NATIONAL UNIVERSITY OF IRELAND GALWAY
SCHOOL OF MATHEMATICS, STATISTICS AND APPLIED MATHEMATICS
Research
day 2013
Abstracts
of Posters
Genome wide DNA
methylation patterns of colonic epithelial cells
of Ulcerative Colitis patients
Alan
Barnicle
Supervisors: Laurence Egan, Cathal Seoighe
Ulcerative colitis associated cancer (UCAC) is the subtype of
colorectal cancer (CRC) that is associated with inflammatory bowel
disease (IBD). Within 30 years of disease onset, more than 20 of IBD
patients develop UCAC, and more than 50 of these patients will die from
UCAC. The strong connection between inflammation and cancer progression
has been well documented; however, an increasing body of evidence
suggests that epigenetic changes, specifically DNA methylation, may
play an important role in the pathogenesis of UCAC. Here we investigate
genome wide methylation levels of ulcerative colitis (UC) patients to
develop an integrative model for DNA methylation induced UCAC.
Pinch biopsies were acquired from recruited UC patients in University
Hospital Galway. Highly purified epithelial populations were
isolated from these biopsies and assessed by means of flow cytometry
and phase contrast microscopy. Genomic DNA was then extracted from
these cells for selective enrichment of methylated DNA through a
restriction enzyme based assay called HELP (HpaII tiny fragment
Enrichment by Ligation-mediated PCR). The HELP assay isolates sequences
neighboring sites digested by the methylation-sensitive HpaII
restriction enzyme for massive parallel sequencing. It can be used to
quantifying methylation at more than 1.8 million loci in the human
genome and allows for recognition of both CG dense and CG diminished
genomic regions (Suzuki et al 2010).
The epigenetic landscape generated from this study should provide new
molecular mechanisms and markers for ulcerative colitis associated
colon cancer and potentially reveal new strategies for the design of
inflammatory bowel disease treatments.
Supported by IRC grant
Algorithm for computing
cohomology of SL(2, Z[1/m])
Bui
Anh Tuan
Supervisors: Graham Ellis
An algorithm for computing a free ZG-resolution
for any crystallographic group G has been implemented HAP. This
algorithm applies a perturbation technique of CTC Wall to the short
exact sequence
1 --> T --> G --> P -->1 involving the finite point group P
and the free abelian translation subgroup T. More efficient algorithms
could be designed for specific classes of crystallographic groups. For
instance, Mark Röder has designed and implemented an
algorithm for arbitrary Bieberbach groups (i.e. crystallographic groups
that act fixed-point freely on Euclidean space). Röder's algorithm
uses convex hull computations to construct a fundamental domain for a
Bieberbach group. Motivated by the work of Röder, we focus
attention in this paper on those n-dimensional crystallographic groups
G that preserve some n-dimensional lattice L < Rn with the
cubical fundamental domain. We design and implement an algortihm
for producing a free ZG-resolution
of Z for such a group.
- Graham Ellis, James Harris, and Emil Sköldberg. Polytopal
resolutions for finite groups. J. Reine Angew. Math. 598 (2006),
131-137.
- Marc Röder. HAPcryst package. 2007.
- Karel Dekimpe and Nansen Petrosyan. Homology of Hantzsche-Wendt
Groups. Contemporary Mathematics, Volume 501, 2009.
Supported by School of
Mathematics,Statistics and Applied Mathematics - National University of
Ireland, Galway.
Counter-intuitive
results in acousto-elasticity
Artur L. Gower,
the
work was co-authored with: M. Destrade and R.W.Ogden (School of
Mathematics and Statistics, University of Glasgow, Scotland)
The determination of the direction of greatest tension in a deformed
solid is one of the main goals of acoustic non-destructive evaluation
because, for isotropic solids, this direction coincides with the
direction of greatest stress. Finding the direction of greatest stress
is important in geophysics, oil prospecting, structural health
monitoring, and for the non-destructive evaluation of the nonlinear
elastic constants of materials (see e.g. [R.A. Guyer and P.A. Johnson,
Nonlinear Mesoscopic Elasticity, Wiley, 2009]) .
In this poster we present results of the propagation of small-amplitude
elastic waves in the body and on the surface of a deformed solid.
