Aggregate systems and collective behavior

The StarFlag

A research group of scientists led by theoretical physicists called StarFlag is working on the roof of the Roman History Museum of Rome since last October. Every evening, at dusk, they take records of beautiful (and somehow threatening) black clouds of starlings flying in from the countryside to their roosting sites in the city.
They call this new discipline named "Econophysics", it something between bird watching and game theory. The aim of the research is to is to understand if physics rules are able to explain phenomenons of other nature such as stock market trends, election results, biological mechanims, currency floats.

The first results of StarFlag were presented last January 15th in Rome and  Physics Today has recently dedicated their cover article to this project.
I am posting here some relevant passages of the article and some great videos on this spectacular phenomenon.

Anisotropic interactions

Flock cohesiveness was a mystery, says Andrea Cavagna, a statistical physicist at Italy's National Institute for the Physics of Condensed Matter (INFM) . "It's clear that the interaction [between birds] decreases with increasing separation, but how do the birds measure distance? We came in as physicists, our experience was with spin glasses, and we used the same tools." Those tools include techniques from statistical physics, optimization theory, and computer vision. Quantifying the interaction among birds is StarFlag's most important result so far, Cavagna says.

The Rome team found that a given bird interacts not with all birds within a certain distance, as most models had assumed, but rather with a fixed number of neighboring birds, independent of how far apart they may be. "If flocks always had the same density, there would not be a striking difference between this [behavior] and interacting with all birds within a certain distance," says Irene Giardina, another statistical physicist in the 10-strong INFM group. "But when a flock is attacked, it undergoes rapid changes in density. You can watch a flock split, but it comes together again. We asked what sort of interaction can guarantee such a robust resilience to perturbation."

"We looked at our three-dimensional data and considered a given bird, and then we measured the angular positions of its nearest neighbors," she continues. The distribution of angular positions turns out to be anisotropic, a result that StarFlag scientists presented at a couple of conferences over the summer. "There is much more probability of finding its nearest neighbor on the side, rather than in front or back along the direction of motion," says Giardina. "We measured this probability also for the second and third neighbors, and so on. And we found that birds interact with six or seven neighbors. After that, the anisotropy decays. That's the point where the spatial structure becomes isotropic."

It turns out, Giardina says, that these "topological interactions are much more robust to perturbations" than a model in which a bird interacts with other birds within a fixed distance. The anisotropy, she adds, makes sense biologically: "It's related to vision, since the physiology of the eye is not isotropic."

The Rome team is now extending the data analysis to reconstruct trajectories of individual birds. "We don't have results yet," says Cavagna. "We have to find algorithms for dynamical matching. But we will be able to ask new questions, such as 'How long does a bird remain correlated with its neighbors?' and 'How does a flock rearrange itself when it turns?' "

Model behavior

Although computer models of flocking don't yet explicitly build in the anisotropy, StarFlag's modelers have refined their simulations since the collaboration began in 2005; the project's three-year grant from the European Commission runs through this year. "We keep three old rules—hard-core repulsion, longer-range attraction, and we assume that the particles [birds] assume the average direction of their neighbors," says Tamás Vicsek of Hungary's Loránd Eötvös University. "But now we feed into the model details of the dynamics, such as that the birds change direction, in order to understand landing and how they self-organize behavior." In particular, Vicsek and others have extended their models to three dimensions. "We have developed a very nice—fast, beautiful—visualization of flocking data points. The graphics shows birds flapping their wings and contracting when moving away," says Vicsek.

Hugues Chaté, a physicist at the Atomic Energy Commission in Saclay, France, says that to incorporate anisotropy into the attractive and repulsive potentials of his models, "we need to introduce not just an axis for the flight direction, but another for the wings. Then we can modulate the strength of the interactions." So far, he adds, the interactions in his models rely on a "nice mix of topological and metric criteria"—a bird interacts with its neighbors, but the strength of each pair interaction is modulated by distance, and the "interactions are strictly local, which makes the emergence of collective motion more spectacular."

Collective glue

And then there is the question of whether starlings might shed light on human behavior. StarFlag's Jean-Philippe Bouchaud, a theoretical physicist who heads research at a hedge fund in Paris, asks, "How do people coordinate and imitate each other to create collective phenomena that are surprising if you think about individuals? People are extremely influenced by their neighbors, by fashions and fads. This might have an impact on markets—possibly events like crashes or bubbles are due to the coordination of people. We are looking for situations where you can measure, or try to measure, the ways people interact and create a collective effect."

Bouchaud is currently focusing on two examples of human behavior. One involves how others' choices affect what music people download. The other—topical to France's summer elections—is how people are influenced by others when they vote. Along the same lines, a group of economists in Pisa, Italy, is studying the collective behavior of banks as indicated by where they open branches. Starling flocking is more complex, says Bouchaud, "because it's a three-dimensional organization of birds in space. But the idea is to work up from the behavior of individual birds to the behavior of the flock." The connection to studies of people is indirect, he adds. "Behind these projects is the same fascination with collective effects that glues the whole project together. We have a lot of things to share when we meet."