Supernetworks -- The Science of Complexity

I've been thinking a lot about complexity lately and recently completed an invited paper, "Supernetworks: The Science of Complexity."

In doing the research for this paper, which presents some of the highlights of methodological advances and applications over the past decade, what amazed me was how research conducted in one discipline can have major impacts in others.

Specifically, I was interested in overviewing the breadth and depth of applications of supernetworks, and associated methodologies, since I wrote the Supernetworks: Decision-Making for the Information Age book with Dr. June Dong back in 2002.

What I pleasantly discovered was that the methodology of projected dynamical systems, which I wrote a book on with Dr. Ding Zhang in 1996, results of which were also included in the second edition of my Network Economics book, is now being utilized and applied in evolutionary game theory, in neuroscience and robotics, and in ecological predator-prey networks! Projected dynamical systems (unlike classical dynamical systems) can handle constraints underlying dynamical systems and the theory allows for the investigation of qualitative properties, including stability of systems, and has associated with it appropriate algorithmic schemes.

Our book, Projected Dynamical Systems and Variational Inequalities with Applications, was the second volume in the International Series in Operations Research & Management Science. As reported in the book (and since), my collaborators and I have used projected dynamical systems to model dynamic traffic problems, dynamic supply chain networks and financial networks, electric power generation and distribution systems, and a variety of spatial and aspatial economic problems.

Sometimes it may take awhile for a methodology developed in one discipline to be discovered by other disciplines but when it allows for breakthroughs, it is very gratifying, I must say!

Food Webs as Nature's Supply Chains and Network Economics: Research that Crosses Disciplines

In a recent paper, The Impact of Boundary Spanning Scholarly Publications and Patents, published in PLoSone, the authors: Shi, Adamic, Tseng, and Clarkson state in the abstract that Human knowledge and innovation are recorded in two media: scholarly publication and patents, ... which carefully cite prior work upon which the innovation is built. The authors conclude after their careful analysis of two very large citation datasets that a publication's citing across disciplines is tied to its subsequent impact. I had been told that the impact of one's work has really made a difference if it is used in other fields so it is gratifying to have such insights now documented. This brings me to another discipline and application that is making use of my results in Network Economics (which was the title of the very first book that I wrote, which was published in 1993 with the second edition appearing in 1999).

I came across a truly original and fascinating paper while researching food supply chains, entitled, NEATS: A Network Economics Approach to Trophic Systems, which is now in press in the journal Ecological Modelling and is co-authored by a group of researchers based in France: Mullon, Shin, and Cury. The paper applies some of the results in my Network Economics: A Variational Inequality Approach book to formulate and determine equilibria in predator prey complex webs. One reads regularly about the impact of science on economics but this paper demonstrates how economics and, especially, network economics, can be used to combine both biological constraints that couple biomass balance equations with complementarity principles using Walras' law. The authors investigate the solutions to simple food chains, bilayer networks, complex food webs, and even to cannibalism (the links loop back to the specific nodes in such networks)!

The authors derive the equilibrium conditions using path concepts, provide theoretical results, and apply the model to the coastal fishery system of Chile. The paper is beautifully illustrated with networks depicting the different species and their volumes along with the resulting species biomass under numerous scenarios. In this framework, one can then investigate the effects of climate change on the species and address numerous ecological questions, from those revolving around differences in productivity, the underlying causes of biological diversity, as well as various controls in marine ecosystems.

The lead author, with associates, will even be offering a course on the subject, Economic versus Ecological Networks: Integrating Economy and Ecology in Scenario Building for Marine Ecosystems, next month on the subject (in France) and the flyer even has my name on it.

A very nice presentation by the authors on the economic approach to the equilibrium of trophic networks can be found here.

In my Network Economics book I discuss applications using variational inequality theory to traffic networks, spatial price equilibrium problems, migration problems, oligopolies, knowledge networks, and even to financial networks. I guess the third edition will need to include applications to biological ecological systems, as well!

Of course I have corresponded with these authors to congratulate them on their excellent paper!

Also, for those of you who read my previous post, I am delighted that Dr. Helander of IBM has how made her slides on Food Safety in a Global Supply Chain available. We thank her!