysis of PDEs have a lot of bootstrap arguments. At least one way to write bootstrap arguments can result in a circular graph; on the other hand, there are also ways to write bootstrap arguments that are not circular.

In any case, these are all great ideas for further code development! One giant improvement would be for me to add support to semantic referencing and store also information about different edge types. But if we want to really dive into the thick of these issues, I think we will get very quickly stuck in the realm of formal proofs and proof-assistants and proof-checkers. 
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Some random thing I've been working on the past week.

Those familiar with my academic work may notice that my field has some very long papers. I myself is not entirely free of blame. But reading these long papers can be quite taxing, especially when trying to keep track of the logical relationships between theorems and lemmata, or to sometimes even just to remember what "Lemma 3.6.13" said. (No, you can't remember it, and so you have to flip through half of a 300 page paper to find that lemma.)

Trying to make life slightly easier for future readers of my work (especially graduate students who will be taking my class next spring), I've been working on a couple of solutions in tandem.

1. I have now some LaTeX code for "Descriptive Referencing" which I will be using in my Lecture Notes. The functionality is quite simple: when calling \label, one adds a second argument containing a short descriptor of the thing being labeled. When calling \ref, the description will be printed in the margin. (There's some intelligence involving not placing the description more than once per page and other small things.) Currently it is only available in the form of a special document class since it only really works when you have ample margin space to work with, and the standard classes are not good in that regards (with the possible exception of amsart.)

2. The LaTeX code also defines a new proof environment, which can track the \ref commands used within. This is then used to output auxiliary data files that store the cross reference logic used in the proofs. This brings us to what I want to show off in this post.

With (not too much) javascript, this data can be displayed as an interactive graph showing how different parts of the paper fit together. The link below shows the output from a dummy test document. Features:

a) Different colors for different "theorem types".
b) Search function for ease of locating a theorem (this is meant to be used together with the book/lecture notes, so we search by labels like "Theorem 1.3").
c) Display of the description, and the page number on which the full statement can be found.
d) MathJax support! So mathematics included in the short descriptions are properly rendered.

All the codes involved are very much in the beta stage. The source code (provided without any guarantees) can be found on https://gitlab.msu.edu/wongwil2/www-textools
(apologies that I haven't updated the READMEs completely yet. Will get around to it another time.)
Search Double click on node to show entry details. (None selected) • TeX label.
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+Ian Agol Ha, the first time I had this idea was when reading one of his works. It would actually be non-trivial to do that, due to his writing style. Christodoulou is a fan of the "exposition ... computation ... exposition ... computation... exposition oh and by the way we just proved Lemma 2.1.57 Statement of lemma" type of writing. Which makes retrofitting any structure tracking to his works really hard even assuming I have the access to the TeX files.

But maybe a "live" demo would be more interesting. I'll take some time to do this for my most recent shocks paper.
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+Patrick Honner may like this. As of my writing, there are three answers posted on Math.SE giving the "correct answer". It is shameful that "calculus" is often taught by "plug-and-chug using these set of rules". It is doubly shameful when the instructors, who should know better, employ such methodology without a tiny bit of sanity check.

In fact, this could've been a beautiful teachable moment. The mechanical evaluation of the integral without regard of the singularity does come out as "0". But this should be coupled with some excursions into improper integrals, on how sometimes the value depends on the limit. And then you can show the graph of the function https://www.wolframalpha.com/input/?i=(+cos(x)+-+sin(x)+)+%2F+(cos(x)+%2B+sin(x)) and ask the student to say why "0" is an aesthetically pleasing answer (the function is "odd" about the singular point).

But no! The answer sheet says 0. Sheesh!
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+Andres Caicedo  It is actually not that easy to cook up a good example where the contribution from the Cauchy principal value is not zero. If you take a ratio of elementary (real analytic) functions, when the singularity is not removable near the blow-up point it looks like 1 / x^k for some k >0. When k is even the integral blows up. When k is odd the p.v. contribution is zero, so that the "naive thing" will give always the "right answer".
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From Karl Pearson, writing on June 23, 1886 in the Preface to Isaac Todhunter's A History of The Theory of Elasticity and of The Strength of Materials, volume I:

"My greatest difficulty arose with regard to the rigid line which Dr Todhunter had attempted to draw between mathematical and physical memoirs... What seemed to me peculiarly needful at the present time was to place before the mathematician the results of physical investigations, that he might have some distinct guide to the direction in which research is required. There has been far too much invention of 'solvable problems' by the mathematical elastician; far too much neglect of the physical and technical problems which have been crying out for solution."
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Yes. I've seen them Maseratis on campus. Haven't seen a Lamborghini yet. Actually, if I owned a Huracan, I probably wouldn't want to drive it on the Michigan roads (too many pot holes and too bumpy; who knows where it might get stuck). 
The latest obsession for China's 'Great Gatsby generation' who come to the US to study: fast, expensive cars. How does a $190,000 Lamborghini sound?
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This article got me thinking: are airlines in fact doing their share in alleviating the problem?

