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GPS Algorithms

Posted on 2/10/11 in Research Articles

The Global Positioning System (GPS) is global navigation system consisting of at least twenty-four satellites orbiting in six planes around the earth. GPS is extensively used by both the military and the FAA, with growing applications in civilian markets. The importance of GPS in everyday […]

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orbits

The Fractal® acoustic barrier

Posted on 3/25/09 in Research Articles

The study of the vibrations in domains with boundaries or interfaces of irregular geometry is a complex mathematical problem, for which many questions are still unsolved. Nevertheless, it has been known for a long time that objects of irregular shape or geometry are “bad resonators”. […]

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Modeling Placental Growth and Structure

Posted on 1/12/09 in Research Articles

Early life influences adult diseases. Such serious public health priorities as diabetes, heart disease, breast and prostate cancer, osteoporosis, and depression have all been related by recent medical studies to the development of the fetus. Environmental influences, such as maternal diseases, can cause irreversible metabolic […]

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Bregman Iteration and Applications to Imaging and Sparse Representation

Posted on 1/9/09 in Research Articles

A breakthrough in the sparse representation of data was made in the Fall of 2004 by David Donoho and by Emmanuel Candes and Terence Tao, in part at IPAM’s Multiscale Geometry and Analysis program. Their important results reduce a computationally difficult problem to an easily […]

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Magnetic Resonance Imaging of a sharp disk, using a traditional method (left) and a new method based on Compressed Sensing and Bregman iteration (right), from work of T. Goldstein.