Research Highlights

Homological Mirror Symmetry
June 2007During the academic year of 20062007 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 […]

Stratification Learning
June 2007Data 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 […]

Low Xray Exposure Imaging
June 2007The ability to “see” inside a human body has been of tremendous value to medical diagnostic. For example, it is almost impossible to properly diagnose brain tumor without being able to image the patient’s head, and very difficult to plan the complex surgery of removing the tumor without accurate threedimensional visualization of the brain itself. […]

Traffic Gridlock
May 2007In studying traffic flow in a large city grid, the following questions arise. Is there a largest traffic density that permits free flow? Is there a density above which gridlock is inevitable? In 1992 Biham, Middleton and Levine introduced a simplified model for the study of these questions, called the BML model. […]

Improved Electron Gun Design
April 2007Electron beams are employed in vacuum devices to generate very high power microwaves for many critical applications, including amplifiers in communications, television, radar guns and computer monitors, and high energy accelerators. The quality of these electron beams directly impacts the output power and efficiency that can be achieved. In a SAMSI workshop, a group of […]

Shedding Light on Blackouts
June 2006The control of communication and power networks through regulation and deregulated market mechanisms presents tremendous challenges and affects almost every citizen of the United States. Theoretical understanding in this area is built on the mathematical field called stochastic networks, a field whose growth has been closely tied to the Institute for Mathematics and its Applications […]

An Eye for Aphids
June 2006Soybeans are a key livestock feed in the US, an important human food source in many parts of the world, and–in the form of biodiesel fuel–a promising source of renewable energy. Informed pest management increases yield and reduces pesticide application: farmers use population estimates obtained by counting the aphids on sample soybean leaves in planning […]

Expander Graphs
May 2006A central computational theme is “parallel processing”: allowing a large number to processors to work simultaneously and thus potentially speed up computation. A major issue for this development is the architecture of the communication network among these processors. The problem of how to design such a network is translated into a mathematical problem of finding […]