Case in point: I live smack in the middle of Michigan. Say I want to fly to Philadelphia, I can choose between

1. Driving 70 minutes to Detroit and take a direct flight from Detroit to Philly
2. Driving 30 - 70 minutes to any of the smaller airports in the area (Kalamazoo, Grand Rapids, Lansing), take a one-stop flight via Detroit.

Reason would usually suggest that it costs the airlines more to carry me and my luggage for two legs compared to one, especially since the two tickets share the Detroit to Philly leg. And as many many before me have noticed, the one stop flight is invariably cheaper.

Now, there is the argument that "a direct flight is a service that the airline charges premiums for". But that only really make sense when

1. The two flights being compared have same starting and ending points.
2. The diversion for the itinerary with more hops funnels passengers down under-utilized routes, thus saving the airline money in the long run.

To make a driving analogy, what the airlines are doing seems to be akin to setting up a toll road where the toll you pay is not based on how long you drove along the road, but also on which side streets you took to get to the toll road.

However incompetent or diabolical one may imagine American airlines, it is hard to justify the bottom line when they are burning more jet fuel on my behalf while charging me less money, and doing so without freeing up capacity on the route (since as soon as I get off that flight from Grand Rapids I hop on the very same flight from Detroit to Philly that I would be taking otherwise for more money). So this got me thinking: is there any hidden economic costs that I've naively ignored in my computation above?

And maybe, just maybe, this cost is the cost associated to delays and cancellations from the long security lines at major airports.

Recently I have grown fond of flying to and from small regional airports. In addition to the savings on the plane tickets, very rarely had I any problem with the security lines there. I've even survived, on occasion, arriving at the airport only 5 minutes before boarding time.

Now, I don't know the numbers at all so I have nothing to back this up but speculation. But it is conceivable that the arbitrary bottle neck imposed by the TSA at the entrance of an airport is costing airlines enough money that they try to encourage flyers to arrive to that airport through alternative means (namely flying in instead of driving in). In the toll-road analogy, this would be like slapping on a congestion charge for entering and exiting at the busiest interchanges and giving a discount to those using a nearby, but less popular exit.

But this also suggest an alternate (and rather unpleasant) solution to the congestion problem at airports, and that is to simply make the security perimeter larger. After the Belgium attacks, there had been discussion on whether security perimeters should be enlarged for airports. The discussion there is mostly focused on issue of security (hundreds or thousands of people stuck in one place outside the secure perimeter for an extended period of time is a great terrorist target). But as the article below pointed out: the TSA may be asking for more man power, but the fact is that there are just so many ways to get into the secure area and the sheer volume of people we are trying to move make it a strict trade-off between length of wait and meticulousness of the inspections. Now, if we were to enlarge the secure area, there is a chance to redesign the infrastructure so that more "lanes" are available for entry. This could potentially alleviate the congestion at the major airports.

In a manner, this is exactly what TSA-pre is doing: offloading the security screening to a different spacetime point from where the congestion is happening. (Though I find the fact that they are charging a rather hefty fee for it unconscionable, both morally and economically.)

And in fact, in a way that I don't know is with or without intent, this is what is happening with the airline pricing structure. That passengers are attracted by the lower ticket prices to fly from smaller regional airports allow the relatively underused security lines at those airports to be used as, effectively, additional security lanes for the major hubs.

Building upon this, an idea for "enlarging the security perimeter" could simply be to have satellite security checkpoints where the passengers can go through security off the site of the airport, and be funneled to the airport by specially designated buses or trains that drop them off behind the TSA checkpoint. 
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I don't know if there's collusion. Remember though that a plane has a fixed number of seats and the marginal extra costs per passenger vs an empty seat are small, so it may well even be worth taking a small number of passengers whose fares aren't quite covering their share of the costs rather than an empty seat without a fare at all.

Here's a traveller's article (so not definite info) that talks about this theory: http://crankyflier.com/2012/01/03/why-does-a-connecting-flight-cost-more-than-a-nonstop-ask-cranky/
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Work
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Mathematician
Employment
  • Michigan State University
    Assistant Professor, 2015 - present
  • École polytechnique fédérale de Lausanne
    Postdoctoral scientist, 2011 - 2015
  • University of Cambridge
    Postdoctoral research associate, 2009 - 2011
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Male
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6accdæ13eff7i319n4o4qrr4s9t12vx... at least, it pays the bills.
Introduction
Mostly I identify as a mathematician. My specialties are partial differential equations (especially nonlinear hyperbolic systems), geometric analysis, and mathematical physics (especially general relativity). You can find me somewhat active on MathOverflow.

I am an apprentice computer ninja. My computers usually run some flavour of Linux or Unix, I know my way around LaTeX quite well, and I am known to do a bit of scripting (I used to be a "clobber things together in bash" sort of guy, but now I prefer Python). I do the vast majority of my text editing in Vim, and prefer Mutt as my e-mail client.

I aspire to be a polyglot. Right now I speak English, French, and Chinese. I hope to add Japanese and Greek to that list.
Education
  • Princeton University
    Mathematics (PhD), 2005 - 2009
  • Princeton University
    Mathematics (AB), 2001 - 2005