DIMACS Series in
Discrete Mathematics and Theoretical Computer Science

VOLUME Fifty Five
TITLE: "Discrete Mathematical Problems with Medical Applications"
EDITORS: Ding-Zhu Du, Panos M. Pardalos, and Jie Wang

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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

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Document last modified on January 5, 2001.