I am going to bump this post back to the top as a reminder – we look forward to seeing you at the Jurix 2011 Network Analysis and Law Tutorial …

“Prior to the 2011 Jurix Conference on Legal Knowledge and Information Systems, Professor Daniel Martin Katz (Michigan State University, College of Law) and Michael Bommarito (University of Michigan – Center for the Study of Complex Systems) will present a tutorial on Network Analysis and Law.

“While historically allied with fields such as mathematical sociology, developments in network science have been generated by a wide range of disciplines, with major recent contributions offered by fields such as applied mathematics and statistical physics. Applied graph theorists often refer to networks as dependency graphs because they formalize the underlying linkages between objects.  Whether the objects in question are webpages on the internet, individuals in a social network such as Facebook or software dependencies in computer programming, the study of networks is the ‘science of our times.’

Building upon the developments in this interdisciplinary field, legal scholars and social scientists have recently begun to apply the tools of network science to bring new insight to a variety of long standing questions including the social structure of legal elites and the ‘evolution’ of the common law. This introductory tutorial is designed to help acquaint intellectually curious scholars with developments in this rapidly emerging field.”

Please join us in Vienna, Austria – December 13, 2011 @ Universität Wien for the Network Analysis and Law Tutorial as we help kick off Jurix 2011 Week.“

• (a) Community Detection in Networks
• (b) Computational Linguistics / Natural Language Processing
• (c) Diffusion Models and Mathematical Modeling with Data
• (d) Exponential Random Graph (p*) Models
• (e) Big Data/ Information Retrieval / Webscraping

Although, we do not work with more advanced languages within the course, those who need to conduct complex analysis are directed to alternatives such as R, Python, Java, etc.

Anyway, the slides are designed to be fully self-contained and thus allow for individually paced study of the relevant material. If you work through the slides carefully you should be able to learn the software as well as many of the core principles associated with the science of complex systems. The material should be available online indefinitely. If you have questions, feel free to email me.

Those of you interested in developing/increasing your computational social science skills should consider attending the 2011 International Joint Conference on Neural Networks where Peter Erdi (Kalamazoo College & Hungarian Academy of Sciences) will be administrating the very useful workshop displayed above.  I have learned a tremendous amount from Peter Erdi and would thus recommend the workshop to you.

Abstract: “The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system’s entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network’s degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes.”

The visualization above is something we are calling the “six degrees” of Marbury v. Madison.  It was originally produced for use in our paper Distance Measures for Dynamic Citation Networks. Due to space considerations, we ended up leaving it on the cutting room floor.  However, the visual is designed to highlight the idea of a “sink.”

Sinks are one of the core concepts which we outline in Distance Measures for Dynamic Citation Networks, 389 Physica A 4201 (October 1 2010). Looking through the prism of a citation network, sinks are the root to which a given legal concept, academic idea or patent based innovation can be drawn. From each citation in a non-sink node, it is possible to trace the chains of citations back to their root (which we call a sink).  In the visualization above, the root or sink node is the famed United States Supreme Court decision Marbury v. Madison.  Starting from the center and working out to the edge, the first ring are cases that directly cite Marbury v. Madison. The next ring are cases which cite cases that cite Marbury v. Madison.  The next ring are cases which cite cases which cases that cite Marbury v. Madison and so on…

Anyway, one of the major contributions of our Distance Measures for Dynamic Citation Networks paper is that it allows us to use these sinks to create pairwise distance/similarity measure between the ith and jth unit. In this instance, the units in this directed acyclic network are the ith and jth decisions of the United States Supreme Court.

Now, it is important to note cases contain many citations and thus can be oriented relative to many different sinks. So, even if a case can be traced to the Marbury sink – this does not preclude it from being traced to other sinks as well.  Also, it is possible to construct a variety of mathematical functions to characterize the sink based distance between units. For instance, the importance of a sink might decay as its shortest path length increases. An alternative measure might weight the importance of each sinks by the number of unique ancestors shared between nodes i and j that are descended from a given sink of interest. Indeed, many fine-grained choices are possible but they require justification drawn from the given substantive problem.

As mentioned above, this method has potential applications  including tracing the spread of technological innovation in patent citations or the spread of ideas in a set of academic articles. However, given our primary interest surrounds the judicial citations, we are working on the follow up to the “sinks” paper. In this follow up paper, we hope to carry these and other ideas forward into a definitive community detection method for judicial citation networks.

To preview, at least two major dynamics must be considered in any null model for community detection.  First, case-to-case citations can help contribute to the fractal nature of legal systems. In other words, we are pretty far from any sort of gaussian null model. However, this is easy enough to confront with an alternative null — some highly skewed distribution (i.e. power law or power law with a cutoff, etc.)

Here is the difficult part — the cross fertilization of legal concepts. This is a time evolving network where ideas are referenced/imported from otherwise unrelated or previously unrelated domains. The examples of cross-fertilization are numerous. One of my personal favorite non-SCOTUS examples is the use of the tort doctrine of “trespass to chattels” in the context of web scraping.

Anyway, we hope to have more to come on the topic of SCOTUS community detection in the weeks and months to come.  In the meantime, please check out a Dynamic 3D Hi Definition  United States Supreme Court Visualization.