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The preliminary analyses on a multiscale model of intestinal crypt dynamics are here presented. The model combines a morphological model, based on the Cellular Potts Model (CPM), and a gene regulatory network model, based on Noisy Random Boolean Networks (NRBNs). Simulations suggest that the stochastic differentiation process is itself sufficient to ensure the general homeostasis in the asymptotic states, as proven by several measures.
Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of uncertainty in
In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review the recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two cases stud
We develop the pruned continuous Haar transform and the fast continuous Fourier series, two fast and efficient algorithms for rectilinear polygons. Rectilinear polygons are used in VLSI processes to describe design and mask layouts of integrated circ
A general-purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity characterized by in-plane periodicity that cannot be effectively treated
Systematic enumeration and identification of unique 3D spatial topologies of complex engineering systems such as automotive cooling layouts, hybrid-electric power trains, and aero-engines are essential to search their exhaustive design spaces to iden