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Their screens display a cloud of about 50 concepts she has selected from the course, such as prediction, network, behavior, and neurological disease. They draw lines to connect related words and phrases, stretching the lines to put distance between dissimilar concepts.

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Bassett will compare the structure of the maps at different points in the course, gauge the influence of class readings and lectures, and look for correlations between network structure and test scores. The work seems miles away from Bassett's physics degree. But underlying that study—and nearly every other project in her lab—is a branch of math called graph theory. The approach, with roots in the 18th century, describes the structure of networks of discrete, interacting parts, be they friends linked on social media or grains in a sand pile.

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Researchers first calculate the relationships between all nodes in a network: in the simplest case, either a zero not connected or a one connected. Then, they ask questions about the features of the network: Is it a sparse web or a dense jungle of connections? Do certain nodes have an unusually large number of connections? Do nodes tend to organize themselves into tight-knit modules that mostly talk among themselves?

In the s, a few researchers started to create such graphs to describe the layout of animal nervous systems. The brains of mammals were far too large and complex to map neuron by neuron, so researchers analyzed the connections between dozens of broad areas in the monkey and cat cortex according to the flow of tracer molecules along neurons. Sporns, now at Indiana University in Bloomington, was among the first to use graph theory to analyze connections in the human brain.

Few data sets were available, he says. But he and his collaborators hoped the approach could help explain how the brain's structure gives rise to thought and awareness.

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By the mids, applications of graph theory were getting more ambitious. Neuropsychiatrist Edward Bullmore's group at the University of Cambridge in the United Kingdom used it to analyze human brain activity recorded with functional magnetic resonance imaging fMRI , a technique that can indicate which regions are active in unison. National Institutes of Health. She took off running with graph theory, Bullmore recalls, stretching its uses to new types of brain data.

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In one study, Bassett analyzed MRI data from people with and without schizophrenia. The condition seems to arise from broadly disorganized brain activity, not a defect in any one region. Bassett and colleagues showed that graph theory offered a new way to describe that disorganization. Brains with schizophrenia showed more random patterns of connectivity than healthy ones, and their hubs—the most highly connected regions—were less likely to be in the frontal cortex, the area that exerts executive control over the brain. That finding aligned with some of the symptoms of schizophrenia: deficits in executive functions such as planning, decision-making, and regulating behavior.

But it didn't explain them. And some neuroscientists were unimpressed by early results from network science. Graphs of brain networks were "obviously a radical simplification of the nervous system," Bullmore says. Bassett saw a different limitation to graph theory. So, as Bassett moved to her postdoc at UC Santa Barbara, she added another type of analysis to her study of networks: dynamical systems theory, a way of modeling how network structure changes. In a key experiment, Bassett studied people as they learned to tap their fingers quickly in a specific order by reading sequences of notes on a staff.

The sequences weren't exactly Brahms rhapsodies; each was just 12 notes long. But participants took time to master them. During three training sessions, they lay in an fMRI scanner and practiced their finger work. Bassett's group captured changes over time in the sets of brain areas that preferentially conversed with each other while participants learned.

The researchers created a mathematical measure of overall "flexibility"—how likely regions were to change their "module allegiance" and sync up with a different set of partners. A brain's flexibility during a practice session, the researchers found, predicted how much faster the person would be able to play the note sequences in the next session. The research, published in , hinted that measurable, predictable features of the brain's configuration can prime it for learning.

That "started to get a lot of people's attention," Bassett says, including representatives of the MacArthur Fellows Program, who pointed to the work in selecting Bassett for the award. Bassett, who was just getting her lab at UPenn off the ground, found herself in the academic spotlight. Her parents, who had separated when she was 18, cheered her on.

Bassett is now a hub in a lively network—a role that doesn't always suit her. On an endless circuit of invited talks, she seeks solitude in her hotel room. She shies away from group interactions, preferring one-on-one communication with trainees and collaborators. But some of those pairwise connections have had far-reaching effects. In , on a bench overlooking the Pacific Ocean in Santa Barbara, she and mechanical engineer Fabio Pasqualetti, then a fellow postdoc, realized they shared an ambition.

