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Forthcoming events in this series
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Dynamics on networks: synchronization of oscillators in biology
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Multiphase flow - a variety of applications, and some simple numerical techniques
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Agent-based modelling of cell migration and angiogenesis
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Stochastic models of cell cycle regulation in eukaryotes
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Self-simplification and 0-1 laws in multiscale reaction networks
Abstract
Multiscale ensembles of reaction networks with well separated constants are introduced and typical properties of such systems are studied. For any given ordering of reaction rate constants the explicit approximation of steady state, relaxation spectrum and related eigenvectors (``modes") is presented. The obtained multiscale approximations are computationally cheap and robust. Some of results obtained are rather surprising and unexpected. First of all is the zero-one asymptotic of eigenvectors (asymptotically exact lumping; but these asymptotic lumps could intersect). Our main mathematical tools are auxiliary discrete dynamical systems on finite sets and specially developed algorithms of ``cycles surgery"
for reaction graphs. Roughly speaking, the dynamics of linear multiscale networks transforms into the dynamics on finite sets of reagent names.
A.N. Gorban and O. Radulescu, Dynamic and static limitation in multiscale reaction networks, Advances in Chemical Engineering, 2008 (in press), arXiv e-print: http://arxiv.org/abs/physics/0703278
A.N. Gorban and O. Radulescu, Dynamical robustness of biological networks with hierarchical distribution of time scales, IET Syst.
Biol., 2007, 1, (4), pp. 238-246.
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Angiogenesis and vascular remodelling in normal and cancerous tissues
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Asymptotics of cardiac excitability equations
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Biodiversity in microbial communities with non-transitive interactions and rock-paper-scissors games
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Mathematical Modelling of mesenchymal stem cell differentiation
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Theoretical models for understanding the development of neuronal positioning
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Cycles from resonant amplification of demographic stochasticity
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Mathematical Modelling of fungal mycelia : a question of scale
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