Sufficient stochastic maximum principle in a regime-switching diffusion model

We prove a sufficient stochastic maximum principle for the optimal control of a regime-switching diffusion model. We show the connection to dynamic programming and we apply the result to a quadratic loss minimization problem, which can be used to solve a mean-variance portfolio selection problem

Reflection and Ducting of Gravity Waves Inside the Sun

Internal gravity waves excited by overshoot at the bottom of the convection zone can be influenced by rotation and by the strong toroidal magnetic field that is likely to be present in the solar tachocline. Using a simple Cartesian model, we show how waves with a vertical component of propagation can be reflected when traveling through a layer containing a horizontal magnetic field with a strength that varies with depth. This interaction can prevent a portion of the downward-traveling wave energy flux from reaching the deep solar interior. If a highly reflecting magnetized layer is located some distance below the convection zone base, a duct or wave guide can be set up, wherein vertical propagation is restricted by successive reflections at the upper and lower boundaries. The presence of both upward- and downward-traveling disturbances inside the duct leads to the existence of a set of horizontally propagating modes that have significantly enhanced amplitudes. We point out that the helical structure of these waves makes them capable of generating an alpha-effect, and briefly consider the possibility that propagation in a shear of sufficient strength could lead to instability, the result of wave growth due to over-reflection.Comment: 23 pages, 5 figures. Accepted for publication in Solar Physic

On evolutionary system identification with applications to nonlinear benchmarks

This paper presents a record of the participation of the authors in a workshop on nonlinear system identification held in 2016. It provides a summary of a keynote lecture by one of the authors and also gives an account of how the authors developed identification strategies and methods for a number of benchmark nonlinear systems presented as challenges, before and during the workshop. It is argued here that more general frameworks are now emerging for nonlinear system identification, which are capable of addressing substantial ranges of problems. One of these frameworks is based on evolutionary optimisation (EO); it is a framework developed by the authors in previous papers and extended here. As one might expect from the ‘no-free-lunch’ theorem for optimisation, the methodology is not particularly sensitive to the particular (EO) algorithm used, and a number of different variants are presented in this paper, some used for the first time in system identification problems, which show equal capability. In fact, the EO approach advocated in this paper succeeded in finding the best solutions to two of the three benchmark problems which motivated the workshop. The paper provides considerable discussion on the approaches used and makes a number of suggestions regarding best practice; one of the major new opportunities identified here concerns the application of grey-box models which combine the insight of any prior physical-law based models (white box) with the power of machine learners with universal approximation properties (black box)

Coloring translates and homothets of a convex body

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in \RR^n.Comment: 11 pages, 2 figure

Performance based specification for road foundation materials

UK Pavement foundations are currently designed using a method specification whereby tightly specified materials are constructed using specific compaction methods and layer thickness. This process does not necessarily guarantee the performance of the materials, but it is assumed to be adequate based on past experience. However, it can be inefficient, leading to unnecessary restrictions when using stabilised, recycled or marginal materials and/or the inappropriate use of good quality aggregates. The UK Highways Agency (HA) funded a recently completed three-year research project to produce a draft performance-based specification for road foundations. The performance-based specification aims to enable more appropriate and efficient use of a wider range of materials, both natural and recycled. The performance parameters required of the materials were established as the stiffness and the resistance to permanent deformation, with both measured, ideally, in the laboratory for design purposes and during construction to ensure their performance on site. Pre-construction trials to demonstrate adequate material performance (both as individual layers and as a composite structure) are expected to feature prominently when the new approach is adopted. A further HA-funded project started in January 2000 to evaluate the implementation of this new specification. This paper outlines the philosophy of the draft performance-based specification produced, including what needs to be measured and how and when it should be measured. Its impact on the highways industry is then discussed

Learning model discrepancy: A Gaussian process and sampling-based approach

Predicting events in the real world with a computer model (simulator) is challenging. Every simulator, to varying extents, has model discrepancy, a mismatch between real world observations and the simulator (given the ‘true’ parameters are known). Model discrepancy occurs for various reasons, including simplified or missing physics in the simulator, numerical approximations that are required to compute the simulator outputs, and the fact that assumptions in the simulator are not generally applicable to all real world contexts. The existence of model discrepancy is problematic for the engineer as performing calibration of the simulator will lead to biased parameter estimates, and the resulting simulator is unlikely to accurately predict (or even be valid for) various contexts of interest. This paper proposes an approach for inferring model discrepancy that overcomes non-identifiability problems associated with jointly inferring the simulator parameters along with the model discrepancy. Instead, the proposed procedure seeks to identify model discrepancy given some parameter distribution, which could come from a ‘likelihood-free’ approach that considers the presence of model discrepancy during calibration, such as Bayesian history matching. In this case, model discrepancy is inferred whilst marginalising out the uncertain simulator outputs via a sampling-based approach, therefore better reflecting the ‘true’ uncertainty associated with the model discrepancy. Verification of the approach is performed before a demonstration on an experiential case study, comprising a representative five storey building structure

