Department of Mathematics & Statistics Colloquia 2020/21
07/10/2020
Title: Modelling genotype x environment interaction
Speaker: Dr Danilo Sarti, Maynooth University
ABSTRACT:
Obtaining new cultivars is one of the bases of human food supply. Such varieties are obtained through a dynamic process of several stages called plant breeding. Within this process, a crucial issue is the assessment of the interaction between genotypes and environments via multi environmental trials. The aim of the seminar will be to present an overview on genotype x environment interactions, how to assess evidence on that and show statistical models that are used to model such interactions. Some results from project INNOVAR related to new wheat varieties will be discussed.
14/10/2020
Title: A Statistician does the Leaving Cert
Speaker: Professor Cathal Walsh, University of Limerick
ABSTRACT:
The Leaving Certificate 2020 calculated grades process involved assigning marks to students in 2020 using a statistical modelling process.
This involved the use of prior attainment information for school cohorts, combined with estimates of current performance to derive a calculated mark for each individual within each subject.
When the Leaving Certificate Grades were released, the Department of Education published documents which described the information that was used, how the modelling evolved, and technical information on the process as intended and as finally realised.
Soon afterwards I was asked to review the statistical approaches used.
In this talk, I describe what the publicly available information tells us about the models used. I highlight how some statistical summaries behave; some in ways that are expected, and some that may be counterintuitive on first examination.
21/10/2020
Title: Numerical Semigroups and Music
Speaker: Dr Maria Bras Amoros, Rovira I Virgili University
ABSTRACT:
We will elaborate on the algebraic structure of the sequence of harmonics when combined with equal temperaments. Fractals and the golden ratio appear surprisingly on the way. The sequence of physical harmonics is an increasingly enumerable submonoid of (R+,+) whose pairs of consecutive terms get arbitrarily close as they grow. These properties suggest the definition of a new mathematical object which we denote a tempered monoid. Mapping the elements of the tempered monoid of physical harmonics from R to N may be considered tantamount to defining equal temperaments. The number of equal parts of the octave in an equal temperament corresponds to the multiplicity of the related numerical semigroup. Analyzing the sequence of musical harmonics we will derive two important properties that tempered monoids may have: that of being product-compatible and that of being fractal. We will demonstrate that, up to normalization, there is only one product-compatible tempered monoid, which is the logarithmic monoid, and there is only one nonbisectional fractal monoid which is generated by the golden ratio. The example of half-closed cylindrical pipes imposes a third property to the sequence of musical harmonics, the so-called odd-filterability property. We will prove that the maximum number of equal divisions of the octave such that the discretizations of the golden fractal monoid and the logarithmic monoid coincide, and such that the discretization is odd-filterable is 12. This is nothing else but the number of equal divisions of the octave in classical Western music.
04/11/2020
Title: Changes in curriculum and assessment for school mathematics: Ireland in international context
Speaker: Ms. Elizabeth Oldham, Trinity College Dublin
ABSTRACT:
Students who came through the Irish education system recently have experienced the impact of "Project Maths," the major curriculum initiative for second-level mathematics that was introduced gradually over a period of several years, starting in 2008. Changes in the content addressed in the Leaving Certificate affected the intake to third level substantially, and increasingly, from 2012 to 2014. However, except for the small number of students who attended the so-called Phase 1 schools, the first full cycle of implementation - the revised Junior Certificate followed by the revised Leaving Certificate - was completed only in 2017 for those who did not do Transition Year and 2018 for those who did. The extended period of change has made it difficult for third-level lecturers to adjust their expectations about incoming students' knowledge, skills and dispositions towards mathematics. It also means that evaluation of the initiative is problematic. The problems are exacerbated by the fact that the Junior Certificate course has already been altered (in the context of Junior Cycle reform across the curriculum).
This talk does not attempt to provide an evaluation of Project Maths. Rather, it seeks to explain the rationale for key developments, framing them by taking a historical perspective and examining the changing context for mathematics education internationally as well as nationally. It focuses on significant changes in content and assessment since the foundation of the state and in particular over the last sixty years. The main emphasis will be on the Higher Leaving Certificate; with regard to assessment, the talk draws on the invaluable archive of state examination papers compiled by David Malone and Hazel Murray. Lively discussion will be welcomed!
