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.

  1. Graham Ellis, James Harris, and Emil Sköldberg. Polytopal resolutions for finite groups.  J. Reine Angew. Math. 598 (2006), 131-137.
  2. Marc Röder. HAPcryst package. 2007.
  3. 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.

  1. 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.
  1. K. Bauer, D. Sen, P. Zvengrowski. A Generalized Goursat Lemma, 2011. Preprint arXiv:1109.002v1
  2. S. Bouc, R. Stancu, J. Thèvenaz. Simple biset functors and double Burnside ring. Journal of Pure and Applied Algebra, 217 (2013) 546-566.
  3. 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.
  1. Diaconis, P. and Sturmfels, B. (1998). Algebraic Algorithms for sampling from Conditional Distributions. The Annals of Statistics, 26, 363-397.
  2. 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.

  1. Murray, J. D., 1989. \emph{Mathematical Biology}. Berlin: Springer.
  2. 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. 
  3. 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.
  1. 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.
  1. 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.
  2. 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
  3. (2009), no. 3, 472-484.
  4. 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
  5. (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.
  1. 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.
  2. 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.
  3. 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.

  1. 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
  2. B. Y. Chen and T. Nagano, Totally geodesic submanifolds of symmetric spaces. II, Duke Math. J. 45 (1978), 405-425.
  3. 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).
  1. Scott MacLachlan and Niall Madden. Robust solution of singularly perturbed problems using multigrid methods. Submitted for publication, August 2012.
  2. Hans-Görg Roos. A note on the conditioning of upwind schemes on Shishkin meshes. IMA J. Numer. Anal., 16(4):529--538, 1996.
  3. 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.
  1. Irizarry, Rafael A., et al. Exploration, normalization, and summaries of high density oligonucleotide array probe level data. Biostatistics 4.2 (2003): 249-264.
  2. Hoheisel, Jörg D. Microarray technology: beyond transcript profiling and genotype analysis. Nature Reviews Genetics 7.3 (2006): 200-210.
  3. 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.
  1. 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.
  1. Warwick de Launey and Dane Flannery, Algebraic design theory, Mathematical Surveys and Monographs, vol. 175, American Mathematical Society, Providence, RI, 2011.
  2. 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].
  1. W.J.Stronge, Impact Mechanics, Cambridge University Press 2000, pp: 1--3 .
  2. 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.
  3. 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.
  1. 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. 
  2. 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;
  3. 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.

  1. 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.
  2. 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.
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  2. M.Crainic, On the perturbation lemma, and deformations,  arXiv:math/0403266v1 (2004), pp 13.
  3. 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