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CTW: Mathematical Challenges in Biomolecular/Biomedical Imaging and Visualization (February 18-22, 2013)

Organizers: Anne Gelb, Michael Knopp, Arthur Olson, and Guowei Wei

The emergence of complexity in self-organizing biological systems poses exciting challenges to their quantitative description and prediction. The imaging and visualization of complex biomolecules, such as proteins, DNAs, RNAs, molecular motors and viruses, are crucial in understanding and conceptualization of biomolecular systems, which in turn can have significant impact in biomedicine, rational drug design, drug discovery and gene therapy. On the other hand, biomedical imaging and visualization are indispensable tools for examining, revealing and diagnosing diseases, and for monitoring the effectiveness of medical treatments. Mathematics provides foundations for visualization and principles for the design of biomolecular/biomedical imaging modalities, such as single-molecule fluorophores, confocal imaging, X-ray crystallography and tomography, cryoelectron microscopy, and magnetic resonance force microscopy, nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), ultrasonography, positron emission tomography (PET), etc. Currently, mean curvature flow, Willmore flow, level set, generalized Laplace-Beltrami operator and partial differential equation transform are commonly used mathematical techniques for biomolecular surface generations and visualization. Additionally, wavelets, frames, harmonic analysis and compressive sensing are popular tools for biomolecular visualization and image processing. Moreover, topology, differential geometry, and geometric measure theory are powerful approaches for the multiscale modeling of biomolecular structure, dynamics and transport. Finally, persistently stable manifold, topological invariant, Euler characteristic, Frenet frame and machine learning are vital to the dimensionality reduction of extremely massive biomolecular data. These ideas have been successfully paired with current investigations and discovery of molecular biosciences. Mathematical challenges include the well-posedness of mathematical models under physical and biological constraints, lack of maximum-minimum principle, numerical analysis of multiply coupled partial differential equations, effectiveness of approximation theory and the modeling of complex biomolecular phenomena.

This weeklong MBI workshop, in conjugation with the Mathematics Planet Earth (MPE) 2013 initiative, will seek greater understanding of imaging and visualization. It provides a forum to bring together mathematicians, biological and biomedical scientists to exchange ideas and results related to research in biomolecular/biomedical imaging and visualization, and to foster interdisciplinary research collaborations. It will also stimulate information flow of "biology to mathematics" and facilitate advances in biological science as a result of "mathematics to biology".

Accepted Speakers

  • Chandrajit Bajaj, Computer Science, University of Texas
  • Jason Cantarella, Mathematics, University of Georgia
  • Larry Carin, Electrical and Computer Engineering, Duke University
  • Duan Chen, Mathematical Biosciences Institute
  • Zhan Chen, Mathematics, University of Minnesota
  • Wah Chiu, Bayor College of Medicine
  • Anne Gelb, Mathematical and Statistical Sciences, Arizona State University
  • Weihong Guo, Mathematics, Case Western Reserve University
  • Chiu-Yen Kao, Mathematics, The Ohio State University
  • Deok-Soo Kim, Industrial Engineering, Hanyang University
  • Michael Knopp, Radiology, The Ohio State University
  • Benzhuo Lu, Inst. of Computational Mathematics, Chinese Academy of Sciences
  • Perumal Nithiarasu, College of Engineering, Swansea University
  • Arthur Olson, Molecular Biology, The Scripps Research Institute
  • Stanley Osher, Mathematics, UCLA
  • Jack Quine, Mathematics, Florida State University
  • Rosemary Renaut, Mathematical and Statistical Sciences, Arizona State University
  • Amit Singer, Mathematics and PACM, Princeton University
  • Guohui Song, Mathematics and Computer Science, Clarkson University
  • Yiying Tong, Computer Science and Engineering, Michigan State University
  • Reidun Twarock, Mathematics and Biology, University of York
  • Adityavikram Viswanathan, Computing and Mathematical Sciences, California Institute of Technology
  • Niels Volkmann, Sanford Burnham Medical Research Institute
  • Edward Walsh, Neuroscience, Brown University
  • Yang Wang, Mathematics, Michigan State University
  • Michelle Wang, Physics, Cornell University
  • Kelin Xia, Mathematics, Michigan State University
  • Jack Xin, Mathematics, UC Irvine
  • Zeyun Yu, Computer Science, University of Wisconsin
  • Shan Zhao, Mathematics, University of Alabama
  • Haomin Zhou, Mathematics, Georgia Institute of Technology