school of mathematics, statistics and applied mathematics...

School of Mathematics, Statistics and Applied Mathematics

Seventh Annual Research Day21 April 2016

Programme

Lectures take place in AC201Co�ee, lunch, posters and reception take place in the Orbsen Building Atrium

9.15-9.30 Dr Ray RyanWelcome by the Head of School

9.30-9.45 Prof Lokesh JoshiWelcome by the Vice-President for Research

9.45-10.30 Prof Werner Nahm FRS (Dublin IAS)Title: Quantum fields and automorphic formsAbstract: Quantum fields are among the most essential tools for modern physics, but havenot made it into the toolkit of mathematicians yet. The talk will show how mathematicianscan handle them. As an example the construction of automorphic forms for the mappingclass group of Riemann surfaces will be described, starting with tori and modular forms.

10.30-11.00 Co�ee (Orbsen Building)11.00-11.30 Dr Marianne Leitner (NUIG)

Title: Graphene and GrothendieckAbstract: The quantum Hall e�ect is one of the most spectacular features of solid statephysics. It has a nice description in terms of Chern classes and the slope of vector bundles, adominant theme of 20th century mathematics. Graphene displays a peculiar quantum Halle�ect which seems to demand new mathematical structures.

11.30-12.00 Dr Jim Cruickshank (NUIG)Title: Geometric Rigidity TheoryAbstract: Consider a collection of objects that are joined together by hinges. Is theresulting structure rigid? This is the basic question at the heart of geometric rigidity theory.There is a growing literature that considers various types of objects, hinges and notions ofrigidity. The theory draws on real algebraic geometry, graph theory, matroid theory andlinear algebra. It is also notable for its diverse domains of application - from protein flexibilityto structural engineering to modern art. I will present a brief survey of some of the highlightsof the mathematical theory and mention some problems that remain open.

(continued overleaf)

12.00-12.30 Cara Dooley (NUIG)Title: Analysing Observational StudiesAbstract: Randomised control trials, where the experimenter allocates eachindividual at random to the treatment or control group, are considered thegold-standard for design of studies interested in estimating treatment e�ects.However, there are many situations where we cannot allocate treatment at ran-dom, for example, for ethical or cost reasons. In these situations we carry outan observational study. To properly analyse an observational study, thoughtneeds to be given to both the design and analysis of the data. Using tools in-cluding propensity scores and matching we can create a quasi-randomised trialand remove bias from the estimate of the treatment e�ect.

12.30-14.00 Lunch14.00-14.45 Prof Giuseppe Saccomandi (Universita di Perugia & NUIG)

Title: On the Equations Governing Nonlinear Symmetric Kirchho�’s ElasticRodsAbstract: A systematic study of the equations governing nonlinear geometricKirchho�’s Elastic Rods is provided. We discuss the integrability of the generalcase and we investigate some special solutions. In particular we characteriseall the possible solutions that are Lancret’s helices.

14.45-15.30 Research blitz (Organizer: Dr Rachel Quinlan)Short research talks by:

• Michel Destrade, Oblique Wrinkles

• Ronan Egan, A Brief Introduction to Error-Correcting Codes

• Olga O’Mahony, Minimal Graphs of Exponent 2

• James O’Shea, Homogeneous Polynomials of Degree 2

• Gotz Pfei�er, The Sections Lattice of the Klein 4-Group

• James Ward, A Lowbrow Limit

• Giuseppe Zurlo, Designing the Stress

15.30-17.00 Poster session (Orbsen Building)16:00-17.00 Reception & poster prizes (Orbsen Building)

Research Day 2016: Introduction 1

1 Introduction

Welcome to the annual Research Day of the School of Mathematics, Statistics and Applied Mathematics. Weare delighted to welcome as our guest speakers this year Professor Giuseppe Saccomandi from Universita dePerugia (who is also an Adjunct Professor in the School) and Professor Werner Nahm FRS, from the DublinInstitute for Advanced Studies.

The research activity in the School is driven by our three research clusters:

• The De Brun Centre for Mathematics supports mathematical research across a spectrum of areas,including Algebra, Analysis, Geometry, Topology and Mathematics Education.

• The Biostatistics/Bioinformatics Cluster covers the areas of Biostatistics and Bioinformatics and isengaged in collaborative work with researchers in Genomics and other areas, and with clinicians, throughthe Clinical Research Facility (CRF).

• The Stokes Applied Mathematics Cluster applies advanced mathematical skills to the modellingof computational, physical and biological phenomena, with the aim of fostering interdisciplinary researchacross the NUI Galway campus and beyond.

Some highlights from the year:

• We were delighted to welcome two new postdoctoral research fellows: Idemauro Rodrigues de Lara (work-ing with John Hinde) and Arkady Zgonnikov (working with Petri Piiroinen, and with Denis O’Hora inPsychology).

• We have been very fortunate in continuing to attract high quality PhD students and 2015 was no excep-tion, with nine new research students joining us. The School won four IRC Postgraduate Scholarships,surpassing all other schools. Our vibrant graduate school includes students from as far afield as Iran,China, Vietnam, Argentina, Libya, Iraq and Brazil along with students from all parts of Ireland.

• We welcomed four new members to the School: Pilib O Broin (Bioinformatics), Cara Dooley (Statistics),Marianne Leitner (Mathematics) and James O’Shea (Mathematics).

• Two new researchers joined the School as adjunct members: Giuseppe Saccomandi from Universita dePerugia (Adjunct Professor in Applied Mathematics) and Alexander Rahm from Universite de Luxembourg(Adjunct Lecturer in Mathematics).

• We were placed third in the whole of Ireland in the QS Subject Rankings.

• The School hosted four conferences:

– The 30th Summer Conference on Topology and Its Applications, funded by SFI.– The Workshop on Vertex Operator Algebras, with funding from SFI and IRC.– Groups in Galway, supported by the Irish Mathematical Society. This renowned conference has been

running annually since 1978.– The second annual NUI Galway SIAM Student Chapter Conference.

• Members of the School published over 100 papers and gave over 50 invited lectures at internationalinstitutions and conferences.

Ray Ryan,Head of School

Research Day 2016: Posters 2

2 Poster Session

Mapper Algorithm and GroupoidMethods for Data Analysis

Nisreen AlokbiSupervisors: Graham Ellis

Topological methods are powerful tools for the analy-sis of high-dimensional data sets. One of these meth-ods is the Mapper algorithm which can be used toreduce high dimensional cloud data to a simplicialcomplex. The fundamental groupoid of the simplicialcomplex should enable one to access subtle homotopi-cal invariants of cellular spaces arising in applicationof topology.The aim of the project is to design and implement al-gorithms that input large finite sets S of experimentaldata from an unknown manifold M and, using un-supervised learning, attempt to return homotopicalinvariants of M based on the fundamental groupoid.

[1] G. Singh, F. Mmoli, G. Carlsson. TopologicalMethods for the Analysis of High DimensionalData Sets and 3D Object Recognition. Euro-graphics Symposium on Point-Based Graphics,pp. 91-100, 2007.

[2] P. Higgins. Presentations of groupoids, with ap-plications to groups. Cambridge PhilosophicalSociety, Mathematical Proceedings of the Cam-bridge Philosophical Society Volume 60, Issue01, 7-20, 1994.

[3] R. Brown. Topology and groupoids. Printed byBooksurge LLC, Charleston, S. Carolina, thirdedition, 2006.

Cohomology Operations Of FiniteGroups

Daher Al BaydliSupervisors: Prof. Graham Ellis, Dr.Emil

Skoeldberg

The main goal of the project is to develop algorithmsand software that can be used by mathematicians whowish to investigate the standard cohomology opera-tions (cup products, Bockstein operation, Steenrodsquares, Stiefel-Whitney classes of a real representa-tion, Chern classes of a complex representation,...) inthe cohomology groups.

[1] Hatcher, Allen. Algebraic topology, CambridgeUniversity Press. New York, NY, USA, 2010.

[2] Graham, Ellis. An introductionto Computational Homotopy, Na-tional University of Ireland, Galway.(http://hamilton.nuigalway.ie/, 2015

[3] Brown, Kenneth S. Cohomology ofGroups,Springer,1994.

Robust Solution of a Fourth-orderSingularly Perturbed Di�erential

Equation

Faiza AlssaediSupervisor: Niall Madden

We consider the numerical solution of a singularlyperturbed fourth-order di�erential equation by a fi-nite di�erence method. Our study is motivation by aproblem that arises in the study of wave-current in-teractions [2]. The di�erential equation in question,a variant on the Orr-Sommerfeld equation of hydro-dynamic stability (see, e.g., [1]) is a complex-valued,parameterised problem, with mixed boundary con-ditions. Moreover, the solution and its derivativespossess boundary layers.The goal of this presentation is to show that classicalmethods are not suitable for solving this problem, andto outline the basis for a successful strategy basedon the application of a finite di�erence scheme on aspecially designed non-uniform mesh [3].

References

[1] P. G. Drazin and W. H. Reid. Hydrodynamic sta-bility. Cambridge University Press, 2nd edition,2004.

[2] N. Madden, M. Stynes, and G.P. Thomas. Onthe application of robust numerical methods toa complete-flow wave-current model. In Proc.BAIL, Toulouse, 2004.

[3] J. J. H. Miller, E. O’Riordan, and G. I. Shishkin.Fitted numerical methods for singular perturba-tion problems. World Scientific Publishing Co.Pte. Ltd., Hackensack, NJ, revised edition, 2012.

The universal Grobner basis of abinomial edge ideal

Isaac BurkeSupervisor: Dr Emil Skoldberg


We describe the universal Grobner basis of a bino-mial edge ideal. We conjecture a similar result for aparity binomial edge ideal and prove this conjecturefor the case when the underlying graph is the com-plete graph. The statistical background to this re-search problem is briefly explained and we also men-tion possibilities for further work. This is joint workwith Mourtadha Badiane and Emil Skoldberg.

[1] Jurgen Herzog, Takayuki Hibi, Freyja Hreins-dottir, and Thomas Kahle, Binomial edge idealsand conditional independence statements, Ad-vances in Applied Mathematics 45 (2010), no.3, 317â��333.

[2] Thomas Kahle, Camilo Sarmiento, and To-bias Windisch, Parity binomial edge ideals, ap-peared online, Journal of Algebraic Combina-torics (2015), 1â��19.

[3] Mourtadha Badiane, Isaac Burke, and EmilSkoldberg, The universal Grobner basis of a bi-nomial edge ideal, arXiv:1601.04575, submitted.

Supported by the Irish Research Council and the NUI GalwayHardiman Scholarship Scheme.

Consensus of dynamic multi-agentsystems

Richard BurkeSupervisor: Petri T. Piiroinen

My research project is a study of dynamic multi-agentsystems in the context of evolving networks. Decen-tralised adaptive controls are utilised to feed informa-tion about the respecive agents’ states and commu-nication lines between them to drive the larger groupfrom initial configurations of disarray toward moredesirable states of order. In particular we wish to ef-fect a consensus in the network and investigate quali-tative approximations of the consensus dynamics thatreduce the order of our systems but track essentialfeatures such as the speed and profile of the largersystem’s convergence.

[1] Y. Cao, W. Yu, w. Ren and G. Chen, “Anoverview of recent progress in the study ofdistributed multi-agent coordination”, IEEETransactions on industrial informatics, vol. 9,no. 1 (2013) pp. 427�438.

[2] R. Olfati-Saber and R. M. Murray, “Consensusproblems in networks of agents with switchingtopology and time-delays”, IEEE Transactionson automatic control, vol. 49, no. 9 (2004)pp. 1520-1533.

[3] J. Yau, Z.H. Guan and D.J. Hill, “Passivity-based control and synchronization of generalcomplex dynamical networks”, Automatica,vol.45, no. 9 (2009) pp. 2107-2113.

Genome assembly and characterisationof Leishmania species

Simone CoughlanSupervisors: Tim Downing, Cathal Seoighe

E�ective molecular tools for monitoring the emer-gence of novel pathogens in domestic and peridomes-tic reservoir hosts are urgently required. Taxonomi-cally classifying unknown samples of ambiguous ori-gin and identifying optimal protocols for their genomeassembly using short-read data is required for com-parison with known species. DNA was sampled fromtwo Colombian dogs with leishmaniasis and from anEthiopian rodent and sequenced. Chromosome-levelsca�olding and annotation was achieved through de-novo assembly of the genome from paired-end Illu-mina Hiseq libraries coupled with iterative optimisa-tion and correction procedures. Phylogenetic mark-ers were extracted from the genomes and comparedwith markers from a panel of known Leishmaniaspecies, identifying two of them as members of the L.braziliensis complex: L. nai� and L. guyanensis andthe other as L. adleri, a member of the Sauroleishma-nia subgenus. All steps were tested and augmentedusing the positive control of another Leishmania ref-erence sequence (L. braziliensis [1] ) and it’s shortread data. This ensured the final draft genomes hadcontiguity comparable with other high-quality pub-lished genomes. Short read coverage and allelic di-versity determined variation across four levels in thehigh quality draft genomes: ploidy, whole chromo-some copy number, structural changes and SNPs. L.nai�, L. guyanensis and L. adleri were diploid butaneuploidy, a rudimentary stress response also seen insamples from human hosts, was observed in all threespecies, illustrating the lack of di�erentiation betweenparasites infecting humans and other animals, whichis a crucial factor for disease eradication programmes.

1 Rogers, M. B., Hilley, J. D., Dickens, N. J.,Wilkes, J., Bates, P. a, Depledge, D. P., â�ÍMottram, J. C. (2011). Chromosome and genecopy number variation allow major structuralchange between species and strains of Leish-mania. Genome Research, 21(12), 2129â��42.doi:10.1101/gr.122945.111

Supported by NUIG College of Science funding


Lida FallahSupervisors: Prof. John Hinde, Dr. Haixuan Yang

Time to event, or survival, data is common in the bi-ological and medical sciences. Here, we consider theanalysis of time to event data from two populationsundergoing life-testing, mainly under a joint Type-IIcensoring scheme for heterogeneous situations, con-taining susceptible and non-susceptible items to fail-ure. We consider a mixture model formulation andmaximum likelihood estimation using the EM algo-rithm and conduct a simulation to study the e�ect ofthe form of censoring scheme on parameter estima-tion and study duration.

[1] Kuo, L. and Peng, F. (2000). A mixture-modelapproach to the analysis of survival data. Gen-eralized Linear Models: A Bayesian Perspec-tive, (Eds. D. K. Dey, S. K. Ghosh and B. K.Mallick), 255 – 267. New York: Marcel Dekker.

[2] Rasouli, A. and Balakrishnan, N. (2010). Exactlikelihood inference for two exponential popu-lations under joint progressive Type-II censor-ing. Communications in Statistics- Theory andMethods, 39, pp. 2172 – 2191.