11/11/2020
Title: Clustering Longitudinal Life-Course Sequences Using Mixtures of Exponential-Distance Models
Speaker: Dr Keefe Murphy, Maynooth University
ABSTRACT:
Sequence analysis is an increasingly popular approach for the analysis of life courses represented by an ordered collection of activities experienced by subjects over a given time period. Several criteria exist for measuring pairwise dissimilarities among sequences. Typically, dissimilarity matrices are employed as input to heuristic clustering algorithms, with the aim of identifying the most relevant patterns in the data.
Here, we consider a survey data set containing information on the career trajectories of a cohort of Northern Irish youths tracked between the ages of 16 and 22. We propose an alternative clustering approach, suited to the analysis of such categorical sequence data from a holistic perspective, which is both model-based and distance-based. Our approach models the sequences themselves directly and employs distance metrics based on weighted variants of the Hamming distance.
This coherent "MEDseq" framework is developed with the aims of estimating the number of typical career trajectories, identifying the relevant features characterising the typical trajectories, and assessing the extent to which such patterns are shaped by the individuals' background characteristics. Simultaneously incorporating the sampling weights and the covariates in the clustering process allows new insights to be gleaned from the Northern Irish data.
18/11/2020
Title: Counting paths in lattices to obtain symmetric polynomial identities
Speaker: Eoghan McDowell, Royal Holloway, University of London
ABSTRACT:
The Lindström--Gessel--Viennot lemma states that the number of non-intersecting tuples of paths in a given lattice is equal to the determinant of a certain matrix. In this talk I will explain the elegant combinatorial argument behind this result, and use it to obtain a new symmetric polynomial identity. This identity generalises both the binomial determinant duality of theorem of Gessel and Viennot and the symmetric function duality theorem of Aitken. I will also mention some motivation from the problem of plethysm in the representation theory of the general linear group.
25/11/2020
Title: House price modelling in the Dublin city area: what is the impact of an address?
Speaker: Dr James Sweeney, University of Limerick
ABSTRACT:
Assessments of the state of play in the Dublin housing market are mainly qualitative at present, based on simple summaries of property prices. Existing property price estimators are limited in terms of the factors they use to estimate the value of a property for the purposes of property tax payment, being primarily based on the dwelling type, number of bedrooms & bathrooms, as well as a comparison to nearby houses for which sales price may be known. No uncertainty in the price prediction is typically provided, a substantial caveat given that property price predictions in areas where property turnover is low should be highly uncertain. Furthermore, a substantial issue of interest is whether there are subjective biases in terms of the prices people are willing to pay for a property - for example, will people overpay for perceived "good" addresses? Existing "hedonic" models for property prices cannot address this question as all of the factors impacting on price are not known (Gelfand et al (2014)).
In this talk I will present a proof of concept spatial model for house prices in the Dublin metropolitan area, which is applied to a dataset of 4,000 properties containing price information and a number of house features. The model appears promising for price prediction given a number of simple property features and provides some interesting results in terms of the factors deemed important in the value of a property.
02/12/2020
Title: Topology and coding in brain networks
Speaker: Dr Chad Giusti, University of Delaware
ABSTRACT:
A common strategy neurons in the brain use for representing information is through patterns of coactivity. One of the major goals of quantitative neuroscience is the development of quantitative frameworks for detecting, characterizing, and understanding these coding strategies. In this talk, I will describe an approach to addressing these problems using tools from algebraic and geometric topology. In particular, I will describe the common "stimulus space" model for neural activity in which neurons' response to stimuli is measured via the metric in some intrinsic space. In this case, the activity profiles of neurons describe a topological space, and I will explain how classical and modern computational tools from topology allow us to detect and analyze that space via observations of the activity of the neurons. No background in neuroscience or algebraic topology will be expected.
