## Research Seminars in the School of Mathematical Sciences

The School of Mathematical Sciences host regular research seminars delivered by internal and external researchers on topics across mathematical sciences. Seminars take place on the Kevin Street campus and are open to all.

## Seminar 7/12/18: Infinite mixtures of infinite factor analysers (IMIFA)

Infinite Mixtures of Infinite Factor Analysers (IMIFA)

Isobel Claire Gormley

Insight Centre for Data Analytics, University College Dublin

Friday 7 December 2018

1pm, Blue Room, 4th floor, Main Building, DIT Kevin Street

Abstract:

Factor-analytic Gaussian mixture models are often employed as a model-based approach to clustering high-dimensional data. Typically, the numbers of clusters and latent factors must be specified in advance of model fitting, and the optimal pair selected using a model choice criterion. For computational reasons, models in which the number of latent factors is common across clusters are generally considered.

Here the infinite mixture of infinite factor analysers (IMIFA) model is introduced. IMIFA employs a Poisson-Dirichlet process prior to facilitate automatic inference on the number of clusters. Further, IMIFA employs shrinkage priors to allow cluster specific numbers of factors, automatically inferred via an adaptive Gibbs sampler. IMIFA is presented as the flagship of a family of factor-analytic mixture models, providing flexible approaches to clustering highdimensional data.

Applications to benchmark and real data sets illustrate the IMIFA model and its advantageous features: IMIFA obviates the need for model selection criteria, reduces model search and associated computational burden, improves clustering performance by allowing cluster-specific numbers of factors, and quantifies uncertainty in the numbers of clusters and cluster-specific factors.

## Seminar 28/9/18: Handling missing network data

Handling missing network data

Robert Krause

University of Groningen

Friday 28 September 2018

2pm, Blue Room, 4th floor, Main Building, DIT Kevin Street

Abstract:

My work focuses on handling missing data in cross-sectional, longitudinal and multiplex networks. We focus on the development and evaluation of multiple imputation procedures for the current state of the art model families (Stochastic Actor-Oriented Models and Exponential Random Graph Models). In this talk I will give an overview about our work.

## Seminar 9/3/18: A numerical study of in-plane wave propagation in mooring cables

A numerical study of in-plane wave propagation in mooring cables

Biswajit Basu

Trinity College Dublin

Friday 9 March 2018

2.15pm, Blue Room, 4th floor, Main Building, DIT Kevin Street

Abstract:

This talk focuses on wave propagation in mooring cables. For cables in ocean applications, there are three sources of nonlinearities affecting the cable response: the hydrodynamic effect, geometric stiffening effect, and seabed effect. To this end, numerical solutions are pursued, where the partial differential equations describing the dynamics of the submerged mooring cable are formulated in Lagrangian coordinates and solved using space-time finite difference methods. Specifically, a two-dimensional cable is considered and the wave propagation is studied when the cable is subjected to harmonic excitation at the fairlead. The wave propagation with seabed effects is also compared to that in a fully suspended cable. The nonlinear mechanisms governing the propagation of waves are discussed based on the numerical results. Further, some results on hydrodynamic analysis using Lagrangian based smooth particle hydrodynamics (SPH) are presented. Comparisons are made with some recent results and the impact of nonlinear hydrodynamics on offshore applications is emphasized.

## Seminar 27/4/18: On mathematical models for microelectromechanical systems

On mathematical models for microelectromechanical systems

Prof Joachim Escher

Leibniz University Hannover

Friday 27 April 2018

1pm, Blue Room, 4th floor, Main Building, DIT Kevin Street

Abstract:

A review of some recent results on mathematical models for microelectromechanical systems with general permittivity profile will be presented. These models consist of a quasilinear parabolic evolution problem for the displacement of an elastic membrane coupled with an elliptic moving boundary problem that determines the electrostatic potential in the region occupied by the elastic membrane and a rigid ground plate.

Local well-posedness, global existence, the occurrence of finite-time singularities, and convergence of solutions to those of the so-called small-aspect ratio model, respectively, are addressed. Furthermore, a topic is addressed that is of note not till non-constant permittivity profiles are taken into account — the direction of the membrane's deflection or, in mathematical parlance, the sign of the solution to the evolution problem.

## Seminar 8/12/17: Trends in undergraduate students' basic mathematical skills on entry to third level education over the past two decades

Trends in undergraduate students' basic mathematical skills on entry to third level education over the past two decades

Fiona Faulkner

Dublin Institute of Technology

Friday 8 December 2017

1pm, KE3-008, 3rd floor, Main Building, DIT Kevin Street

Abstract:

In 1997 diagnostic testing was first implemented in the University of Limerick due to service mathematics lecturers' anxiety regarding Science and Technology students' mathematical competency levels. The test is a tool to identify those who are struggling with the basic mathematical concepts needed for third level education. An examination of over 8,000 students involved in the diagnostic testing in UL between 1998 and 2008 highlighted a steady decline in students' basic mathematical competency levels on entry to third level education. This data was also used to explore the role of prior mathematics achievement in predicting performance in third level mathematics (Faulkner et al 2010). Later examinations of the diagnostic test data, between 2003 and 2013, found that the proportion of students tested that are predicted to be at risk of failing their service mathematics end-of-semester examinations had continued to increased. Furthermore, when students' performance in secondary level mathematics was controlled, it was determined that the performance of beginning undergraduates in 2013 was statistically significantly below that of the performance of the beginning undergraduates recorded 10 years previously (Treacy and Faulkner 2015). This research also examines the declining standard in basic mathematics skills in light of curriculum changes in second level education (Treacy, Faulkner and Prendergast 2016).