Wolfram Just and others provide a preface to collection of articles that came out of a conference held early October, 2010. In this introduction, they lay the logical foundation for a forum on “delayed” complex systems. That is, they argue that since the only universally accepted truth of complex systems is that they have several interconnected parts, then it must be reasonable to consider the time taken for information, resources, and so on to pass along these connections. Depending on the system we introduce delay into, a sort of paradox discovered at this conference, the delay may cause the system to stabilize. But, for other systems, this same delay may trigger unpredictable, chaotic behavior. In other words, there is no hard and fast rule for the effects of a delay.
Yang-Yu Liu and others also consider a system’s interconnections, such as relationships between genes, power-lines in a city power-grid, and Facebook friends. Their concern, however, is with the shape that these links make—that is, the network’s topology—and, subsequently, how this shape effects the system’s ability to be controlled. They develop mathematical and statistical techniques for estimating how many “drivers” would be required to transition the components from one collective state to another at will. For example, in networks of genes, only a small percent of the genes would be required. In contrast, almost everyone would need to be controlled to perfectly direct a social network, and the Internet is just so weird it’s hard to say how controllable it is.
Alessandro Vespignani, in a Nature article, collects and summarizes the state of research (for early 2010) into the relationships between network topology and “integrity.” When the bird flu finally breaks loose, will it be better to live in a small town, where everyone knows everyone else, or in a large city, where there is a larger population? Or, a related two-fold question, how do we connect massive computer networks so that good information—like, for example, those funny cat pictures on Facebook—is delivered quickly, but also in a way that bad information—like, for example, that Myspace virus—does not take down the Internet? ∎
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