Supported by the Irish Research Council.

Mathematical Modelling ofNanoparticle Endocytosis

Paul GreaneySupervisors: Martin Meere, Giuseppe Zurlo, Yury

Rochev

Nanoparticles have been the subject of much recentresearch due to their wide-ranging potential applica-tions in areas such as high-resolution cellular imaging,drug delivery, and tumour targeting. In general, theuptake of such particles by cells occurs via endocy-tosis. The material to be taken up is surrounded bya portion of the cell membrane, forming an invagina-tion and eventually pinching o� to form an endocyticvesicle. In animal cells, receptor-mediated endocyto-sis is the mechanism which facilitates the uptake ofmacromolecules via clathrin-coated pits and vesicles.Macromolecules bind to transmembrane receptor pro-teins, which span from the exterior to the interior ofthe cell membrane.The vast majority of biomembrane modelling is basedon the model proposed by Helfrich for the free energy

W per unit area of a membrane, given by

W = kc

2 (2H ≠ c0)2 + kK,

where c0 is the spontaneous curvature, H and K arethe mean and Gaussian curvatures, respectively, andk, kc are the bending rigidities. While there are manyforces involved in the endocytosis process, includ-ing electrostatic, van der Waals, hydrophobic forces,and receptor-ligand binding, these may be approxi-mated as a single adhesion force which drives endo-cytosis. Mathematical modelling provides a rationalframework for the optimisation of this process. Wemodel this situation by assuming negligible tensionand spontaneous curvature, and taking the total en-ergy to be the sum of the bending energy Ebe of themembrane plus the adhesion energy Ead of the par-ticles, where the bending energy is calculated as theintegral

Ebe = 2kc

⁄H2dA

over the area A of the membrane. For a particlelengthscale of tens of nanometers, the adhesion poten-tial is significant in the uptake process, and is takento be a Morse potential with characteristic potentialdepth U , given by

V (d) = U(e≠2d/fl ≠2e≠d/fl),

where d is the distance of the particle from the mem-brane and fl is the range of the adhesion poten-tial. The adhesion energy is then given by Ead =s

V (d) dA, which can easily be extended for a sys-tem of multiple particles.

[1] W. Helfrich. Elastic Properties of Lipid Bi-layers: Theory and Possible Experiments, Z.Naturforsch. C, 1973, 28 (11-12), 693-703.

[2] S. Zhang, H. Gao, and G. Bao, Physical Prin-ciples of Nanoparticle Endocytosis, ACS Nano,2015, 9 (9), 8655-8671.

[3] M. Raatz, R. Lipowsky, and T. R. Weikl, Coop-erative wrapping of nanoparticles by membranetubes, Soft Matter, 2014, 10, 3570-3577.

Supported by the College of Science, NUI Galway

Maximum rank of completions ofentry pattern matrices

Ha Van HieuSupervisors: Dr. Rachel Quinlan


Given a set S = {x1,x2, · · · ,xk}, we denote by Mn(S),or Mn(x1,x2, · · · ,xk) the set of n◊n matrices whoseentries are from S. The following definition appearsin [?].Definition 1. Let x1,x2, · · · ,xk be distinct indeter-minates. We call a matrix in Mn(x1,x2, · · · ,xk) anentry pattern matrix.Thus an entry pattern is a matrix whose entries areindeterminates some of which may be equal. The pat-tern class of an entry pattern matrix A, denoted byCF(A), is the set of the matrices obtained by specify-ing the values of the indeterminates of A by elementsin some field F. Each element in CF(A) is called aF-completion of A.Definition 2. The maximum F-rank of A is the max-imum rank of F-completions of A. The generic rankof A is the rank of A when considered as a matrix inMn(F), where F is the field of rational functions inthe indeterminates that appear in A over F.

The maximum F-rank cannot exceed the generic rank, and these are equal if the field F is big enoughor the number of indeterminates is smaller than 3.This poster will present some precise conditions un-der which the maximum F-rank and the generic rankcoincide, and some constructions of examples over fi-nite fields in which they di�er.

[1] Z. Huang and X.Zhan, Nonsymmetric normalentry patterns with the maximum number ofdistinct indeterminates, Linear Algebra and itsApplications 485 (2015), 359-371.

Dynamic Nomograms

Amirhossein JalaliSupervisors: Alberto Alvarez-Iglesias, John Hinde

and John Newell

In this poster I will introduce my ’DynNom’ packagein R which makes it possible to present the results ofstatistical models as a dynamic nomogram that canbe interacted with in a web browser. Dynamic nomo-gram is a translational tool for the interpretabilityit adds to a statistical model. It aims to facilitatesthe integration of Biostatistics within clinical researchand enhance communication of research findings in anaccurate and accessible manner to diverse audiences(e.g. policy makers, patients and the media). Thepackage allows an investigation into the results of theproposed model, the relative importance of each ex-planatory variable (e.g. modifiable risk factors) andan assessment of model assumptions through accom-panying model diagnostics.

[1] Banks, J. (2006) Nomograms. Encyclopedia ofStatistical Sciences. 8.

[2] Jalali, A. et al. (2015) DynNom: DynamicNomograms for Linear, Generalized Linear andProportional Hazard Models. R package ver-sion 2.0.

[3] Newell, J. Hinde, J. (2014) Translational Statis-tics and Dynamic Nomograms. Proceedings ofthe Conference on Applied Statistics in Ireland(CASI).

Penalized regression procedures withmultiply imputed data

Olga KalininaSupervisors: Dr. Emma Holia and Dr. John

Newell

Prognostic models play an important role in medicaldecision making process. Missing predictors and cen-sored responses are common problems within prog-nostic modelling studies. Simple methods, such ascomplete cases analysis, are commonly used as thedefault procedure in many statistical software pack-ages. Several studies have shown that such approachloses e�ciency, and may lead to biased estimates ifthere is a relationship between missing values and theresponse. Multiple imputation is an attractive ap-proach, which replaces each missing value in predic-tor by M credible values estimated from the observeddata. Then M imputed data sets are analysed sep-arately and the parameters estimates and their stan-dard errors combined using ’Rubin’s Rule’. However,it is still unclear how to conduct variable selectionover multiply imputed data sets under the frameworkof penalized regressions. Several methods have beenproposed and used in the literature. Wood(2008) per-formed classical backward stepwise selection methodwhere i) at each step, the inclusion and exclusion ofthe variable is based on combined overall estimateswith standard errors using Rubin’s Rule, and ii) astacking method is used where the multiply imputeddata sets into one using a weighting scheme to ac-count for the fraction of missing data in each explana-tory variable. Chen(2013) and Wan(2015) proposedmethods combining multiple imputation and penal-ized regressions. Chen(2013) treated estimates fromthe same variable across all imputed data sets as agroup, and applied the group lasso penalty to yielda consistent variable selection, while Wan(2015) pro-posed weighted elastic net method to the stacking


method after multiple imputation with a weight ac-counting for the proportion of the observed informa-tion for each subject. Penalized regression techniqueslike lasso, elastic net and group lasso achieve parsi-mony as they shrink some regression coe�cients tozero. However, it may lead to inconsistent variableselection if they are applied directly to the multiplyimputed data sets.

[1] Chen Q, Wang S (2013). Variable selectionfor multiply-imputed data with application todioxin exposure study. J Stat Comput Simulat2015, 85(9), pp. 1902 – 1916.

[2] Wan Y, Datta S, Conklin DJ, Kong M (2015).Variable selection models based on multiple im-putation with an application for predicting me-dian e�ective dose and maximum e�ect. StatMed 2008, 27, pp. 3227 – 3246.

[3] Wood AM, White IR, Royston (2008). Howshould variable selection be performed withmultiply imputed data? Stat Med 2008, 27, pp.3227 – 3246.

Gent models for the inflation ofspherical balloons

Robert ManganSupervisor: Michel Destrade

We revisit an iconic deformation of nonlinear elastic-ity: the inflation of a rubber spherical thin shell. Wefind the link between the exact solution of nonlin-ear elasticity and the membrane and Young-Laplacetheories often used a priori in the literature. In par-ticular, by expanding to first order in the thicknessparameter, we recover the classical relation T = Pr/2,where T is the wall tension, P is the internal pressureand r is the radius of the sphere.We use the 3-parameter Mooney and Gent-Gent phe-nomenological models to explain the stretch-straincurve of a typical inflation, as these two models covera wide spectrum of known models for rubber, in-cluding the Varga, Mooney-Rivlin, one-term Ogden,Gent-Thomas and Gent models. We find that thebasic physics of inflation exclude the Varga, one-termOgden and Gent-Thomas models. We compare theperformance of both models on fitting the data forexperiments on rubber balloons and animal bladder.We conclude that the Gent-Gent model is the mostaccurate and versatile model on o�er for the mod-elling of rubber.

[1] R. Mangan, M. Destrade, Gent models for theinflation of spherical balloons, InternationalJournal of Non-Linear Mechanics, 68 (2015),52–58.

[2] W.A. Osborne, The elasticity of rubber bal-loons and hollow viscera, Proceedings of theRoyal Society of London, Series B, 81 (1909)485–499.

Compact Homogeneous Spaces withPositive Euler Characteristic and their

‘Strange Formulae’

Mohammad Adib MakrooniSupervisor: John Burns

This poster presents my collaborative publicationwith Dr. J. Burns [1]. In this research work, we provea generalisation of the ”Strange formula” of Freuden-thal and de-Vries for compact homogeneous spaceswith positive Euler characteristic. We also apply theresults to computing a topological invariant used tostudy hyper-Kahler structures. We also make use ofa sharpened version of Borel and de Siebenthal Theo-rem in [2], where the the isotropy representation of Kon the tangent space to G/K is described, in whichK denotes a maximal connected subgroup of maximalrank in a compact simple Lie group G.

[1] J. M. Burns and M. A. Makrooni, Compact Ho-mogeneous Spaces with Positive Euler Charac-teristic and their ‘Strange Formulae’, Quart. J.Math. 66 (2015), 507-516.

[2] J.A. Wolf. Spaces of Constant Curvature,McGraw-Hill. New York, 1967.

Deconvolution of genome-wideepigenetic data from simulated

heterogeneous samples

Barbara Zambiasi MartinelliSupervisors: Cathal Seoighe and Pilib Ã� Broin

Biological samples are typically heterogeneous and inmany cases it is informative to determine di�erencesin the relative abundances of distinct cell types be-tween groups of biological samples that display fea-tures of biological or biomedical interest. The state ofmethylation in genomic sites characteristic of a spe-cific cell type could be exploited to obtain highly ac-curate estimates of cell type proportions across sam-ples by using statistical or mathematical methods.


Making use of the Expectation-Maximization (EM)algorithm, and following the hypothesis that interme-diate methylation/low entropy (IM/LE) loci are likelyto be highly informative for identifying and quan-tifying cell subtypes present in a meta-epigenome,deconvolution of genome-wide epigenetic data canbe performed. In this work, whole genome bisul-phite sequencing (WGBS) of two cell lines, IMR90and NA12878, was used in the mixture simulation.Firstly, all the CpGs of chromosome 21, the sequencereads and their respective methylation status were re-trieved. Simulated heterogeneous samples were gen-erated by computationally mixing the methylationdata from the two cell lines in varying proportions.Percentage of methylation in each CpG of the mix-ture was calculated and, using a sliding window ap-proach, genome regions with IM were identified. Forthis step, the parameters were settled as: a) windowsize of 10 CpG sites, b) window shift of 1 site, c)methylation values between 30

Propensity Score Matching Methodsfor Observational Studies

Michael Mc CagueSupervisors: Dr. John Newell

Propensity Score Matching is an increasingly popularstatistical concept used as a pre-processing step forcausal inference in observational studies. The goal isto match subjects in the case and control groups asclosely as possible on their given observed character-istics so as to approximate the conditions of a ran-domised controlled trial to better estimate the true’treatment’ e�ect of being in the case group. Thereare many di�erent matching algorithms and settingsadvocated in current literature and in this poster, us-ing a sample of data arising from an observationalstudy, I will present a comparative study of some ofthese methods and their merits relative to when nomatching is performed, aided by graphical summariesusing R and Tableau software.

[1] Rosenbaum, P. R. and Rubin, D. B. (1983b).The central role of the propensity score in obser-vational studies for causal e�ects. Biometrika70, 41â��55.

[2] Ho DE, Imai K, King G, Stuart EA.MatchIt: nonparametric preprocessing forparametric causal inference. J Stat Software2011;42:1â��28.

[3] Stuart, Elizabeth A. 2010. â��MatchingMethods for Causal Inference: A Review

and a Look Forward.â�� Statistical Science25(1):1â��21. (CASI).

A Bayesian approach to imputation ofsurvival data

Shirin MoghaddamSupervisors: Prof. John Hinde, Dr. Milovan

Krnjajic and Dr. John Newell

In survival analysis, due to censoring, standard meth-ods of plotting individual survival times are invalid.Therefore, graphical display of time-to-event datausually takes the form of a Kaplan-Meier survivalplot. By treating the censored observations as missingand using imputation methods, a complete datasetcan be formed. Then standard graphics may usefullycomplement Kaplan-Meier plots. Here, we considerusing a Bayesian framework to present a flexible ap-proach to impute the censored observations using pre-dictive distributions.

[1] Christensen, R. et al. (2010).Bayesian Ideasand Data Analysis: an introduction for scien-tists and statisticians. CRC Press.

[2] Lunn, D. et al. (2012). The BUGS Book:A Practical Introduction to Bayesian Analysis.CRC Press.

[3] Royston, P. et al. (2008). Visualizing lengthof survival in time-to-event studies: a comple-ment to Kaplanâ��Meier plots. Journal of theNational Cancer Institute, 100, pp. 92 – 97.

Analysis of Allele Specific Translationacross Human Individuals

Ngoc NguyenSupervisors: Cathal Seoighe

Genetic variants are considered as an importantsource of phenotypic variations and may give riseto human genetic diseases and complex phenotypes.Allele specific translation (AST) analysis, a methodintegrating genome and transcriptome data has be-come an important tool for studying genome func-tion, because it quantifies the di�erences in proteinproduction e�ciency between alternative alleles ofa gene distinguished by heterozygous sites. Severalstudies presented integrative analysis of RNA-seq andribosome profiling data to reveal distinct regulatorygenetic variants that can impact protein abundance


through their e�ect on translation (Battle et al. 2015;Albert et al. 2014; Cenik et al. 2015). However, un-avoidable presence of PCR artifacts (introduced inlibrary amplification process) is the most common is-sue in ribosome profiling data, which can confounddownstream AST analysis and up-to-date, there isstill no correction method suggested for it. Here wepresented the initial analysis of transcriptomic andribosome profiling datasets from lymphoblastoid celllines (LCLs) samples of 60 individuals to reveal a listof SNPs that potentially causing and/or associatedwith human diseases and complex phenotypic traits.Moreover, we also demonstrated the inspection of sys-tematic bias introduced by PCR artifacts across sam-ples.

