Engineers use control theory to predict how systems will respond to various inputs, which in turn helps them make robots that can catch baseballs, cars that take sharp corners with ease, and planes that don’t fall from the sky. Barabási had never heard of it, so his new friend led him to a whiteboard and drew out the basic equations. Barabási noticed how similar they were to the ones he used to map networks, and he decided to incorporate them into his own work.
Like prediction, control required evaluating an object as a system with nodes of varying importance. A car for instance: “It is made of 5,000 components,” Barabási says, “yet you as a driver have access to only three to five nodes”—the steering wheel, the gas pedal, the brake, and maybe the clutch and shifter. “With those three to five knobs, you can make this system go anywhere a car can go.” What he wanted to know was if he could look at any network, not just engineered ones, and find those control nodes. Among the thousands of proteins operating within a cell, could he find the steering wheel, the gas pedal and the brake?
Barabási asked Yang-Yu Liu, a physicist in his lab, and Jean-Jacques Slotine, a control theorist at the Massachusetts Institute of Technology, to help him locate “control nodes” within networks. Control nodes take instructions or signals from outside the network (for example, a foot on the gas pedal) and transmit them to nodes within the network (the fuel-injection system). To find them, Liu borrowed an algorithm, developed by Erdös and Rényi five decades prior, that acts as a signal moving through the network. It starts at one node and follows a random edge to another node, at which point it “erases” every other edge but the one it came in on and the one it will go out on. The algorithm runs through the entire network over and over until it finds the minimum set of starting points needed to reach every node in the system. Control these starting points, and you control the entire network.
The group tested the algorithm on 37 different networks, including a constellation of alliances within a prison population, the metabolic pathways in yeast, and several Internet communities, including Slashdot and Epinions. They found that denser, more interconnected networks tended to have fewer control nodes per capita. For instance, the brain of the highly studied worm C. elegans, a network of 297 neurons, has only 49 control nodes. The network of genes operating in a yeast cell produces 4,441 proteins, but Barabási found that he would need to control 80 percent of them, or 3,500, to control the system.
This sounds like too many points to be useful, like a car with 3,500 steering wheels, but Barabási points out two things: Whereas the neuronal map of C. elegansis complete, scientists have determined only about 5 percent of the connections in the yeast cell’s gene network. The more data scientists feed into the model, the better they can map connections in the network and the fewer control nodes they might need to operate the system. “We know these maps are incomplete,” Barabási says. “But they’re getting richer every day.” He also says his theory applies to total control of a network. Scientists who want partial control—say, to elicit a particular protein expression within a cell—would need to master far fewer nodes.
As with most of Barabási’s work, it will take time to make it useful. Finding the points of control is one thing. Actually exerting influence over a given network, be it Facebook or the human immune system, is an entirely different challenge.
The first breakthroughs will most likely take place in medicine. By identifying control nodes in cell growth systems, scientists could return mature cells to their embryonic state, creating a new source of stem cells. “Some diseases are all about lack of control,” Barabási says. “If you were able to gain control over them at the cellular or neuronal level, you might be able to cure the disease.”
Control can be used for ill as well as good, of course. Marketers could learn how to better manipulate consumers, and governments could develop new techniques to cow citizens. It’s up to us, Barabási says, to define how control should be applied and how it shouldn’t be. “What we have to realize is that control is a natural progression of understanding processes,” he says. “But control is a question of will, and will can be controlled by laws. We have to come together as a society to figure out how far we can push it."single page
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