We uncover examples of solids where the wave speed does not have its
greatest value along the direction of greatest stretch, and/or can be
extremal along directions which are oblique to the directions of
greatest stretch. This goes against what was commonly accepted. This
phenomena occurs because the coupling of acoustics and elasticity is a
non-linear phenomenon even at its lowest order, and it can thus
generate counter-intuitive results.
Supported by Hardiman Research
Scholarship.
Effect of degree of
Negative energy balance on hepatic miRna expression
in postpartum dairy cattle and their potential targets involved in
lipid metabolism
Attia
Fatima
Supervisors: Cathal Seoighe, Dermot Morris, Charlie Spillane
Negative energy balance is a metabolic disorder of early post -partum
dairy cattle which has pleiotropic effects on liver gene expression.
micro RNAs (miRNAs) are small non coding RNA which can regulate
gene expression at post transcription level. In this study 5 miRNAs
were up-regulated in liver tissues of dairy cattle under severe
negative energy balance two weeks postpartum. The
up-regulated miRNAs miR-31, miR-17 and miR-140 are
implicated in liver diseases. The up-regulated miRNA, miR-2885 is
cattle specific and its putative target gene FADS2 (fatty acid
desaturase 2) is 6 folds down-regulated under NEB, FADS2 is critical for
lipid biosynthesis which is very important to maintain energy
balance and normal liver function. This study will help
understand better the NEB in cattle.
- McCarthy, S., Waters, S., Kenny, D., Diskin, M., Fitzpatrick, R.,
Patton, J., Wathes, D. and Morris, D. (2010). Negative energy balance
and hepatic gene expression patterns in high-yielding dairy cows during
the early postpartum period: a global approach. Physiol Genomics.42A
(3): 188–199.
Bisets and double
Burnside algebras
Brendan
Masterson
Supervisor: Götz Pfeiffer
Let G be a finite group and $k$be a field. A (G, G)-biset is both a
left and right G-set, such that the G-actions commute. The double
Burnside ring B(G, G) is the Grothendieck ring of the category of
finite (G, G)-bisets with respect to disjoint unions and the tensor
product of bisets over G. We present recent results in the theory of
double burnside algebras, including a method for the decomposition of
kB(G, G), complete with worked example.
- K. Bauer, D. Sen, P. Zvengrowski. A Generalized Goursat Lemma,
2011. Preprint arXiv:1109.002v1
- S. Bouc, R. Stancu, J. Thèvenaz. Simple biset functors and
double Burnside ring. Journal of Pure and Applied Algebra, 217 (2013)
546-566.
- R. Boltje, S.Danz. Ghost algebras of double Burnside algebras via
Schur Functors, 2012. Preprint arXiv:1203.1346v1.
Variable Selection
Techniques for Multiply Imputed Data
Deirdre
Wall
Supervisor: John Newell
Missing data can be a serious problem, in particular in retrospective
observational studies where the percentage of subjects with complete
data can be of concern. Multiple Imputation (MI) is a popular technique
in missing data problems. MI uses models based on observed data to
replace missing values with credible values. This process is repeated a
number of times to create several imputed datasets. An approach to
model selection is to identify the final model based on the imputed
datasets. Results will be presented from a simulation study to compare
the performance of variable selection techniques in multiple imputed
data and a new method of imputation where random forests are used to
impute a single dataset.
Supported by NBCRI
Recent Developments in Algebraic
Statistics
Isaac
Zebulun Burke
Supervisor: Dr. Emil Sköldberg
Algebra has traditionally had numerous applications in statistics.
However, it is only in recent years that computational algebraic
geometry and related combinatorial techniques have been used to examine
statistical models and inference problems. Central to this advancement
is the fact that polynomials and ratios of polynomials appear
frequently in statistical methods, from model representations to
inferential procedures. Initial work in this area was concerned with
constructing algebraic algorithms for sampling from discrete
exponential families conditional on a sufficient statistic [1]. This
eventually led to the monograph Pistone et al. [2], where the term
``algebraic statistics" was officially coined. Here we present a
introduction to this rapidly expanding field from the algebraist's
perspective and consider some recent developments.
- Diaconis, P. and Sturmfels, B. (1998). Algebraic Algorithms for
sampling from Conditional Distributions. The Annals of Statistics, 26,
363-397.
- Pistone, G., Riccomagno, E. and Wynn, H. P. (2000). Algebraic
Statistics (Computational Commutative Algebra in Statistics). Chapman
and Hall CRC.
