ODE parameter inference using adaptive gradient matching with Gaussian processes

Parameter inference in mechanistic models based on systems of coupled differential equa- tions is a topical yet computationally chal- lenging problem, due to the need to fol- low each parameter adaptation with a nu- merical integration of the differential equa- tions. Techniques based on gradient match- ing, which aim to minimize the discrepancy between the slope of a data interpolant and the derivatives predicted from the differen- tial equations, offer a computationally ap- pealing shortcut to the inference problem. The present paper discusses a method based on nonparametric Bayesian statistics with Gaussian processes due to Calderhead et al. (2008), and shows how inference in this model can be substantially improved by consistently inferring all parameters from the joint dis- tribution. We demonstrate the efficiency of our adaptive gradient matching technique on three benchmark systems, and perform a de- tailed comparison with the method in Calder- head et al. (2008) and the explicit ODE inte- gration approach, both in terms of parameter inference accuracy and in terms of computa- tional efficiency

The provision of distance education within the HE sector - some areas for concern

This paper presents a summary of the findings of a recent survey of the way in which UK higher education institutions (HEIs) are offering distance education (DE) courses, the types of courses being offered, and their modes of delivery. From analysis of the findings of this survey, it is apparent that the emphasis of HEIs is very much on the exploitation of available teaching technology in the delivery of DE courses. However, teaching at a distance is quite different from face-toface teaching, and the evidence suggests that many HEIs fail to implement any meaningful academic staff training for the new role of DE tutor. The authors consider the difficulties this presents to academic staff who are required to move from face-to-face teaching to online facilitating. The paper concludes with an examination of the current provision of staff development and training within UK HEIs and suggests the type of academic staff training required if DE courses are to become truly core activities

Three-dimensional incompressible Navier-Stokes computations of internal flows

Several incompressible Navier-Stokes solution methods for obtaining steady and unsteady solutions are discussed. Special attention is given to internal flows which involve distinctly different features from external flows. The characterisitcs of the flow solvers employing the method of pseudocompressibility and a fractional step method are briefly described. This discussion is limited to a primitive variable formulation in generalized curvilinear coordinates. Computed results include simple test cases and internal flow in the Space Shuttle main engine hot-gas manifold

Potential applications of computational fluid dynamics to biofluid analysis

Computational fluid dynamics was developed to the stage where it has become an indispensable part of aerospace research and design. In view of advances made in aerospace applications, the computational approach can be used for biofluid mechanics research. Several flow simulation methods developed for aerospace problems are briefly discussed for potential applications to biofluids, especially to blood flow analysis

Superconformal Primary Fields on a Graded Riemann Sphere

Primary superfields for a two dimensional Euclidean superconformal field theory are constructed as sections of a sheaf over a graded Riemann sphere. The construction is then applied to the N=3 Neveu-Schwarz case. Various quantities in the N=3 theory are calculated and discussed, such as formal elements of the super-Mobius group, and the two-point function.Comment: LaTeX2e, 23 pages; fixed typos, sorted references, modified definition of primary superfield on page

Parameter inference in mechanistic models of cellular regulation and signalling pathways using gradient matching

A challenging problem in systems biology is parameter inference in mechanistic models of signalling pathways. In the present article, we investigate an approach based on gradient matching and nonparametric Bayesian modelling with Gaussian processes. We evaluate the method on two biological systems, related to the regulation of PIF4/5 in Arabidopsis thaliana, and the JAK/STAT signal transduction pathway

Phase decorrelation, streamwise vortices and acoustic radiation in mixing layers

Several direct numerical simulations were performed and analyzed to study various aspects of the early development of mixing layers. Included are the phase jitter of the large-scale eddies, which was studied using a 2-D spatially-evolving mixing layer simulation; the response of a time developing mixing layer to various spanwise disturbances; and the sound radiation from a 2-D compressible time developing mixing layer

A Feynman-Kac Formula for Anticommuting Brownian Motion

Motivated by application to quantum physics, anticommuting analogues of Wiener measure and Brownian motion are constructed. The corresponding Ito integrals are defined and the existence and uniqueness of solutions to a class of stochastic differential equations is established. This machinery is used to provide a Feynman-Kac formula for a class of Hamiltonians. Several specific examples are considered.Comment: 21 page