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Complex Networks 

The effects of simultaneity

Eliminating synchronism in networks could improve crowd control and control brain disorders

View Pictures / UIG via Getty ImagesThe synchronization of the steps of thousands of people crossing the Millennium Bridge in London, in 2002, made the bridge swayView Pictures / UIG via Getty Images

There seems to be a very simple way to prevent activity in networks as complex and diverse as the Internet or the human brain from becoming synchronized, which causes them to stop working properly. In a study published in the journal Scientific Reports, researchers at the Federal University of Ceará (UFC) and the Swiss Federal Institute of Technology Zurich (ETH) propose that it is possible to break the synchronization of a system by interfering at some key points, without acting on the whole. “Examples of synchronization can be found in a wide range of phenomena, such as the firing of neurons, laser cascades, chemical reactions and opinion formation,” the researchers say in the article. “But, in many cases, the formation of a coherent state is undesired and must be attenuated.”

In any system that operates to some extent like a network, synchronism can usually be created (and often is). And this process is frequently detrimental to its continued operation. The purpose of the work of mathematician Vitor Louzada and physicists José Soares Andrade Junior, Nuno Araujo and Hans Herrmann was to try to develop a strategy to disrupt the synchronism and keep the system healthy.

Nowadays, when it comes to networks, we immediately think of interconnected computers. But, strictly speaking, any set of connected elements in which the activity of one influences the others can be treated, from the mathematical point of view, as a network. An example mentioned by the researchers was the opening of the Millennium Bridge in London in 2002. A crowd gathered at one end of the bridge in order to cross it as soon as it was opened. When the bridge was opened, everyone began a frantic walk across the bridge and, because of the size of the crowd, synchronization occurred between the steps of the walkers. As a result, the in-step vibration led to a scary lateral swaying of the structure.

In other situations, the synchronization of a network could be much more dangerous. This is true of a neurological disease known as epilepsy. In epileptic attacks, neurons synchronize, firing impulses simultaneously. The result is a seizure. In Parkinson’s disease, where there is a gradual loss of control of movements, the problem is similar: synchronization in neuronal firing leads to lack of motor control. To fight these problems, doctors have developed devices known as brain pacemakers that, when implanted in the brain, emit electrical impulses that break synchronism and restore normal brain activity. However, current systems need to take into account all brain activity before they can act. The result is a slow response and a less precise level of control over whether or not to intervene in the neuronal network.

The unique feature of the paper published in Scientific Reports is its demonstration, first in theory and then through computer simulations and  experiments with living beings, that it is possible to avoid the synchronization process without interfering with the entire network. In addition to reducing the intervention needed, the response can be initiated locally, without even taking into account the entire network. In the study, the researchers suggest that it is possible to include what they call contrarians in the network, points where data contrary to the synchronization trend can be input. If one were to apply this principle to the example of the Millennium Bridge, it would be as if the government had trained some actors to always walk out of synch with the crowd. With a few contrarians intelligently distributed along the bridge, one could prevent the system from entering into a synchronous state and oscillating.

Local Interventions
The same applies to epilepsy. Instead of implanting a clumsy pacemaker in the skull to take the whole network into account, miniature devices that interact with individual neurons could be developed, affecting only close connections (the local state), and able to act as contrarians at the appropriate time to eliminate the risk of synchronization. The success of this strategy would depend on installing the devices at the interconnection points or hubs, the regions containing the largest number of network connections.

The group tested this strategy in the nervous system of a worm widely used for scientific research, the Caenorhabditis elegans, a multicellular being whose body is relatively simple. With a total of about a thousand cells, it was the only living organism whose nervous system had been completely mapped. As complete knowledge of its neural network is available, it was possible to identify where to install the contrarians to prevent the synchronism of its brain cells. According to the researchers, this was proof of an important principle. The test showed that the calculations made by the group were correct and that more efficient brain pacemakers could possibly be created in the future.

But there are still challenges to be overcome. In an immense network such as the human brain, the challenge of identifying the hubs is much greater. “The difficulty in carrying out this task depends on the complexity of the network involved,” says Andrade. “One possible way to find these hubs is through spatial monitoring of brain activity, which might reveal regions where neuronal activity is typically higher.”

Applying this strategy seems to be simpler in the case of computer networks, regardless of their size. As these networks can be mapped more easily, it becomes less difficult to identify the hubs and interfere in their operation, dissipating potential hacker attacks that attempt to overload the system by inducing synchronization. However, the social application of this new knowledge could be controversial. No one is likely to oppose trying to prevent the Millennium Bridge from swinging. But what about someone who takes advantage of a group of contrarians positioned at strategic points in an audience with the intent of disrupting a thunderous round of applause?

Scientific article
LOUZADA, V.H.P. et al. How to suppress undesired synchronization. Scientific Reports. v. 2 (658). 2012.