[1] Albert FW, Muzzey D, Weissman JS, KruglyakL. 2014. Genetic Influences on Translation inYeast. PLoS Genet 10: e1004692.

[2] Battle A, Khan Z, Wang SH, Mitrano A, FordMJ, Pritchard JK, Gilad Y. 2015. Impact ofregulatory variation from RNA to protein. Sci-ence 347: 664?667.

[3] Cenik C, Cenik ES, Byeon GW, Grubert F,Candille SI, Spacek D, Alsallakh B, Tilgner H,Araya CL, Tang H, et al. 2015. Integrativeanalysis of RNA, translation, and protein lev-els reveals distinct regulatory variation acrosshumans. Genome Res.

This project is supported by Irish Research Council

Minimal Graphs of Exponent 2

Olga O’MahonySupervisor: Dr Rachel Quinlan

A non-negative matrix A is called primitive if Ak ispositive for some positive integer k; the least such k iscalled the exponent of A. A graph is said to be primi-tive of exponent k if its adjacency matrix is primitiveof exponent k. If u and v are vertices of such a graphG, then there exists a path of length k from u to v inG.We say a graph G is minimal of exponent 2, or is anme2 graph, if G has exponent 2, and if you delete anyedge, then G no longer has exponent 2.This poster deals with the problem of e�ciently em-bedding a tree as an induced subgraph of an me2graph. We present a theorem, and give an exampleto show how to construct an e�cient embedding.Supported by The College of Science NUIG

Rigidity of Surface Graphs

Qays ShakirSupervisor: James Cruickshank

This poster presents a survey of some of the key con-cepts of geometric rigidity theory. In the case of barand joint frameworks, the three dimensional rigidityproblem remains one of the major open problems inthe area. We propose to investigate this problem inthe special case of graphs that are derived from tri-angulations of surfaces.

[1] A. Nixon,E. Ross, One brick at a time: a sur-vey of inductive constructions in rigidity theory,Rigidity and symmetry, 22 (2014) , 303-324.

[2] H, Gluck. Almost All Simply Connected ClosedSurfaces are Rigid. Heidelberg, Germany:Springer-Verlag, (1975) 225-239.

[3] W. Whiteley, Vertex splitting in isostatic frame-works, Structural Topology,16 (1991), 23-30.

[4] J. Cruickshank D. Kitson, S. Power, TheGeneric Minimal Rigidity of a Partially Trian-gulated Torus, to be appear.

Adaptive Ranges for ClinicalBiomarkers using Bayesian Approaches

Davood Roshan SangachinSupervisors: Dr. John Newell, Prof. Fracis J.

Sullivan

Biomarkers are measurements reflecting an interac-tion between a biological system and a potential haz-ard. They are typically measured and evaluated asindicators of normal/abnormal biological processes.Biomarkers may be measured on a bio-sample (e.g.blood), may be a recording (e.g. blood pressure),or an imaging test (e.g. echocardiogram). Ascertain-ment of the pattern and temporal changes of biomark-ers play a vital role as indicators of risk markers, dis-ease state or disease progression.A reference range, generated from a cross-sectionalanalysis of healthy individuals free of the disease ofinterest, is typically used as a basis for comparison tointerpret a set of test results for a particular patient.An arbitrary percentile cut-point (typically the 95thor 97.5th percentile) is chosen to define abnormal-ity. When biomarkers are collected longitudinally for


patients, dynamic reference ranges are needed for ef-fective diagnosis which adapt to account for betweenand within subject variability.In this poster, methods for generating adaptiveranges using tolerance intervals and Bayesian ap-proaches are discussed. Initially the patient specificreference range is based on the tolerance interval gen-erated for the population in question which adaptsover time as more data are collected for that indi-vidual. These adaptive ranges have the potential todetect a meaningful change earlier.This methodology will be applied to the construc-tion of adaptive range for Prostate Specific Antigen(PSA) biomarker in patient with prostate cancer andin blood testing in elite athletes.

[1] Sottas P, Baume N, Saudan C, SchweizerC, Kamber M, Saugy M. (2007). Bayesiandetection of abnormal values in longitudinalbiomarkers with an application to T/E ratio.Biostatistics, Volume 8, pp. 285 - 296

[2] Zorzoli M. (2011). Biological passport param-eters. Journal of Human Sport and Exercise,Volume 6, pp. 205-217.

Hochschild cohomology rings ofalgebras k[x1, . . . ,xn]/(x1 . . .xn)

Tran Thi Hieu NghiaSupervisors: Dr. Emil Skoldberg, Dr. Alexander

D. Rahm

Let k be a commutative ring with unity and f ink[x] a monic polynomial. The ring structure of theHochschild cohomology for the k-algebra k[x]/(f)was determined (in [1]). We want to consider thisproblem in a more general case, for the algebrak[x1, . . . ,xn]/(x1 . . .xn). In this poster, we review thebasic definitions of Hochschild cohomology for alge-bras and describe some early results on this researchproblem. The results are in a joint work with EmilSkoldberg and Isaac Burke.

[1] Th. Holm, Hochschild cohomology rings of al-gebras k[X]/(f), Contributions to Algebra andGeometry, Vol. 41, No. 1, pp. 291 - 301 (2000).

[2] J. A. Guccione, J. J. Guccione, M. J. Redondo,O. E. Villamayor, Hochschild and Cyclic Ho-mology of Hypersurfaces, Advances in Mathe-matics 95, pp. 18 - 60 (1992).

Supported by The College of Science, National University ofIreland, Galway.

Genus Two Zhu Theory for FermionicVertex Operator Superalgebras

Michael WelbySupervisors: Prof. Michael Tuite

The theory of n-point functions for a Vertex Op-erator (Super-)Algebra (VO(S)A) has been well-documented at genus zero and one. These functionshave a natural description in terms of functions fromclassical number theory. The theory is that there is ahigher genus analogue of these objects, following theresults of Zhu [3], who developed a recursion formularelating n-point functions to (n ≠ 1)-point functionsat genus one.The aim of the project is essentially togeneralise the results of [2] to a genus two environ-ment, that is: Zhu recursion on a genus two VOSA.Higher genus versions of the objects such as “twistedWeierstrass functions” are expected be found, whichwill have some relation to forms on the genus two sur-face. These functions should play a role in the Zhureduction of genus two VOSA n-point functions.

1 T. Gilroy, M.P. Tuite: Genus Two Zhu Theoryfor Vertex Operator Algebras, arXiv 1511.07664.

2 G. Mason, M.P. Tuite and A. Zuevsky: Torusn-point functions for R-graded vertex operatorsuperalgebras and continuous fermion orbifolds,Commun.Math.Phys. 283 (2008) 305-342.

3 Y. Zhu.: Modular invariance of characters ofvertex operator algebras, J. Amer.Math.Soc. 9(1996) 237-302.

LymAnalyzer: a tool forcomprehensive analysis of next

generation sequencing data of T cellreceptors and immunoglobulins.

Yaxuan YuSupervisors: Rhodri Ceredig, Cathal Seoighe

The adaptive immune system includes populationsof B and T cells capable of binding foreign epitopesvia antigen specific receptors, called immunoglobulin(IG) for B cells and the T cell receptor (TCR) for Tcells. In order to provide protection from a wide rangeof pathogens, these cells display highly diverse reper-toires of IGs and TCRs. This is achieved through

Research Day 2016: Abstracts of PhD and MSc Theses 10

combinatorial rearrangement of multiple gene seg-ments in addition, for B cells, to somatic hyper-mutation. Deep sequencing technologies have rev-olutionized analysis of the diversity of these reper-toires; however, accurate TCR/IG diversity profil-ing requires specialist bioinformatics tools. Here wepresent LymAnalzyer, a software package that sig-nificantly improves the completeness and accuracyof TCR/IG profiling from deep sequence data andincludes procedures to identify novel alleles of genesegments. On real and simulated data sets LymAna-lyzer produces highly accurate and complete results.Although, to date we have applied it to TCR/IGdata from human and mouse, it can be appliedto data from any species for which an appropriatedatabase of reference genes is available. Implementedin Java, it includes both a command line version anda graphical user interface and is freely available athttps://sourceforge.net/projects/lymanalyzer/.

[1] Yu, Yaxuan, Rhodri Ceredig, and CathalSeoighe. ”LymAnalyzer: a tool for comprehen-sive analysis of next generation sequencing dataof T cell receptors and immunoglobulins.” Nu-cleic acids research (2015): gkv1016.

3 Abstracts of PhD Theses

Analysis and Interpretation of Epigenomic Patternsin Colonic Epithelia

Alan BarnicleSupervisor: Laurence Egan and Cathal Seoighe

The methylation of cytosine nucleotides at the 5’ po-sition of DNA is a crucial epigenetic mechanism forthe control of gene expression. Epigenome-wide asso-ciated studies have demonstrated that specific methy-lome patterns exist in certain disease states, thatmethylome signatures can predict cancer susceptibil-ity and that methylation patterns are capable of char-acterizing epigenomic events that stimulate the sur-vival of cancer cells. Little is known about the e�ectof chronic inflammation on DNA methylation.In this work, we analysed the e�ect of chronic inflam-mation on DNA methylation patterns in ulcerativecolitis (UC), a condition that predisposes to coloncancer. Due to the cell type specific nature of DNAmethylation patterns, this PhD initially focussed ondesigning an epithelial cell isolation method that wascapable of enriching a purified epithelial populationboth in diseased and non-diseased states. Secondly,we wished to test the hypothesis that distinct colonicregions have specific methylation signatures, whilealso comparing DNA methylation patterns in isolatedepithelial cells and in whole colonic mucosal biopsies.Finally, using the chronic inflammatory condition ofulcerative colitis (UC) as a pathogenic phenotype,this PhD aimed to identify potential epigenomic andgenomic dysregulation that occurs in intestinal ep-ithelial cells in inflamed areas of the colon.Isolation of epithelial cells from mucosal biopsies re-sulted in purified populations of crypts consisting of90% pure epithelium. Using these fractions isolatedat 4Â�C to minimize degradation of nucleic acids, itwas demonstrated that stable and integral mRNAand gDNA could successfully be extracted in bothdiseased and non-diseased states. Using genome-widetechnology, specific DNA methylation signatures inthe proximal and distal colon in samples from healthycolon were identified. Computational deconvolutionwas also used to characterize accurate epithelial cellestimates from whole colonic biopsies, while also high-lighting the increased DNA methylation variabilitycaused by samples comprised of a mixture of celllineages. Results from this study identified region-specific epigenomic patterns of HOX genes (specif-ically HOXB and HOXC families). These patternsrepresent a valuable tool for interpreting experimen-tal data on diseases that exhibit region-specific ex-pression in the colon such as inflammatory bowel dis-ease and colorectal cancer. By performing genome-


wide DNA methylation and transcriptome profilingof purified intestinal epithelial cells, it was demon-strated that significant DNA methylation and geneexpression variation occurs in UC. Genes showing in-verse correlation between DNA methylation and geneexpression levels were also identified, most notablypromoter hypermethylation and down regulation ofRARB. This gene was previously identified as a tu-mour suppressor in colorectal adenocarcinoma as wellas in breast, lung and prostate cancer. However this isthe first finding of RARB potentially playing a func-tional role in UC. This integrative epigenomic datasetwill enhance our understanding of UC pathophysiol-ogy, potentially adding to our knowledge of the linksbetween chronic inflammation and carcinogenesis.

The Genomic Architecture of Nucleolar OrganiserRegions on the Short Arms of Human Acrocentric

ChromosomesSofia NazarÃ� de Pereira Barreira

Supervisor: Brian McStay and Cathal Seoighe

Nucleolar Organiser Regions (NORs) are comprisedof ribosomal gene (rDNA) arrays and adjacent se-quences. Nucleoli, the sites of ribosome biogenesisand key regulators of cellular growth and prolifer-ation, form around NORs. In humans, NORs arepositioned on the short arms of the five acrocentricchromosomes (13, 14, 15, 21 and 22). These chromo-some arms are not included in the human referencegenome and have only recently started to be mappedand characterised.This thesis has focussed on contributing to the char-acterisation and extension of these underexplored ge-nomic regions. Previous work had suggested that asmany as one third of rDNA repeats are rearranged.These could impact on nucleolar and ribosomal for-mation and protein synthesis. By performing nextgeneration sequencing on DNA extracted from pu-rified nucleoli, I demonstrated that there is no ev-idence for rearranged rDNA repeats in human celllines. This conclusion was emphasised by a detailedanalysis of more recent long read DNA sequence datasets. The second objective of this thesis was to de-scribe the spatial organisation of sequences distal tothe clusters of rDNA repeats. These sequences ex-hibit a euchromatic-like chromatin organisation, aretranscriptionally active and appear to function as ananchor for the linked rDNA array during interphase.In the post genomic age, much e�ort now focuses ondescribing the chromatin status and 3D organizationof the genome in a variety of human cell types andit is common practice to make the raw sequencing

data from these genome-wide studies publicly avail-able. Exploiting Hi-C data sets designed to capturegenome organisation revealed the existence of a tran-scription dependent stem-loop structure encompass-ing over 200 kb of NOR distal sequence that may playa role in NOR regulation. The third objective was toextend the sequences distal to NORs and characterisethem. Using a combination of nucleolar sequencingreads and Hi-C data, this region was extended by 180Kb. Analysis of data from the ENCODE project sug-gests that this region is transcriptionally active andmarks the beginning of interchromosomal variabilityon the short arms of acrocentric chromosomes.These results provide a platform for investigating therole of NORs in nucleolar formation and maintenanceand serve as a starting point for the identification andcharacterisation of the unknown regions of the p-armsof acrocentric chromosomes.

Theoretical and numerical analysis of rigid-bodyimpacts with friction

Shane BurnsSupervisor: Dr Petri Piiroinen

This thesis gives a flavour of the area of rigid body im-pacts with friction, an area which has far reaching ap-plications in engineering, sports science and every daylife. The focus of this work will be on the two mainstreams of this field, theoretical and numerical. Thisthesis will present an overview of the general subjectof rigid-body impact, including discussion and anal-ysis of the validity of ones choice of impact law andthe numerical techniques required for the simulationof rigid-body impacting systems.Two impact laws will be introduced in Chapter 3 anda direct comparison will be made in order to examinethe varying dynamics that can be achieved using botha basic and a complex impact law and to explore someof the problems that can occur with a more basicformulation. It will be demonstrated that for certainregions in parameter space the two formulations areequivalent, however, for many other regions the twoformulations can vary greatly.A hybrid event-driven numerical scheme is one inwhich smooth dynamics are described by di�eren-tial equations, which can be solved numerically usingstandard techniques, and non smooth events whichare described my maps. In Chapter 5, a hybrid event-driven numerical scheme for the implementation ofthe Energetic impact law described in Chapter 3 ispresented. Moreover, the framework necessary for thelong term simulation of mechanical systems with im-pacts and chatter is derived.


