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Network Complexity and Robustness

John Doyle, California Institute of Technology

DR. DOYLE: I am going to try to set the stage for this meeting. The work that I am going to talk about is the result of a lot of collaborations. I certainly won’t give justice to those people here. All the good ideas and all the good work that I am going to talk about is done with them, so when I say “we” I mean “they.” A lot of them are here today; two of them have posters and Jean Carlson is going to talk later. Walter Willinger is here. I am going to talk a lot about work with them.

There are buzzwords related to network complexity—network-centric, systems biology, pervasive, embedded. What I am interested in is the core theory challenges that underlie those common themes. I am going to be a little narrow in my focus in the sense that I am going to concentrate on biological networks and technological networks: I want to stick with stuff where we mostly know how the parts work, so that means not much social networks. There is a remarkably common core of theoretical challenges, so from the math-stat side I think there are some really common themes here. There has been recent dramatic progress in laying the foundation, yet there has also been amazingly, at the same time, a striking increase in what I would call unnecessary confusion. I will talk a little bit about both of these.

One of the common themes I am going to talk about is the fact that we see power laws all over. I think a lot of people at this workshop are going to be talking about that, because it is a common trait across all advanced technology and biology. Another common theme is that many of these systems in biology and advanced technology are robust yet fragile. What I mean by that is they work really well most of the time but that they fail occasionally, and when they do fail it can be catastrophically. We will hear more about that from other speakers and poster presenters. What I am going to do today, though, is talk about motivation for new theory and also education. We need to educate each other about even some fairly elementary aspects of statistics and mathematics. To get this started on the broadest level possible, I am going to stick with stuff that only assumes the background provided by a Caltech undergraduate education.

Let’s start with some data. The figures below show the 20th century’s hundred largest disasters worldwide. What I have plotted here are three kinds of disasters: technological disasters in tens of billions of dollars, natural disasters in hundreds of billions of dollars (and natural disasters can be even bigger), and power outages over some period of time and tens of millions of customers. What you see on a log-log chart are roughly straight lines with slopes of minus one.

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