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Pattern formation by lateral inhibition with feedback: a mathematical model of delta-notch intercellular signalling.
TLDR
A simple and general mathematical model of contact-mediated lateral inhibition that postulates that receipt of inhibition diminished the ability to deliver inhibition and gives rise to a feedback loop that can amplify differences between adjacent cells is constructed. Expand
Cyclic dermal BMP signalling regulates stem cell activation during hair regeneration
TLDR
Results show that BMPs may be the long-sought ‘chalone’ inhibitors of hair growth postulated by classical experiments, and provide an example of hierarchical regulation of local organ stem cell homeostasis by the inter-organ macroenvironment. Expand
Mathematical Models of Avascular Tumor Growth
TLDR
The aim of the review is to provide a relatively comprehensive list of existing models and discuss several representative models in greater detail and some possible future avenues of mathematical modeling of avascular tumor development are outlined. Expand
Inherent noise can facilitate coherence in collective swarm motion
TLDR
A coarse-grained approach to the study of directional switching in a self-propelled particle model assuming an underlying one-dimensional Fokker–Planck equation for the mean velocity of the particles is adopted, revealing that individual locusts appear to increase the randomness of their movements in response to a loss of alignment by the group. Expand
A practical guide to stochastic simulations of reaction-diffusion processes
TLDR
A practical introduction to stochastic modelling of reaction-diffusion processes is presented, starting with the classical Gillespie algorithm for the stochastically modelling of chemical reactions and progressing to more advanced methods and problems. Expand
Traveling wave model to interpret a wound-healing cell migration assay for human peritoneal mesothelial cells.
TLDR
A "wound-healing" experiment that quantifies the migration of human peritoneal mesothelial cells over components of the extracellular matrix was performed, and a relationship between the rate of cell proliferation and the diffusion coefficient was obtained. Expand
Travelling waves in a wound healing assay
TLDR
It is shown that a very simple wound healing assay does indeed give rise to constant speed travelling waves, the first verification of Fisher's equation in a medical context. Expand
Reaction and diffusion on growing domains: Scenarios for robust pattern formation
TLDR
It is found numerically that frequency-doubling is realized for a finite range of exponential growth rate and shown that in one dimension domain growth may be a mechanism for increased robustness of pattern formation. Expand
Chaste: A test-driven approach to software development for biological modelling
TLDR
Chaste (‘Cancer, heart and soft-tissue environment’) is a software library and a set of test suites for computational simulations in the domain of biology and has been developed using agile programming methods. Expand
Non-linear incidence and stability of infectious disease models.
TLDR
It is remarkable that the system dynamics is independent of how the incidence rate depends on the number of susceptible individuals, and it is demonstrated that under the constant population size assumption, these models exhibit asymptotically stable steady states. Expand
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