This thesis also gives an overview of the phenom-ena known as the Painleve Paradox in Chapter 6 andpresents a numerical experiment to show the occur-rence of the paradox for a mechanical system.

Mathematical models of seasonal migrationJohn Donohue

Supervisor: Dr Petri Piiroinen

The phenomenon of seasonal migration has attracteda wealth of attention from biologists. However, thedynamics of migratory populations have been littleconsidered. In this thesis, we use di�erential equa-tions to model the variation in abundance of season-ally migrating populations.Our contribution to the field begins with a representa-tion of seasonal breeding. We use piecewise-smoothdi�erential equations to model the variation in thesize of a population that has a short interval eachyear during which successful reproduction is possible.We first consider a one-species model which illustratesthe dynamics of a population of specialist feeders overthe course of a single breeding season and use it to ex-amine how reproductive success depends on the pop-ulation’s distribution of breeding dates. We then in-troduce time-dependent switches to extend the modelto a broader class of species. This allows us to con-sider the e�ect of climate change on populations thatannually travel long distances.We then shift focus to consider interactions betweenmigrants and species at higher levels in the food web.Predatory pressure influences almost all populationsto some extent. Here, however, interactions may oc-cur for just a brief period each year before the popula-tions involved become spatially separated. The rangeof a migrating population may overlap with that ofa population of predators for a single season. Weoutline a framework for examining how this kind of“transient” predation influences the dynamics of theprey population. We are then able to examine howa migratory population may be overwhelmed by thefleeting influence of members of other species.Finally, as an alternative to the aforementioned mod-els, we outline a di�erent approach to modelling mi-gration, namely using partial di�erential equationsinstead of ordinary di�erential equations. In this way,we provide two distinct templates for the future ex-ploration of the dynamical features of such popula-tions.

Incremental elastic surface waves and static wrinkles

Artur L. GowerSupervisor: Professor Michel Destrade

This article-based thesis comprises a collection of fourarticles, each of which constitutes a chapter writtenand formatted in manuscript form. The general aimunderlying these articles is to understand and predicthow incremental elastic surface waves propagate orstatic wrinkles form on a deformed elastic substrate.The formation of these small-amplitude disturbancescan be the end goal, such as in sending signals orcreating functional coatings, or they can be used tomeasure and characterise the underlying elastic sub-strate. This thesis focuses on using surface waves orstatic wrinkles to characterise soft solids, such as bi-ological tissues.Chapter 1 predicts a new phenomenon: oblique wrin-kles, which should appear in a large range of materi-als. Yet oblique wrinkles have not been seen experi-mentally so far on soft solids. Another issue raisedwas why are the predicted critical strains greaterthan the experimentally observed critical strains? Weshowed that this is likely due to a skin e�ect causedby dehydration.In Chapter 2 the e�ects of a sti�er skin on an elasticsubstrate on surface wrinkles was initially studied,and therein we also studied the possibility of usingsurface wrinkles to characterise fibre reinforced ma-terials.The results from Chapter 3 show that measuringthe propagation speed of surface waves only alongthe principal directions of deformation leads to manychallenges in non-destructive evaluation of strain andstress, because these directions are not necessarilyaligned with the directions of fastest and slowestpropagation. However, the methods for calculatingsurface waves along any direction presented in thatchapter are now su�ciently mature and robust to beable to use the full Rayleigh wave-field in order tocharacterise solids. There are now experiments inplace that measure surface waves on tissue, and awide range of techniques to infer the surface elasticproperties from these measurements for a range ofmaterials. Yet, to date, surface wave measurementshave not been adequately linked to the elastic prop-erties of soft tissue, such as the residual stress or thereinforcing fibre properties.Chapter 4 shows a surprisingly simple relationship be-tween the angle of the surface wrinkle wave-front andthe fibre orientation, a trend which becomes strongerthe sti�er the fibres. Yet predicting how these wrin-kles appear on soft fibre reinforced solids required ahighly technical and involved numerical method. Apromising alternative model is that of a soft tissue


reinforced by fibres idealized to be infinitely strongerthan the surrounding soft matrix.

Completions of Partial MatricesJames McTigue

Supervisor: Rachel Quinlan

A partial matrix over a field F is a matrix whose en-tries are either elements of the field or independentindeterminates. A completion of a partial matrix isany matrix that results from assigning a field ele-ment to each indeterminate. The set of completionsof an m ◊ n partial matrix forms an a�ne subspaceof Mm◊n(F).This thesis investigates partial matrices whose sets ofcompletions satisfy particular rank properties - specif-ically partial matrices whose completions all haveranks that are bounded below and partial matriceswhose completions all have the same rank. The max-imum possible number of indeterminates in such par-tial matrices is determined, and the partial matricesthat attain these bounds are fully characterized forall fields. These characterizations utilize a dualitybetween properties of a�ne spaces of matrices thatare related by the trace bilinear form.Precise conditions (based on field order, rank andsize) are provided to determine if a partial matrixwhose completions all have rank r must possess anr◊r partial submatrix whose completions are all non-singular.Finally a characterization of maximal nonsingularpartial matrices is provided - a maximal nonsingu-lar partial matrix is a square partial matrix each ofwhose completions has full rank, with the propertythat replacement of any constant entry with an inde-terminate results in a partial matrix having a singularcompletion.

Discrete vector fields and cohomology of certainarithmetic and crystallographic groups

Bui Anh TuanSupervisor: Graham Ellis

This thesis makes the following contributions to thearea of Computational Algebraic Topology:

[1] All algorithms written in this thesis are im-plemented and are publicly available as docu-mented functions for the GAP computer alge-bra system, and are distributed with the systemas part of its HAP package.

[2] We devise and implement an algorithm for com-puting a finite ZG-equivariant CW-space withnice cell stabilizer groups and a contracting dis-crete vector field, where G = SL2(Z[1/m]) forany positive integer m. (See Algorithm 3.2.1.)

[3] We implement a function which inputs a non-free ZG-resolution and outputs finitely manyterms of a free ZG-resolution Rú of Z, whereG = SL2(Z[1/m]) for any positive integer m.(See Algorithm 2.1.1.)

[4] We devise and implement an algorithm forcomputing finitely many terms of a free ZH-resolution Rú of Z for H a finite index subgroupof G = SL2(Z[1/m]). (See Algorithm 3.2.2.)

[5] We devise and implement an algorithm that at-tempts to find a cubical fundamental cell fora cubical crystallographic group G. (See Algo-rithm 4.3.1).

[6] We devise and implement an algorithm that in-puts a crystallographic group G together witha cubical fundamental cell and outputs a finiteZG-equivariant CW-space with nice cell stabi-lizer groups and a contracting discrete vectorfield. (See Algorithm 4.4.1).

[7] We implement a function for calculating finitelymany terms of a free ZG- resolution Rú ofZ with contracting homotopy, where G is ann-dimensional cubical crystallographic group.This resolution can be used to compute the co-homology ring structure of G. (See Algorithm4.5.1.)

[8] We give the complete list of 3-dimensional cu-bical Bieberbach groups with their cohomologyring structures.(See Section 4.7.)

4 Abstracts of Masters Theses

Ability to construct mathematical proof at seniorIrish undergraduate level: a qualitative study

Michelle DuaneSupervisor: Dr Aisling McCluskey

This research uses a qualitative approach to inves-tigate senior Irish undergraduate mathematics stu-dentsÂü approaches to proof construction in the ana-lytical subject metric spaces. In particular, the studyis concerned with the impact that logical statementshave on a studentÂüs ability to succeed in proof-making.

Research Day 2016: Research Activity 14

First, a review of the literature looks at the relevantareas of research: approaches to proof construction,the role of intuition and informal representations inthe proving process, and undergraduate studentsÂüdi�culties in constructing proofs.The qualitative research was carried out by meansof audio-recorded task-based interviews with sixparticipants from the mathematics module MetricSpaces, at National University of Ireland, Galwayduring 2013. The students were in the penultimateor final year of their chosen degree programme. Par-ticipants were asked to write down and discuss theirideas for proofs relating to a number of di�erent tasksprovided. The tasks were designed with particularfocus on the logical form of mathematical statementsand to be accessible without reliance on memory. Allrelevant mathematical definitions were provided tothe students at the interviews. The interviews weretranscribed and coded inductively from the Â�bottomupÂö, using a grounded-theoretic approach.The analysis of interview data provides some evidenceto suggest that students possess a number of di�cul-ties in working with implications and notably withthose that include universally quantified statements.In particular, students in general placed dispropor-tionate emphasis on the hypotheses of implications,while simultaneously ignoring the chosen goals. Stu-dents also showed di�culty in working with partic-ular mathematical definitions, like continuity andsequential convergence, when trying to create validproofs. The research also suggests that some studentshave a concept image of proof by contradiction that islinked to the notions of converse or counterexample,and that this indirect proof method is not properlyunderstood, in general.

Superconformal Symmetry in Vertex OperatorSuper AlgebrasPhilip Vernon

Supervisor: Prof Michael Tuite

This thesis gives a brief review of Vertex Algebrasand Vertex Operator Algebras and discusses their re-lationship with modular forms and elliptic functions.We also investigate super-symmetric extensions ofthe celebrated Virasoro algebra, namely the Neveu-Schwarz N = 1, N = 2 and N = 4 super-conformalalgebra. We also construct fermionic models for eachof these super-conformal Vertex Operator Super Al-gebras.

5 Research Activity from 1 Jan2015 to 31 Dec 2015

Permanent and Contract Sta�

Burns, John

Current Research Interests

My current research interests are Algebra (Lie alge-bras, Lie groups, Weyl groups) and Di�erential Ge-ometry (Homogeneous manifolds, Symmetric spaces).Research in these areas is ongoing with various au-thors:Adib Makrooni and I are studying relations betweenroot theoretic data, such as the Coxeter number andthe exponents, of parabolic sub-root systems andthose of the parent root systems. Applications in-clude formulae for the defect of projective varieties.Patrick Browne and I are working on graded Lie Alge-bras and their application to the geometry of homoge-neous submanifolds of noncompact symmetric spaces.These spaces are interesting as they contain a largeclass of Einstein manifolds.

Publications

Most significant recent publications

[1] Burns, John M.; Makrooni, Mohammad A.Compact homogeneous spaces with positive Eu-ler characteristic and their ‘strange formulae’.Q. J. Math. 66 (2015), no. 2, 507?516.

Research Activities

// Invited talks: Workshop on Geometry,U.C.C. Boole celebrations Oct. 2015. //Ref-ereeing: 1 paper. //Reviewing: 1 paper.//Conferences and workshops: Irish GeometryConference (Limerick) 2015. Groups in Gal-way, May 2015. //Postgraduate supervision: 1Ph.D. student.

1. Burns, John M.; Makrooni, Mohammad A. Com-pact homogeneous spaces with positive Euler charac-teristic and their ‘strange formulae’. Q. J. Math. 66(2015), no. 2, 507?516.2. Maximal Order Abelian Subgroups of CoxeterGroups as Discrete Maximal Tori (with G. Pfei�er).Available at arXiv:1601.078123. Parabolic Sub-root Systems (with M. Makrooni)


Cruickshank, James


[1] Geometric graph theory - in particular rigidityof bar-joint frameworks and other related struc-tures.

[2] Random geometric graphs.

Publications

No publications appeared in 2015. Two papers ac-cepted for publication during 2015:

• Cruickshank, James; Loane, John; Ryan, Ray.Positive polynomials on Riesz spaces. Acceptedby Positivity subject to minor changes

• Cruickshank, James; Kitson, Derek; Power,Stephen. The generic rigidity of triangulatedspheres with blocks and holes. Accepted byJournal of Combinatorial Theory, Series B sub-ject to minor changes.

Research Activities

Graduate Students: Qays Shakir, Christine Marshall(cosupervised with Colm O Riordan, Discipline of In-formation Technology)Conferences:

• Rigidity Workshop, Lancaster University, June2015. (Invited speaker).

• Geometric Rigidity Workshop, Ban� Interna-tional Reseach Station, July 2015 (Invitedspeaker).

• Global Rigidity Workshop, Ban� InternationalResearch Station, July 2015 (participant).

Editorships: Editorial board of the Bulletin of theIMSJournal Submissions: 1 paper to Discrete and Com-putational Geometry.

Destrade, Michel


I apply the principles of Continuum Mechanics to themodelling of soft matter, including soft silicones, gels,and biological tissues such as the human skin andbrain matter. I am mainly working in problems andapplications of elastic wave propagation, elastic sta-bility, and proper computational solid mechanics.

Publications

Number of publications appearing in calendar year2015: seven articles in international scientific jour-nals.Most significant recent publications

[1] A.L. Gower, P. Ciarletta, M. Destrade. Initialstress symmetry and its applications in elastic-ity, Proceedings of the Royal Society A, 471(2015) 20150448.

[2] Y. Jiang, G. Li, L.-X. Qian, S. Liang, M. De-strade, Y. Cao. Measuring the linear and non-linear elastic properties of brain tissue withshear waves and inverse analysis, Biomechan-ics and Modeling in Mechanobiology 14 (2015)1119-1128.

[3] M. Destrade, M.D. Gilchrist, J.G. Murphy,B. Rashid, G. Saccomandi. Extreme softnessof brain matter in simple shear, InternationalJournal of Non-Linear Mechanics, Special Issuein Honour of Martine Ben Amar [invited con-tribution] 75 (2015) 54-58.

[4] R. Mangan, M. Destrade, Gent models forthe inflation of spherical balloons, InternationalJournal of Non-Linear Mechanics, Special Issuein Honour of Alan Gent [invited contribution]68 (2015) 52-58.

The three (or fewer) pieces of work published during2013-2017 that I plan to submit to the internal reviewof the school’s research next year.

[1] L. Vergori, M. Destrade, P. McGarry, R.W.Ogden. On anisotropic elasticity and ques-tions concerning its Finite Element implemen-tation, Computational Mechanics, 52 (2013)1185-1197.

[2] A.L. Gower, P. Ciarletta, M. Destrade. Initialstress symmetry and its applications in elastic-ity, Proceedings of the Royal Society A, 471(2015) 20150448.

[3] Y. Jiang, G. Li, L.-X. Qian, S. Liang, M. De-strade, Y. Cao. Measuring the linear and non-linear elastic properties of brain tissue withshear waves and inverse analysis, Biomechan-ics and Modeling in Mechanobiology 14 (2015)1119-1128.