09/12/2020
Title: Dynamic Treatment Regimes vs. The Real World: Practical Challenges in Precision Medicine
Speaker: Dr Michael Wallace, University of Waterloo
ABSTRACT:
Precision medicine describes the practice of tailoring treatment decisions to patient-level characteristics such as symptom severity, age, or prior medication. This may be formalized through dynamic treatment regimes (DTRs): sequences of treatment decision rules that take patient information as input and output treatment recommendations. Numerous methods have been proposed for the estimation of optimal DTRs: those that optimize some pre-specified health outcome. However, many real-world challenges, from the data, to analysis, and into practice, have remained largely unstudied. In this talk, we will discuss specific obstacles to DTR estimation and implementation in practice. First, we outline the ubiquitous challenge of measurement error, where observed values differ from the 'true' values we wish to observe. Next, we discuss the assumption of no interference: that the treatment of one individual does not affect the outcome of another. This assumption is often violated, such as in the study of infectious diseases where treating one patient may not only lower their risk of infection, but by extension the risk of infection for those they come into contact with. Finally, we discuss how patient-level preferences (such as the trade-off between treatment efficacy and risk of side effects) can, and should, influence our recommendations.
16/12/2020
Title: Density estimation on manifolds
Speaker: Dr Galatia Cleanthous, Maynooth University
ABSTRACT:
The objective of non-parametric density estimation is the data-based estimation of a pdf that belongs in large class of functions. The corresponding theory has been highly developed during the last decades and has been extensively used in applications in a wide range of fields.
The problem of density estimation has been studied on Euclidean spaces, cubes, spheres, balls and other settings. Sophisticated methods using kernels, wavelets, needlets and smoothness spaces have been used in approaching the problem.
In this talk, we will present the extension of the study on manifolds or more general metric spaces. We will present our resent results and some open problems in the area.
03/02/2021
Title: Partition identities and crystal bases
Speaker: Dr Jehanne Dousse, Université Claude Bernard Lyon 1 (UCBL)
ABSTRACT:
A partition of a positive integer n is a non-increasing sequence of positive integers whose sum is n. A Rogers-Ramanujan type identity is a theorem stating that for all n, the number of partitions of n satisfying some difference conditions equals the number of partitions of n satisfying some congruence conditions. In the 1980's, Lepowsky and Wilson established a connection between the Rogers-Ramanujan identities and representation theory. Other representation theorists have then extended their method and obtained new identities yet unknown to combinatorialists, and Primc introduced a new method in connection with crystal base theory. After a general introduction on partitions and their generating functions, we will show how one can use combinatorial techniques to prove partition identities and character formulas from crystal base theory.
10/02/2021
Title: "And oh the stories we could tell": Why numbers need a narrative
Speaker: Brian Tarran, Editor of Significance Magazine
ABSTRACT:
Data scientists and statisticians must learn to harness the power and potential of storytelling. In this talk, Brian Tarran, editor of the statistics magazine Significance, shares ideas from journalists, science communicators, visual storytellers and screenwriters to explain how to communicate effectively with the public and policymakers.
17/02/2021
Title: Using Facebook advertising data to estimate migration
Speaker: Dr Monica Alexander, University of Toronto
ABSTRACT:
Measuring and monitoring migration is important for policy and planning purposes. However, often detailed or timely data on migration outcomes do not exist. In this talk I will discuss the potential for using data from Facebook's advertising platform to estimate and project short-term migration patterns. The potential utility of these data will be highlighted through two case studies: 'nowcasting' migrant stocks in the US, and estimating out-migration from Puerto Rico following Hurricane Maria.
24/02/2021
Title: On the Lie algebra structure of outer derivations of finite group algebras
Speaker: Professor Markus Linckelmann, City, University of London
ABSTRACT:
Very few finite-dimensional algebras over a field are expected to arise as direct factors of finite group algebras. In fact, prominent finiteness conjectures would imply that in any fixed dimension, only finitely many isomorphism classes of algebras should arise in this way. Even in very small dimensions, where this is known to hold, this tends to require some substantial effort, since it is generally very difficult to decide for any given algebra whether it arises as a direct factor of some finite group algebra or not. Amongst many invariants which can be useful for this endeavour is the Lie algebra structure of the first Hochschild cohomology space - this is simply the space of derivations on the algebra modulo inner derivations. We describe some progress in recent years. Time permitting, we describe a construction principle for operators of degree -1 on Ext-spaces of modules which can be used to calculate the Lie algebra structure of the first Hochschild cohomology of certain finite p-group algebras. This is joint work with Radha Kessar and Dave Benson.
