22nd ECMI Conference second day

The conference continues. We would like again to write a few words about our guest invited to give Planar Lectures on Tuesday.

Ruth Baker

Professor of Applied Mathematics at University of Oxford who specialises at using mathematical methods in biomedical sciences. She focusses on the development and application of technologies to transform understanding of how cell-level biomechanical and biochemical mechanisms drive morphogenesis at the cell and tissue level. She will give a lecture Quantitative comparisons between models and data to provide new insights in cell and developmental biology.

In her talk she will use examples relating to cell motility and proliferation to showcase how quantitative comparisons between models and data can help tease apart subtle details of biological mechanisms. Nowadays, this type of analysis is especially important due to the advent of a host of new experimental technologies which caused an explosion in the amount and types of quantitative data now being generated. This sets a new challenge for the field – to develop, calibrate and analyse new models to interpret these data.

Henrik Madsen

Expert in statistical analysis of dynamical systems. This includes signal processing, time series analysis, model building, estimation, grey-box modelling, digital twins, prediction, optimisation and control. Author or co-authored of approximately 650 papers and 12 books. He will give a lecture Forecasting for the Weather-Driven Energy System.

He will describe methods for multivariate probabilistic forecasting of load, prices and renewable power generation. Such tools for integrated forecasting across domains (wind, solar, load, prices, etc.) will become essential, and replace more silo-oriented tools for individual areas like wind power. Full multivariate probabilistic forecasts are important to obtain reliability and profitability in the operation of the future low-carbon energy system. The lecture will describe some of the recent developments in forecasting using both spatial and temporal hierarchies.

Research in Wrocław: numerical methods for fractional derivatives

Taking the opportunity, organisers would like to additionally advertise some of the research in Wrocław which will be discussed on Tuesday. At Minisymposium 10: Computational mathematics for partial differential equations: theory and applications Łukasz Płociniczak and Mateusz Świtała from Hugo Steinhaus Center will talk about different aspects of discretisation schemes which are used in differential equations with fractional order derivatives.

Fractional derivatives are mathematical operators which generalise the notion of derivative by allowing its order to be any real number. They differ substantially from the classical integer-order derivatives by being non-local operators: the current value of the fractionally differentiated function depends on all of its previous values. Thus, fractional order derivatives and equations can model systems with memory. In particular, they are are used to construct widely used models of phenomena in which long, power-law dependance is experimentally measured. This is often observed in complex media such as crowded liquids (e.g. cellular cytoplasm) or porous media (e.g. soil). Industrial applications include for example structural engineering and material durability research.

The same non-locality which makes fractional derivatives useful is also a source of challenges in the related numerical methods. On Tuesday, new methods for porous media and Erdélyi–Kober equations will be discussed.

Figure: Numerical errors of the discretised time-fractional porous medium equation as a function of step length h.
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