Supported by the Irish Research
Council (IRC)
Partial matrices whose
completions all have the same rank
James
McTigue
Supervisors: Dr Rachel Quinlan
A partial matrix over a field F
is a matrix whose entries are either elements of the field F or independent indeterminates. Let
A be an m × n partial matrix over a field F whose completions all have the
same rank r less or equal min(m,n). We answer the following questions:
1. What condition on the order of F
is sufficient for A to contain an r × r partial sub-matrix whose
completions are all non-singular?
2. If the order of F is not
sufficient to guarantee that A contains an r × r partial
sub-matrix whose completions are all non-singular what are the
necessary conditions on the dimension of A to ensure that it does
contain such a partial sub-matrix?
This is joint work with Dr Rachel Quinlan.
Supported by The College of Arts,
Social Sciences, and Celtic Studies, NUIG
Seasonal migration
models
John
Donohue
Supervisor: Dr Petri Piiroinen
Population models where two or more species exhibit predator-prey
relationships have long been of interest to researchers working on both
dynamical systems and ecological modelling [1]. Most of these models
have been static where the different species have been constrained to a
specific area. However, even though seasonal migration is a common
occurrence in nature [2, 3], surprisingly few attempts have been made
to model predator-prey systems that incorporate such behaviour. The
possibility for predator-prey problems that allow for one or more of
the species to undergo mass migration open up a range of new
possibilities from a dynamical point of view. Furthermore,
systems of this type can be modeled in a variety of different ways.
Here we focus on two different approaches, namely, ordinary and partial
differential equations, where the former can be seen as a compartment
model and the latter a spatial model. In both cases the inclusion of
the seasonal periodicity is key in understanding their behaviour. The
dynamics arising from the different migration models will be compared,
with particular emphasis placed on the stability of periodic solutions
and bifurcations.
- Murray, J. D., 1989. \emph{Mathematical Biology}. Berlin:
Springer.
- Egevang, C., Stenhouse, I.J., Phillips, R.A., Petersen, A., Fox,
J.W. and Silk, J.R.D., 2009. Tracking of Arctic Terns Sterna paradisaea
reveals longest animal migration. Proceedings of the National Academy
of Sciences of the United States of America, 107(5),
pp.2078-2081.
- Madsen T. and Shine R., 1996. Seasonal migration of predators and
prey - a study of pythons and rats in tropical Australia. Ecology,
77(1), pp.149-156.
Supported by the Irish Research
Council.
Topologies as Value
Quantales : the epsilon-delta obsession.
Jorge,
Bruno
Supervisors: Aisling McCluskey
We present an equivalence of categories O: T
--> Top between the
category of Value Quantales, T,
and the category of topological spaces,Top.
We also construct the value quantale equivalent of topological
products, coproducts, equalizerers, direct and inverselimits.
- R. C. Flagg, Quantales and Continuity Spaces. Algebra
Universalis, 1997.
Supported by IRCSET, Embark Initiative
A Mathematical Model
of CENP-A Loading in Mammalian Centromeres
Kevin
Doherty
Supervisors: Dr Martin Meere, Dr Petri Piiroinen
The presence of CENP-A at centromeres is vital for the proper
construction of the kintechore complex and, in turn, microtubule
binding and correct segregation of sister chromatids in mitosis. Loss
of CENP-A from centromeres results in defects in chromosome congression
to the metaphase plate and missegregation in anaphase which can result
in micronuclei [1]. A number of factors play important roles in CENP-A
association with and loading into centromeres, for example, HJURP [2]
and the Mis18 complex [3]. A mathematical model of CENP-A incorporation
in centromeres is presented that uses a dynamical systems approach. The
model
contains two compartments, one for the nucleoplasm and another for the
centromeric binding sites.
- V. Régnier, P. Vagnarelli, T. Fukagawa, T. Zerjal,
E. Burns, D. Trouche, W. Earnshaw, and W. Brown, CENP-A is required for
accurate chromosome segregation and sustained kinetochore association
of BubR1, Molecular and Cellular Biology 25 (2005), no. 10, 3967-3981.
- D.R. Foltz, L.E.T Jansen, A.O. Bailey, J.R. Yates III, E.A.