Sparse Gaussian Process Emulators for surrogate design modelling

Efficient surrogate modelling of computer models (herein defined as simulators) becomes of increasing importance as more complex simulators and non-deterministic methods, such as Monte Carlo simulations, are utilised. This is especially true in large multidimensional design spaces. In order for these technologies to be feasible in an early design stage context, the surrogate model (oremulator) must create an accurate prediction of the simulator in the proposed design space. Gaussian Processes (GPs) are a powerful non-parametric Bayesian approach that can be used as emulators. The probabilistic framework means that predictive distributions are inferred, providing an understanding of the uncertainty introduced by replacing the simulator with an emulator, known as code uncertainty. An issue with GPs is that they have a computational complexity of O(N3) (where N is the number of data points), which can be reduced to O(NM2) by using various sparse approximations, calculated from a subset of inducing points (where M is the number of inducing points). This paper explores the use of sparse Gaussian process emulators as a computationally efficient method for creating surrogate models of structural dynamics simulators. Discussions on the performance of these methods are presented along with comments regarding key applications to the early design stage

Dilogarithm Identities in Conformal Field Theory and Group Homology

Recently, Rogers' dilogarithm identities have attracted much attention in the setting of conformal field theory as well as lattice model calculations. One of the connecting threads is an identity of Richmond-Szekeres that appeared in the computation of central charges in conformal field theory. We show that the Richmond-Szekeres identity and its extension by Kirillov-Reshetikhin can be interpreted as a lift of a generator of the third integral homology of a finite cyclic subgroup sitting inside the projective special linear group of all $2 \times 2$ real matrices viewed as a {\it discrete} group. This connection allows us to clarify a few of the assertions and conjectures stated in the work of Nahm-Recknagel-Terhoven concerning the role of algebraic $K$-theory and Thurston's program on hyperbolic 3-manifolds. Specifically, it is not related to hyperbolic 3-manifolds as suggested but is more appropriately related to the group manifold of the universal covering group of the projective special linear group of all $2 \times 2$ real matrices viewed as a topological group. This also resolves the weaker version of the conjecture as formulated by Kirillov. We end with the summary of a number of open conjectures on the mathematical side.Comment: 20 pages, 2 figures not include

Tissue chemistry and carbon allocation in seedlings of Pinus palustris subjected to elevated atmospheric CO2 and water stress

Longleaf pine (Pinus palustris Mill.) seedlings were grown in 45-1 pots and exposed to ambient or elevated (365 or 730 uamol CO2 mol-1 ) CO2 concentration in open-top chambers for 20 months. Two water-stress treatments (target values of -0.5 or -1.5 MPa xylem pressure potential) were imposed 19 weeks after initiation of the study. At harvest, tissues (needles, stems, taproots, coarse roots, and fine roots) were analyzed for carbon (C), nitrogen (N), nonpolar extractives (fats, waxes, and oils), nonstructural carbohydrates (sugars and starch), structural components (cellulose and lignin), and tannins. The greatest dry weights and lowest N concentrations occurred in tissues of plants grown at elevated CO 2 or with adequate water. Although allocation of C fractions among tissues was generally unaffected by treatments, concentrations of the analyzed compounds were influenced by treatments in needles and taproots, but not in stems and lateral roots. Needles and taproots of plants exposed to elevated CO2 had increased concentrations of nonstructural carbohydrates. Among plant tissues, elevated CO2 caused reductions in structural C concentrations and foliar concentrations of fats, waxes and oils

The effects of a 12-Month weight loss intervention on cognitive outcomes in adults with overweight and obesity

Obesity is associated with poorer executive functioning and reward sensitivity. Yet, we know very little about whether weight loss through diet and/or increased exercise engagement improves cognitive function. This study evaluated whether weight loss following a dietary and exercise intervention was associated with improved cognitive performance. We enrolled 125 middle-aged adults with overweight and obesity (98 female) into a 12-month behavioral weight loss intervention. Participants were assigned to one of three groups: energy-restricted diet alone, an energy-restricted diet plus 150 min of moderate intensity exercise per week or an energy restricted diet plus 250 min of exercise per week. All participants completed tests measuring executive functioning and/or reward sensitivity, including the Iowa Gambling Task (IGT). Following the intervention, weight significantly decreased in all groups. A MANCOVA controlling for age, sex and race revealed a significant multivariate effect of group on cognitive changes. Post-hoc ANCOVAs revealed a Group x Time interaction only on IGT reward sensitivity, such that the high exercise group improved their performance relative to the other two intervention groups. Post-hoc ANCOVAs also revealed a main effect of Time, independent of intervention group, on IGT net payoff score. Changes in weight were not associated with other changes in cognitive performance. Engaging in a high amount of exercise improved reward sensitivity above and beyond weight loss alone. This suggests that there is additional benefit to adding exercise into behavioral weight loss regimens on executive functioning, even without additional benefit to weight loss