Networked Networks Are Prone to Epic Failure

“When networks are interdependent, you might think they’re more stable. It might seem like we’re building in redundancy. But it can do the opposite,” said Eugene Stanley, a Boston University physicist and co-author of the study, published April 14 in Nature.

Most theoretical research on network properties has focused on single networks in isolation. In reality, many important networks are tied to each other. Anecdotal evidence — the crash of communications networks (.pdf) in lower Manhattan after 9/11, the plummeting of markets around the world after the Black Monday stock market collapse of 1987 — hints at their fragility, but the underlying mathematics are largely unexplored.

The Nature researchers modeled the behavior of two networks, each possessing what’s known as “broad degree distribution”: A few nodes have many connections, some have an intermediate amount of links and many have just a few. Think of the networks as having only a few branches, but many leaves. On their own, such networks are known to be stable. A random failure is likely to disable a leaf, leaving the rest of the network’s connections mostly intact.

In the new study, the researchers connected two of these networks. While many node failures were required to crash the networks when they were independent, a few failures crashed the networks when they were linked.

Read More http://www.wired.com/wiredscience/2010/04/networked-networks/#ixzz0ll3dRTsM

S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, and S. Havlin, "Catastrophic Cascade of Failures in Interdependent Networks," Nature 464, 1025-1028 (2010). PDF -- Accompanied by "News \& Views" article by A. Vespignani on pp. 984-985. PDF

http://en.wikipedia.org/wiki/Electrical_grid

An electrical grid is an interconnected network for delivering electricity from suppliers to consumers.

http://en.wikipedia.org/wiki/Network_science

Network science is a new and emerging scientific discipline that examines the interconnections among diverse physical or engineered networks, information networks, biological networks, cognitive and semantic networks, and social networks. This field of science seeks to discover common principles, algorithms and tools that govern network behavior. The National Research Council defines Network Science as "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena."

http://en.wikipedia.org/wiki/Biological_neural_network

Biological neural network

In neuroscience, a neural network describes a population of physically interconnected neurons or a group of disparate neurons whose inputs or signalling targets define a recognizable circuit. Communication between neurons often involves an electrochemical process. The interface through which they interact with surrounding neurons usually consists of several dendrites (input connections), which are connected via synapses to other neurons, and one axon (output connection). If the sum of the input signals surpasses a certain threshold, the neuron sends an action potential (AP) at the axon hillock and transmits this electrical signal along the axon.

In contrast, a neuronal circuit is a functional entity of interconnected neurons that influence each other (similar to a control loop in cybernetics).


From "Texture of the Nervous System of Man and the Vertebrates" by Santiago Ramón y Cajal. The figure illustrates the diversity of neuronal morphologies in the auditory cortex.

http://en.wikipedia.org/wiki/Perceptron

The perceptron is a type of artificial neural network invented in 1957 at the Cornell Aeronautical Laboratory by Frank Rosenblatt.