- Statistical analysis of time-course/functional data.
- Smoothing using the mixed effects model.
- Finite mixture model clustering of time-course data.
- Modelling -omics data, e.g. RNA-seq data, mass spectrometry data, ChiP-seq data, etc.
- Statistical modelling in biomechanics.
As an applied mathematician specialising in mathematical modelling, I consider myself prone to be interested in any problem which requires modelling, and that means almost any scientific problem at all. The main part of my research interests lies in mathematical geoscience, and stems from my doctoral research in glaciology: my thesis 'Glacier dynamics' was finished in 1977, back in the days before word processing, personal computers and the like, and I typed it on a typewriter with two keyboards, one Roman and one with Greek and mathematical symbols.
Since then I have become interested in many other areas of geophysics, geology, petrology, volcanology, as well as geomorphology and Earth surface processes in general.
The genuine applied mathematician is a multi-faceted creature, and I am no different. I have been interested in various parts of biology and physiology, and with a background in Oxford and a current post in MACSI, industrial problems also form a major part of my interests.
Romina Gaburro's research area is in inverse problems, partial differential equations and their applications to imaging and material properties identification. Inverse problems are employed to identify physical properties of materials that cannot be directly observed. These are the model parameters and are very often the coefficients of a partial differential equation describing the model.
The material under investigation is typically probed with an electromagnetic field that interacts with the material according to the governing equation describing the model. This interaction is measured and used to determine the material properties/ inhomogeneities in the material (data inversion). Examples of inhomogeneities include an oil or geothermal reservoir in the subsurface of the Earth, a tumour in the human body or a crack/defect in a material. Inverse problems have indeed wide applications in geophysics, medical imaging, nondestructive testing, radar, acoustics, signal processing, machine learning, etc. The study of inverse problems is a very active area of modern applied mathematics and one of the most interdisciplinary field of science.
My group works on mathematical models for stochastic dynamics, particularly on complex networks. As co-director of MACSI, I am also interested in applying mathematical tools and techniques to solving real-world problems, in collaboration with partners from industry, science and engineering.
I am an applied mathematician. I use maths - usually differential equations - to describe, understand and predict the behaviour of physical systems. My specialties are systems involving fluid flow, systems involving deformation of solid bodies, and systems involving chemical reactions. I am motivated by real-world problems, by situations where counter-intuitive behaviour can be explained using maths, and by taking phenomena that are usually annoying and using them to our advantage.
You can find details of some of my research projects on my research page. Here is a list of the areas I work or have worked in:
Fluid Mechanics: Viscous flow, capillary flows, fluid-structure interaction
Solid Mechanics: Elasticity, plasticity, wrinkle mechanics
Chemistry: Decontamination problems, batteries
Industrial mathematics: Glass manufacture, metal forming
Dr. Purtill's current research area is statistical profiling in longitudinal population studies such as Growing Up in Ireland (GUI) and The Irish LongituDinal Study of Aging (TILDA). She also has considerable research experience in the design and analysis of randomised control trials, meta-analyses, validity and reliability studies, power calculations and sample sizing for clinical and observational studies.
My interest is to develop mechanistic models for dairy and pharmaceutical industries using ANN, Monte Carlo method, Discrete Element methods and population balance approach. I have been also working on developing numerical methods for the integro-partial differential equations well known as population balance equations and conducting their convergence analysis. My other research interest is to find approximate, semi-analytical and analytical solutions for linear and nonlinear differential and integro-partial differential equations.