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Applied Math at the Movies (including supplement)

This morning I had an article entitled The Mysterious Equilibrium of Zombies in the Boston Globe Ideas section about applied math in movies. I mentioned a number of movies, math and articles. For those who are interested in more details, here are some references, film clips and stills:

Casino Royale and Fractals

Harry Potter and The Millennium Bridge

The Dark Knight and Game Theory

Zombie Epidemiology

Six Degrees of Separation

Balance Theory

Mega-Regions

Richard Florida, in this weekend’s WSJ, discusses the Rise of the Mega-Region. Florida argues that nation-states and cities are somewhat passé, and that the relevant quantity that should be considered is the mega-region. A mega-region is an area “that hosts business and economic activity on a massive scale, generating a large share of the world’s economic activity and an even larger share of its scientific discoveries and technological innovation.”

I think the most important part of this concept is that these mega-regions need not be in a single country, and that therefore freedom of movement and trade is vital (see Florida’s suggestions at the end of the piece). For long-time readers of this blog, you will remember that the Buffalo-Toronto region is one of Florida’s mega-regions, and can be significantly helped by these freedoms.

Community Urinalysis

The NYT Magazine’s Year in Ideas is my favorite issue of the year, and this one is no exception. One idea that I particularly enjoyed is the concept of community urinalysis. By examining the sewage water of a city, scientists can examine which drugs its inhabitants are using. As Clive Thompson writes:

…when [Jennifer] Field’s team tested a mere teaspoonful of water from a sewage plant — which it ultimately did in many American cities — the sample revealed the presence of 11 different drugs, including cocaine and methamphetamine.

The research team called this technique community urinalysis. From a privacy standpoint, it’s a very clever approach to monitoring drug usage, because while it is involuntary — drug users can’t help urinating — it also manages to preserve the public’s anonymity. “It’s the closest to the urinal you can get without violating privacy,” says Field, who presented her findings at an August meeting of the American Chemical Society.

I look forward to a whole slew of maps that show, at a glance, the drug usage of different cities. And better yet, ones that show the drug use over time (which they have already begun measuring).

Network Theory in Cities

Jason Kottke recently pondered what the minimum number of New York City residents one would need to choose, such that these people know every single person in the city:

Any guesses as to the smallest group size? Better yet, is there any research out there that specifically addresses this question? Or is it impossible…are there people living in the city (shut-ins, hermits) who don’t know anyone else?

People have been commenting about it on the blog, where the consensus seems to be about 10,000 people (this sounds pretty reasonable). My two-cents (which can be seen as the first comment on kottke) are reproduced here:

 This is actually a well-established problem in graph theory called the vertex-cover problem. It is NP-hard, which means that there are no really good algorithms for it (although some approximate algorithms are good within a factor of two). In terms of answering this for NYC itself, my guess would be something on the order of 1000 or so. But I don’t have a good reason for that number, just a feeling. You could probably do better by assuming a power-law distribution for the number of acquaintances and derive a better estimate, but I haven’t thought about that in detail.

CDC To Cut Funding for Disease Tracking

The CDC is planning to scale back its main disease surveillance system, BioSense, and will now only focus on tracking diseases that occur in the largest cities in the United States. While this might be due to budget cuts, this strikes me as a foolhardy decision. To focus only on the larger cities is to miss the sources of possible outbreaks. While in decades past this might have still provided enough time to stem the outbreak, nowadays, when travel is routine and widespread, epidemics can spread to the entire United States extremely rapidly (here are some flu simulations, for example). By limiting detection to only large cities, this might remove the element of early-warning and possibly make it too late for proper counter-measures (by the time the outbreak is detected, it has already gone national or international). If the CDC has done simulations and studies that show that the lead-time gained is negligible, that would be good to know and would assuage my concerns, but I have not heard anything about that. If you are aware of anything like this, please let me know.

Census 2010: How to Word Simple Questions

A recent article in the WSJ, entitled Census 2010 Plays Six Not-So-Easy Questions (behind paywall), discusses the difficulty of choosing and wording the questions that will go into the 2010 Census. This kind of information is important for many things, from allocating members of Congress to policy planning to learning about the growth and decline of cities. Unfortunately, if the questions are ambiguous or confusing, large groups of people end up not responding, or giving the wrong answer. So they’re trying to be really careful about it:

“You only get one chance with the census,” says Preston Waite, the associate director of the decennial census. “If the wording isn’t right, it’s 10 more years before you can ask that question again. You only get one chance at bat.”

An interesting read.

Braess’s Paradox

Braess’s Paradox, named after Dietrich Braess, is when you add roads or capacity for cars, and thereby worsen traffic (or alternatively, you lower traffic costs by removing roads). Formally, this simply means that the current traffic equilibrium state is not the optimal one. Dietrich Braess, on his website, notes that this concept has applications to computer networks in addition to traffic networks.