They wondered whether network science could go beyond describing the brain to offering ways to change it. Pasqualetti studies control theory, a branch of engineering that uses sensors and feedback to guide the behavior of a system, whether that's an electrical grid or a fighter jet. Was it possible, he and Bassett wondered, to apply principles of control theory to brain networks? In their initial study, published in , Bassett and Pasqualetti modeled brain structure with data from an MRI-based technique that traces the diffusion of water through the brain to identify regions connected by bundles of neuronal fibers.

By feeding that information into an equation from control theory, they identified areas of the brain that, when active, might help it shift into various other states. Scientists are already experimenting with zapping the brain to improve various conditions, including severe depression and disability after stroke. But the approach, which often relies on magnetic stimulation of the scalp, involves trial and error.

Control theory could help researchers decide where in the brain to stimulate, and at which intensities, to reliably steer it into a healthier state. Still, Zorzi says, "It's not ready yet. That work should include studying how many points of stimulation are necessary to induce a desired brain state, he adds.

Bassett and her team are now refining their control theory approach and using it to predict the spreading patterns of activity in epileptic seizures. The results, they hope, will show how doctors could place seizure-stifling electrical implants more precisely or slice out less brain tissue during surgery. Before any clinical trials, Bassett and colleagues will also have to defend the work against a familiar charge: that it oversimplifies the brain.

Signals don't pass predictably along every connection between neurons.

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Some get amplified; others run into gating mechanisms that inhibit them, and equations from control theory don't fully capture those details. In response, Bassett channels Ptolemy. The game, called Quantum Moves , is based on a real problem in quantum computing: how fast a laser can move an atom between wells in an egg-box-like structure without changing the energy of the atom, which is in a delicate quantum state.

Endless possible combinations of movement and timing exist, and scientists have designed computer algorithms to try to solve the problem. In the game, an atom is represented by what looks like a liquid sloshing around in a well, which reflects the wave-like nature of a quantum particle.

In one level, players move a cursor to control a second well, which they use to collect the sloshing liquid and take it back to a base. Once they find ways to transfer the liquid, a computer can then convert their mouse movements to solutions to the real-world quantum egg box.

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The researchers then fed the human solutions into a computer for further refinement. Not only were more than half of the human-inspired solutions more efficient than those produced by just computer algorithms, but the two best hybrid strategies were faster than what the quickest computers had been able to achieve working alone. Games enable researchers to appeal to the public for help in solving scientific problems.

What abilities humans bring to the mix is unclear. Although an interest in physics seems to correlate with ability in the game, success did not correlate with years spent studying quantum physics. Quantum concepts may seem less bizarre to people in a game than they do in other contexts, because it is an environment in which they expect rules to be broken, adds Sabrina Maniscalco of the Turku Centre for Quantum Physics in Finland, who runs an event aimed at making games that might benefit quantum physics.

To Sherson, the results also suggest that physicists could use their own intuition more. To that end, his team is building a version of the game in which physicists can tweak the scenario to represent different set-ups, potentially offering them new insights into their work. Other quantum physicists agree that the finding that people can develop an intuition for quantum processes is surprising, but think that scientists already use intuition to solve quantum problems, at least at the mathematical level.

By playing the game, people perhaps gain a form of that intuition, says Seth Lloyd, a physicist at the Massachusetts Institute of Technology in Cambridge. He notes that before babies learn to expect an object to stay where it is, they have a form of quantum intuition, which they lose. Unite to build a quantum Internet. Lloyd also says that much of the success of Quantum Moves is due to its clever design, which successfully translates a quantum problem to a visual one, but which could fail with more-complex quantum problems.

Physicists who are trying to develop quantum-computing algorithms already play around with graphical interfaces to help them to improve on existing solutions, says Charles Tahan, a theoretical physicist at the University of Maryland in College Park.