Bassett, S. Wood, B.E. Black, and D.W. Cleveland, Centromere-specific
assembly of CENP-A nucleosomes is mediated by HJURP, Cell 137
- (2009), no. 3, 472-484.
- Y. Fujita, T. Hayashi, T. Kiyomitsu, Y. Toyoda, A. Kokubu, C.
Obuse, and M. Yanagida, Priming of centromere for CENP-A recruitment by
human hMis18α, hMis18β, and M18BP1,
Developmental Cell 12
- (2007), no. 1, 17-30.
Supported by The College of Science,
National University of Ireland, Galway.
Extensive variation in
DNA diversity patterns in chromosomes of parasite samples from patients
Students
of MA216 module on Mathematical Molecular Biology II
Supervisors: Dr Tim Downing
Patterns of DNA variation can describe population history, rates of
evolution and highlight mutations associated with disease. In
populations, multiple complementary approaches can isolate mutations
with differential rates of co-inheritance and contrasting drivers of
variability. In 2002-03, 12 Leishmania donovani parasites samples were
isolated from patients in Nepal with acute disease. These strains have
a unique geographic and
genetic profile among leishmaniasis cases, being a distinct lineage all
from the uplands of Nepal (aka the “Yeti” strains). Using the DNA
sequences for each chromosome, we compared the relative variation,
recombination rates and inter-sample genetic distances. Differing
patterns of diversity were mirrored by extensive disparities in
mutations co-inheritance rates across chromosomes. Linkage between
mutations tended not to decline with distance between mutations, which
indicated clonal non-sexual reproduction. However, phylogenetic trees
were incompatible between chromosomes: each presented differing
patterns of relatedness between the 12 strains. This pattern was
symptomatic of episodic but rare outbreeding and recombination during
co-infection of multiple parasites on the background of clonality. All
research presented was performed by students taking this module.
The Pirie-Kieren
Theory: a possible framework for exploring growth of mathematical
understanding in Metric Spaces
Michelle Duane
Supervisor: Dr Aisling McCluskey
This research seeks to explore how senior Irish undergraduate
mathematics students respond to the type of learning required by Metric Spaces, a subject both
enabling and demanding advanced
mathematical thinking. It seeks to examine the development of
and facility with proof and proving in such students. Data will be
collected by means of semi-structured interviews, analysis of students
written mathematical work and
non-participant periodic observation of the classroom. There are a
number of theoretical frameworks within the field of mathematics
education that could be applied to the data collected from this study.
The Pirie-Kieren Theory is one such framework that I have chosen to
discuss here. It is a dynamical theory for the growth of mathematical
understanding that could be utilised to analyse students' understanding
of key concepts in Metric Spaces.
- Martin, L. (2008). Folding back and the dynamical growth of
mathematical understanding: Elaborating the Pirie-Kieren Theory. The
Journal of Mathematical Behavior, 27 (1), 64-85.
- Pirie, S., and Kieren, T. (1994). Growth in mathematical
understanding: How can we characterise it and how can we represent it?
Educational Studies in Mathematics, 26 (2/3), 165-190.
- Tall, D. (Ed.). (1991). Advanced Mathematical Thinking.
Dordrecht: Kluwer Academic Publishers.
Supported by the NUI, Galway Hardiman
Research Scholarship
Coxeter exponents and
flags of root systems
Mohammad Adib Makrooni
Supervisor:Dr John Burns
The exponents of a compact Lie group G (or its Weyl group W(G)) can be
variously defined in terms of its cohomology, the cohomology of its
(full) flag variety or in terms of lattice points in certain associated
rational simplices. It seems reasonable therefore (in any of the above
settings) to look for descriptions of the exponents related
geometrically to important sub-objects (polars and meridians) of
G, and this we do. We also
apply this new description to compute exponents to certain B-stable
ideals (for B a Borel subalgebra) that arise naturally in the study of
projective subvarieties of flag varieties.
- R. Bott, On Torsion in Lie Groups, Proceedings of the National
Academy of Sciences of the United States of America, Vol. 40, No. 7
(1954), pp. 586-588
- B. Y. Chen and T. Nagano, Totally geodesic submanifolds of
symmetric spaces. II, Duke Math. J. 45 (1978), 405-425.