Research Activities

Research grants: COST Action/European ScienceFoundation (Co-I, unsuccessful), Postgraduate


Hardiman Fellowship for Robert Mangan (unsuc-cessful), Postgraduate IRC Fellowship for RobertMangan (successful), NUI Galway start-up grant(PI), NUI Galway College of Science Scholarshipfor Robert Mangan (declined), NUI TravellingScholarship for Robert Mangan (shortlisted), ItalianInstitute of Higher Mathematics INdAM VisitingProfessor Programme (PI).Numbers of graduate students: 1 (Artur Gower andthen, Robert Mangan);Research Fellow: 1 (Valentina Balbi) Confer-ences/Seminars: 18;Outreach talks: 10;Research Visits: 4 (Modena, Tianjin, Glasgow,Manchester);Research Visitors: 5 (Saccomandi/Perugia, Ver-gori/Glasgow, Napoli/Lecce, Carfagna/Turin,Su/Hanzhou);Papers refereed: 14;International Grant referee: 2 (International Centrefor Mathematical Sciences, Tec 21 Laboratory ofExcellence);PhD External Examiner: 1 (Paris 6);Professorial Promotion External Examiner: 1 (Mi-lan);Editorial Board Member: 6 (Proceedings of theRoyal Society A, Quarterly Journal of Mechanicsand Applied Mathematics, International Journal ofApplied Mechanics, International Journal of Non-Linear Mechanics, Journal of the Acoustical Societyof America, SIAM Journal of Applied Mathematics);Memberships: Acoustical Society of America, Societyfor Industrial and Applied Mathematics, Interna-tional Society for the Interaction of Mechanics andMathematics;External positions: Reviews Editor (Proceedings ofthe Royal Society A); Contributing Editor (Interna-tional Journal of Non-Linear Mechanics); VisitingProfessor of Mechanical Engineering (UniversityCollege Dublin); Directeur de Recherche, Institutd’Alembert, CNRS, Paris, France (on leave); Inter-national Brain Mechanics and Trauma Lab (Oxford);Biomechanics Research Centre (NUI Galway).

Dooley, Cara


My research interests include design and analysisof observational studies and analysis of longitudinaldata, survey data and survival data.

Publications

4 publications were published in 2015 with a furthertwo in press. Most significant recent publications

[1] Donoghue OA, Jansen S, Dooley C, De Rooij S,Van Der Velde N, Kenny RA. 2014. Atrial Fib-rillation Is Associated With Impaired Mobilityin Community-Dwelling Older Adults. Journalof the American Medical Directors Association.15(12) (2015)929â��933.

[2] Aku�o, KO, Nolan, J, Stack, J, Moran, R,Feeney, J, Kenny, RA, Peto, T, Dooley, C,O’Halloran, AM, Cronin, H, Beatty, S. Preva-lence of age-related macular degeneration in theRepublic of Ireland. British Journal of Oph-thamology. 99(8) (2015) 1037-1044.

[3] McCrory, C., Dooley, C., Layte, R.& Kenny,R.A. The Lasting Legacy of Childhood Adver-sity for Disease Risk in Later Life. Health Psy-chology 34(7) (2015) 687-696.

[4] O’Sullivan, V, Nolan, B, Barrett, A, Dooley, C.2014. Income and Wealth in the Irish Longi-tudinal Study on Ageing. Economic and SocialReview 45(3) (2015) 329-348.

Ellis, Graham


I am interested in computational algebraic topology,and particularly in: (i) calculations related to the co-homology of discrete groups and; (ii) calculations ofhomotopy theoretic invariants of topological spacesarising from scientific data sets.

Publications


[1] Brendel, Piotr; Dlotko, Pawel; Ellis, Graham;Juda, Mateusz; Mrozek, Marian. Computingfundamental groups from point clouds. Appl.Algebra Engrg. Comm. Comput. 26 (2015),no. 1-2, 27-48.

[2] Ellis, Graham; Murillo, Aniceto; Real, Pedro;Saenz-de-Cabezon, Eduardo. Editorial [Com-putational algebraic topology and its applica-tions]. Appl. Algebra Engrg. Comm. Comput.26 (2015), no. 1-2, 1-3.


[3] Ellis, Graham. Cohomological periodicities ofcrystallographic groups. J. Algebra 445 (2016),537-544.

[4] Ellis, Graham. GAP package HAP: Ho-mological Algebra Programming version1.11.13, 03/11/2015. http://www.gap-system.org/Packages/hap.html

Research Activities

In 2015 Dr Bui Anh Tuan completed his PhD stud-ies under my supervision. His thesis is on “Dis-crete vector fields and the cohomology of certainarithmetic and crystallographic groups”. Ms NisreenAlokbi started studying a PhD with me on the topicof “groupoid methods in applied topology”. Mr Da-her Freh started to work under my co-supervison on“Cohomology operations on groups”. I also started toco-supervise Mr Pablo Torres on “Detection of eventsin Twitter”.I started joint research on classification of knottedgraphs with Dr Vitaliy Kurlin (Durham) and DrVanessa Robbins (Canberra).I gave talks at conferences in Jena (February), Han-nover (May), Belfast (September). I continued edi-torial work for the three journals HHA, JHRS andAAECC and the GAP Council.

Flannery, Dane


Active in two main fields: linear groups (especiallycomputational aspects), and algebraic design theory.Continuing to expand the new area of computingwith infinite matrix groups. This encompasses thedevelopment of innovative techniques and implemen-tation of algorithms for the study of solvable-by-finitegroups and arithmetic subgroups of linear algebraicgroups.The book Algebraic design theory by de Launey andFlannery describes a unifying paradigm for pairwisecombinatorial designs, of which Hadamard matricesand their generalisations form a special case. We haveestablished machinery to analyse the regular sub-group structure of the automorphism group of suchdesigns. This forms the basis of e�ective solutionsto existence and classification problems for cocyclicdesigns.

Publications

Most significant recent publications:

[1] On linear shift representations, Journal of Pureand Applied Algebra 219, 3482â��3494, 2015(with R. Egan).

[2] Classifying cocyclic Butson Hadamard matri-ces, Springer Proceedings in Mathematics andStatistics (PROMS): Algebraic Design Theoryand Hadamard Matrices, in press, 2015 (withR. Egan and P. O Cathain).

[3] Algorithms for arithmetic groups with the con-gruence subgroup property, Journal of Algebra421, 234–259, 2015 (with A. S. Detinko andA. Hulpke).

[4] Integrality and arithmeticity of solvable lineargroups, Journal of Symbolic Computation 68,138–145, 2015 (with W. de Graaf and A. S.Detinko).

Research Activities

• Invited speaker at

· Groups, Computation and Geometry,June 9–13 2014, Colorado State Univer-sity, USA;

· Algebraic Design Theory and HadamardMatrices, July 8–11 2014, University ofLethbridge, Canada;

· Algorithms for Linear Groups, November16–21 2014, Ban� International ResearchStation, Canada.

• Organizer, Algebraic Design Theory withHadamard Matrices: Applications, CurrentTrends and Future Directions, Ban� Interna-tional Research Station, July 11–13 2014.

• Editor, Journal of the Australian MathematicalSociety.

• Irish Research Council New Foundations 2015grant.

• Supervisor of doctoral student Ronan Egan(Hardiman & Irish Research Council postgrad-uate scholarships).

• Distinguished visitor: Professor RobertCraigen, University of Manitoba (AlgebraicDesign Theory).

• 5 papers refereed.

• 2 Mathematical Reviews.

Golden, Aaron

http://www.gap-system.org/Packages/hap.html

http://www.gap-system.org/Packages/hap.html



On leave of absence.

Publications

Research Activities

Hayes, Michael



Publications

Research Activities

Hinde, John


Statistical modelling, particularly generalized linearmodels and random e�ects and mixture models; sta-tistical computing and statistical software; likelihoodtheory and inference; applications of statistics in bi-ological, medical and social sciences.

Publications

Journal papers: 1; Conference Papers: 5; Software 1.Most significant recent publications

[1] Alvarez-Iglesias, A., Hinde, J., Scarrott, C. andNewell, J. (2015) Summarising censored sur-vival data using the mean residual life function.Statistics in Medicine, 34(11), 1965â��-1976

[2] Co�ey, Norma, Hinde, John and Holian, Emma(2014) Clustering longitudinal profiles using P-splines and mixed e�ects models applied totime-course gene expression data. Computa-tional Statistics and Data Analysis, 71, 14–29.

[3] Islam, Nahidul; Whitehouse, Michael; Mehen-dale, Sanchit; Hall, Michael; Tierney, Joanna;O’Connell, Enda; Blom, Ashley; Bannis-ter, Gordon; Ceredig, Rhodri; Hinde, John;Bradley, Benjamin (2014) Post-traumaticImmunosuppression is Reversed by Anti-coagulated Salvaged Blood Transfusion;Deductions from studying Immune Status afterKnee Arthroplasty. Clinical and ExperimentalImmunology, 177(2), 509â��-520.

[4] Hinde, J (2015) All statistical models arewrong, some are usable! In Proceedings ofthe 30th International Workshop on StatisticalModelling, Volume 1, Linz, Austria, 67–85.

Research Activities

• Graduate students: 3; Visiting Postdoc: 1

• Journal submissions: 7 under review; 3 underrevision

• Conferences: Keynote 5; Invited Speaker 3;Contributed presentations 2

• Seminar talks: 7; Public Lecture: 1

• Research Visits: ESALQ/USP, Brazil –July/August 2015; University of ChristchurchCanterbury – Feb/April 2016.

• Conference Organisation: Organising Presi-dent, IBC2016 Vicotoria, Canada; co-chair ofScientific Programme Committee RBras 2016,Salvador, Brasil; member of Scientific Pro-gramme Committee IWSM 2017, Groeningen,The Netherlands.

• Editorships: Statistics and Computing (As-sociate); Computational Statistics and DataAnalysis (Associate & Guest Editor); Statisti-cal Modelling (Advisory Board); Econometricsand Statistics (Guest Editor). Referee for nu-merous journals.

• President of the International Biometric Society(2013-2017)

Holian, Emma


Mixture modelling to cluster longitudinal data pro-files and to model the group features via generalizedlinear mixed models and penalized smoothing models,leading to the formulation of the Regression ClusterModel (RCM). Analysis into capability of the RCMto handle missing data within profiles or profiles mea-sured at variable time-points. Extension of the RCMto longitudinal profiles measured on discrete or cat-egorical scales. P-Splines and mixed e�ects modelclustering. Applications in microarray analysis.Prognostic models in Breast Cancer, variable selec-tion methods in survival models for data with variousmissingness mechanisms.


Publications

[1] “Her-2 Breast Cancer Treatments Induced Vari-ations in the Patterns of Survival and Metas-tasis in Her-2 Positive Breast Cancers” A.McGuire, O. Kalinina, E. Holian, K. Sweeney,C. Malone, R. McLaughlin, A. Lowery, J. A. L.Brown, M. J. Kerin. (2015) Conference Paperin Irish Journal of Medical Science 184:S397-S397, Sept 2015

[2] “Exosome-mediated tra�cking of microRNAsby breast cancer cells. D. P. Joyce, C. L. Glynn,J. Brown, E. Holian, P. Dockery, M. J. Kerin,R. M. Dwyer (2015) Cancer Research 75 (9 Sup-plement): P4-07-05 May 2015

[3] “Investigation of exosome-encapsulated mi-croRNAs as potential circulating biomarkers ofbreast cancer.” D. P. Joyce, M. Higgins, C. L.Glynn, J. Brown, E. Holian, P. Dockery, M. J.Kerin, R. M. Dwyer (2015) British Journal ofSurgery, April 2015

[4] “Colorectal cancer cells actively secreteexosome-encapsulated microRNAs which areassociated with epithelial-mesenchymal tran-sition.” C. Clancy, J. Brown, E. Holian ,M.R. Joyce, M.J. Kerin, R.M. Dwyer (2014)Conference: European Journal of SurgicalOncology (EJSO)

Research Activities

Supervision:Ph.D student Olga Kalinina, Prognostic modelsin Breast Cancer, variable selection methods insurvival models for data with various missingnessmechanisms.

Memberships: Irish Statistical Association.A�liations: Sta� member Biostatistics Unit. HRBClinical Research Facility, Galway, (CRFG).Collaborative work: Statistical Consultation, Dr.Roisin Dwyer, REMEDI, NUIG, microarray analysisin Mesenchymal Stem Cells and Breast Cancer.

Jennings, Kevin


I am interested in di�erence sets, particularly thosewith classical parameters. The study of these involves

techniques from finite fields, linear algebra, combina-torics and finite groups. Last year I had been work-ing on a problem in linear algebra, to do with enu-merating the number of distinct ranks arising in two-dimensional subspaces of Mn(F ). More recently Ihave begun working on a problem in design theory,with a hope to discovering some interesting designsover non-abelian groups.

Publications

Research Activities

Krnjajic, Milovan



Publications

Research Activities

Leitner, Marianne

I joined NUIG on September 01, 2015.


My research aims at bridging the gap between math-ematics and physics in the area of quantum field the-ory. My previous work relates to the quantum Halle�ect in graphene like materials and features inter-esting number theoretical and geometrical aspects,part of which are not yet fully explored. More recentwork is devoted to a sound mathematical formulationof conformal field theory on Riemann surfaces of ar-bitrary genus, using tools from algebraic geometry.This is a joint project with Werner Nahm (DIAS).I recently became interested in learning about issuesrelated to the elliptic genus. I plan to approach thesubject within the framework of K-theory and thecorresponding Index Theory.

Publications

“Index Theory with Applications to Mathematics andPhysics” by D.D.Bleecker and B. Booss-Bavnbek, Int.Press of Boston 2013, 792 pp. (book review), IrishMath. Soc. Bulletin 75 (Summer 2015), 63–70.


Research Activities

I accepted to supervise the Master thesis of Mr Ab-dullah Alharbi which would have involved some com-puter algebra (Abdullah left in December). I gave aseminar talk at NUIG in October. I attended MichaelTuite’s lecture series on VOAs. Before joining NUIGin September, I held a postdoctoral scholarship atDIAS. I was the main organiser of the Irish QuantumFoundation Meeting celebrating the institute’s 75th

anniversary in May, (and the successful main appli-cant for an SFI workshop grant). I came to Galwayfor the VOAs & MMFs conference the same month. Iattended a seminar on automorphic forms in Utrechtand I gave a talk at DIT in April. Currently I ama Research Associate of the School of TheoreticalPhysics at DIAS.

Madden, Niall


I work in the area of numerical analysis, and, in par-ticular, on the solution of partial di�erential equa-tions by finite di�erence and finite element methods.Much of my focus is on so-called singularly perturbedproblems. Solutions to these problems feature bound-ary and/or interior layers, and their numerical so-lution requires the development of quite specialisedmethod.Within this area, I work in two main branches: dis-cretizations (meaning algorithms that reduce di�er-ential equations to linear systems of equations) andsolvers (meaning algorithms that compute solutionsto these linear systems).

