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Photo, caption follows:

A three-dimensional computer simulation of what happens when a tornado passes over a building. Both images show aerial views looking down on the roof; the arrows represent wind velocities and the colors represent air pressure, with red being the highest. In the top image the eye of the tornado is dead center on the building, which is surrounded by a series of violent eddies. In the bottom image, the tornado has just passed the building and is headed toward the upper right. Knowledge gained from simulations such as this one helps scientists understand the tornado-induced loads on buildings, which could in turn help reduce tornadoes' enormous yearly toll on life and property.
Credit: R. Panneer Selvam, Paul C. Millett, Computational Mechanics Laboratory, University of Arkansas


Pattern Hunting and Statistical Learning
Since the advent of modern data-recording technology, vast quantities of scientific measurements have been collected and stored. Much more is on the way. Analyzing the data, however, is far harder than storage. It demands new mathematical techniques for processing giant information sets and novel systems for extracting essential patterns from enormous volumes of surrounding data. NSF supports research in the following fields, along with many others.

  • Rare Events. Many experiments in the physical sciences, such as those at the LIGO gravitational wave observatory, are searching for phenomena that are believed to occur rarely or to leave small traces when they do. Classical methods of statistics are meant to uncover frequent repetitions, not rare examples. Using a variety of mathematical and computational approaches, investigators are looking for the best ways to filter out a dominant background in search of small contributions that carry special content. Some approaches are modeled on biological signal-processing, such as a hawk's ability to spot small prey against a complex background from high above; or the human auditory capacity to follow a conversation in a loud environment.
  • Weather and Climate Simulation. Atmospheric and ocean scientists are collaborating with statisticians on methods for making sense of an ever-increasing amount of day-to-day information in order to improve weather prediction and climate models. For example, competing models can give different predictions for a hurricane's track. Researchers want to compare them on the basis of performance. But new mathematical tools are needed to measure predictive accuracy for simulations that compute quantities such as temperature, barometric pressure, wind speed and direction, and humidity over a map grid of thousands of points. For these circumstances, familiar, simple ideas like "average" are inadequate.
  • High-Dimensional Data Sets. Data collections such as weather measurements over a given volume are often described as "high-dimensional data sets." If a sensor records temperature, barometric pressure, and relative humidity, then there are three "dimensions" involved. If there are 1,000 recording sites, then there is a total of 3,000 independent numbers, or dimensions. Identifying patterns within those measurements is a daunting mathematical problem.

    But it may be simplified. Imagine a room containing 400 people. Each has two "dimensions" of location (a north-south value and an east-west value), so they form an 800-dimensional data set. However, if the people start square-dancing in groups of four, the number of relevant dimensions is greatly reduced. Weather patterns can produce similarly ordered behavior. To return to the dance floor analogy, the challenge is to devise a mathematical system that can analyze the changing positions of the dancers, detect the regularity of their movements, and perhaps even identify the dance being performed.

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