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A New Mathematical Tool...Useful?

Celebrate the development of a new mathematical tool...it can help us understand the "chaotic" structure underlying time-dependent, interrelated, complex data. Examples of sources of such data include legislators' votes over their careers, instantaneous activity of the stock market, or levels of oxygenated blood flow in the brain.

Dartmouth researchers named their tool the Partition Decoupling Method (PDM), which is able to both unscamble and capture patterns in "data-flow" that represent the "subtle interdependencies among the different components of a complex system."

The PDM involves statistical learning tools and spectral analysis, an area of mathematics that models heat flow on different kinds of geometric surfaces. In its simplest form, the PDM analyzes data in a complex system, identifies sectors where the flow circulates more than expected (base assumption is random), collapses these sectors, and then creates new networks of these sectors (now as nodes). The result is bi-directional information-wise...zooming in to gain detailed analyses of the sectors' interrelations and zooming out for a broad wholistic view of the overall flow of data.

Thus far, the researchers have applied the PDM primarily to the equities market, a complex system rich in both numerical data and a web of interdependent markets, industries, and currencies. The PDM was robust, identifying not only the known structures and patterns but also new structures.

Daniel Rockmore, part of the research team, commented: "We think this tool can be useful, when applied in the financial realm, to portfolio and risk management. We expect similar results as it is applied to different complex systems like the brain, or even the collections of brains that are societies."

My question or bottom-line: How can I use PDM to avoid the continual financial market "downfalls" that keep depleting my life-time of savings?

Source: ScienceDaily, December 18, 2008