Publications

Three publications appearing in calender year 2015.Most significant recent publications

[1] James Adler, Scott MacLachlan, and NiallMadden. A first-order system Petrov-Galerkindiscretization for a reaction-di�usion problemon a fitted mesh. IMA Journal of NumericalAnalysis, 2015. 10.1093/imanum/drv045.

[2] Niall Madden and Stephen Russell. A mul-tiscale sparse grid finite element method for atwo-dimensional singularly perturbed reaction-di�usion problem. Adv. Comput. Math.,41(6):987–1014, 2015.

[3] Naresh M. Chadha and Niall Madden.An optimal time-stepping algorithm for un-steady advection-di�usion problems. J.Comput. Appl. Math., 294:57–77, 2016.10.1016/j.cam.2015.07.029.

[4] Pandelitsa Panaseti, Antri Zouvani, NiallMadden, and Christos Xenophontos. AC1-conforming hp finite element method forfourth order singularly perturbed boundaryvalue problems. Appl. Numer. Math., 104:81–97, 2016. 10.1016/j.apnum.2016.02.002.

Research Activities

In April, I gave a research talk at the 12th AnnualWorkshop on Numerical Methods for Problems withLayer Phenomena, a two-day conference dedicated tothe 65th birthday of Hans-Gorg Roos. (The 14th in-stance of this meeting will take place in Galway inApril 2017!) In June, I gave a talk at the 26th Bi-ennial Numerical Analysis Conference, Strathclyde,where I also organised a mini-symposium on singu-larly perturbed di�erential equations. I gave invitedseminars in the University of Limerick, in March, andUniversity College Dublin in December.During 2015, I worked with three research students:Thai Anh Nhan, who defended his thesis in Septem-ber, Stephen Russell, who is preparing the final draftof his thesis, and Faiza Alssaedi, who started inFebruary.I refereed papers for several international journalsduring 2015, including the Journal of Scientific Com-puting, Journal of Applied Mathematics & Compu-tation, Applied Numerical Mathematics, Journal ofMathematical Modelling and Analysis, Journal ofDi�erence Equations and Applications, Journal ofComputer Mathematics, and Numerical Algorithms.

McCluskey, Aisling


My research interests reside primarily within analytictopology, with a particular fascination in how ordertheoretic structures mesh with topology. Other ongo-ing research concerns continua theory in the contextof both a natural associated order (a notion of ”be-tweenness”), and of discrete dynamical systems.Additionally, my research interests encompass re-search in undergraduate mathematics education.Specifically, I am interested in the developmentof and facility with proof and proving in abstract

10.1093/imanum/drv045

http://dx.doi.org/10.1016/j.cam.2015.07.029

http://dx.doi.org/10.1016/j.apnum.2016.02.002

http://www.math.tu-dresden.de/layer-phenomena/



http://numericalanalysisconference.org.uk/

http://numericalanalysisconference.org.uk/


analysis-based mathematical subjects typically takenin mathematics-major degree programmes.

Publications

Number of publications appearing in calendar year2015: 2Most significant publications

[1] A. McCluskey and B. McMaster, ”Undergradu-ate topology: a working textbook”, Oxford Uni-versity Press, 2014.

[2] J. L. Bruno and A. E. McCluskey, ”Topolo-gies as points within a Stone space: lattice the-ory meets topology”, Topology Appl. 160 (2)(2013), 273 - 279.

Research Activities

Publications: 2 published; 1 submitted.Graduate students: Daron Anderson PhD; MichelleDuane graduated with MSc by research in November2015.Conferences: Host of 18th Galway Topology Collo-quium at NUI Galway in June 2015.Host of the international 30th Summer Conferencein Topology and Its Applications at NUI Galway inJune 2015.Member of International Steering Committee ofDELTA 2015Research funding: 10,000 euros awarded by SFIConferences and Workshops programme; 2100 eurosfrom FÃπilte Ireland; 300 euros from IMS; 0 eurosfrom IRC New Foundations.Research visitors: S. Greenwood, Auckland, May2015 (5 weeks); John Grant McLoughlin, Canada,September - November 2015 (6 weeks); I. Weiss,University of South Pacific, June 2015 (4 days).Reviewer of papers submitted to Topology and itsApplications and International Journal of Researchin Undergraduate Mathematics Education.

Mc Gettrick, Michael


Quantum information and quantum computation: Inparticular quantum algorithm design, quantum walksand quantum games. Computer algebra.

Publications

Number of publications appearing in calender year2015: 2Most significant recent publications

[1] “Generic quantum walks with memory on reg-ular graphs”, Li, D., Mc Gettrick, M., Gao, F.,Xu, J., and Wen, Q-Y., accepted in Phys. Rev.A (2016)

[2] “Quantum walks on two kinds of two-dimensional models”, Li, D., Mc Gettrick,M., Zhang, W-W., Zhang, K-J. InternationalJournal of Theoretical Physics Volume: 54Issue: 8 pp 2771-2783 (2015)

[3] “One-dimensional lazy quantum walks and oc-cupancy rate”, Li, D., Mc Gettrick, M., Zhang,W-W., Zhang, K-J. Chinese Physics B Vol-ume: 24 Issue: 5 (2015)

Research Activities

I gave an invited lecture on “Quantum walks” atthe George Boole Mathematical Sciences Conference(GBMSC) in UCC, August 2015. I refereed a numberof papers on quantum walks. In May 2015 I partici-pated in the conference TQC2015 (Theory of Quan-tum Computation, Communication and Cryptogra-phy) in Brussels. I am a member of both the Irishand American Mathematical Societies.

Meere, Meere


Analysis of reaction di�usion models describing drugrelease from a�nity hydrogels. Modelling drug re-lease from novel drug eluting stents. Modelling en-docytosis and the mechanics of membranes. Mod-elling di�usion in crystalline solids. Modelling poly-mer degradation.

Publications

Five papers in peer reviewed journals in 2015.Most significant recent publications

[1] Sean McGinty, Tuoi T.N. Vo, Martin Meere,Sean McKee & Christopher McCormick, Somedesign considerations for polymer-free drug-eluting stents: a mathematical approach, ActaBiomaterialia, doi:10.1016/j.actbio.2015.02.006(2015)


[2] Tuoi T.N. Vo & M.G. Meere, A mathematicalmodel for the release of peptide-binding drugsfrom a�nity hydrogels, Cellular and MolecularBioengineering, doi:10.1007/s12195-014-0375-2(2015)

[3] O. Gladkovskaya, P. Greaney, Y. K. Gun’ko,G. M. O’Connor, M. Meere & Y. Rochev,An experimental and theoretical assessmentof quantum dot cytotoxicity, Toxicology,doi:10.1039/c5tx00149h (2015)

[4] Tuoi T.N. Vo & M.G. Meere, The mathemati-cal modelling of a�nity-based drug delivery sys-tems, Journal of Coupled Systems and Multi-scale Dynamics, 3, 5 - 22 (2015)

Research Activities

Two PhD students, one co-supervised by Dr GiuseppeZurlo, and another co-supervised by Dr Tuoi Vo. Re-viewed two papers. Mentor at the Student ModellingWorkshop, MACSI. Mentor at the Stokes ModellingWorkshop, NUIG. Delivered invited talk to CMALS,the University of Glasgow. One week research visitto the University of Strathclyde, December 2015.

Newell, John


My primary areas of research in Biostatistics are inthe theory and application of statistical methods inclinical trials of health service and population healthinterventions and in the development of novel ana-lytic approaches in Sports and Exercise Science. Myresearch interests include statistical modelling, sta-tistical computing, design and analysis of cluster ran-domised trials, smoothing techniques and derivativeestimation, survival analysis, tree based classificationproblems and sports analytics.

Publications

4 publications appeared in calendar year 2015Most significant recent publications

[1] Alvarez-Iglesias, A., Newell, J., Scarrott, C. andHinde, J. (2015), Summarising censored sur-vival data using the mean residual life function.Statistics in Medicine, 34: 1965â��1976.

[2] Newell, J., Korir, P., Moore, B., Pedlar, C.(2015) App for the calculation of blood lactate

markers. Journal of Sports Sciences, 33:6, 568-569.

[3] Murphy AW, Cupples ME, Murphy E, NewellJ, Scarrott C, Vellinga A, Gillespie P, ByrneM, Smith SM (2015) ’Six-year follow-up of theSPHERE RCT: secondary prevention of heartdisease in general practice’. BMJ Open.

[4] Healy, D, Clarke-Moloney, M, Gaughan, B,O’Daly, S, Hausenloy, D, Sharif, F, Newell, J,O’Donnell, M, Grace, P, Forbes, JF, Cullen,W, Kavanagh, E, Burke, P, Cross, S, Dow-dall, J, McMonagle, M, Fulton, G, Manning,BJ, Kheirelseid, EAH, Leahy, A, Moneley, D,Naughton, P, Boyle, E, McHugh, S, Madhaven,P, O’Neill, S, Martin, Z, Courtney, D, Tubas-sam, M, Sultan, S, McCartan, D, Medani,M, Walsh, S (2015) ’Preconditioning ShieldsAgainst Vascular Events in Surgery (SAVES),a multicentre feasibility trial of precondition-ing against adverse events in major vascularsurgery: study protocol for a randomised con-trol trial’. Trials, 16.

Research Activities

• Current research grants: PI (1), Co-PI (1), Col-laborator (3), Co-Applicant (7).

• Number of graduate students: 6

• Journal submissions: 7

• Conferences: 2

• Visits: 4

• Invited talks: 2

• Research visits: 4

• Memberships: International Society for ClinicalBiostatistics, Irish Statistical Association

• External posts: Adjunct Senior Research Fellowin the Department of Mathematics and Statis-tics, University of Canterbury, Christchurch,New Zealand.

O Broin, Pilib


My research interests are focused in two main areas:algorithm development and high-performance com-puting for the analysis of next-generation sequencingdata, and statistical machine learning for the identi-fication of biomarker signatures in clinical data.


Publications


[1] Tomohisa Takahashi*, Shota Okabe*,Pilib O Broin*, Akira Nishi, Kenny Ye,Michael Beckert, Takeshi Izumi, HiroakiMachida, Gina Kang, Jose L. Pena, AaronGolden, Takefumi Kikusui, Noboru Hiroi.‘Structure and function of neonatal socialcommunication in a genetic mouse model ofautism spectrum disorders’. Mol. Psych. (inpress)

[2] Pilib O Broin, Terry Smith, and AaronGolden. ‘Alignment-free clustering of tran-scription factor binding motifs using a genetic-k-medoids approach’. BMC Bioinformatics.16(1):22 (2015)

[3] Pilib O Broin, Bhavapriya Vaitheesvaran,Subhrajit Saha, Kirsten Hartil, Emily I.Chen, Devorah Goldman, William Harv Flem-ing, Irwin J. Kurland, Chandan Guha, andAaron Golden. ‘Intestinal Microbiota-DerivedMetabolomic Blood Plasma Markers for PriorRadiation Injury’. Int. J. Radiat. Oncol. Biol.Phys. 91(2):360-367 (2015)

[4] Behnam Nabet, Pilib O Broin, Jaime M.Reyes, Kevin Shieh, Charles Y. Lin, ChristineM. Will, Relja Popovic, Teresa Ezponda, JamesE. Bradner, Aaron A. Golden, and Jonathan D.Licht. ‘Deregulation of the Ras-Erk signalingaxis modulates the enhancer landscape’. Cellreports 12(8):1300-1313 (2015)

Research Activities

Published manuscripts:6Conference presentations:8Invited talks:1Graduate Students:1 PhD (co-supervised)Professional Memberships: NYAS, ISCB, VIBE

O’Regan, Donal


Nonlinear functional analysis (theory, methods andapplications).

Publications


[1] 1. On abstract di�erential equations with noninstantaneous impulses (with E. Hernandez andM. Pierri), Topological Methods in NonlinearAnalysis, 46(2015), 1067–1088.

[2] 2. Asymptotic behavior of a three specieseco-epidemiological model perturbed by whitenoise (with Q. Zhang, D. Jiang and Z. Liu),Journal of Mathematical Analysis and Appli-cations, 433(2016), 121–148.

[3] 3. Existence results for a Neumann probleminvolving the p(x)–Laplacian with discontin-uous nonlinearities (with G. Barletta and A.Chinni), Nonlinear Analysis Series B: RealWorld Applications, 27(2016), 312–325.

[4] 4. Weak solutions for fractional di�erentialequations in nonreflexive Banach spaces viaRiemann-Pettis integrals (with R.P. Agarwal,V. Lupulescu and G. ur Rahman), Mathema-tische Nachrichten, 289(2016), 395–409.

Research Activities

Park, Sejong


My research topics involve representation theory fi-nite groups and its connection with group theory andalgebraic topology. Specifically, I am working on fu-sion systems and related homological algebra, includ-ing cohomology of groups, and more generally, de-rived limits of functors over categories, Mackey func-tors and biset functors.

Publications


[1] Mislin’s theorem for fusion systems via Mackeyfunctors, Comm. Algebra, to appear

[2] Realizing fusion systems inside finit groups,Proc. Amer. Math. Soc., to appear


[3] Mackey functors and sharpness for fusion sys-tems, Homology, Homotopy Appl. 17 (2015),no. 1, 147–164 (joint with Antonio Dıaz)

[4] Counting conjugacy classes of cyclic subgroupsfor fusion systems, J. Group Theory 17 (2014),no. 4, 661–666

Research Activities

• Research grant: Ulysses 2014 (as a projectleader, with Goetz Pfei�er and Brendan Mas-terson)

• Published paper: 1

• Submitted papers: 2

• Invited talks: 2

[1] Cohomology of fusion systems, Groups andgeometries, Ban�, Canada, 4â��-8 May2015

[2] Biset functors and fusion systems, Func-torial Methods in Representation Theory,EPFL, Switzerland, 1-â��4 Sep 2015

• Other talks: 6

• Conference participation: 4

[1] Representations of Finite Groups, Ober-wolfach, Germany, 6–10 Apr 2015

[2] Groups and geometries, Ban�, Canada, 4–8 May 2015

[3] Groups, Representations, and Cohomol-ogy, Isle of Skye, UK, 23–26 Jun 2015

[4] Functorial Methods in RepresentationTheory, EPFL, Switzerland, 1–4 Sep 2015

• Research visits

[1] Universite de Picardie, Amiens, France,19â��-25 Apr 2015

[2] Universidad de Malaga, Spain, 8-â��15July 2015

[3] Universitat Autonoma de Barcelona,Spain, 14–17 Oct 2015

• Visitors: 5

• Papers refereed: 2

O’Shea, James


I am interested in a number of questions withinquadratic form theory. Most fundamentally, I am in-terested in understanding the isotropy behaviour offorms with respect to extensions of their ground field,addressing questions in the following vein: if a givenpolynomial (homogeneous of degree two) attains aroot over a field extension, what other polynomials(homogeneous of degree two) attain a root over thisfield extension in consequence? I am currently in-vestigating the isotropy of forms over function fieldsof conics, an important class of field extensions. Iam also seeking to clarify the nature of the relation-ship that exists between the classes of “round” and“group” forms. I am also interested in topics in Lin-ear Algebra, and am considering questions concerningthe rank of matrices over finite fields.