03/03/2021
Speaker: Aaron Tyrrell, University of Notre Dame
ABSTRACT:
We will look at some results regarding the renormalised area of minimal submanifolds of Poincaré-Einstein manifolds.
10/03/2021
Speaker: Dr John S. Butler, Technological University Dublin
ABSTRACT:
I will discuss the application of statistical and analysis methods to investigate an on-going debate whether children with Autism spectrum disorder (ASD) have unreliable sensory processing. The general notion is that signal averaging procedures typically used in neurophysiological and neuroimaging studies obscure the fact that there are ongoing and presumably relatively dramatic fluctuations in responsiveness to individual events. If this is correct a number of straightforward predictions can be made about the evoked brain signals; 1) the averaged evoked response should be broader and have a delayed peak for all components; 2) people with ASD should have a greater variability of phase dispersion across single trials.
Here, we examined this thesis in a matched cohort of typically developing children and children with ASD, using high-density EEG recordings of visual and somatosensory evoked responses. We first used classical statistical methods and Bayes Factors to investigate differences or similarities of the groups’ evoked responses [1]. We then processed the single trials to look at amplitude or phase differences at different frequencies.
Finally, we simulated an unreliable evoked response by introducing temporal and amplitude variability at a single trial level. This simulated data was then compared with the observed TD and ASD data and illustrated the predictions of the unreliable evoked response and the sensitivity of the measures and data to small perturbations.
Our data show highly similar reliability in the neural responses to visual and somatosensory stimuli in our matched groups, while the simulated data show differences predicted by the unreliability thesis. These results allowed us to embrace the null and argue against a straightforward unreliability hypothesis and instead favors an argument taking into account subtleties and specializations that are present in a complex disorder such as autism.
If there is time, I will talk about my more recent work in embracing the null [2] and some of my ongoing work simulating neuronal responses [3].
References
[1] John S. Butler, Sophie Molholm, Gizely N. Andrade, John J. Foxe, An Examination of the Neural Unreliability Thesis of Autism, Cerebral Cortex, Volume 27, Issue 1, January 2017, Pages 185-200, https://doi.org/10.1093/cercor/bhw375
[2] Fearon, C., Butler, J.S., Waechter, S.M. et al. Neurophysiological correlates of dual tasking in people with Parkinson's disease and freezing of gait. Exp Brain Res 239, 175-187 (2021). https://doi.org/10.1007/s00221-020-05968-8
[3] Website: https://johnsbutler.netlify.app
24/03/2021
Title: Mathematics Support in the time of COVID-19
Speaker: Claire Mullen, University College Dublin
ABSTRACT:
The dramatic and swift changes brought on by COVID-19, in particular the move to fully online modes of teaching and learning for mathematics and statistics support (MSS), have presented students and tutors with a host of new opportunities for thinking and working. We, at the Mathematics Support Centre at University College Dublin (UCD), Ireland, and the Mathematics Education Support Hub at Western Sydney University (WSU), Australia, conducted a study aiming to gain insight from both MSS student users and tutors about their experience of wholly online learning and teaching in the COVID-19 era with particular emphasis on support. The study represents a ‘perspectives’ study, the idea being that before we examine specific aspects of this experience, it would be best to know what the issues are. Employing a qualitative analysis framework of 23 one-on-one interviews with tutors and students from both institutions in Australia and Ireland, we identified five key themes as central to the shared experiences and perspectives of the participants. In this talk I will give some background to previous online mathematics support provision prior to the pandemic in both UCD and WSU. I will then discuss the identified themes in relation to the new normal with the intention of supporting MSS practitioners, researchers and students in the future. The themes are; Usage of online MSS, Mathematics is different, Pedagogical Changes, Social Interactions, and the Future of online MSS.
