## CONNECTING WOMEN IN MATHEMATICS ACROSS CANADA

December 7-8, 2006

**Talk Abstracts**

**Shaheena Bashir**, McMaster University

*Permutation Tests in Gene Microarrays*

Gene microarrays study is a burgeoning & challenging field.
The purpose is to identify the differentially expressed genes to
identify the causes of some disease, etc. The challenges occur due
to a number of reasons; gene expressions for a very large number
of genes are available as compared to very small sample size, and
possibility of high level of non-normal random noises. Permutation
tests are useful in this context when traditional ANOVA can not
be used. In this talk, I will discuss how permutation tests can
be constructed to test the hypotheses of differential expressions
in microarrays.

**Kadiri, Habiba **- University of Montreal

*Effective estimates of some prime counting functions and applications*

It is widely expected that every integer may be represented
as a sum of seven cubes. In 1943, Linnik proved that it was true
for sufficiently large integers. The problem of finding the size
of the smallest integer for which it is true is related to some
effective estimates on prime counting functions. I will discuss
an explicit version of Vinogradov's theorem on the sum of three
primes and how it is also related to the distribution of prime numbers.

**Kim, Hee Jung** - McMaster University

*Topological triviality of smoothly knotted surfaces in 4-manifolds*

Some generalizations of the Fintushel-Stern rim surgery are
known to produce smoothly knotted surfaces. We show that if the
fundamental groups of their complements are standard, then these
surfaces are topologically unknotted.

**Labibi, Batool** - University of Alberta

*Decentralized Stabilization of a Class of Nonlinear Interconnected
Systems*

This work considers decentralized output feedback stabilization
of a class of nonlinear interconnected systems using linear matrix
inequalities. Based on small gain theorem, sufficient condition
for closed-loop stability is derived. By solving an appropriately
defined LMI problem, a decentralized output feedback controller
is designed and an estimation for the attraction domain of the nonlinear
system is given. An application to a large scale telescope is given
to show the effectiveness of the proposed methodology.

**Masuda, Ariane **Carleton University

*Analogies between the ring of integers and the ring of polynomials
over a finite field*

In this talk we compare and contrast the ring of integers and
the ring of polynomials over a finite field. We discuss several
questions which have analogous versions in both settings**.**

** Pullenayegum, Eleanor** - University
of Waterloo

*Cost-effectiveness analysis in clinical trials and longitudinal
data: filling in some gaps*

In a country with ever-increasing health spending, studying the
cost-effectiveness analysis of medical therapies is a vital area
of health research. As health researchers designed trials to assess
cost-effectiveness and gather data, statisticians began to wonder
how to analyse this type of data: cost data has several features
that make it difficult to model using standard statistical methods.
Whilst the necessary statistical methods now exist, there are existing
statistical ideas --some very basic -- that can be used to improve
the efficiency of estimation considerably.

**Savu, Anamaria** - University of Northern
British Columbia

*Some remarks on the solid-on-solid model*

Matching priors are a natural choice in the absence of specific
prior information, since they lead to inferences equivalent to frequentist
inferences to the second order. When the model depends on a scalar
parameter, Jeffrey’s prior is the unique first order matching
prior. However, when the model depends on a vector parameter, the
matching priors (not unique) are obtained as solutions to a complicated
system of differential equations. In this talk we show the uniqueness
of a first order probability matching prior for purposes of higher
order approximate inference for parametric settings with a scalar
component of interest. We exemplify by a simulation study and a
numerical example.

CONNECTING WOMEN IN MATHEMATICS ACROSS CANADA

December 7-8, 2006