It is shown that for any outerplanar graph G there is a one to one mapping of the vertices of G to the plane, so that the number of distinct distances between pairs of connected vertices is at most three. This settles a problem of Carmi, Dujmovic, Morin and Wood. The proof combines (elementary) geometric, combinatorial, algebraic and probabilistic arguments.

D. Michal FREEDMAN*, Alice SIGURDSON, R. Sowmya RAO, Michael HAUPTMANN, Bruce ALEXANDER, Aparna MOHAN, Michele MORIN DOODY and Martha S. LINET Division of Cancer Epidemiology and Genetics, Radiation Epidemiology Branch, National Cancer Institute, Bethesda, MD, USA Division of Cancer Epidemiology and Genetics, Biostatistics Branch, National Cancer Institute, Bethesda, MD, USA Division of Environ...

Attributes of words, such as frequency and imageability, can influence memory for order. In serial recall, Hulme, Stuart, Brown, and Morin (Journal of Memory and Language, 49(4), 500-518, 2003) found that high-frequency words were recalled worse, and low-frequency words better, when embedded in alternating lists than pure lists. This is predicted by associative chaining, wherein each recalled l...

Roddy Hiram, Edmond Rizcallah, Chantal Sirois, Marco Sirois, Caroline Morin, Samuel Fortin, and Eric Rousseau Department of Physiology and Biophysics, Université de Sherbrooke, Sherbrooke, Quebec, Canada; Department of Pathology, Université de Sherbrooke, Sherbrooke, Quebec, Canada; Service of Thoracic Surgery Faculty of Medicine and Health Sciences, Université de Sherbrooke, Sherbrooke, Quebec...

For decades, the sphere eversion has been a favorite subject for mathematical visualization. The 1998 video The Optiverse shows minimax eversions, computed automatically by minimizing elastic bending energy using Brakke’s Evolver. We contrast these geometrically optimal eversions with earlier ones, including those by Morin, Phillips,

It is shown that for any outerplanar graph G there is a one to one mapping of the vertices of G to the plane, so that the number of distinct distances between pairs of connected vertices is at most three. This settles a problem of Carmi, Dujmović, Morin and Wood. The proof combines (elementary) geometric, combinatorial, algebraic and probabilistic arguments.

Caroline Morin, Christelle Guibert, Marco Sirois, Vincent Echave, Marcio M. Gomes, and Eric Rousseau Le Bilarium, Department of Physiology and Biophysics, Service of Thoracic Surgery, and Department of Pathology, Université de Sherbrooke, Sherbrooke, Quebéc, Canada; and Laboratoire de Physiologie Cellulaire Respiratoire, Institut National de la Santé et de la Recherche Médicale U885, Université...