## Symposium Celebrating New Fellows of the Royal Society of Canada

February 26, 2007

## Abstracts

**Andrew Granville, **Université
de Montréal

*The anatomy of common objects in pure mathematics*

Common mathematical objects such as integers, permutations, graphs
and polynomials appear, on the surface, to be quite different from
each other. Each has its own context and one can say many interesting
things about how each is used within that context. However, in this
talk, we explore the inner workings of these mathematical objects,
what we will call their "anatomy", and discuss their similarities
and differences.

**Ming Li,** University of Waterloo

*Modern Homology Search*

Homology search, finding similar parts between two sequences, is
the most fundamental task in bioinformatics. A large fraction of
the world's supercomputing time is consumed by homology search.

Traditional homology search technology is a heuristic science.
Given a gene sequence, the search is either too slow (dynamicprogramming)
or not sensitive enough. When it does return something, the results
are simply some fragments of alignments.

We have introduced a new mathematical theory of optimized spaced
seeds that achieve high sensitivity and high speed simulataneously
for homology search. This methodology is now serving thousands of
queries daily. We also introduce another idea of integrating an
HMM into our homology search strategy that returns structured gene
matches, instead of random fragment matches.

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Joint work with Bin Ma and John Tromp and X.F. Cui, T. Vinar, and
D. Shasha

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**Mary E. Thompson, **University of Waterloo

*Generalizing from a sample to a population: reflections on history*

Although the idea of making inference about a survey population
from a sample is a very old one, most of the evolution of the theory
and practice of sampling took place over the twentieth century.
In the talk I will describe some of the important historical advances
and their consequences for survey methods today.