Many networks are designed to be pretty failsafe—if any failures do occur there is enough resiliency in the network that it is routine to bypass them and life can go on as usual. However networks do not live in a vacuum and not uncommonly one network ends up somehow connected to another network, which is somehow connected to another, and so on. What happens now? Is the resulting “super-network” really all that super? As the title of this Wired magazine article hints, researchers are beginning to figure out that the answer is no.
A dramatic real-world example of a cascade of failures (‘concurrent malfunction’) is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations.
The quote above is actually from a Nature article which is one of a few (here’s another, where the picture above comes from) mentioned in the Wired article. All is not doom and gloom, however. With greater understanding comes a greater power to avoid catastrophes like the Italian shutdown.
According to Raissa D’Souza, a University of California, Davis mathematician who studies interdependent networks, the findings are “a starting point for thinking about the implications of interactions.” D’Souza hopes such research will pull together mathematicians and engineers. “We now have some analytic tools in place to study interacting networks, but need to refine the models with information on real systems,” she said.
This NY Times article details the efforts of Dr. Giulio Tononi to develop a means to measure a person’s level of consciousness as easily as a blood pressure sleeve measures a person’s blood pressure. Dr. Tononi is one of the world’s experts on consciousness, especially that peculiar form of half-consciousness known as sleep. While most people, researchers included, have long thought of consciousness as a kind of synchronization of brain waves, Dr. Tononi noticed that in particular kinds of unconsciousness, like during epileptic seizures, brain waves were even more synchronized than during wakeful periods. It seemed a new paradigm for consciousness was required. And for that paradigm, Dr. Tononi turned to information theory.
While in medical school, Dr. Tononi began to think of consciousness in a different way, as a particularly rich form of information. He took his inspiration from the American engineer Claude Shannon, who built a scientific theory of information in the mid-1900s. Mr. Shannon measured information in a signal by how much uncertainty it reduced. There is very little information in a photodiode that switches on when it detects light, because it reduces only a little uncertainty…. Our neurons are basically fancy photodiodes, producing electric bursts in response to incoming signals. But the conscious experiences they produce contain far more information than in a single diode. In other words, they reduce much more uncertainty.
Tononi has developed a measure called phi that seems to track how rich in information a mental state is, and the article mentions some preliminary medical work that is lending support to his model. The research is in its infancy and much more work is needed, but the same could be said for all science-based inquiries into consciousness. The point here is that the Dr. Tononi’s work “translating the poetry of our conscious experiences into the precise language of mathematics” holds promise—at the very least, enough promise to warrant featuring in this article.
Soccer has long been one of the team sports with the least amount of statistics, especially statistics on individual players. Unlike (American) football or baseball, say, there are no regular stops in play that break the game into easily digestible chunks; and unlike basketball, say, the ‘important events’ in soccer—like goals, saves, or shots on goal—are relatively rare, and don’t necessarily reveal which team or players are doing well.
Now Luis Amaral and Josh Waitzman from Northwestern University are bridging that gap using, of all things, the mathematics behind social networks. By treating each pass between players as a “link” it is possible to then measure which players are most “central” to the network created and thus, whose presence most helps the team go. Their new metric appears to correlate fairly well with the soccer establishment’s subjective opinions. Is fantasy soccer around the corner? The story was picked up by a number of news outlets, including the Washington Post, Scientific American, and UPI, as well as the online arms of the Discovery Channel and Sports Illustrated. Amaral and Waitzman’s original paper can be found here.
Addendum: A network approach using passing data was also employed by Javier López Peña and Hugo Touchette from Queen Mary University during the 2010 World Cup to analyze teams’ strategies and predict match winners. According to the article “Mathematical Formula Predicts Clear Favorite for the FIFA World Cup” at ScienceDaily, the network predictions’ accuracy rivaled that of the psychic octopus that caught the eye of the news. Dr. Peña was interviewed on CNN Espanol about the mathematical (non-cephalopod) prediction method.
This story by Clive Thompson from the NY Times Magazine examines networks and the signals that travel over them–only the network and the signals aren’t made of wires and electric impulses, the network is the social network of friends and relations and the signals are behaviors. A number of scientists have been using the mathematics of networks to analyze the impact that the behaviors of peoples’ friends and relations have on their own behaviors, and how certain behaviors sometimes get “transmited” through the network in ways startlingly like more physical networks. This article (free registration required) describes some of those scientists and their findings.
This TIME magazine article describes a literal marriage between math and medicine: the couple made up of transplant surgeon Dory Segev and his mathematician wife Sommer Gentry. Together, Segev and Gentry developed a new way to more efficiently match kidney donors with the more than 60,000 Americans awaiting transplants. Gentry was also interviewed by various radio, TV, and newspaper outlets.