5,579 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
Bayesian Analysis of ODE's: solver optimal accuracy and Bayes factors
In most relevant cases in the Bayesian analysis of ODE inverse problems, a
numerical solver needs to be used. Therefore, we cannot work with the exact
theoretical posterior distribution but only with an approximate posterior
deriving from the error in the numerical solver. To compare a numerical and the
theoretical posterior distributions we propose to use Bayes Factors (BF),
considering both of them as models for the data at hand. We prove that the
theoretical vs a numerical posterior BF tends to 1, in the same order (of the
step size used) as the numerical forward map solver does. For higher order
solvers (eg. Runge-Kutta) the Bayes Factor is already nearly 1 for step sizes
that would take far less computational effort. Considerable CPU time may be
saved by using coarser solvers that nevertheless produce practically error free
posteriors. Two examples are presented where nearly 90% CPU time is saved while
all inference results are identical to using a solver with a much finer time
step.Comment: 28 pages, 6 figure
Adaptive Detection of Instabilities: An Experimental Feasibility Study
We present an example of the practical implementation of a protocol for
experimental bifurcation detection based on on-line identification and feedback
control ideas. The idea is to couple the experiment with an on-line
computer-assisted identification/feedback protocol so that the closed-loop
system will converge to the open-loop bifurcation points. We demonstrate the
applicability of this instability detection method by real-time,
computer-assisted detection of period doubling bifurcations of an electronic
circuit; the circuit implements an analog realization of the Roessler system.
The method succeeds in locating the bifurcation points even in the presence of
modest experimental uncertainties, noise and limited resolution. The results
presented here include bifurcation detection experiments that rely on
measurements of a single state variable and delay-based phase space
reconstruction, as well as an example of tracing entire segments of a
codimension-1 bifurcation boundary in two parameter space.Comment: 29 pages, Latex 2.09, 10 figures in encapsulated postscript format
(eps), need psfig macro to include them. Submitted to Physica
COEL: A Web-based Chemistry Simulation Framework
The chemical reaction network (CRN) is a widely used formalism to describe
macroscopic behavior of chemical systems. Available tools for CRN modelling and
simulation require local access, installation, and often involve local file
storage, which is susceptible to loss, lacks searchable structure, and does not
support concurrency. Furthermore, simulations are often single-threaded, and
user interfaces are non-trivial to use. Therefore there are significant hurdles
to conducting efficient and collaborative chemical research. In this paper, we
introduce a new enterprise chemistry simulation framework, COEL, which
addresses these issues. COEL is the first web-based framework of its kind. A
visually pleasing and intuitive user interface, simulations that run on a large
computational grid, reliable database storage, and transactional services make
COEL ideal for collaborative research and education. COEL's most prominent
features include ODE-based simulations of chemical reaction networks and
multicompartment reaction networks, with rich options for user interactions
with those networks. COEL provides DNA-strand displacement transformations and
visualization (and is to our knowledge the first CRN framework to do so), GA
optimization of rate constants, expression validation, an application-wide
plotting engine, and SBML/Octave/Matlab export. We also present an overview of
the underlying software and technologies employed and describe the main
architectural decisions driving our development. COEL is available at
http://coel-sim.org for selected research teams only. We plan to provide a part
of COEL's functionality to the general public in the near future.Comment: 23 pages, 12 figures, 1 tabl
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