8,650 research outputs found
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art
Stochasticity is a key characteristic of intracellular processes such as gene
regulation and chemical signalling. Therefore, characterising stochastic
effects in biochemical systems is essential to understand the complex dynamics
of living things. Mathematical idealisations of biochemically reacting systems
must be able to capture stochastic phenomena. While robust theory exists to
describe such stochastic models, the computational challenges in exploring
these models can be a significant burden in practice since realistic models are
analytically intractable. Determining the expected behaviour and variability of
a stochastic biochemical reaction network requires many probabilistic
simulations of its evolution. Using a biochemical reaction network model to
assist in the interpretation of time course data from a biological experiment
is an even greater challenge due to the intractability of the likelihood
function for determining observation probabilities. These computational
challenges have been subjects of active research for over four decades. In this
review, we present an accessible discussion of the major historical
developments and state-of-the-art computational techniques relevant to
simulation and inference problems for stochastic biochemical reaction network
models. Detailed algorithms for particularly important methods are described
and complemented with MATLAB implementations. As a result, this review provides
a practical and accessible introduction to computational methods for stochastic
models within the life sciences community
Stochastic simulation of the influence of cure kinetics uncertainty on composites cure
A stochastic cure simulation methodology is developed and implemented to investigate the influence of cure kinetics uncertainty due to different initial resin state on the process of cure. The simulation addresses heat transfer effects and allows quantification of uncertainty in temperature overshoot during the cure. Differential Scanning Calorimetry was used to characterise cure kinetics variability of a commercial epoxy resin used in aerospace applications. It was found that cure kinetics uncertainty is associated with variations in the initial degree of cure, activation energy and reaction order. A cure simulation model was coupled with conventional Monte Carlo and an implementation of the Probabilistic Collocation Method. Both simulation schemes are capable of capturing variability propagation, with the collocation method presenting benefits in terms of computational cost against the Monte Carlo scheme with comparable accuracy. Simulation of the cure of a carbon fibre–epoxy panel shows that cure kinetics uncertainty can cause considerable variability in the process outcome with a coefficient of variation in temperature overshoot of about 30%
A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics
We propose a new sensitivity analysis methodology for complex stochastic
dynamics based on the Relative Entropy Rate. The method becomes computationally
feasible at the stationary regime of the process and involves the calculation
of suitable observables in path space for the Relative Entropy Rate and the
corresponding Fisher Information Matrix. The stationary regime is crucial for
stochastic dynamics and here allows us to address the sensitivity analysis of
complex systems, including examples of processes with complex landscapes that
exhibit metastability, non-reversible systems from a statistical mechanics
perspective, and high-dimensional, spatially distributed models. All these
systems exhibit, typically non-gaussian stationary probability distributions,
while in the case of high-dimensionality, histograms are impossible to
construct directly. Our proposed methods bypass these challenges relying on the
direct Monte Carlo simulation of rigorously derived observables for the
Relative Entropy Rate and Fisher Information in path space rather than on the
stationary probability distribution itself. We demonstrate the capabilities of
the proposed methodology by focusing here on two classes of problems: (a)
Langevin particle systems with either reversible (gradient) or non-reversible
(non-gradient) forcing, highlighting the ability of the method to carry out
sensitivity analysis in non-equilibrium systems; and, (b) spatially extended
Kinetic Monte Carlo models, showing that the method can handle high-dimensional
problems
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