What’s New

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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fractal barrier-1

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.

Describing protein motions with nonlinear dimensionality reduction

Posted on 7/18/08 in Research Articles

Twenty years ago, commenting on macromolecular dynamics, Francis Crick wrote that “what seems to physicists a hopelessly complicated process may have been what Nature found simplest.” Indeed, if one uses molecular dynamics simulations (that follow the molecular motion of biological systems in the high dimensional […]

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Image courtesy of Mark Moll, Payel Das and Hernan Stamati (Rice University, Houston, Texas).