NATIONAL UNIVERSITY OF IRELAND GALWAY
SCHOOL OF MATHEMATICS, STATISTICS AND APPLIED MATHEMATICS
Research
day 2014
Research
Presentations
Some mathematical
models for drug delivery
Martin
Meere
School of
Mathematics, Statistics and Applied Mathematics
Drug-eluting stents are now commonly used in the treatment of coronary
artery disease. These devices increase the flow of blood through
blocked arteries and provide mechanical support to the artery wall.
They also protect the artery from re-blockage due to inflammation by
releasing an anti-inflammatory drug into the surrounding tissue from a
polymer that coats the stent. However, the permanent presence of a
polymer in the body is now thought to increase the likelihood of
a dangerous blood clot forming on thestent. Consequently, a new
generation of stents are being developed that do not rely on a polymer
to release the drug.
In these polymer-free stents, the drug is either sprayed directly onto
a bare metal surface or infused in a metallic porous medium. Polymer
free stents are a relatively new technology and no mathematical models
have yet been developed to describe drug release from them. In this
talk, some preliminary ideas for the modelling of polymer free stents
are presented. The proposed models are based principally on dissolution
theory and the theory of diffusion in porous media.
Clustering
longitudinal profiles using P-splines and mixed effects models applied
to time-course
gene expression data
Emma
Holian, Norma Coffey and John Hinde
School of Mathematics, Statistics and
Applied Mathematics
Time-course microarray analyses involve measuring the expression levels
of thousands of genes repeatedly through time. Multivariate clustering
methods such as principal components analysis, k-means clustering,
finite mixture models etc.\\ have difficulties handling missing values,
require uniform sampling for all genes, fail to account for the
correlation between measurements made on the same gene or do not
facilitate the removal of noise from the measured data thus ignoring
any smoothness that may be evident in the expression profiles. This
talk proposes the use of curve-based clustering, which can handle the
latter issues. We use the linear
mixed effects model representation of penalized spline smoothing to
estimate the gene expression curves which provides a framework for
simultaneously determining a smooth estimate of the mean expression
profile in each cluster, determining estimates of the gene-specific
expression profiles within a cluster through the use of additional
random effects and clustering expression profiles using mixtures of
mixed effects models.\\
Coffey, N., J. Hinde, and E. Holian. ``Clustering longitudinal profiles
using P-splines and mixed effects models applied to time-course gene
expression data.'' Computational Statistics & Data Analysis 71
(2014): 14-29.
DNA variation in a
pathogen outbreak: past, present and predictions
Tim
Downing
School of Mathematics, Statistics and
Applied Mathematics
Mixing between genetically distinct pathogens within a population leads
to novel combinations with altered host virulence and drug resistance.
Such unique specimens represent either undiscovered lineages or
re-assortments between established groups: comparison with known DNA
patterns (haplotypes) provides a framework for determining ancestry and
predicting biological traits. Current methods of allele frequency
correlation, variant distribution modality and admixture modelling are
effective for breeding between sub-species, but are untested for
monomorphic populationswhere discriminatory mutations are rare.
Haplotype distribution, size and length provided sufficient power to
distinguish samples with just 3.4 mean pairwise SNPs/Mb in a sample of
191 Indian subcontinent clinical isolates of Leishmania donovani
sampled in 2002-11 during two drug treatment eras. Model-based
population clustering identified six genetically homogeneous
populations with little evidence of recent interbreeding. These
originated in the 1850s and showed a genetic bottleneck-recovery
signature from anti-parasite pesticide spraying campaigns ending in the
1960s. Population-free membership assignment, phylogenetic trees and
admixture statistics indicated six recent isolates were discovered
whose haplotypes were mixes of these populations, despite as few as 60
genome-wide polymorphisms differentiating the main groups. These six
hybrids were distinguishable from seven rare lineages
whose haplotype structure did not resemble any previous sample.
Predicting resistance to future second-line or combination drug
therapies using genetic data is now a tangible goal.
Categorising
properties of road systems
Jorge
Bruno, Aisling McCluskey
School of Mathematics, Statistics and
Applied Mathematics
A road system on a nonempty
set X is a family R of
nonempty subsets of X such that:
- a is in R for all a in
X,
- for all a, b in X, there is R in R
such that a, b in R.
Each road system (X, R) gives
rise to an R-relation R on X
as follows: [a,b,c]R holds
if each road R containing a and c also contains b.
We explore some properties that are characteristic of R-relations using
a categorical framework.
circular designs
balanced for neighbours at distances one and two
Rosemary
A. Bailey
University of St. Andrews, Scotland
TBA