- B. Kostant, The Principal Three-Dimensional Subgroup and the
Betti Numbers of a Complex Simple Lie Group, American Journal of
Mathematics, Vol. 81, No. 4 (Oct., 1959), pp. 973-1032
Incomplete-LU
preconditioning for a singularly perturbed problem
Nhan
Anh Thai
Supervisor: Niall Madden
I am studying the iterative solution of linear systems arising
from the finite difference discretization of singularly perturbed
two-dimensional reaction-diffusion problems on a layer adapted mesh.
Our model problem is:
-ε 2 ∆u + b(x,y)u = f(x,y), on
Ω=(0,1) 2,
and u(∂Ω)=0
(1)
Discretization of (1) for a mesh with N interval in each direction
leads to a linear system to be solved:
AU=F
(2)
where A is banded, symmetric and positive definite (N-1) 2
× (N-1) 2 matrix. These systems can be solved by
direct methods. However, the computational cost becomes prohibitively
large as the degrees of freedom grow. Also, they don't necessarily
behave well for small ε [1].
Alternatively, one can use a iterative scheme. There are many possible
schemes, but perhaps the most widely used is the method of Conjugate
Gradient (CG) [3]. However, unpreconditioned CG behaves badly since the
condition number of symmetrized problem (2) depends badly on ε [2]. To overcome this constraint, we consider
Incomplete-LU factorization preconditioning. I present some
numerical results demonstrating the suitability of this approach for
(1), and provide an outline of some of the mathematical analysis for
ILU(0).
- Scott MacLachlan and Niall Madden. Robust solution of singularly
perturbed problems using multigrid methods. Submitted for publication,
August 2012.
- Hans-Görg Roos. A note on the conditioning of upwind schemes
on Shishkin meshes. IMA J. Numer. Anal., 16(4):529--538, 1996.
- Yousef Saad. Iterative methods for sparse linear systems. Society
for Industrial and Applied Mathematics, Philadelphia, PA, second
edition, 2003.
Supported by the Irish Research
Council, Grant No. RS/2011/179
Summarising Microarray
Probes Using A Statistical Learning Approach
Paul
K. Korir
Supervisors: Prof. Cathal Seoighe, Dr. Tim Downing
Microarrays are an affordable and flexible high-throughput technology
that simultaneously measure the abundance of thousands of genes. Each
gene on a microarray is represented by tens to hundreds of probes,
which have to be summarised into a single measure. Numerous
summarisation algorithms have been developed with varying success. We
present an alternative approach to summarisation that uses statistical
learning algorithms instead of functional models. Our approach builds
gene-specific models from gold standard estimates, such as those
obtained using high-throughput sequencing (HTS) technology, then uses
the learned
models to predict the expression for a new set of probes.
We show that this strategy not only outperforms conventional
summarisation algorithms but also extends the the reach of microarrays.
Furthermore, it easily lends itself to estimating the abundance of
individual transcript isoforms. Two biological applications are also
presented that show how this technique increases statistical power in
genome-wide experiments.
- Irizarry, Rafael A., et al. Exploration, normalization, and
summaries of high density oligonucleotide array probe level data.
Biostatistics 4.2 (2003): 249-264.
- Hoheisel, Jörg D. Microarray technology: beyond transcript
profiling and genotype analysis. Nature Reviews Genetics 7.3 (2006):
200-210.
- Marioni, John C., et al. RNA-seq: an assessment of technical
reproducibility and comparison with gene expression arrays.Genome
Research 18.9 (2008): 1509-1517.
Supported by SFI.
The impact of the Aire
gene on alternative splicing
Peter
Keane
Supervisors: Cathal Seoighe, Rhodri Ceredig
The Autoimmune Regulator gene (Aire) is a transcription factor that
induces the expression of otherwise tissue specific genes in the
thymus. Mutations in this gene lead to APECED, a severe multi-organ
specific autoimmune disease. Although Aire has been shown to influence
the alternative splicing of a tissue specific gene (Zumer et al. 2011),
the global impact of Aire on alternative splicing and the degree to
which this contributes to Aire's function remains unknown. Using data
in the public domain, we present evidence for a widespread impact of
Aire on alternative splicing in the thymus.
- Zumer. K, Plemenitas. A, Saksella. K, Peterlin. B. M. (2011).
Patient mutation in AIRE disrupts P-TEFb binding and target gene
transcription. Nucleic Acids Research. 39(8), 7908-7919.