Publications


[1] Multiples of Pfister forms, Journal of Algebra449, 214-236 (2016).

[2] The weak isotropy of quadratic forms over fieldextensions, Manuscripta Mathematica 145, 143-161 (2014).

[3] Isotropy over function fields of Pfister forms,Journal of Algebra 361, 23-36 (2012).

[4] Sums of squares in certain quaternion and oc-tonion algebras, C. R. Acad. Sci. Paris, Ser. I349, 239-242 (2011).

Research Activities

I am currently supervising one student in the prepa-ration of her M.Sc. thesis. I have given talks at boththe School Seminar and the Linear Algebra Semi-nar within the School. I am currently a committeemember of the Irish Mathematical Society, and thusattend the Society’s scientific and general meetings.I look forward to attending one or more of the up-coming algebra conferences that will be held in Lens,Ghent and Telc this summer. I recently refereed anarticle on the Hurwitz problem in quaternion alge-bras.

Pfei�er, Gotz



Computational algebra, representations of finitegroups and associative algebras, combinatorics andgeometry of finite Coxeter groups.

Publications


[1] (with Marcus Bishop, J. Matthew Douglass andGerhard Rohrle) Computations for Coxeter ar-rangements and Solomon’s descent algebra III:Groups of rank seven and eight, J. Algebra 423(2015), 1213–1232.

[2] (with J. Matthew Douglass and GerhardRohrle) Cohomology of Coxeter Arrangementsand Solomon’s Descent Algebra, Trans. Amer.Math. Soc. 366 (2014), no. 10, 5379–5407.

Research Activities

Research grants: IRC Ulysses Grant (with S. Park);Numbers of graduate students: 1; Journal submis-sions: 2; Conferences: 2; Invited talks: 2; Researchvisits: 2; Papers refereed: 5; Math review: 4; Editor-ships: Mathematical Proceeedings of the Royal IrishAcademy; Memberships: Irish Mathematical Society,American Mathematical Society;

Pfei�er, Kirsten


Publications


[1] Sinead Breen, Ann O’Shea, Kirsten Pfei�er(2016) ’Students’ views of example generationtasks’. In: Teaching Mathematics and its Ap-plications.

[2] Pfei�er, K. and Quinlan R. (2015) Proof-Evaluation as a Step towards Proof Authorship.In: MAA Notes. Volume ‘Beyond Lecture:Techniques to Improve Student Proof-WritingAcross the Curriculum’.

[3] Pfei�er, K. and Quinlan R. Proof evaluationtasks as tools for teaching? Proceedings of theNinth Congress of the European Society for Re-search in Mathematics Education (CERME 9).February 4th - 8st 2015, Prague (Czech Repub-lic).

Research Activities

• Post-doc researcher in a joined project (“Ananalysis of the opportunities for creative reason-ing in undergraduate Calculus courses”) fundedby 3U NStep .

• Organiser of the 10th Annual Irish Workshopon Mathematics Learning and Support Centres(May27th in NUI Galway).

• Committee member of the Irish MathematicsLearning Support Network (IMLSN).

Piiroinen, Petri T


My main research interests are in the area of dis-continuous dynamical systems with application torigid-body mechanics, evolving networks, populationdynamics, economics, psychology and biological sys-tems. An overarching aim of my research is to bridgethe gap between mathematics and numerical analy-sis on one hand and biology, engineering and socialsciences on the other to make mathematical theoriesmore applicable to non-theoreticians.

Publications

Most significant publications

• Burns, S. and Piiroinen P.T., A hybrid schemefor simulation of planar rigid bodies with im-pacts and friction using impact mappings, In-ternational Journal of Non-Linear Mechan-ics 77, pp. 312–324, December 2015. (DOI:10.1016/j.ijnonlinmec.2015.09.011)

• Doherty, K., Meere, M. and Piiroinen, P.T.,Some Mathematical Models of IntermolecularAutophosphorylation, Journal of Theoretical Bi-ology 370, pp. 27–38, April 2015.(DOI: 10.1016/j.jtbi.2015.01.015)

• Donohue, J.G. and Piiroinen, P.T., Mathemat-ical modelling of seasonal migration with appli-cations to climate change, Ecological Modelling299, pp. 79–94, March 2015.(DOI: 10.1016/j.ecolmodel.2014.12.003)

Research Activities

During 2015 I supervised 4 PhD students and 1 MScstudent. The MSc student and two of the PhD stu-dents graduated. During the year I visited researchers


in Sao Paulo (Brazil), Naples (Italy) and Bangalore(India).

Quinlan, Rachel


Linear algebra and its interactions with combina-torics, graph theory, field theory and the representa-tion theory of finite groups. Specific current projectsinvolve completion problems for partial matrices andentry pattern matrices, as well as classifications ofnilpotent spaces in positive characteristic. I also haveinterests in university mathematics education.

Publications


[1] Kirsten Pfei�er and Rachel Quinlan. Proofevaluation tasks as tools for teaching? Proceed-ings of the Ninth Congress of the European So-ciety for Research in Mathematics Education.pp178-184 (2015) ¡hal-01281065¿

[2] J. McTigue and R. Quinlan. Partial matricesof constant rank, Linear Algebra and its Appli-cations, Vol. 446, 177–191 (2014).

[3] J. Cruickshank, A. Herman, R. Quinlan, F.Szechtman, Unitary groups over local rings,Journal of Algebra and its Applications, Vol.13, Issue 02 (2014)

[4] J. McTigue and R. Quinlan, Partial matriceswhose completions all have the same rank, Lin-ear Algebra and its Applications, Vol 438, no.1, pages 348–360 (2013)

Research Activities

I am currently supervising the PhD research of twostudents, Olga O’Mahony and Ha Van Hieu. I wasalso the supervisor of James McTigue who com-pleted his PhD in 2015. I am the coordinator of theweekly linear algebra seminar which ran throughoutSemester 2 this year. In 2015 I gave research presenta-tions at the Ninth Congress of the European Societyfor Research in Mathematics Education in Prague,and in the UCD Algebra seminar (as well as locally).In Summer 2015 I supervised the Summer internsipof Cian O’Brien. I have recently refereed articles forthe Journal of Algebra and for Linear Algebra and itsApplications and reviewed three articles for Mathe-matical Reviews in 2015. I am the author of one bookreview in the Bulletin of the IMS in 2015.

Rover, Claas



Publications

Research Activities

Ryan, Ray


Publications


[1] ”Introduction to tensor products of Banachspaces”, Springer Monographs in Mathematics,Springer-Verlag, London, 2002.

[2] with C. Boyd, ”Geometric theory of spacesof integral polynomials and symmetric tensorproducts”, J. Functional Analysis 179 (2001),no. 1, 18–42.

[3] with B. Grecu, ”Polynomials on Ba-nach spaces with unconditional bases”,Proc. Amer. Math. Soc 133 (2005), no. 4,1083–1091.

[4] with C. Boyd, ”The norm of the product ofpolynomials in infinite dimensions”, Proc. Ed-inburgh Math. Soc. (2) 49 (2006), no. 1, 17–28.

Research Activities

• “Polynomial and Holomorphic Mappings onRiesz Spaces”, minicourse at 11th ILJU Schoolof Mathematics, Gyeongju, Korea, September2016.

• “Free and Projective Vector Lattices”, DublinAnalysis Seminar, UCD, June 2015.

• ”Regular Holomorphic Functions on ComplexBanach Lattices”, Workshop on Infinite Dimen-sional Analysis, Buenos Aires, July 2014.

Rahm, Alexander D.

Started a postdoctoral fellowship at the University ofLuxembourg on 1 September 2015.



Algebra, Geometry & Topology, e.g. homology ofarithmetic groups, isometries of hyperbolic space.

Publications


[1] Alexander D. Rahm and Matthias Wendt, Arefinement of a conjecture of Quillen. ComptesRendus Mathematique (2015)

[2] Alexander D. Rahm, Complexifiable character-istic classes. Journal of Homotopy and RelatedStructures (2014)

[3] Alexander D. Rahm, Accessing the cohomologyof discrete groups above their virtual cohomo-logical dimension. Journal Of Algebra (2014)

[4] Alexander D. Rahm, The homological torsionof PSL2 of the imaginary quadratic integers.Transactions of the American Mathematical So-ciety (2013)

Research Activities

Grants: ICHEC grant of 900,000 processor hours(value: 30,000 Euro); IHES grant for one-monthfunded research stay; MFO grant for two-weeksfunded research collaboration stay at Oberwolfach,joint with Rob de Jeu, Herbert Gangl and DanYasaki. PhD student: Daher Al-Baydli (jointly super-vised with Emil Skoldberg); Master student: Kather-ine Wilkie. Papers in progress: Manuscripts withMatthias Wendt, resp. Ethan Berkove submittedto journals; preprint with Rob de Jeu; preprint onorbifolds which is under completion joint with FabioPerroni. Talks: 3 international conference/workshopcontributions in 2014 (3 confirmed so far in 2015), 2invited seminar talks in 2014 (3 confirmed so far in2015). Papers refereed for Mathematische Annalen,Journal fÃ�r die reine und angewandte Mathematik(Crelle’s Journal), Journal of Pure and Applied Alge-bra (JPAA), Homology, Homotopy and Applications(HHA), Discrete & Computational Geometry. Edito-rial board member of Research Matters, NUI Galway.Member of IMS, EMS, SMF and DMV.

Seoighe, Cathal


My research interests are in several areas of bioin-formatics/computational biology: Genomics and epi-

genetics, including gene expression deconvolution,mRNA splicing and analysis of chromatin structureusing high throughput sequencing data; developmentand application of probabilistic models of evolution;genetic variation in human molecular phenotypes, in-cluding gene expression, splicing and mutation rates;computational immunology, including tools for anal-ysis of immune receptor diversity. Bioinformatics isinterdisciplinary and I collaborate with several otherresearch groups on campus. A major focus of recentcollaborations involves the analysis of data from highthroughput sequencing technologies. These technolo-gies can be used to sequence genomes or for studyinggene expression or the binding of proteins to DNA.

Publications

4 journal articles appeared in 2015.Most significant recent publications

[1] LymAnalyzer: a tool for comprehensive analy-sis of next generation sequencing data of T cellreceptors and immunoglobulins. Yu Y, CeredigR, Seoighe C. Nucleic Acids Res. 2016 Feb29;44(4)

[2] Promiscuous mRNA splicing under the controlof AIRE in medullary thymic epithelial cells.Keane P, Ceredig R, Seoighe C. Bioinformatics.2015 Apr 1;31(7):986-9

[3] Seq-ing improved gene expression estimatesfrom microarrays using machine learning. KorirPK, Geeleher P, Seoighe C. BMC Bioinformat-ics. 2015 Sep 4;16:286.

[4] Population genetics inference for longitudinally-sampled mutants under strong selection.Lacerda M, Seoighe C. Genetics. 2014Nov;198(3):1237-50.

Research Activities

My research group consisted of six PhD students in2015. Current research grants are from the EU (MarieSklodowska Curie), IRC, Science Without Borders(Brazil), PRTLI (through the graduate programme insimulation science) and SFI (H2020 Catalyst Award).Academic community service included membership ofthe editorial board of Briefings in Bioinformatics, re-view of grants for the Natural Sciences and Engineer-ing Research Council of Canada and refereeing for arange of journals. Member of the International Soci-ety for Computational Biology. Gave a keynote talkat ISMB satellite meeting for Integrative RNA Biol-ogy.


Sheahan, Jerome


Sequences of various kinds, including iid and depen-dent sequences.

Publications

Three research publications

Research Activities

Skoldberg, Emil


I work on combinatorial commutative (and non-commutative) algebra. In particular, I am interestedin homological properties of such algebraic structures,recently in particular the study of the existence ofdi�erential graded algebra structures on minimal res-olutions of certain classes of monomial ideals in thecommutative polynomial ring.

Publications

Research Activities

Tuite, Michael


Vertex operator algebras (VOAs), conformal field the-ory, Riemann surfaces, elliptic, Jacobi and modularfunctions in number theory and combinatorics. Inthe past year I completed a major paper with TomGilroy where we describe a genus two version of Zhutheory for VOAs. I am also working on the solutionof a partial di�erential equation describing all genustwo partition functions for the (2,5) minimal modelVOA with Tom Gilroy at UCD, quasi-Jacobi formsin VOAs with Kathrin Bringman and Matt Krauel ofUniversity of Cologne and on VOA book collabora-tion with .Geo� Mason at UC Santa Cruz

Publications


[1] G. Mason and M.P. Tuite, Free bosonic ver-tex operator algebras on genus two Riemannsurfaces II. â��Conformal Field Theory, Au-tomorphic Forms and Related Topicsâ��, Con-tributions in Mathematical and ComputationalSciences 8 183-225, (Springer Verlag), (2014).

[2] M.P. Tuite and Hoang Dinh Van, On excep-tional vertex operator (super) algebras, ”Devel-opments and Retrospectives in Lie Theoryâ��,Developments in Mathematics Volume 38 351-384 (Springer Verlag) (2014).

Research Activities

[1] Invited talks at University of Cologne, a work-shop on Mathieu Moonshine Durham Univer-sity and a VOA conference in Chengdu China.

[2] 1 PhD student with IRC funding

[3] 2 journal submissions

Ward, James


Algebra, Subnormal Subgroups, History of Mathe-matics.

Publications

Research Activities

Yang, Haixuan


My focus is in Bioinformatics & Statistical Modelling,especially of network data such as protein-protein in-teractions, co-expression, and functional similarity.A bio-molecular network can be viewed as a collec-tion of nodes, representing the bio-molecules, con-nected by links, representing relations between thebio-molecules. I am working on inferring valuable in-formation from bio-molecular networks.

Publications


[1] Y Jiang et al. An expanded evaluation of pro-tein function prediction methods shows an im-provement in accuracy. arXiv, 2016.


[2] SP Smieszek, H Yang, A Paccanaro, PF De-vlin. Progressive promoter element combina-tions classify conserved orthogonal plant circa-dian gene expression modules. Journal of TheRoyal Society Interface 11 (99), 2014.

[3] P Radivojac et al. A large-scale evaluation ofcomputational protein function prediction. Na-ture Methods 10 (3), 2013.