31/03/2021
Title: The ultrahyperbolic equation after Fritz John
Speaker: Guillem Cobos, IT Tralee
ABSTRACT:
Fritz John showed in 1938 that the ultrahyperbolic equation arises as the compatibility for functions on line space to come from line integrals of functions in Euclidean 3-space. The introduction of the canonical neutral Kaehler metric on the space of oriented lines clarifies the relationship and broadens the paradigm to allow new insights. In particular, conformal maps of the neutral metric are used to generate new solutions to the equation. The link with tomography is explained, and the possibility of image reconstruction from attenuation values along lines intersecting a fixed line in space is discussed.
14/04/2021
Title: Approaches to feedback in the mathematical sciences: just what do students really think?
Speaker: Dr Michael Grove, University of Birmingham
ABSTRACT:
Within the mathematical sciences there exist particular challenges associated with the provision of timely and detailed feedback, both of which are important given the widespread use of formative, and typically weekly, problem sheet assessments to aid and structure the mathematical development of learners. In this talk I will report on the outcomes from a cycle of action research that was designed to enhance the feedback received by students and their subsequent engagement with it in a large research-intensive mathematical sciences department. Student views on the current feedback they receive will be discussed, but more broadly the findings offer insight into alternative feedback practices that mathematical sciences departments might wish to explore.
21/04/2021
Title: How Can Novel Statistical Methods Improve Analyses in Environmental Sciences
Speaker: Dr Erica Ashe, Rutgers University
ABSTRACT:
Characterizing the spatio-temporal variability of relative sea level (RSL) and estimating local, regional, and global RSL trends requires statistical analysis of RSL data. Formal statistical treatments are needed to account for the spatially and temporally sparse distribution of data and for geochronological and elevational uncertainties. I frame improvements in statistical methods by themes: Uncertainty, Correlations, and Progress.
First, I introduce a newly developed statistical framework to estimate past RSL change based on the modern distributions of RSL proxy elevations in relation to RSL, using corals as an illustrative example. The new statistical model incorporates nonparametric empirical likelihoods through a distribution-fitting module, a sampling module, and a sample-wise prediction module. Using Markov chain Monte Carlo (MCMC) sampling, we approximate the posterior distributions on these parameters and RSL, conditioned on the observed data. Through the use of a robust set of validation and sensitivity tests, we show that the nonparametric model, while sometimes overestimating uncertainties, performs better than past methods in these tests.
Then, I outline the importance of Bayesian and empirical Bayesian hierarchical models, particularly in a spatio-temporal context, to analyze diverse, noisy observations with errors in both dependent and independent variables. The hierarchical frameworks employed improves upon past RSL models by more richly representing the correlation structure of RSL across space and time. Bayesian hierarchical models are suitable for developing complex process-level models, accounting for uncertainties in model parameters, incorporating prior knowledge, and sharing information over various dimensions. My models are able to rigorously quantify spatial and temporal variability, combine geographically disparate data, and separate the RSL field into various components associated with different driving processes.
Last, I demonstrate the value of statistical emulation in environmental science through the emulation of an Antarctic Ice Sheet (AIS) model simulator. Gaussian process emulators easily mimic the behavior of the ice-sheet model and provide continuous probability distributions of past and future sea-level equivalents from AIS from discrete simulation ensembles. I present the results of two ice-sheet emulators (for the last interglacial period [LIG, 130kya] and the future [1950-2100]) to demonstrate the value of emulation and geological data for constraining projections of Antarctica's role in future sea level rise. I show that posterior estimates of future AIS sea-level equivalent are highly dependent on how geological data can constrain LIG contributions, and that statistical emulation is a powerful tool for incorporating physics into statistical models.
05/05/2021
Title: Diagnostics for nominal data analysis
Speaker: Patricia Peres Araripe, University of São Paulo
ABSTRACT:
In the agronomic or biological areas, experiments with a categorical response are usual. The categorical variable is obtained by a finite number of categories and classified as polytomous when it has more than two categories. The generalized logit models, class members of Generalized Linear Models, are commonly used to fit a polytomous variable with a nominal scale (without order between the categories). After choosing a statistical model, an important step is the residuals and diagnostics analysis. However, this method for assessing the adequacy of these models is still emerging and extremely necessary in the class of discrete models. It is presented the recently developed residuals by Chen, Wang, and Zhang (2020) and illustrated them using a literature example. Then, it will be discussing the results of the simulation studies using distance measures in the residuals analysis.