European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
13:30   MS50: Numerical methods to advance mathematical biology research (Part 2)
Chair: Alf Gerisch
25 mins
Bayesian sequential learning framework to parametrise a model of melanoma invasion into human skin
Alexander Browning
Abstract: We present a novel framework to parameterise a mathematical model of melanoma cell invasion into human skin. Our technique uses a suite of increasingly sophisticated experimental data to sequentially estimate the proliferation rate, diffusivity and a parameter that quantities the invasion of the cells into human skin. Our Bayesian sequential learning approach is simple to implement, computationally efficient and leads to well-defined parameter estimates. In contrast, taking a naïve approach that attempts to estimate all parameters from a single set of data from the same experiment fails to produce meaningful results.
25 mins
Persistent Homology for Large Datasets
Alvaro Torras Casas
Abstract: Topological Data Analysis deals with the shape of data. An important tool is "Persistent Homology", which detects topological features such as cycles, holes and connected components. This has been applied successfully to areas such as protein compressibility, pattern detection, machine learning techniques, and many more. However, persistent homology has some computational limitations; the algorithm is expensive in terms of memory when it comes to analysing big data sets. In this talk we build up a basic guide to the technique, its strengths and weaknesses, resulting in a new parallelization method. Apart from the computational advantages of this approach, we will see that this provides local information which might be of interest for particular applications.
25 mins
A population dynamics model of cell-cell adhesion and its numerical analysis
Hideki Murakawa
Abstract: Cell-cell adhesion and cell sorting processes are essential in organ formation during embryonic development and in maintaining multicellular structure. We proposed a nonlocal advection-diffusion problem as a possible continuous mathematical model for these phenomena. In this talk, we briefly give a derivation of the model. And then, we provide and analyze a numerical scheme for the model. This talk is based on joint works with Rafael Bailo, Jose A. Carrillo, Hideki Murakawa, Makoto Sato, Markus Schmidtchen, Hideru Togashi and Olena Trush.
25 mins
Kinetic models with non-local sensing determining cell polarization and speed according to independent cues
Nadia Loy, Luigi Preziosi
Abstract: Cells move by run and tumble, a kind of dynamics in which the cell alternates runs over straight lines and re-orientations. This erratic motion may be influenced by external factors, like chemicals, nutrients, the extra-cellular matrix, in the sense that the cell measures the external field and elaborates the signal eventually adapting its dynamics.\\ We propose a kinetic transport equation implementing a velocity-jump process in which the transition probability takes into account a double bias, which acts, respectively, on the choice of the direction of motion and of the speed. The double bias depends on two different non-local sensing cues coming from the external environment. We analyze how the size of the cell and the way of sensing the environment with respect to the variation of the external fields affect the cell population dynamics by recovering an appropriate macroscopic limit and directly integrating the kinetic transport equation. A comparison between the solutions of the transport equation and of the proper macroscopic limit is also performed.