Supported by PRTLI cycle 5
Cocyclic Development
of Pairwise Combinatorial Designs
Ronan
Egan
Supervisors:Dr Dane Flannery
A design for us is a square matrix over some ring, satisfying explicit
combinatorial constraints. A PCD (pairwise
combinatorial design [1]) is a design whose rows taken pairwise
satisfy a balance condition such as orthogonality. For example,
Hadamard matrices and their generalizations are PCDs. The most
effective method known to date of generating PCDs is cocyclic development. An n ×
n { ± 1}-matrix M is cocyclic
over a group G with cocycle ψ: G × G
--> { ± 1} if M=[ψ(g,h)ψ
(gh)]g,h ϵ G for some set map φ. The cocycles from a group G to an abelian group U
form a group Z(G,U) under pointwise composition. Unfortunately
cohomological equivalence does not preserve orthogonality. We are
investigating the relatively new idea of shift representations, which are
derived from an action of G on Z(G,U) (discovered by Horadam [2]) that
preserves both cohomology and orthogonality.
- Warwick de Launey and Dane Flannery, Algebraic design theory,
Mathematical Surveys and Monographs, vol. 175, American Mathematical
Society, Providence, RI, 2011.
- K.J. Horadam, The shift action on 2-cocycles, Journal of Pure and
Applied Algebra, vol. 188, pp. 127-143, Elsevier, 2003.
Supported by an N.U.I.Galway Hardiman
Scholarship
An Energetic/Impulsive
formulation of the Impact Law
Shane
Burns
Supervisor:Dr Petri Piiroinen
Impact Mechanics is concerned
with the reaction forces and impulses which develop during a collision
and the governing dynamics which ensue [1]. We derive an impact
law for a general 2D rigid body using the Amontons-Coulomb friction law. The
law relates the tangential and normal components FT and
FN, respectively, of the reaction forces occurring at
impact using a coefficient of friction µf, which gives
the relation FT =
s µf FN
, where s is given by
the sign of the tangential velocity [1]. By integrating out the
time dependance we arrive at an Impulsive interpretation of the Amontons-Coulomb friction law [2].
This work analyses the impact law in an effort to give scientists and
engineers informative predictions on collision dynamics. The
limitations of this approach are discussed and bounds on the Impulse
ratio µ are derived and analysed. This is an extension of the
work of [3].
- W.J.Stronge, Impact Mechanics, Cambridge University Press 2000,
pp: 1--3 .
- R.M. Brach, Formulation Of Rigid Body Impact Problems Using
Generalized Coefficients, Int.J.Impact Engng Sci Vol 36, No.1,
pp.61-71, 1998.
- R.M. Brach, Friction, Restitution and Energy Loss in Planar
Collisions, J.Appl.Mech., ASME, Vol.51, 1984, pp. 164--170.
Harnessing related
species and samples data to create and optimise a draft genome sequence
for Leishmania colombiensis
Simone
Coughlan
Supervisors: Tim Downing, Cathal Seoighe
Advances in DNA sequencing technologies require genome assembly
strategies that exploit related species and sample data to develop and
improve new draft sequences. The majority of current DNA sequencing
methods create large volumes of short overlapping sequences: for de
novo assembly, these require either long DNA sequences, or guidance
(contiguation) using related species information. Contiguation uses
related genomes to align, order and orient genome assemblies in
development: here we apply this approach to a paired-end short read
library to create a draft genome sequence for Leishmania colombiensis.
Initial de novo
assemblies and sequence alignments with other Leishmania indicated that
this new species was genetically distinct, and was approximately
equidistant from L. tarauntolae and the L. braziliensis complex. The
Leishmania colombiensis genome sequence was sampled from a dog in
Colombia (MCAN/CO/1986/CL223) and was improved with a sample from the
same species (MCAN/CO/1985/CL085). We improved these assemblies by
correcting miscalled bases, closing gaps and clarifying repetitive
regions by examining the differences during re-mapping of sample DNA
sequences to the reference genome sequences. Using information from
multiple subspecies identifies chromosomal differences unique to L.
colombiensis that would have been incorrectly aligned data from asingle
sample alone. This efficient scheme produces draft genome sequences
that reflect more accurately intra-species variation and also allows
the improved comparison of nucleotide and structural diversity.
Discovering the genetic basis for phenotypic variability is crucial for
tackling the acute global disease burden caused by leishmaniasis.
