Research Highlights

Sparse Representations
November 2007What do researchers studying infrared spectroscopy, seismic imaging, error correcting codes, and MRI’s have in common? They all can get better results if they have the right math. Fourier analysis, discovered in analyzing the flow of heat, revolutionized how mathematics is used in a variety of sciences by breaking complicated functions into a sum of […]

EvoGeo
November 2007Can polyhedral geometry and commutative algebra—usually regarded as pure mathematics—help biologists? We at the IMA certainly think so, and the emerging applications of these mathematical areas to evolutionary biology was a major theme during a workshop bringing 135 mathematicians, statisticians, biologists, and computer scientists to the IMA in March 2007 as part of our yearlong […]

Honeybee Olfaction
October 2007A honeybee may forage on 1,000s of flowers for nectar and pollen in its lifetime. Scent is one of the primary means that it uses for identifying rewarding flowers. How honeybees and other animals learn to associate complex and variable scents with important events is still not well understood. Honeybees are an excellent model system […]

New Tools for Old Problems
October 2007When mathematicians notice connections between two distinct areas of their discipline, you can be sure something interesting will develop. That is exactly what happened at a recent workshop at the American Institute of Mathematics (AIM). The scientific advisory board of AIM noticed that new methods in ergodic theory, a subject arising from […]

Neuronal Network
October 2007Modeling the Dynamic Range of a Neuronal Network for Breathing For humans and other mammals, breathing is essential to life. The breathing rhythm relies on an area of the brain stem known as the preBötzinger complex, a network of neurons exhibiting rhythmic bursts of activity that […]

Symmetry in 248 Dimensions
October 2007A Calculation the Size of Manhattan Mathematicians have mapped the inner workings of one of the most complicated structures ever studied: the object known as the exceptional Lie group E8. This achievement is significant both as an advance in basic knowledge and because of the many […]

MindBending Math
October 2007When viewed from the outside, a human brain appears as a volume with a highly wrinkled surface having numerous long crevices. Sulcal fundi are 3D curves that lie in the depths of the cerebral cortex; informally, the fundus of a sulcus is the curve of maximal average depth that spans the length of the sulcus. […]

Reallife NUMB3RS
October 2007In December 2005, while the IMA was in the midst of a thematic program on imaging science, a homicide investigator from Richmond, Virginia, contacted the institute about an unsolved murder. The best clue available seemed to be a service station security camera video showing the perpetrator fleeing the crime scene in a car. Unfortunately the […]

Alimentary Math
October 2007Meat and soybeans are two important food sources in many parts of the world, and in the form of biodiesel fuel, soybeans are a promising source of renewable energy. Two groups of longterm visitors to the IMA during our 20052006 program on imaging are contributing to the improved production of these important foodstuffs. […]

Spatial Model for Rabies
October 2007A human bitten by an animal with rabies will almost certainly die within days unless immediately treated with a multistage vaccine regimen initially developed by Louis Pasteur in 1885. To combat the spread of rabies today, which nationwide affects over 40,000 people annually and countless wild and domestic animals, the United States spends over $300 […]