Research Activities

Presented the work ”A Graph-based Logistic Regres-sion Model and Its Application to Protein FunctionPrediction” in CASI2015. Presented the work ”Apost-processing method of NMF for molecular cancersubtype discovery” in VIBE2015. Visited TsingHuaUniversity. Refereed papers for ”IEEE Transactionson Neural Networks and Learning Systems”, ”Gene”,and ”Bioinformatics”.

Zurlo, Giuseppe


I am deeply interested in those phenomena that canbe modeled by Continuum Mechanics and Thermo-dynamics. My research is focused on the modeling ofmaterial behavior at the intersection of ContinuumMechanics with Biology, Medicine and Electromag-netism. More in detail, I work on the theory of growthin biological materials, on the mechanical behavior ofcell membranes, with recent emphasis on endocytosis,on finite plasticity theory, on the theory of finite elas-ticity with a specific focus on the mechanics of thinbodies, on the electromechanics of highly deformablematerials.

Publications


[1] S Colonnelli, G Saccomandi, G Zurlo, The roleof material behavior in the performances of elec-troactive polymer energy harvesters Journal ofPolymer Science Part B: Polymer Physics 53(18), 1303-1314

Research Activities

[1] invited talk to the MathematischesForschungsinstitut Oberwolfach (MFO, Ober-wolfach Research Institute for Mathematics)November 2015

[2] co-supervisor (with Dr Martin Meere) of 1 PhDthesis (student: Paul Greaney)

[3] 3 journal submissions

[4] research visits in Ecole Polytechnique, InstitutCurie (Paris), Universit�a di Perugia, Politec-nico di Bari

[5] reviewer for various scientific journals (Proceed-ings of the Royal Society A, Journal of Elastic-ity, Journal of Physics D, ... )

[6] member of the Italian group of MathematicalPhysics (GNFM)

Visitors

Murphy, Jerry

Dates of visit: 10-11 May 2015 Dr Murphy is Lecturerin Mechanical Engineering at DCU and Adjunct Lec-turer in the School of Mathematics, Statistics andApplied Mathematics. He visited Professor MichelDestrade to work on the mechanical behaviour of fi-brous soft matter.

Research Interests

A complete treatment of the problem of Dominantnegative Poynting e�ect for soft tissues, published inJournal of Engineering Mathematics [95 (2015) 87-98]

Saccomandi, Giuseppe

Dates of visit: 14-17 August 2015 Professore Sac-comandi is Professor in Mechanical Engineering atthe Universita di Perugia and Adjunct Professor inthe School of Mathematics, Statistics and AppliedMathematics. He visited Professor Michel Destradeto work on the mechanical behaviour of rubbers.

Research Interests

A complete treatment of the problem of MethodicalFitting for Mathematical Models of Rubber-like Ma-terials, under review.

Lusetti, Irene


Dates of visit: 01-31 August 2015 Ms Lusetti is a Mas-ters Student in Mathematical Engineering at Politec-nico di Milano. She visited Professor Michel Destradeto work on the mechanical stability of soft matter,with support from the College of Science.

Research Interests

A complete treatment of the problem of Stability ofbent layered solids, in preparation.

Su, Yipin

Dates of visit: 01 November 2015-02 April 2016 MrSu is a PhD Student in Mechanical Engineering atZhejiang University. He visited Professor Michel De-strade to work on the mechanical behaviour of electro-active soft solids, with support from his university.

Research Interests

A complete treatment of the problem of Stability softdielectrics for half-spaces and plates, two articles inpreparation.

Carfagna, Melania

Dates of visit: 15 November 2015-15 February 2016Ms Carfagna is a PhD Student in Mathematica Engi-neering at Politecnico di Torino. She visited ProfessorMichel Destrade to work on the the stability of softsolids, with support from her university.

Research Interests

A complete treatment of the problem of oblique wrin-kles for half-spaces and layered substrates, under re-view.

Balbi, Valentina

Dates of visit: 12 November 2015-12 January 2016Ms Balbi is a Post-doctoral fellow at the UniversitePierre et Marie Curie. She visited Professor MichelDestrade to prepare a grant proposal, with supportfrom Enterprise Ireland.

Research Interests

A complete proposal submitted to the EuropeanCommission for a Marie Curie Initial Training Net-work.

Visiots to Sejong Park

Dates of visit:

[1] 21–28 Apr 2015: Serge Bouc, Radu Stancu

[2] 29 Sep – 4 Oct: Antonio Dıaz

[3] 29 Sep – 2 Oct: Radu Stancu

[4] 6–10 Oct 2015: Hiroyuki Nakaoka

Research Interests

[1] Representation theory of finite groups

[2] Fusion systems and related homological algebra

[3] Biset functors (Mackey functors)

I am collaborating with Goetz Pfei�er on biset func-tors, in particular the structure of the double Burn-side ring B(G,G) of a finite group G.

MacLachlan, Scott, Memorial University ofNewfoundland

Dates of visit: 22–19 April.

Research Interests

Scott worked with Niall on completing revisions to apaper on a least-squares finite element method, andwith Thai and Niall on a multigrid preconditionerfor reaction-di�usion problems in one and two dimen-sions. He also gave a seminar to the SIAM Chapter.

Linß, Torsten, FernUniversitat in Hagen

Dates of visit: 30 November – 1 December.

Research Interests

Torsten worked with Niall on long-running projectinvolving the analysis of a time-stepping alternating-direction method.

Miszczak, Jarek

Dates of visit: 9/11/2015 to 13/11/2015


Research Interests

Dr. Miszczak visited NUI, Galway to carry out re-search with Dr. M. Mc Gettrick on quantum walksand quantum evolutionary game theory: He gave aseminar on “Why quantum mechanics is (not) spe-cial”


Postgraduate Students

• Daher Al-Baydli [email protected]

• Faiza Alssaedi [email protected]

• Daron Anderson [email protected]

• Alan Barnicle [email protected]

• Sofia Barreira [email protected]

• Anh Tuan Bui [email protected]

• Issac Burke [email protected]

• Richard Burke [email protected]

• Shane Burns [email protected]

• Simone Coughlan [email protected]

• John Donohue [email protected]

• Liam Doonan [email protected]

• Ronan Egan [email protected]

• Lida Fallah lida [email protected]

• Artur Gower [email protected]

• Paul Greaney [email protected]

• Ha Van Hieu [email protected]

• Amirhossein Jalali [email protected]

• Olga Kalinina [email protected]

• Peter Keane [email protected]

• Adib Makrooni [email protected]

• Barbara Martinelli [email protected]

• Brendan Masterson [email protected]

• Shirin Moghaddam [email protected]

• Michael McCague [email protected]

• Ngoc Thanh Nguyen [email protected]

• Anh Thai Nhan [email protected]

• Olga O’Mahony [email protected]

• Davood Roshan [email protected]

• Stephen Russell [email protected]

• Qays Shakir [email protected]

• Eoghan Staunton [email protected]

• Philip Vernon [email protected]

• Michael Welby

• Yaxuan Yu [email protected]


Seminars

[1] Oliver Mason, Maynooth University. TheMarkov Chain Tree Theorem in the MaxAlgebra and Semirings, 22/01/2015. (Con-tact: Niall Madden)

[2] Paul Hurley, IBM Research – Zurich. Re-imagining the radio telescope andsampling from Gaussian processes,05/02/2015. (Contact: Jerome Sheahan)

[3] Kevin Jennings, NUIG. Some commentson the ranks of subspaces of Mn(F),05/03/2015. (Contact: Haixuan Yang)

[4] Baptiste Rognerud, EPFL, Switzerland.Equivalences between blocks of coho-mological algebras, 12/03/2015. (Contact:Sejong Park)

[5] Tom Brady, DCU. Triangulating the per-mutahedron, 19/03/2015. (Contact: EmilSkoldberg)

[6] Fabio Perroni, University of Trieste, Italy.Topology of the moduli space of curveswith a given group of automorphisms,26/03/2015. (Contact: Alexander Rahm)

[7] Timothy J. Healey, Cornell University, USA.Wrinkling of Highly Stretched ElasticSheets, 01/04/2015. (Contact: GiuseppeZurlo)

[8] Laurence Hurst, University of Bath, UK. Whythere is more to gene evolution than pro-tein function: splicing and dual-codingsequence, 09/04/2015. (Contact: CathalSeoighe)

[9] Scott MacLachlan, Memorial University,Canada. Parallel-in-time integration us-ing multigrid, 23/04/2015. (Contact: NiallMadden)

[10] Piotr Gawron, Polish Academy of Sciences,Poland. Generalized open quantum walkson Apollonian networks, 29/04/2015. (Con-tact: Michael Mc Gettrick)

[11] Alberto Paccanaro, Royal Holloway Universityof London, UK. Inference and structure dis-covery in biological networks, 14/05/2015.(Contact: Haixuan Yang)

[12] Ruben Sanchez-Garcia, University ofSouthampton, UK. Topology and Geom-etry of Networks and Data, 20/05/2015.(Contact: Alexander Rahm)

[13] Matthias Wendt, Universitaet Duisburg-Essen,Germany. Buildings and K-theory of ellip-tic curves, 28/05/2015. (Contact: AlexanderRahm)

[14] Sina Greenwoody, University of Auckland, NewZealand. Generalised inverse limits andcontinua, 04/06/2015. (Contact: Aisling Mc-Cluskey)

[15] Sushing Chen, University of Florida, USA. BigData and Precision Medicine, 12/06/2015.(Contact: Cathal Seoighe)

[16] Nesrin Manav, Gazi University, Turkey. FixedPoint Theorems on Modular MetricSpaces, 03/09/2015. (Contact: RaymondRyan)

[17] Dessislava Kochloukova, State University ofCampinas, Brazil. Weak commutativity ingroups, 10/09/2015. (Contact: Grahamj Ellis)

[18] Javier Aramayona, Institut de MathÃ�ma-tiques de Toulouse, France. The abelianiza-tion of automorphism groups of right-angled Artin groups, 17/09/2015. (Contact:Grahamj Ellis)

[19] Neil Oâ�èConnell, Warwick University,UK. Increasing subsequences, Youngtableaux, and related topics, 24/09/2015.(Contact: Raymond Ryan)

[20] Marianne Leitner, NUIG. CFT on Riemannsurfaces, 01/10/2015. (Contact: Grahamj El-lis)

[21] Hiroyuki Nakaoka, UniversitÃ� de Picardie /Kagoshima University, France / Japan. Pread-ditive categories as a categorification ofrings; quotients, spans and their applica-tions, 08/10/2015. (Contact: Sejong Park)

[22] John McLoughlin, University of NewBrunswick, Canada. Enriching the Scopeof Mathematical Experiences withProblems, 15/10/2015. (Contact: AislingMcCluskey)

[23] Pilib Ã� Broin, NUIG. The role of theTbx1 gene in a mouse model of autismspectrum disorder, 22/10/2015. (Contact:Cathal Seoighe)

[24] Antonio DÃ�az, Universidad de MÃπlaga,Spain. Simplicial complexes and Quillen’scomplexes, 29/10/2015. (Contact: SejongPark)


[25] James O’Shea, NUIG. Field Invariants andPfister forms, 05/11/2015. (Contact: RachelQuinlan)

[26] Eric Ladizinsky, D-Wave Systems Inc.,USA. Evolving Quantum Computers,10/11/2015. (Contact: Michael Mc Gettrick)

[27] Jaroslaw Miszczak, Polish Academy of Science,Poland. Why quantum mechanics is (not)special?, 12/11/2015. (Contact: Michael McGettrick)

[28] Yoshifumi NAKATA, The University of Tokyo,Japan. Unitary designs: constructionsand applications in quantum informationtheory, 26/11/2015. (Contact: Michael McGettrick)

[29] Vitaly Kurlin, University of Durham, UK.Computing invariants of knotted graphsgiven by sequences of points in 3-dimensional space, 03/12/2015. (Contact:Grahamj Ellis)

[30] Giovanni Russo, IBM Research – Dublin.Analysis and control of networked sys-tems: from biology to smart cities,09/12/2015. (Contact: Petri Piiroinen)

[31] Miguel Bustamante, UCD. Precession Res-onance and Strong Energy Transfersin Nonlinear Wave Systems, 17/12/2015.(Contact: Michel Destrade)

[32] Fionnuala Connolly, Harvard University, USA.Developing Design Rules for Soft FluidicActuators, 18/12/2015. (Contact: Michel De-strade & Raymond Ryan)

Conferences and Workshops

• Stokes Modelling WorkshopDates: 15–18 June, 2015Organisers and mentors:Shane Burns, Paul Greaney, Niall Madden,Martin Meere, Richard Burke, Shane Burns,Michel Desdrade, John Donohue, Michael McGettrick, Eoghan Staunton, Michael Tuite, andGiuseppe Zurlo.Twenty four undergraduate students from vari-ous Irish universities came to Galway for a weekto study techniques in modelling, and to solve

problems in pollution, drug release from poly-mers, aircraft wing vibration, flight networks,and structural isomers. They were mentoredby sta� and students of the Stokes Cluster forApplied Mathematics.

• NUI Galway SIAM Student Chapter AnnualConference 2015Date: 3 December 2015Invited speakers: Dr Dana Mackey (DIT) andProf. James Gleeson (UL)Contributed talks: Brendan Murray (UCD),Naoise Holohan (TCD), Niall McInerney (UL),Martina Curran (NUI Galway), Gary O’Kee�e(UL), Alan Compelli (DIT) Kevin Devine (UL).Organisers:Richard Burke, Christine Marshall,Paul Greaney, Niall Madden, Faiza Alssaedi,Shane Burns, Stephen Russell, Bram Siebert,Eoghan Staunton and Michael Welby

• Group in GalwayDate: 22 - 23 May 2015Invited speakers: Nicolas Bergeron (Univer-sitÃ� de Paris 7), Serge Bouc (UniversitÃ� dePicardie - Jules Verne), Hans Cuypers (Tech-nische Universiteit Eindhoven), Tom de Medts(Ghent University), Peter Kropholler (Univer-sity of Southhampton), Goetz Pfei�er (NUIGalway), Radu Stancu (UniversitÃ� de Picardie- Jules Verne), Alain Valette (UniversitÃ� deNeuchÃÊtel).Organisers: Sejong Park & Alexander Rahm

• ”Vertex operator algebras and mock modularforms” workshopDate: 22-23 May 2015Funded by IRC and SFI.Speakers: Drazen Adamovic (University of Za-greb, Croatia), Nicolas Bergeron (UniversitÃ�de Paris 7, France), Thomas Creutzig (Univer-sity of Alberta, Canada), Terry Gannon (Uni-versity of Alberta, Canada), Matt Krauel (Uni-versity of Cologne, Germany), Ching Hung Lam(Academia Sinica, Taiwan), Sameer Murthy(Kings College London, UK), Roberto Volpato(SLAC and Stanford University, USA)Nicolas Bergeron was a joint speaker withGroups in Galway.

school of mathematics, statistics and applied mathematics...

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