Genomics of the human
nucleolar organizer region
Sofia
Barreira
Supervisors: Brian McStay, Cathal Seoighe
Nucleolar Organiser Regions, NORs, comprised of tandem arrays of
ribosomal DNA and responsible for the formation of a major functional
domain of the nucleus dedicated to ribosome biogenesis, the nucleolus,
are positioned on the short arms of the five human acrocentric
chromosomes (13, 14, 15, 21 and 22). These regions and those adjacent
to the NORs are missing from the current human genome assembly. The
identification and characterisation of these sequences is of critical
importance, as nucleoli have a central role in growth-regulation and a
long-established connection to tumorigenesis, and more importantly,
ribosomes serve as the primary site of biological protein synthesis. My
work focuses in the organisation of rDNA repeats, in extending and
characterising the sequences on the distal side (DJ) of the NORs and
establishing
the organisation of DJ chromatin.
- McStay, B., and Grummt, I. (2008). The Epigenetics of rRNA Genes:
From Molecular to Chromosome Biology. Annual Review of Cell and
Developmental Biology 24, 131157.
- Data from the ENCODE Project: Rosenbloom KR, Sloan CA, Malladi
VS, Dreszer TR, Learned K, Kirkup VM, Wong MC, Maddren M, Fang R,
Heitner SG, Lee BT, Barber GP, Harte RA, Diekhans M, Long JC, Wilder
SP, Zweig AS, Karolchik D, Kuhn RM, Haussler D, Kent WJ. ENCODE Data in
the UCSC Genome Browser: year 5 update. Nucleic Acids Res. 2012;
- McCord RP, Nazario-Toole A, Zhang H, Chines PS et al. Correlated
alterations in genome organization, histone methylation, and DNA-lamin
A/C interactions in Hutchinson-Gilford progeria syndrome. Genome Res
2013 Feb; 23(2):260-9.
Supported by IRC
Multiscale Sparse Grid
Methods for Singularly Perturbed Reaction-Diffusion Problems
Stephen
Russell
Supervisors: Dr. Niall Madden
Standard finite element methods for partial differential equations,
such as the Galerkin finite element method, are often impractical
for high-dimensional problems: for fixed accuracy, the computational
complexity grows exponentially with the dimension of the problem.
Sparse grid methods were designed to overcome this
difficulty; even for two-dimensional singularly perturbed problems,
research has shown they can match the accuracy of standard FEMs but are
much more efficient.
The ``classic'' sparse grid methods are classified as multiscale,
whereas recent studies [1,2] use simpler, but still effective,
two-scale methods. The focus in this poster will be on the more
sophisticated multiscale approach. The main ingredient in
designing and analysing such methods is the construction of a
special interpolation operator.
For Poisson's equation, we present a new, simple proof of a standard
result: that the multiscale finite element method has the same
order of accuracy as the standard Galerkin method but with
significantly lower computational cost. We conclude with
numerical results indicating that the sparse-grid method achieves the
same accuracy as the full Galerkin method, and
demonstrating the savings in computational effort.
- Franz, S., Liu, F., Roos, H.-G., Stynes, M., and Zhou, A. (2009).
The combination technique for a two-dimensional convection-diffusion
problem with exponential layers. \emph{Appl. Math.},
54(3):203--223.
- Liu, F., Madden, N., Stynes, M., and Zhou, A. (2009). A two-scale
sparse grid method for a singularly perturbed reaction-diffusion
problem in two dimensions. \emph{IMA J. Numer. Anal.}, 29(4):986--1007.
Supported by College of Science,
National University of Ireland, Galway
Integrative analysis
of gene expression and half-life data reveals trans-acting genetic variants that
affect RNA stability in human populations
Thong
T. Nguyen
Supervisors: Andrew Flaus, Cathal Seoighe
Genetic variation in gene expression makes an important contribution to
phenotypic variation and susceptibility to disease. Recently, a subset
of \emph{cis}-acting expression quantitative loci (eQTLs) has been
found to result from polymorphisms that affect RNA stability.
