Sculplexity: Sculptures of Complexity using 3D printing

We show how to convert models of complex systems such as 2D cellular automata into a 3D printed object. Our method takes into account the limitations inherent to 3D printing processes and materials. Our approach automates the greater part of this task, bypassing the use of CAD software and the need for manual design. As a proof of concept, a physical object representing a modified forest fire model was successfully printed. Automated conversion methods similar to the ones developed here can be used to create objects for research, for demonstration and teaching, for outreach, or simply for aesthetic pleasure. As our outputs can be touched, they may be particularly useful for those with visual disabilities.Comment: Free access to article on European Physics Letter

Coupling iterated Kolmogorov diffusions

The Kolmogorov (1934) diffusion is the two-dimensional diffusion generated by real Brownian motion B and its time integral integral B d t. In this paper we construct successful co-adapted couplings for iterated Kolmogorov diffusions defined by adding iterated time integrals integral integral B d s d t,... as further components to the original Kolmogorov diffusion. A Laplace-transform argument shows it is not possible successfully to couple all iterated time integrals at once; however we give an explicit construction of a successful co-adapted coupling method for (B, integral B d t, integral integral B d s d t); and a more implicit construction of a successful co-adapted coupling method which works for finite sets of iterated time integrals

Forecasting in the presence of recent structural change

We examine how to forecast after a recent break. We consider monitoring for change and then combining forecasts from models that do and do not use data before the change; and robust methods, namely rolling regressions, forecast averaging over different windows and exponentially weighted moving average (EWMA) forecasting. We derive analytical results for the performance of the robust methods relative to a full-sample recursive benchmark. For a location model subject to stochastic breaks the relative MSFE ranking is EWMA < rolling regression < forecast averaging. No clear ranking emerges under deterministic breaks. In Monte Carlo experiments forecast averaging improves performance in many cases with little penalty where there are small or infrequent changes. Similar results emerge when we examine a large number of UK and US macroeconomic series

A switch to reduce resistivity in smoothed particle magnetohydrodynamics

Artificial resistivity is included in Smoothed Particle Magnetohydrodynamics simulations to capture shocks and discontinuities in the magnetic field. Here we present a new method for adapting the strength of the applied resistivity so that shocks are captured but the dissipation of the magnetic field away from shocks is minimised. Our scheme utilises the gradient of the magnetic field as a shock indicator, setting {\alpha}_B = h|gradB|/|B|, such that resistivity is switched on only where strong discontinuities are present. The advantage to this approach is that the resistivity parameter does not depend on the absolute field strength. The new switch is benchmarked on a series of shock tube tests demonstrating its ability to capture shocks correctly. It is compared against a previous switch proposed by Price & Monaghan (2005), showing that it leads to lower dissipation of the field, and in particular, that it succeeds at capturing shocks in the regime where the Alfv\'en speed is much less than the sound speed (i.e., when the magnetic field is very weak). It is also simpler. We also demonstrate that our recent constrained divergence cleaning algorithm has no difficulty with shock tube tests, in contrast to other implementations.Comment: 8 pages, 7 figures, accepted for publication in MNRA

Information sheets for patients with acute chest pain: randomised controlled trial

Objectives: To determine whether providing an information sheet to patients with acute chest pain reduces anxiety, improves health related quality of life, improves satisfaction with care, or alters subsequent symptoms or actions. Design: Single centre, non-blinded, randomised controlled trial. Setting: Chest pain unit of an emergency department. Participants: 700 consecutive patients with acute chest pain and no clear diagnosis at initial presentation. Interventions: After a diagnostic assessment patients were randomised to receive either standard verbal advice or verbal advice followed by an information sheet. Main outcome measures: The primary outcome was anxiety (hospital anxiety and depression scale). Secondary outcomes were depression (hospital anxiety and depression scale), health related quality of life (SF-36), patient satisfaction, presentation with further chest pain within one month, lifestyle change (smoking cessation, diet, exercise), further information sought from other sources, and planned healthcare seeeking behaviour in response to further pain. Results 494 of 700 (70.6%) patients responded. Compared with those receiving standard verbal advice those receiving advice and an information sheet had lower mean hospital anxiety and depression scale scores for anxiety (7.61v8.63, difference 1.02, 95% confidence interval 0.20 to 1.84) and depression (4.14 v 5.28, difference 1.14, 0.41 to 1.86) and higher scores for mental health and perception of general health on the SF-36. The information sheet had no significant effect on satisfaction with care, subsequent symptoms, lifestyle change, information seeking, or planned actions in the event of further pain. Conclusions: Provision of an information sheet to patients with acute chest pain can reduce anxiety and depression and improve mental health and perception of general health but does not alter satisfaction with care or other outcomes. Trial registration Current Controlled Trials ISRCTN85248020

Ridge Fusion in Statistical Learning

We propose a penalized likelihood method to jointly estimate multiple precision matrices for use in quadratic discriminant analysis and model based clustering. A ridge penalty and a ridge fusion penalty are used to introduce shrinkage and promote similarity between precision matrix estimates. Block-wise coordinate descent is used for optimization, and validation likelihood is used for tuning parameter selection. Our method is applied in quadratic discriminant analysis and semi-supervised model based clustering.Comment: 24 pages and 9 tables, 3 figure

Constrained Hyperbolic Divergence Cleaning for Smoothed Particle Magnetohydrodynamics

We present a constrained formulation of Dedner et al's hyperbolic/parabolic divergence cleaning scheme for enforcing the \nabla\dot B = 0 constraint in Smoothed Particle Magnetohydrodynamics (SPMHD) simulations. The constraint we impose is that energy removed must either be conserved or dissipated, such that the scheme is guaranteed to decrease the overall magnetic energy. This is shown to require use of conjugate numerical operators for evaluating \nabla\dot B and \nabla{\psi} in the SPMHD cleaning equations. The resulting scheme is shown to be stable at density jumps and free boundaries, in contrast to an earlier implementation by Price & Monaghan (2005). Optimal values of the damping parameter are found to be {\sigma} = 0.2-0.3 in 2D and {\sigma} = 0.8-1.2 in 3D. With these parameters, our constrained Hamiltonian formulation is found to provide an effective means of enforcing the divergence constraint in SPMHD, typically maintaining average values of h |\nabla\dot B| / |B| to 0.1-1%, up to an order of magnitude better than artificial resistivity without the associated dissipation in the physical field. Furthermore, when applied to realistic, 3D simulations we find an improvement of up to two orders of magnitude in momentum conservation with a corresponding improvement in numerical stability at essentially zero additional computational expense.Comment: 28 pages, 25 figures, accepted to J. Comput. Phys. Movies at http://www.youtube.com/playlist?list=PL215D649FD0BDA466 v2: fixed inverted figs 1,4,6, and several color bar