Mexico Update Following Joaquin Guzmán’s Capture

As you probably know by now, the Sinaloa cartel’s leader Joaquin Guzmán was captured in Mexico last Saturday. How will violence in Mexico shift following Guzman’s removal?

(Alfredo Estrella/AFP/Getty Images)

(Alfredo Estrella/AFP/Getty Images)

I take up this question in an article forthcoming in the Journal of Quantitative Criminology. According to that research (which used negative binomial modeling on a cross-sectional time series of Mexican states from 2006 to 2010), DTO leadership removals in Mexico are generally followed by increased violence. However, capturing leaders is associated with less violence than killing them. The removal of leaders for whom a 30 million peso bounty (the highest in my dataset, which generally identified high-level leaders) been offered is also associated with less violence. The reward for Guzmán’s capture was higher than any other contemporary DTO leader: 87 million pesos. Given that Guzmán was a top-level leader and was arrested rather than killed, I would not expect a significant uptick in violence (in the next 6 months) due to his removal. This follows President Pena Nieto’s goal of reducing DTO violence.

My paper was in progress for a while, so the data is a few years old. Fortunately Brian Phillips has also taken up this question using additional data and similar methods, and his results largely corroborate mine:

Many governments kill or capture leaders of violent groups, but research on consequences of this strategy shows mixed results. Additionally, most studies have focused on political groups such as terrorists, ignoring criminal organizations – even though they can represent serious threats to security. This paper presents an argument for how criminal groups differ from political groups, and uses the framework to explain how decapitation should affect criminal groups in particular. Decapitation should weaken organizations, producing a short-term decrease in violence in the target’s territory. However, as groups fragment and newer groups emerge to address market demands, violence is likely to increase in the longer term. Hypotheses are tested with original data on Mexican drug-trafficking organizations (DTOs), 2006-2012, and results generally support the argument. The kingpin strategy is associated with a reduction of violence in the short term, but an increase in violence in the longer term. The reduction in violence is only associated with leaders arrested, not those killed.

A draft of the full paper is here.

Who says North is “up”?

There are several childhood lessons that I trace back to dinners at Outback Steakhouse: the deliciousness of cheese fries, the inconvenience of being in the middle of a wraparound booth, and the historical contingency of North as “up” on maps.

Who started using the NESW arrangement that is virtually omnipresent on maps today? Was it due to the fact that civilization as we now know it developed in the Northern hemisphere? (Incidentally, that’s why clocks run clockwise–a sundial in the Southern hemisphere goes the other way around.)

That doesn’t appear to be the case according to Nick Danforth, who recently took on this question at al-Jazeera America (via Flowing Data):

There is nothing inevitable or intrinsically correct — not in geographic, cartographic or even philosophical terms — about the north being represented as up, because up on a map is a human construction, not a natural one. Some of the very earliest Egyptian maps show the south as up, presumably equating the Nile’s northward flow with the force of gravity. And there was a long stretch in the medieval era when most European maps were drawn with the east on the top. If there was any doubt about this move’s religious significance, they eliminated it with their maps’ pious illustrations, whether of Adam and Eve or Christ enthroned. In the same period, Arab map makers often drew maps with the south facing up, possibly because this was how the Chinese did it.

So who started putting North up top? According to Danforth, that was Ptolemy:

[He] was a Hellenic cartographer from Egypt whose work in the second century A.D. laid out a systematic approach to mapping the world, complete with intersecting lines of longitude and latitude on a half-eaten-doughnut-shaped projection that reflected the curvature of the earth. The cartographers who made the first big, beautiful maps of the entire world, Old and New — men like Gerardus MercatorHenricus Martellus Germanus and Martin Waldseemuller — were obsessed with Ptolemy. They turned out copies of Ptolemy’s Geography on the newly invented printing press, put his portrait in the corners of their maps and used his writings to fill in places they had never been, even as their own discoveries were revealing the limitations of his work.

map_projectionsPtolemy probably had his reasons, but they are lost to history. As Danforth concludes, “The orientation of our maps, like so many other features of the modern world, arose from the interplay of chance, technology and politics in a way that defies our desire to impose easy or satisfying narratives.” Yet another example of a micro-institution that rules our world.

Visualizing the Indian Buffet Process with Shiny

(This is a somewhat more technical post than usual. If you just want the gist, skip to the visualization.)

N customers enter an Indian buffet restaurant, one after another. It has a seemingly endless array of dishes. The first customer fills her plate with a Poisson(α) number of dishes. Each successive customer i tastes the previously sampled dishes in proportion to their popularity (the number of previous customers who have sampled the kth dish, m_k, divided by i). The ith customer then samples a Poisson(α) number of new dishes.

That’s the basic idea behind the Indian Buffet Process (IBP). On Monday Eli Bingham and I gave a presentation on the IBP in our machine learning seminar at Duke, taught by Katherine Heller. The IBP is used in Bayesian non-parametrics to put a prior on (exchangeability classes of) binary matrices. The matrices usually represent the presence of features (“dishes” above, or the columns of the matrix) in objects (“customers,” or the rows of the matrix). The culinary metaphor is used by analogy to the Chinese Restaurant Process.

Although the visualizations in the main paper summarizing the IBP are good, I thought it would be helpful to have an interactive visualization where you could change α and N to see how what a random matrix with those parameters looks like. For this I used Shiny, although it would also be fun to do in d3.

One realization of the IBP, with α=10.

One realization of the IBP, with α=10.

In the example above, the first customer (top row) sampled seven dishes. The second customer sampled four of those seven dishes, and then four more dishes that the first customer did not try. The process continues for all 10 customers. (Note that this matrix is not sorted into its left-ordered-form. It also sometimes gives an error if α << N, but I wanted users to be able to choose arbitrary values of N so I have not changed this yet.) You can play with the visualization yourself here.

Interactive online visualizations like this can be a helpful teaching tool, and the process of making them can also improve your own understanding of the process. If you would like to make another visualization of the IBP (or another machine learning tool that lends itself to graphical representation) I would be happy to share it here. I plan to add the Chinese restaurant process and a Dirichlet process mixture of Gaussians soon. You can find more about creating Shiny apps here.