Here we carried out a search for trans-acting
variants that influence RNA stability. We first demonstrate that
differences in the activity of trans-acting
factors that stabilize RNA can be detected by comparing the expression
levels of long-lived (stable) and short-lived (unstable) genes in
high-throughput gene expression experiments. Using gene expression
microarray data generated from eight HapMap3 populations, we calculated
the relative expression ranks of long-lived RNAs versus short-lived
RNAs in each sample. Treating this as a quantitative trait, we applied
genome-wide association and identified a single nucleotide polymorphism
(SNP), rs6137010, on chromosome 20p13 with which it is strongly
associated in two Asian populations (p = 4 × 10-10 in
CHB – Han Chinese from Beijing; p = 1 × 10-4 in JPT –
Japanese from Tokyo). This SNP is a cis-eQTL for
SNRPB in CHB and JPT but not in other six HapMap3 populations. SNRPB is
a core component of the spliceosome, and has previously been shown to
affect the expression of many RNA processing factors.
We propose that a cis-eQTL of
SNRPB is directly responsible for inter-individual variation in
relative expression of long-lived versus short-lived genes in Asian
populations. In support of this hypothesis, knockdown of SNRPB results
in a significant reduction in the relative expression of long-lived
versus short-lived genes. Samples with higher relative expression of
long lived genes also had higher relative expression of coding
compared to non-coding RNA and of RNA from housekeeping compared to
non-housekeeping genes, due to the lower decay rates of coding RNAs,
particularly those that perform housekeeping functions, compared to
non-coding RNAs.
Supported by IRC
Higher Genus Aspects
of Vertex Operator Algebras
Thomas
Gilroy
Supervisors: Michael Tuite
This year I have been working towards finalising the recursion theory
for the genus 2 correlation functions for Vertex Operator Algebras. The
approach has been to build genus 2 correlation functions from genus 1
functions and sewing procedures on tori and then using Zhu's recursion
formulae for genus 1 functions on each of the sewn tori. Complete
formal recursion formulae for the general quasiprimary recursion of
genus 2 n-point correlation functions have been found. These formulae
allow for explicit calculation of genus 2 Ward identities for n primary
vectors and Virasoro n-point correlation functions. The convergence of
these formulae is currently being studied using geometric methods and
the connection between the algebraic and geometric aspects of the
recursion theory are being explored.
Yongchang Zhu, \textit{Vertex Operator Algebras, Elliptic Functions,
and Modular Forms,} Ph.D thesis, Yale University (1990), appeared as:
Modular Invariance of Characters of Vertex Operator Algebras
J.Amer.Maths.Soc 9 (1996).
Geoffrey Mason and Michael P.Tuite, On Genus Two Riemann Surfaces
Formed from Sewn Tori, Commun.Math.Phys. 270 (2007), 587--634.
Geoffrey Mason and Michael P.Tuite, Free Bosonic Vertex Operator
Algebras on Genus Two Riemann Surfaces I, Commun.Math.Phys. 300 (2010),
673--713.
Supported by the Irish Research
Council
Computational homology
of n-types
Van
Luyen Le
Supervisors: Graham Ellis
Let G* be a simplicial group. By treating each group Gi
as a category with one object and constructing the nerve NGi one
obtains a bisimplicial set N G* .
The diagonal
∆NG* =
{( NGi)i}i≥ 0 is a simplicial set whose geometric
realization is a CW-space BG*. The condition on the Moore
complex of G* is sufficient to ensure that BG* is
an n-type. The functor B induces an
equivalence of categories
Ho(Simplicial groups with Moore
complex trivial in degrees ≥ n)
-->Ho(n-types)
where Ho(C) denotes the category obtained from a category C by
localizing with respect to those maps in C, termed quasi-isomorphisms, that induce
isomorphisms on homotopy groups.
We define the integral homology of a simplicial group G* to
be
H_i(G*, Z) = Hi(B(G*),
Z) , i ≥ 0.
In this report, we describe an algorithm for computing the integral
homology of a simplicial group and illustrate an implementation on
simplicial groups arising as the Eilenberg-Mac Lane space and the nerve
of a cat1 group.
- G. Ellis, Homology of 2-types, J. London Math. Soc.
(2) 46 (1992), no. 1, 1--27.
- M.Crainic, On the perturbation lemma, and deformations,
arXiv:math/0403266v1 (2004), pp 13.
- G. Ellis and L.V. Luyen, Computational homology of n-types, J.
Symbolic Computation 47(11): 1309-1317 (2012).
Supported by the NUI Galway, College
of Science, PhD fellowship