Research Highlights

Real-life NUMB3RS

IMA - October 2007

In 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 quality of the video was terrible, and it seemed...

Honeybee Olfaction

MBI - October 2007

A 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 for studying olfaction because their physiology and behavior...

New Tools for Old Problems

AIM - October 2007

When 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 mathematical physics, may have applications in other...

Neuronal Network

MBI - October 2007

Modeling 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 pre-Bötzinger complex, a network of neurons exhibiting rhythmic bursts of activity that initiate inspiration. The frequency of the rhythm varies in response to such challenges as exercise, sleep, or...

Symmetry in 248 Dimensions

AIM - October 2007

A 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 connections between E8 and other areas, including string theory and geometry. The magnitude of the calculation is...

Mind-Bending Math

IMA - October 2007

When 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. The sulcal fundi serve as anatomical landmarks, ‘segmenting’ the cortex into...

Alimentary Math

IMA - October 2007

Meat 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 long-term visitors to the IMA during our 2005-2006 program on imaging are contributing to the improved production of these important foodstuffs. For beef, the rib eye area is an important indicator of the meat quality...

Spatial Model for Rabies

MBI - October 2007

A human bitten by an animal with rabies will almost certainly die within days unless immediately treated with a multi-stage 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 million each year on its prevention and...

Stratification Learning

IMA - June 2007

Data in high dimensions is becoming ubiquitous, from image analysis and finances to computational biology and neuroscience. This data is often given or represented as samples embedded in a high dimensional Euclidean space, point cloud data, though it is assumed to belong to lower dimensional manifolds. Thus, in recent years, there have been significant efforts in the development of methods to...

Homological Mirror Symmetry

IAS - June 2007

During the academic year of 2006-2007 the School of Mathematics conducted a special program in algebraic geometry. This subject, with deep classical roots, is one of the most active areas in contemporary mathematics. Especially notable are its interconnections with number theory, mathematical physics and topology. The scientific activities during the year reflected the depth and breadth of...