A Statistical Mechanics Take on No Child Left Behind — Flow and Diffusion of High-Stakes Test Scores [From PNAS]


The October 13th Edition of the Proceedings of the National Academy of Science features a very interesting article by Michael Marder and Dhruv Bansal from the University of Texas.

From the article … “Texas began testing almost every student in almost every public school in grades 3-11 in 2003 with the Texas Assessment of Knowledge and Skills (TAKS). Every other state in the United States administers similar tests and gathers similar data, either because of its own testing history, or because of the Elementary and Secondary Education Act of 2001 (No Child Left Behind, or NCLB). Texas mathematics scores for the years 2003 through 2007 comprise a data set involving more than 17 million examinations of over 4.6 million distinct students. Here we borrow techniques from statistical mechanics developed to describe particle flows with convection and diffusion and apply them to these mathematics scores. The methods we use to display data are motivated by the desire to let the numbers speak for themselves with minimal filtering by expectations or theories.

The most similar previous work describes schools using Markov models. “Demographic accounting” predicts changes in the distribution of a population over time using Markov models and has been used to try to predict student enrollment year to year, likely graduation times for students, and the production of and demand for teachers. We obtain a more detailed description of students based on large quantities of testing data that are just starting to become available. Working in a space of score and time we pursue approximations that lead from general Markov models to Fokker–Planck equations, and obtain the advantages in physical interpretation that follow from the ideas of convection and diffusion.”

The Clerkship Tournament: Supreme Court Edition [Repost from 6/3]

Picture 1

As part our multipart series on the clerkship tournament, here is a simple bar graph for the top placing law schools in the Supreme Court Clerkship Tourney. It is important to note that we do not threshold for the number of graduates per school. Specifically, we do not just divide by the number graduates per school because we have little theoretic reason to believe that placements linearly scale to differences in size of graduating classes. In other words, given we do not know the proper functional form — we just offer the raw data. For those interested in other posts, please click here for the law clerks tag.

The Map of the Future [From Densitydesign.org]

Map of the Future

Picture 7As we mentioned in previous posts, Seadragon is a really cool product. Please note load times may vary depending upon your specific machine configuration as well as the strength of your internet connection. For those not familiar with how to operate it please see below. In our view, the Full Screen is best the way to go ….

Who Should Win (probably not who will win) the 2009 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel


Benoît Mandelbrot whose classic work on fractals as well as more recent work questioning the Efficient Market Hypothesis offers a lasting contribution to positive economic theory. While the committee is likely considering Eugene Fama and/or Kenneth French (of Fama-French fame), we believe they should instead consider Mandelbrot (or at a minimum split the award between Fama, French &  Mandelbrot).

Robert Axelrod whose work on the evolution of cooperation is among the most cited work in all of the social sciences. Iterated Prisoners Dilemma as well as concepts such Tit for Tat are part of the cannon of almost all introductory courses in game theory.

Robert Shiller for his contributions to behavioral finance including his work challenging the Efficient Market Hypothesis. Of course, Shiller is also well known for his work on the real estate market with Karl Case (including the Case-Shiller Index). This also represents important work worthy of recognition.

Elinor Ostrom for her work on public choice theory, common pool resources and collective action. Her work has offered a substantial contribution to political economy as well as institutional and environmental economics. {Note: (Ladbrokes places her at 50 to 1)}.

UPDATE: ELINOR OSTROM AND OLIVER WILLIAMSON WIN THE 2009 NOBEL PRIZE {In Our Estimation, this is a Very Appropriate Decision }

Visualizing the Campaign Contributions to Senators in the 110th Congress — The TARP EDITION [Repost from 3/26])

Senators of 110th Congress

This is a repost our previous Senators of the 110th Congress Campaign Finance Visualization. Last week we highlighted one specific element of the graph (i.e. Senator Dodd and the TARP Banks). Now, we wanted to bring the full graph back to the front of the page for your consideration.  Here is the content of the old post with a few small additions….

“As part of our commitment to provide original content, we offer a Computational Legal Studies approach to the study of the current campaign finance environment.  If you click below you can zoom in and read the labels on the institutions and the senators.   The visualization memorializes contributions to the members of the 110th Congress (2007 -2009).  Highlighted in green are the primary recipients of the TARP.

In the post below, we offer detailed documentation of this visualization.  One Important Point the Visualization Algorithm we use does force the red team, blue team separation.  Rather, the behavior of firms and senators produces the separation.

Four Important Principles: (1) Squares (i.e. Institutions) introduce money into the system and Circles (i.e. Senators) receive money  (2) Both Institutions and Senators are sized by dollars contributed or dollars received– Larger = More Money  (3) Senators are colored by Party.  (4) The TARP Banks are colored in Green. “

Algorithmic Community Detection in Networks

Communities in Networks

Community detection in networks is an extremely important part of the broader network science literature. For quite a while, we have meant to highlight the extremely useful review article written by Mason Porter (Oxford) Jukka-Pekka Onnela (Harvard/Oxford) and Peter J Mucha (UNC). Rather than offer our description of the article, we thought it best to highlight commentary on the subject provided by the authors.

For example, in describing the paper over at Harvard’s Complexity and Social Networks Blog Jukka-Pekka Onnela posted the following… “Uncovering the “community” structure of social networks has a long history, but communities play a pivotal role in almost all networks across disciplines. Intuitively, one can think of a network community as consisting of a group of nodes that are relatively densely connected to each other but sparsely connected to other dense groups of nodes. Communities are important because they are thought to have a strong bearing on functional units in many networks. So, for example, communities in social networks can correspond to different social groups, such as family, whereas web pages dealing with a given subject tend to form topical communities.  The concept is simple enough, but it turns out that coming up with precise mathematical definitions and algorithms for community detection is one of the most challenging problems in network science. Recently, a lot of the research in this area has been done using ideas from statistical physics, which has an arsenal of tools and concepts to tackle the problem. Unfortunately (but understandably) relatively few non-physicists like to read statistical physics papers.”

These scholars quote Mark Newman noting “[T]he development of methods for finding communities within networks is a thriving sub-area of the field, with an enormous number of different techniques under development. Methods for understanding what the communities mean after you find them are, by contrast, still quite primitive, and much needs to be done if we are to gain real knowledge from the output of our computer programs.”  They later note “the problem of how to validate and use communities once they are identified is almost completely open.”

Anyway, if you are interested in learning more about this important piece of the network science toolkit … we suggest you read this paper!