A convex analysis approach to optimal controls with switching structure for partial differential equations

Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality system that allows an explicit pointwise characterization and whose Moreau-Yosida regularization is amenable to a semismooth Newton method in function space. This approach is especially suited for computing switching controls for partial differential equations. In this case, the optimality gap between the original functional and its relaxation can be estimated and shown to be zero for controls with switching structure. Numerical examples illustrate the effectiveness of this approach

Total variation regularization of multi-material topology optimization

This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is proposed which involves total variation regularization combined with a suitably chosen cost functional that promotes the diffusion coefficient assuming prespecified values at each point of the domain. The main difficulty lies in the delicate functional-analytic structure of the resulting nondifferentiable optimization problem with pointwise constraints for functions of bounded variation, which makes the derivation of useful pointwise optimality conditions challenging. To cope with this difficulty, a novel reparametrization technique is introduced. Numerical examples using a regularized semismooth Newton method illustrate the structure of the obtained diffusion coefficient.

A Web Browser-Based Application for Processing and Analyzing Material Flow Models using the MFCA Methodology

In the context of IT for Green, the potential of the Material Flow Cost Accounting (MFCA) method has not yet been fully unleashed. Using the advantages of mobile data acquisition for material and energy flows, for instance right at a production plant, makes it easier to identify optimization potentials in sustainability management. Tapping this potential, for example through continuous data acquisition of sensor data from sensors in a production plant, can also be made more convenient. Studies conducted that the introduction and application of MFCA has brought significant ecological and economic benefits. They also revealed that there is very little MFCA specialized software on the market. This paper describes the objective and concept of a web browser-based application for the processing and analysis of material flow models and their evaluation with the MFCA methodology

Approximation of elliptic control problems in measure spaces with sparse solutions

Optimal control problems in measure spaces governed by elliptic equations are considered for distributed and Neumann boundary control, which are known to promote sparse solutions. Optimality conditions are derived and some of the structural properties of their solutions, in particular sparsity, are discussed. A framework for their approximation is proposed which is efficient for numerical computations and for which we prove convergence and provide error estimates.This author was supported by Spanish Ministerio de Ciencia e Innovación under projects MTM2008-04206 and “Ingenio Mathematica (i-MATH)” CSD2006-00032 (Consolider Ingenio 2010)

Parabolic control problems in measure spaces with sparse solutions

Optimal control problems in measure spaces lead to controls that have small support, which is desirable, e.g., in the context of optimal actuator placement. For problems governed by parabolic partial differential equations, well-posedness is guaranteed in the space of square-integrable measure-valued functions, which leads to controls with a spatial sparsity structure. A conforming approximation framework allows one to derive numerically accessible optimality conditions as well as convergence rates. In particular, although the state is discretized, the control problem can still be formulated and solved in the measure space. Numerical examples illustrate the structural features of the optimal controls.This author was supported by the Spanish Ministerio de Ciencia e Innovación under project MTM2011-2271

Ice-algal carbon supports harp and ringed seal diets in the European Arctic: evidence from fatty acid and stable isotope markers

Sea-ice declines in the European Arctic have led to substantial changes in marine food webs. To better understand the biological implications of these changes, we quantified the contributions of ice-associated and pelagic carbon sources to the diets of Arctic harp and ringed seals using compound-specific stable isotope ratios of fatty acids in specific primary producer biomarkers derived from sea-ice algae and phytoplankton. Comparison of fatty acid patterns between these 2 seal species indicated clear dietary separation, while the compound-specific stable isotope ratios of the same fatty acids showed partial overlap. These findings suggest that harp and ringed seals target different prey sources, yet their prey rely on ice and pelagic primary production in similar ways. From Bayesian stable isotope mixing models, we estimated that relative contributions of sympagic and pelagic carbon in seal blubber was an average of 69% and 31% for harp seals, and 72% and 28% for ringed seals, respectively. The similarity in the Bayesian estimations also indicates overlapping carbon sourcing by these 2 species. Our findings demonstrate that the seasonal ice-associated carbon pathway contributes substantially to the diets of both harp and ringed seals

Can clinical case discussions foster clinical reasoning skills in undergraduate medical education? A randomised controlled trial

OBJECTIVE Fostering clinical reasoning is a mainstay of medical education. Based on the clinicopathological conferences, we propose a case-based peer teaching approach called clinical case discussions (CCDs) to promote the respective skills in medical students. This study compares the effectiveness of different CCD formats with varying degrees of social interaction in fostering clinical reasoning. DESIGN, SETTING, PARTICIPANTS A single-centre randomised controlled trial with a parallel design was conducted at a German university. Study participants (N=106) were stratified and tested regarding their clinical reasoning skills right after CCD participation and 2 weeks later. INTERVENTION Participants worked within a live discussion group (Live-CCD), a group watching recordings of the live discussions (Video-CCD) or a group working with printed cases (Paper-Cases). The presentation of case information followed an admission-discussion-summary sequence. PRIMARY AND SECONDARY OUTCOME MEASURES Clinical reasoning skills were measured with a knowledge application test addressing the students' conceptual, strategic and conditional knowledge. Additionally, subjective learning outcomes were assessed. RESULTS With respect to learning outcomes, the Live-CCD group displayed the best results, followed by Video-CCD and Paper-Cases, F(2,87)=27.07, p<0.001, partial η2=0.384. No difference was found between Live-CCD and Video-CCD groups in the delayed post-test; however, both outperformed the Paper-Cases group, F(2,87)=30.91, p<0.001, partial η2=0.415. Regarding subjective learning outcomes, the Live-CCD received significantly better ratings than the other formats, F(2,85)=13.16, p<0.001, partial η2=0.236. CONCLUSIONS This study demonstrates that the CCD approach is an effective and sustainable clinical reasoning teaching resource for medical students. Subjective learning outcomes underline the importance of learner (inter)activity in the acquisition of clinical reasoning skills in the context of case-based learning. Higher efficacy of more interactive formats can be attributed to positive effects of collaborative learning. Future research should investigate how the Live-CCD format can further be improved and how video-based CCDs can be enhanced through instructional support

Dense mesopelagic sound scattering layer and vertical segregation of pelagic organisms at the Arctic-Atlantic gateway during the midnight sun

Changes in vertical and spatial distributions of zooplankton and small pelagic fish impact the biological carbon pump and the distribution of larger piscivorous fish and marine mammal species. However, their distribution and abundance remain poorly documented at high latitudes because of the difficulties inherent to sampling relatively fast-moving organisms in ice-covered waters. This study documents the under-ice distribution of epipelagic and mesopelagic organisms at the Arctic-Atlantic gateway in spring, during the midnight sun period, using ice-tethered and ship-based echosounders. An epipelagic surface scattering layer composed of copepods consistently occupied the top 60 m and was associated with cold polar surface water (mean temperature of -1.5°C). A mesopelagic deep scattering layer (DSL), partly composed of fish, persisted between 280 m and 600 m and was associated with modified Atlantic water. Backscattering strength within the DSL was higher than previously reported in the Arctic and north Atlantic, and increased by two orders of magnitude over the continental slope where one of the Atlantic water pathways enters the Arctic Ocean. Mesopelagic organisms did not perform diel vertical migrations. The consistent segregation between copepods at the surface and their predators at mesopelagic depths suggests limited predator-prey interactions during the midnight sun period, even under the ice cover. Predation on copepods by mesopelagic organisms, including fish, could thus be limited to very pulsed events during the seasonal vertical migration of copepods to and from overwintering depths. This suggests that the arctic mesopelagic food web may be decoupled from secondary production in the epipelagic layer throughout most of the year