DSpace Community:http://hdl.handle.net/2440/2992014-10-20T14:33:16Z2014-10-20T14:33:16ZInterpreting scratch assays using pair density dynamics and approximate Bayesian computationJohnston, S.T.Simpson, M.J.McElwain, D.L.S.Binder, B.J.Ross, J.V.http://hdl.handle.net/2440/862512014-10-15T23:00:17Z2013-12-31T13:30:00ZTitle: Interpreting scratch assays using pair density dynamics and approximate Bayesian computation
Author: Johnston, S.T.; Simpson, M.J.; McElwain, D.L.S.; Binder, B.J.; Ross, J.V.
Abstract: Quantifying the impact of biochemical compounds on collective cell spreading is an essential element of drug design, with various applications including developing treatments for chronic wounds and cancer. Scratch assays are a technically simple and inexpensive method used to study collective cell spreading; however, most previous interpretations of scratch assays are qualitative and do not provide estimates of the cell diffusivity, D, or the cell proliferation rate, λ. Estimating D and λ is important for investigating the efficacy of a potential treatment and provides insight into the mechanism through which the potential treatment acts. While a few methods for estimating D and λ have been proposed, these previous methods lead to point estimates of D and λ, and provide no insight into the uncertainty in these estimates. Here, we compare various types of information that can be extracted from images of a scratch assay, and quantify D and λ using discrete computational simulations and approximate Bayesian computation. We show that it is possible to robustly recover estimates of D and λ from synthetic data, as well as a new set of experimental data. For the first time, our approach also provides a method to estimate the uncertainty in our estimates of D and λ. We anticipate that our approach can be generalized to deal with more realistic experimental scenarios in which we are interested in estimating D and λ, as well as additional relevant parameters such as the strength of cell-to-cell adhesion or the strength of cell-to-substrate adhesion.2013-12-31T13:30:00ZRefined MDP-based branch-and-fix algorithm for the Hamiltonian cycle problemEjov, V.Filar, J.A.Haythorpe, M.Nguyen, G.T.http://hdl.handle.net/2440/862432014-10-15T22:49:13Z2008-12-31T13:30:00ZTitle: Refined MDP-based branch-and-fix algorithm for the Hamiltonian cycle problem
Author: Ejov, V.; Filar, J.A.; Haythorpe, M.; Nguyen, G.T.
Abstract: We consider the famous Hamiltonian cycle problem (HCP) embedded in a Markov decision process (MDP). More specifically, we consider the HCP as an optimisation problem over the space of occupation measures induced by the MDP's stationary policies. In recent years, this approach to the HCP has led to a number of alternative formulations and algorithmic approaches. In this paper, we focus on a specific embedding, because of the work of Feinberg. We present a “branch-and-fix” type algorithm that solves the HCP. At each branch of the algorithm, only a linear program needs to be solved and the dimensions of the successive linear programs are shrinking rather than expanding. Because the nodes of the branch-and-fix tree correspond to specially structured 1-randomised policies, we characterise the latter. This characterisation indicates that the total number of such policies is significantly smaller than the subset of all 1-randomised policies. Finally, we present some numerical results.2008-12-31T13:30:00ZDrawing of micro-structured fibres: circular and non-circular tubesStokes, Y.M.Buchak, P.Crowdy, D.G.Ebendorff-Heidepriem, H.http://hdl.handle.net/2440/861492014-10-14T02:02:21Z2013-12-31T13:30:00ZTitle: Drawing of micro-structured fibres: circular and non-circular tubes
Author: Stokes, Y.M.; Buchak, P.; Crowdy, D.G.; Ebendorff-Heidepriem, H.
Abstract: A general mathematical framework is presented for modelling the pulling of optical glass fibres in a draw tower. The only modelling assumption is that the fibres are slender; cross-sections along the fibre can have general shape, including the possibility of multiple holes or channels. A key result is to demonstrate how a so-called reduced time variable τ serves as a natural parameter in describing how an axial-stretching problem interacts with the evolution of a general surface-tension-driven transverse flow via a single important function of τ, herein denoted by H (τ), derived from the total rescaled cross-plane perimeter. For any given preform geometry, this function H (τ) may be used to calculate the tension required to produce a given fibre geometry, assuming only that the surface tension is known. Of principal practical interest in applications is the ‘inverse problem’ of determining the initial cross-sectional geometry, and experimental draw parameters, necessary to draw a desired final cross-section. Two case studies involving annular tubes are presented in detail: one involves a cross-section comprising an annular concatenation of sintering near-circular discs, the cross-section of the other is a concentric annulus. These two examples allow us to exemplify and explore two features of the general inverse problem. One is the question of the uniqueness of solutions for a given set of experimental parameters, the other concerns the inherent ill-posedness of the inverse problem. Based on these examples we also give an experimental validation of the general model and discuss some experimental matters, such as buckling and stability. The ramifications for modelling the drawing of fibres with more complicated geometries, and multiple channels, are discussed.2013-12-31T13:30:00ZNonautonomous analysis of steady Korteweg-de Vries waves under nonlocalised forcingBalasuriya, S.Binder, B.J.http://hdl.handle.net/2440/861402014-10-13T23:24:36Z2013-12-31T13:30:00ZTitle: Nonautonomous analysis of steady Korteweg-de Vries waves under nonlocalised forcing
Author: Balasuriya, S.; Binder, B.J.
Abstract: Abstract not available2013-12-31T13:30:00Z