| 1. |
- Eriksson, Olivia, et al.
(författare)
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Uncertainty quantification, propagation and characterization by Bayesian analysis combined with global sensitivity analysis applied to dynamical intracellular pathway models
- 2019
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Ingår i: Bioinformatics. - : Oxford University Press (OUP). - 1367-4803 .- 1367-4811. ; 35:2, s. 284-292
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Tidskriftsartikel (refereegranskat)abstract
- Motivation: Dynamical models describing intracellular phenomena are increasing in size and complexity as more information is obtained from experiments. These models are often over-parameterized with respect to the quantitative data used for parameter estimation, resulting in uncertainty in the individual parameter estimates as well as in the predictions made from the model. Here we combine Bayesian analysis with global sensitivity analysis (GSA) in order to give better informed predictions; to point out weaker parts of the model that are important targets for further experiments, as well as to give guidance on parameters that are essential in distinguishing different qualitative output behaviours.Results: We used approximate Bayesian computation (ABC) to estimate the model parameters from experimental data, as well as to quantify the uncertainty in this estimation (inverse uncertainty quantification), resulting in a posterior distribution for the parameters. This parameter uncertainty was next propagated to a corresponding uncertainty in the predictions (forward uncertainty propagation), and a GSA was performed on the predictions using the posterior distribution as the possible values for the parameters. This methodology was applied on a relatively large model relevant for synaptic plasticity, using experimental data from several sources. We could hereby point out those parameters that by themselves have the largest contribution to the uncertainty of the prediction as well as identify parameters important to separate between qualitatively different predictions. This approach is useful both for experimental design as well as model building.
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| 2. |
- Laptev, Ari, et al.
(författare)
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Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder
- 2017
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 58:1
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Tidskriftsartikel (refereegranskat)abstract
- Perturbation problems for operators with embedded eigenvalues are generally challenging since the embedded eigenvalues cannot be separated from the rest of the spectrum. In this paper, we study a perturbation problem for embedded eigenvalues for a magnetic Schrödinger operator, when the underlying domain is a cylinder. The magnetic potential is C2 with an algebraic decay rate as the unbounded variable of the cylinder tends to ±∞. In particular, no analyticity of the magnetic potential is assumed. We also assume that the embedded eigenvalue of the unperturbed problem is not the square of an integer, thus avoiding the thresholds of the continuous spectrum of the unperturbed operator. We show that the set of nearby potentials, for which a simple embedded eigenvalue persists, forms a smooth manifold of finite codimension.
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| 3. |
- Maad Sasane, Sara
(författare)
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An age structured cell cycle model with crowding
- 2016
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X. ; 444:1, s. 768-803
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Tidskriftsartikel (refereegranskat)abstract
- We study a two compartment, nonlinear, age structured model for the cell cycle. The phases of the cell cycle G1, S, G2 and M are grouped into two phases, which we call Phase 1 and Phase 2, where Phase 1 consists of the phase G1 and Phase 2 consists of the phases S, G2 and M. It is assumed that Phase 1 has a variable duration while the duration of Phase 2 is fixed. The model consists of a system of nonlinear PDEs describing the number densities ni(t,τ), i=1,2, of cells in Phase i of age τ (counted from when the cell entered the phase) and time t, together with initial and boundary conditions for ni. We first prove that this initial and boundary value problem is equivalent to solving a system of integral equations. We then prove existence and uniqueness of this system of integral equations, and hence also of the original PDE system. Qualitative behaviour of solutions with small initial and input data is studied, and an application to quorum sensing is discussed. Finally, some simple numerical examples are computed using the derived integral equations.
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