Thursday, November 29, 2012

A Bit On Networks

Networks are made of nodes and links. If taking Facebook for example, people are the nodes, and their friendships are the links. Some people have lots of links to other people, some not so much. All together, the number of people who use Facebook is the size of the network, and the connections between them is the density of the network. If every person, on average, has 150 friends, then the network density is 150.

RSA Animate - The Power of Networks - 2012
The TREE of life has become the WEB of life
watch this animated talk
^Manuel Lima, senior UX design lead at Microsoft Bing, explores the power of network visualisation to help navigate our complex modern world.
full talk: RSA

Human brain, internet, and cosmology: Similar laws at work?
November 20, 2012 by Jan Zverina

The structure of the universe and the laws that govern its growth may be more similar than previously thought to the structure and growth of the human brain and other complex networks, such as the Internet or a social network of trust relationships between people, ...

By performing complex supercomputer simulations of the universe and using a variety of other calculations, researchers have now proven that the causal network representing the large-scale structure of space and time in our accelerating universe is a graph that shows remarkable similarity to many complex networks such as the Internet, social, or even biological networks.

"These findings have key implications for both network science and cosmology," noted Krioukov. "We discovered that the large-scale growth dynamics of complex networks and causal networks are asymptotically (at large times) the same, explaining the structural similarity between these networks."

"This is a perfect example of interdisciplinary research combining math, physics, and computer science in totally unexpected ways," said SDSC (San Diego Supercomputer Center) Director Michael Norman. "Who would have guessed that the emergence of our universe's four-dimensional spacetime from the quantum vacuum would have anything to do with the growth of the Internet? Causality is at the heart of both, so perhaps the similarity Krioukov and his collaborators found is to be expected."

^ Network Cosmology
Dmitri Krioukov, et. al.
Scientific Reports 2, Article number: 793
Published 16 November 2012

World’s Subways Converging on Ideal Form
Brandon Keim - May 15, 2012
modified article:

City subway systems converge on a ratio for the number of stations on branch lines to the number in city cores.
Image: Roth et al./JRSI
After decades of urban evolution:

In a May 15 Journal of the Royal Society Interface paper, Barthelemy and NCSR complex systems analyst Camille Roth focused a network analysis lens on city subways...

On the surface, these core-and-branch systems — evident in New York City, Tokyo, London or most any large metropolitan subway — may seem intuitively optimal. But in the absence of top-down central planning, their movement over decades toward a common mathematical space may hint at universal principles of human self-organization.

With equations used to study two-dimensional spatial networks, the class of network to which subways belong, the researchers turned stations and lines to a mathematics of nodes and branches.

Patterns emerged: Roughly half the stations in any subway will be found on its outer branches rather than the core. The distance from a city’s center to its farthest terminus station is twice the diameter of the subway system’s core. This happens again and again.

“Many other shapes could be expected, such as a regular lattice,” said Barthelemy. “What we find surprising is that all these different cities, on different continents, with different histories and geographical constraints, lead finally to the same structure.”

Subway systems seem to gravitate towards these ratios organically, through a combination of planning, expedience, circumstance and socioeconomic fluctuation, say the researchers.

The convergence “is a sign that there are some basic, profound mechanisms that drive the development of urban systems,” said Barthelemy.

^ A long-time limit for world subway networks
Camille Roth, Soong Moon Kang, Michael Batty and Marc Barthelemy
Proceedings of the Royal Society Interface, 15 May 2012

The Network Visualized, Michael Rigley, 2012
Information technology has become a ubiquitous presence. By visualizing the processes that underlie our interactions with this technology we can trace what happens to the information we feed into the network. Beautiful and sinister in equal measure.

Post Script:
The Mathematical Shape of Things to Come
Jennifer Ouellette, Quanta Magazine
October 4, 2013
Scientific data sets are becoming more dynamic, requiring new mathematical techniques on par with the invention of calculus.

Networks Reveal the Connections of Disease
Veronique Greenwood, Quanta, 2015 Jan 29
Enormous databases of medical records have begun to reveal the hidden biological missteps that make us sick.

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