Math is beautiful and fractals are among the most elegant objects in all of mathematics. I have to admit that I am a bit obsessed with them. For those who are interested in learning more about fractals … this Ted Talk from 2007 by Ron Eglash offers both a useful overview and an application to African design.
Robert Axelrod’s 1997 Culture Model is a complex systems classic. Several versions of the model are available including one in Repast J. Perhaps the most user friendly version has recently been posted to Netlogo’s “community models” page. Those interested in experimenting with this Netlogo version of the model can click on the image above (provided you have Java 4.1 or higher installed).
For those not previously familiar with the model … Figure 1 from the article is featured to the left and demonstrates a model run through 80,000 events. Those results are generated in the following manner:
“Patches are assigned a list of num-features integers which can each take on one of num-traits values. Each tag is called a feature, while it’s value is called the trait. The links in the view represent walls between patches where solid black walls mean there is no cultural similarity, and white walls mean the neighbors have the same culture.
The order of actions is as follows:
1) At random, pick a site to be active, and pick one of it’s neighbors
2) With probability equal to their cultural similarity, these sites interact. The active site replaces one of the features on which they differ (if any) with the corresponding trait of the neighbor.”
Those looking for the original article … here is the both the citation and a link: Robert Axelrod, The Dissemination of Culture: A Model with Local Convergence and Global Polarization, J. Conflict Res, 41, 203 (1997).
In the years following its release, several important extensions or applications have been offered. These include contributions from scholars in a wide number of disciplines including applied math, political science, economics and physics. Indeed, while many more articles are available in outlets such as the arXiv … here is a subset for your consideration ….
Damon Centola, Juan Carlos González-Avella, Víctor M. Eguíluz & Maxi San Miguel, Homophily, Cultural Drift and the Co-Evolution of Cultural Groups, J. Conflict Res. 51, 905 (2007).
Konstantin Klemm, Victor M. Eguíluz, Raul Toral, Maxi San Miguel, Globalization, Polarization and Cultural Drift, J. Economic Dynamics & Control 29, 321 (2005).
Konstantin Klemm, Victor M. Eguíluz, Raul Toral & Maxi San Miguel, Role of Dimensionality in Axelrod’s Model for the Dissemination of Culture, Physica A 327, 1 (2003).
As a member of the Society for Evolutionary Analysis in Law (SEAL), I have had the oppurtunity to see a number of interesting presentations by Gregory Todd Jones. Gregory is a Faculty Research Fellow and Adjunct Professor of Law at the Georgia State University College of Law as well as Senior Director of Research and Principal Scientist at the Network for Collaborative Problem Solving. Of particular interest to readers of this blog, he is also the founding director of the Computational Laboratory for Complex Adaptive Systems at Georgia State Law School.
Above is a recent talk by Gregory at the TedX Atlanta in which he (1) assembles a model of sustainability based on collaboration and (2) discusses species behavior … from slugs to chimpanzees. If you are interested in learning more … Gregory has launched a really cool blog … Cooperation Science Blog … Check it out!
We have been working on a larger paper applying many concepts from structural analysis and complexity science to the study of bodies of statutory law such as the United States Code. To preview the broader paper, we’ve published to SSRN and arXiv a shorter, more technical analysis of the properties of the United States Code’s network of citations.
Abstract: The United States Code is a body of documents that collectively comprises the statutory law of the United States. In this short paper, we investigate the properties of the network of citations contained within the Code, most notably its degree distribution. Acknowledging the text contained within each of the Code’s section nodes, we adjust our interpretation of the nodes to control for section length. Though we find a number of interesting properties in these degree distributions, the power law distribution is not an appropriate model for this system.
Here at the CSCS Lab, we are working hard to finish up some projects. In the meantime, we wanted to highlight one of our favorite articles, an article we previously highlighted on the blog. Some of you might ask “what does this have to do with law or social science?” (1) We believe the taxonomy outlined in this article could potentially be applied to a wide set of social phenomena (2) As we say around here, if you are not reading outside your discipline, you are far less likely to be able to innovate within your discipline. So we suggest you consider downloading this paper….
Last week we offered a model of intellectual diffusion built upon a standard fare social epidemiology model. Given recent events within the United States, Mexico and potentially worldwide, we thought it would be worthwhile to highlight the classic S.I.R. (Susceptible, Infected, Recovered) model. Netlogo offers a user friendly version of the model. Using this platform, we hope the exploration of the dynamics of S.I.R. might prove illuminating.
First, various hosts have different levels of interactions (work, home, transit, etc.) and so this network approach represents a blunt measure. To start the model at the default parameters, push the SETUP Button and then the GO Button. As the model runs, the plot tracks the Susceptible, Infected, Recovered. The model contains a variety of “sliders.” The model can be rerun at lots of combinations of parameter levels. Those “sliders” fall into several categories: Network Attributes, Virus Attributes, Node Attributes. The full documentation is available here.
With respect to the swine flu, one important parameter is the delay between when an individual becomes infectious and when that individual is likely to become symptomatic. This parameter can be tuned in the simulation above using VIRUS-CHECK-FREQUENCY slider. From the documentation… “Infected nodes are not immediately aware that they are infected. Only every so often (determined by the VIRUS-CHECK-FREQUENCY slider) do the nodes check whether they are infected by a virus.”
An additional parameter worthy of consideration is the VIRUS-SPREAD-CHANCE. Consider this slider as a rough measure of the underlying infectiousness of the virus in question.
It is important to note the above simulation is an incredible simplification of the world faced by public health officials. Additionally, this version of the model was designed to consider the spread of disease on a computer network. Notwithstanding these limitations, we thought it useful to highlight a computational approach to this important matter of public concern.
I recently attended a conference at the Santa Fe Institute. During the trip, I made a point of eating at the El Farol Bar & Restaurant. This restaurant holds a special place in the lore of complex systems. Thus, I thought I would take the opportunity to highlight the model on the CLS blog.
Here is a subset of the model description…. “The bar is popular — especially on Thursday nights when they offer Irish music — but sometimes becomes overcrowded and unpleasant. In fact, if the patrons of the bar think it will be overcrowded they stay home; otherwise they go enjoy themselves at El Farol. This model explores what happens to the overall attendance at the bar on these popular Thursday evenings, as the patrons use different strategies for determining how crowded they think the bar will be.”
The original paper written by Brian Arthur is located here. An interesting follow up paper employing reinforcement learning is located here. This above is a screen print from the Netlogo model. Netlogo offers an easy interface useful for exploring a variety of agent based models.
The model will run in your browser provided you have Java 1.4.1+.
To run the El Farol model, please go here.
(1) Discussion of a New Paper: Computer Programming and the Law
(2) Visualizing the 110th Congress — The House of Representatives
(3) For Law Students and Law Professors — Data on the Law Clerk Tournament
(4) And More …..