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In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce...
In vitro transmesothelial migration assays of ovarian cancer cells, isolated or
aggregated in multicellular spheroids, are reproduced deducing suitable Cellular Potts
Models (CPM). We show that the simulations are in good agreement with the experimental
evidence and that the overall process is regulated by the activity of matrix
metalloproteinases (MMPs) and by the interplay of the adhesive properties of the cells
with the extracellular matrix and...
We study the influence of time delays on the dynamics of the general Hahnfeldt et al. model of an angiogenesis process. We analyse the dynamics of the system for different values of the parameter α which reflects the strength of stimulation of the vessel formation process. Time delays are introduced in three subprocesses: tumour growth, stimulation and inhibition of vessel formation (represented by endothelial cell dynamics). We focus on possible destabilisation of the positive steady state due...
Epidemiologic data suggest that schools and daycare facilities likely play a major role
in the dissemination of influenza. Pathogen transmission within such small, inhomogenously
mixed populations is difficult to model using traditional approaches. We developed
simulation based mathematical tool to investigate the effects of social contact networks
on pathogen dissemination in a setting analogous to a daycare center or grade school. Here
we show...
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