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IPAM: Where Math Creates Connections
The graph represents the connections between IPAM programs (workshops and long programs) from 2000 to 2013. It also demonstrates the breadth of topics that are discussed at IPAM. Each node in the graph represents an IPAM program, and its size corresponds to the number of participants in the program. Clusters of programs, depicted in different colors, emerge naturally as a result of a graph-theoretic community detection algorithm. This is similar to the analysis of other networks, such as co-authorship networks in scientific publications. Full article

AI for Chemical Design
By combining quantum chemistry with artificial intelligence (AI) or Machine Learning, core participants of the long program, "Navigating Chemical Compound Space for Bio and Materials Design", achieved a scientific breakthrough expected to aid in exploring chemical compound space, i.e. the virtual space populated by all possible chemical compounds.Full article

GPS Algorithms
How accurate are GPS measurements? The answer to this question is important to GPS users and to operators of the GPS constellation, who use it to optimize the geometry of GPS satellites in the sky.Full article

Multiscale representation of macromolecular motion
How many variables do we need to describe macromolecular motion? The answer depends on the time and length scale of interest.Full article

The Fractal® acoustic barrier
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. Full article

Modeling Placental Growth
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. Full article

Compressed Sensing Algorithms
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. Full article

Dimensionality Reduction for Protein Folding
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.” Full article

Better Seismic Imaging
The economic value to the oil industry of 3D seismic imaging is approximately $11 billion annually. How accurately seismic imaging can be done depends on both the quality of the sensing equipment, but also very much on the effectiveness of the mathematical algorithms that are used. Full article

Sparse Representations
What 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. Full article

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