Efficient preconditioning of the linearized Navier-Stokes equations

We outline a new class of robust and efficient methods for solving subproblems that arise in the linearization and operator splitting of Navier-Stokes equations. We describe a very general strategy for preconditioning that has two basic building blocks; a multigrid V-cycle for the scaler convection-diffusion operator, and a multigrid V-cycle for a pressure Poisson operator. We present numerical experiments illustrating that a simple implementation of our approach leads to an effective and robust solver strategy in that the convergence rate is independent of the grid, robust with respect to the time step, and only deteriorates very slowly as the Reynolds number is increased

Refined saddle-point preconditioners for discretized Stokes problems

This paper is concerned with the implementation of efficient solution algorithms for elliptic problems with constraints. We establish theory which shows that including a simple scaling within well-established block diagonal preconditioners for Stokes problems can result in significantly faster convergence when applying the preconditioned MINRES method. The codes used in the numerical studies are available online

PlaNet - Photo Geolocation with Convolutional Neural Networks

Is it possible to build a system to determine the location where a photo was taken using just its pixels? In general, the problem seems exceptionally difficult: it is trivial to construct situations where no location can be inferred. Yet images often contain informative cues such as landmarks, weather patterns, vegetation, road markings, and architectural details, which in combination may allow one to determine an approximate location and occasionally an exact location. Websites such as GeoGuessr and View from your Window suggest that humans are relatively good at integrating these cues to geolocate images, especially en-masse. In computer vision, the photo geolocation problem is usually approached using image retrieval methods. In contrast, we pose the problem as one of classification by subdividing the surface of the earth into thousands of multi-scale geographic cells, and train a deep network using millions of geotagged images. While previous approaches only recognize landmarks or perform approximate matching using global image descriptors, our model is able to use and integrate multiple visible cues. We show that the resulting model, called PlaNet, outperforms previous approaches and even attains superhuman levels of accuracy in some cases. Moreover, we extend our model to photo albums by combining it with a long short-term memory (LSTM) architecture. By learning to exploit temporal coherence to geolocate uncertain photos, we demonstrate that this model achieves a 50% performance improvement over the single-image model

Modified Streamline Diffusion Schemes for Convection-Diffusion Problems

We consider the design of robust and accurate finite element approximation methods for solving convection--diffusion problems. We develop some two--parameter streamline diffusion schemes with piecewise bilinear (or linear) trial functions and show that these schemes satisfy the necessary conditions for $L^{2}$-uniform convergence of order greater than $1/2$ introduced by Stynes and Tobiska. For smooth problems, the schemes satisfy error bounds of the form $O(h)|u|_{2}$ in an energy norm. In addition, extensive numerical experiments show that they effectively reproduce boundary layers and internal layers caused by discontinuities on relatively coarse grids, without any requirements on alignment of flow and grid. (Also cross-referenced as UMIACS-TR-97-71

Efficacy of Elaborated Semantic Features Analysis in Aphasia: a quasi-randomised controlled trial

Background: Word finding difficulty is one of the most common features of aphasia. Semantic Features Analysis (SFA) directly aims to improve word finding in people with aphasia. Evidence from systematic reviews suggests that SFA leads to positive outcomes, yet the evidence comprises single case studies and case series. There is a need to evaluate the efficacy of SFA in controlled group studies/trials. Aims: To evaluate the efficacy of Elaborated Semantic Feature Analysis (ESFA) for word finding in people with aphasia. We investigated: (a) the efficacy of ESFA versus a delayed therapy/control, (b) the efficacy of two therapy approaches– individual versus a combination of individual and group therapy. Methods and procedures: We ran a multi-centre, quasi-randomised controlled trial, nested in a larger study (Thales-Aphasia). Participants were recruited from community settings. They had to be people with aphasia due to stroke at least four months post-onset. Participants were randomized to individual vs combination vs delayed therapy/control groups. Both therapy groups had three hours of ESFA per week for 12 weeks. Delayed therapy/control group had no intervention for 12 weeks and were then randomized to either individual or combination therapy. The primary outcome was confrontation naming. Secondary outcomes were the Boston Naming Test, Discourse, the Functional Assessment of Communication Skills for adults (ASHA–FACS), the Stroke and Aphasia Quality of Life scale (SAQOL-39g), the General Health Questionnaire-12 item, and the EQ-5D. Outcomes and Results: Of the 72 participants of the Thales-Aphasia project, 58 met eligibility criteria for speech-language therapy and 39 were allocated to ESFA. The critical p-value was adjusted for multiple comparisons (.005). For the therapy versus control comparison, there was a significant main effect of time on the primary outcome (p<.001, η2p=.42) and a significant interaction effect (p=.003, η2p=.21). An interaction effect for the SAQOL-39g (p=.015, η2p=.11) and its psychosocial domain (p=.013, η2p=.12) did not remain significant after Bonferroni adjustment. For the individual versus combination ESFA comparison, there were significant main effects of time on the primary outcome (p<.001, η2p=.49), the BNT (p<.001, η2p=.29) and the ASHA-FACS (p=.001, η2p=.18). Interaction and group effects were not significant. Conclusion: Though underpowered, this study provides evidence on the efficacy of ESFA to improve word finding in aphasia, with gains similar in the two therapy approaches. Trial registration: ISRCTN71455409, https://doi.org/10.1186/ISRCTN7145540

Is the structure of 42Si understood?

A more detailed test of the implementation of nuclear forces that drive shell evolution in the pivotal nucleus \nuc{42}{Si} -- going beyond earlier comparisons of excited-state energies -- is important. The two leading shell-model effective interactions, SDPF-MU and SDPF-U-Si, both of which reproduce the low-lying \nuc{42}{Si}($2^+_1$) energy, but whose predictions for other observables differ significantly, are interrogated by the population of states in neutron-rich \nuc{42}{Si} with a one-proton removal reaction from \nuc{43}{P} projectiles at 81~MeV/nucleon. The measured cross sections to the individual \nuc{42}{Si} final states are compared to calculations that combine eikonal reaction dynamics with these shell-model nuclear structure overlaps. The differences in the two shell-model descriptions are examined and linked to predicted low-lying excited $0^+$ states and shape coexistence. Based on the present data, which are in better agreement with the SDPF-MU calculations, the state observed at 2150(13)~keV in \nuc{42}{Si} is proposed to be the ($0^+_2$) level.Comment: accepted in Physical Review Letter

Using a cognitive architecture to examine what develops

Different theories of development propose alternative mechanisms by which development occurs. Cognitive architectures can be used to examine the influence of each proposed mechanism of development while keeping all other mechanisms constant. An ACT-R computational model that matched adult behavior in solving a 21-block pyramid puzzle was created. The model was modified in three ways that corresponded to mechanisms of development proposed by developmental theories. The results showed that all the modifications (two of capacity and one of strategy choice) could approximate the behavior of 7-year-old children on the task. The strategy-choice modification provided the closest match on the two central measures of task behavior (time taken per layer, r = .99, and construction attempts per layer, r = .73). Modifying cognitive architectures is a fruitful way to compare and test potential developmental mechanisms, and can therefore help in specifying “what develops.