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This volume presents selected papers from a three-day workshop held during the DIMACS special years on Mathematical Support for Molecular Biology. Participants from the world over attended, giving the workshop an important international component.
The study of discrete mathematics and optimization with medical applications is emerging as an important new research area. Significant applications have been found in medical research, for example in radiosurgical treatment planning, virtual endoscopy, and more. This volume presents a substantive cross-section of active research topics ranging from medical imaging to human anatomy modeling, from gamma knife treatment planning to radiation therapy, and from epileptic seizures to DNA screening. This book is an up-to-date resource reflecting current research directions.
Foreword vii Preface ix Breast cancer survival and chemotherapy: A support vector machine analysis Y.-J. Lee, O. L. Mangasarian, and W. H. Wolberg 1 A model for learning human vascular anatomy P. Hall 11 Optimization of gamma knife radiosurgery M. C. Ferris and D. M. Shepard 27 Sphere packing using morphological analysis Q. J. Wu 45 Transition to epileptic seizures: Optimization L. D. Iasemidis, D.-S. Shiau, J. C. Sackellares, and P. Pardalos 55 Analysis of magnetic resonance angiography images using skeletonization and distance transforms I. Nystrom and O. Smedby 75 Computing medial surfaces S. Bouix and K. Siddiqi 91 A mixed variable optimization approach to non-rigid image registration A. Rangarajan and H. Chui 105 On computing the nearest neighbor interchange distance B. DasGupta, X. He, T. Jiang, M. Li, J. Tromp, and L. Zhang 125 Two-stage group testing for complexes in the presence of errors A. J. Macula, D. C. Torney, and P. A. Vilenkin 145 On the perfectness of tagged probe interval graphs L. Sheng, C. Wang, and P. Zhang 159 Frequent sets in the presence of clones: An example from medical surveillance S. E. Brossette and A. P. Sprague 165 A survey on combinatorial group testing algorithms with applications to DNA Library Screening H. Q. Ngo and D.-Z. Du 171 Optimization problems in 3D conformal radiation therapy Q. J. Wu, C. H. Sibata, and J. Wang 183 Medical applications of discrete tomography A. Kuba, G. T. Herman, S. Matej, and A. Todd-Pokropek 195 A study of 3D imaging approaches in medicine J. K. Udupa 209 Discrete mathematics in medical imaging: A personal view P. Hall 217