мы и они
22:43 | 20-09-2012 | Internet, Lifeform, Science | No Comments
немного математики:
For any network where some people have more friends than others, it’s a theorem that the average number of friends of friends is always greater than the average number of friends of individuals.
This phenomenon has been called the friendship paradox. Its explanation hinges on a numerical pattern — a particular kind of “weighted average” — that comes up in many other situations.
и, само собой, ее приложений:
Like many of math’s beautiful ideas, the friendship paradox has led to exciting practical applications unforeseen by its discoverers. It recently inspired an early-warning system for detecting outbreaks of infectious diseases.
In a study conducted at Harvard during the H1N1 flu pandemic of 2009, the network scientists Nicholas Christakis and James Fowler monitored the flu status of a large cohort of random undergraduates and (here’s the clever part) a subset of friends they named. Remarkably, the friends behaved like sentinels — they got sick about two weeks earlier than the random undergraduates, presumably because they were more highly connected within the social network at large, just as one would have expected from the friendship paradox. In other settings, a two-week lead time like this could be very useful to public health officials planning a response to contagion before it strikes the masses.