35,943 research outputs found
Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D. melanogaster
Background: Reaction-diffusion systems are frequently used in systems biology to model developmental and signalling processes. In many applications, count numbers of the diffusing molecular species are very low, leading to the need to explicitly model the inherent variability using stochastic methods. Despite their importance and frequent use, parameter estimation for both deterministic and stochastic reaction-diffusion systems is still a challenging problem.
Results: We present a Bayesian inference approach to solve both the parameter and state estimation problem for stochastic reaction-diffusion systems. This allows a determination of the full posterior distribution of the parameters (expected values and uncertainty). We benchmark the method by illustrating it on a simple synthetic experiment. We then test the method on real data about the diffusion of the morphogen Bicoid in Drosophila melanogaster. The results show how the precision with which parameters can be inferred varies dramatically, indicating that the ability to infer full posterior distributions on the parameters can have important experimental design consequences.
Conclusions: The results obtained demonstrate the feasibility and potential advantages of applying a Bayesian approach to parameter estimation in stochastic reaction-diffusion systems. In particular, the ability to estimate credibility intervals associated with parameter estimates can be precious for experimental design. Further work, however, will be needed to ensure the method can scale up to larger problems
Constrained Nonlinear Model Predictive Control of an MMA Polymerization Process via Evolutionary Optimization
In this work, a nonlinear model predictive controller is developed for a
batch polymerization process. The physical model of the process is
parameterized along a desired trajectory resulting in a trajectory linearized
piecewise model (a multiple linear model bank) and the parameters are
identified for an experimental polymerization reactor. Then, a multiple model
adaptive predictive controller is designed for thermal trajectory tracking of
the MMA polymerization. The input control signal to the process is constrained
by the maximum thermal power provided by the heaters. The constrained
optimization in the model predictive controller is solved via genetic
algorithms to minimize a DMC cost function in each sampling interval.Comment: 12 pages, 9 figures, 28 reference
Learning Dynamic Boltzmann Distributions as Reduced Models of Spatial Chemical Kinetics
Finding reduced models of spatially-distributed chemical reaction networks
requires an estimation of which effective dynamics are relevant. We propose a
machine learning approach to this coarse graining problem, where a maximum
entropy approximation is constructed that evolves slowly in time. The dynamical
model governing the approximation is expressed as a functional, allowing a
general treatment of spatial interactions. In contrast to typical machine
learning approaches which estimate the interaction parameters of a graphical
model, we derive Boltzmann-machine like learning algorithms to estimate
directly the functionals dictating the time evolution of these parameters. By
incorporating analytic solutions from simple reaction motifs, an efficient
simulation method is demonstrated for systems ranging from toy problems to
basic biologically relevant networks. The broadly applicable nature of our
approach to learning spatial dynamics suggests promising applications to
multiscale methods for spatial networks, as well as to further problems in
machine learning
A computationally efficacious free-energy functional for studies of inhomogeneous liquid water
We present an accurate equation of state for water based on a simple
microscopic Hamiltonian, with only four parameters that are well-constrained by
bulk experimental data. With one additional parameter for the range of
interaction, this model yields a computationally efficient free-energy
functional for inhomogeneous water which captures short-ranged correlations,
cavitation energies and, with suitable long-range corrections, the non-linear
dielectric response of water, making it an excellent candidate for studies of
mesoscale water and for use in ab initio solvation methods.Comment: 6 pages, 5 figure
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