Professor David Epstein, joint with Health Infomatics
of University of Warwick
will speak on
"Tree Space"
Software used by biologists takes as input chunks of similar DNA. These chunks can be obtained from various sources: different species, or different individuals from the same species (the Eve project), or different viruses within the same individual (studies of HIV). The output from the software is a phylogenetic tree (evolutionary tree a la Darwin). A vertex in the tree corresponds perhaps to a currently living or to an extinct species at a time of speciation. The length of an edge corresponds to the number of mutation events between its two ends. A tree in which each edge has a length is called a weighted tree. Following Billera, Holmes and Vogtmann, we take weighted trees as input for further investigations. There are different ways to define a metric on space of weighted trees. We investigate algorithms for finding the distance between two trees in different metrices, and algorithms for finding the "average" of a finite set of weighted trees. Efficient methods result from interesting geometric theorems. I will discuss a number of possible applications in biology. I am currently investigating possible applications to statistics (namely to analyzing the effectiveness of certain types of cluster analysis under certain conditions), and will report on this in Minneapolis if it pays off.
Professor Christopher Sogge, Johns Hopkins University, will be visiting the Mathematics Department April 24-May 7, 2003. His visit is sponsored by the Ordway Endowment. Professor Sogge's office will be Vincent Hall 260 and you can reach him by phone at 625-2036. Professor Martin Markl, Mathematical Institute of the Academy, Prague, is visiting the School of Mathematics April 30 - May 28, 2003. His visit is partially sponsored by the Visitors Program. Professor Markl's office is VinH 235, and you can reach him by phone at 625-1858. Professor David Epstein, University of Warwick, will visit the Mathematics Department May 6-16, 2003. Professor Epstein's visit is sponosred by the Visitors Program. During his stay, his office will be Vincent Hall 220; you can reach him by phone at 625-4557.
There will be a tutorial on Monday, May 5, 2003 on Data Analysis and Optimization. Please see http://www.ima.umn.edu/optimization/spring/t5.html for further information.
There will also be a workshop on Data Analysis and Optimization from May 6-9, 2003. Please see http://www.ima.umn.edu/optimization/spring/op7.html for further information.