Non-linear wave resonances; Inverse problems; Practical skills for mathematical and data modelling; linear and integer programming; PCA
Day 4 – Foundations of Data Science II (Thursday 9th December)
9.30am: Associate Professor Miguel D Bustamante, UCD. Title: Chaos and synchronisation in nonlinear wave systems
Brief synopsis: Many physical systems consist of nonlinearly interacting oscillations or waves: nonlinear circuits in electrical power systems, high-intensity lasers, nonlinear photonics, gravity water waves in oceans, Rossby-Haurwitz planetary waves in the atmosphere, drift waves in fusion plasmas, etc. These systems are characterised by ubiquitous phenomena: extreme events (localised in space and time), strong nonlinear energy exchanges, and out-of-equilibrium dynamics (chaos and turbulence). In this introductory lecture I will present some of the mechanisms involved in these phenomena, via a combination of analytical and numerical methods applied to the study of the partial differential equations that model these systems.
11.00am: Dr Romina Gaburro, UL. Title: Inverse problems: the mathematical world behind imaging.
Brief synopsis: In this talk we introduce the concept of inverse problem, the mathematical technique behind imaging and material characterisation. We explain the idea of inversion from data/measurements to parameter (describing a physical property of a medium) and the mathematical challenges behind imaging. Such challenges are mostly due to the intrinsic ill-posed and non-linear nature of inverse problems, which require regularisation in order for the inversion/parameter characterisation to be efficient and produce reliable images.
12.00pm: Dr Adamaria Perrotta, UCD. Title: Managing complexity in financial risk management: how to apply PCA to analyse the interest rates term structure dynamics.
Brief synopsis:The methodology called Principal Component Analysis (PCA) is commonly used to analyse data dynamics and reduce the complexity. After a brief overview of the PCA on portfolio analysis, a case study will be presented. It will be shown how to analyse the dynamics of the interest rates term structure, with 13 maturities over a 15 years’ time window, via PCA. In particular, it will be presented how to apply PCA to:
• measure the relative correlation between different maturities of the term structure.
• understand the relevance of different principal components in the term structure dynamics.
• interpret possible movements of the yield curve.
• detect different dynamics regimes across different historical periods.
2.00pm: Associate Professor Dr Paula Carroll, UCD. Title: An introduction to linear and integer programming
Brief synopsis: Many real world problems require us to find optimal solutions subject to limitations such as resource availability. We can formulate mathematical models of these constrained optimisation problems, but some of these models very difficult to solve. In this lecture we introduce Linear and Integer Programming which are modelling and solution techniques for constrained optimisation problems. We demonstrate how the techniques can be applied to a range of applications such as electricity supply and demand balancing.
3.00-5.00pm: Dr Cameron Hall, University of Bristol. Title: Practical skills for mathematical and data modelling.
Brief synopsis: Applied mathematics and data science give us a huge array of tools that we can use for tackling problems and questions. But often real problems are not as neat as the problems we encounter in the classroom, and sometimes working out what the questions should be is as hard as finding answers for them. In this session, we’ll look at some practical first steps for mathematical modelling and data analysis problems. What are good questions to ask in order to gain more understanding about a problem? What are some quick and simple tools and tests that can give you valuable insights into what to do next? How do you prioritise between different possible approaches to a problem? During the course of the session, we’ll look at some general practical principles for mathematical and data modelling and go through some case studies based on some real problems.
The SFI Centre for Research Training in Foundations of Data Science will train a cohort of PhD students with world-class foundational understanding in the horizontal themes of Applied Mathematics, Statistics, and Machine Learning.
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