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New formula helps gauge the winds of change

January 28, 2010
University of Washington
Researchers devise formula to examine just what types of change occur over time among complex and integrated structures.

This set of scientific fields show the major shifts in the last decade of science. Each significance clustering for the citation networks in years 2001, 2003, 2005 and 2007 occupies a column in the diagram and is horizontally connected to preceding and succeeding significance clusterings by stream fields. Each block in a column represents a field and the height of the block reflects citation flow through the field. The fields are ordered from bottom to top by their size with mutually nonsignificant fields placed together and separated by half the standard spacing. A darker color is used to indicate the significant subset of each cluster. All journals that are clustered in the field of neuroscience in year 2007 are colored to highlight the fusion and formation of neuroscience.
Credit: Martin Rosvall, Carl T. Bergstrom. Mapping Change in Large Networks. PLoS ONE, 2010; 5 (1): e8694 DOI: 10.1371/journal.pone.0008694

The Greek philosopher Heraclitus said that change is the only constant. People change, organizations change, the way people and institutions interact changes over time. Change affects social interactions and the natural world, and it even plays a role in how networks such as air traffic control and banking systems function.

University of Washington research has developed a formula to examine just what sorts of changes occur over time among complex and integrated structures. A key to understanding what's happening is to think of the relationships as networks.

"We've been working on the mathematics of it for some time and it's worked out quite well. We're able to use our formula to create maps that show in detail what's going on," said Carl Bergstrom, a UW associate professor of biology.

He is co-author of a paper describing the work, which is being published in the online journal PLoS ONE, published by the Public Library of Science. The lead author is Martin Rosvall of Umeå University in Sweden, who worked on the project while a UW postdoctoral researcher.

To test their formula, the scientists applied the principals to mapping changes in the field of neuroscience, which a decade ago was mostly a specialty for individuals in a number of other disciplines, such as neurology, psychology or cell biology. They looked at thousands of citations for papers published in scholarly journals in the last 10 years to see how the field has evolved.

"What's happened is that neuroscience has gone from an interdisciplinary specialty to a discipline of its own," Bergstrom said. "These maps throw out our preconceptions of what the disciplines are and look at it in terms of what people are citing."

He believes there are many other applications, such as looking at changes in the flow of air traffic in the United States over time, with the emergence of dominantly busy airports such as Chicago and Atlanta. Those airport operations can affect the nation's entire air traffic system. The formula eventually could allow a closer examination of how the system changed with airline deregulation that began in the late 1970s.

Bergstrom is currently working with Federal Reserve economists to analyze the financial flow between Federal Reserve banks and the nation's largest banking institutions, and he believes the new tool could have broad applications in the public health field as well.

"I think there are many opportunities to look at biological networks, genetics and the spread and treatment of cancer for example," he said.

The tool also could be useful in tracking the spread of illnesses such as AIDS and H1N1, the so-called swine flu.

"If you want to understand the way infectious diseases spread through human populations, you have to understand the network of contacts through which those transmissions occur," Bergstrom said.

The work was funded by the National Institute of General Medical Sciences Models of Infectious Disease Agent Study.

Story Source:

The above post is reprinted from materials provided by University of Washington. Note: Content may be edited for style and length.

Journal Reference:

  1. Martin Rosvall, Carl T. Bergstrom. Mapping Change in Large Networks. PLoS ONE, 2010; 5 (1): e8694 DOI: 10.1371/journal.pone.0008694

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University of Washington. (2010, January 28). New formula helps gauge the winds of change. ScienceDaily. Retrieved August 27, 2016 from
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