Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators

We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general

The Seigniory of Sark and the Duchy Of Cornwall: Similarities and Differences Including Observations on the Isles of Scilly

A unified and robust mathematical model for compressible and incompressible linear elasticity can be obtained by rephrasing the Herrmann formulation within the Hellinger-Reissner principle. This quasi-optimally converging extension of PEERS (Plane Elasticity Element with Reduced Symmetry) is called Dual-Mixed Hybrid formulation (DMH). Explicit residual-based a posteriori error estimates for DMH are introduced and are mathematically shown to be locking-free, reliable, and efficient. The estimator serves as a refinement indicator in an adaptive algorithm for effective automatic mesh generation. Numerical evidence supports that the adaptive scheme leads to optimal convergence for Lam\ue9 and Stokes benchmark problems with singularities

Experimental investigation on the effects of shoreface nourishment placement and timing on long-term cross-shore profile development

Acknowledgements The first, second and last authors gratefully acknowledge financial support from the Independent Research Fund Denmark project SWASH: Simulating WAve Surf-zone Hydrodynamics and sea bed morphology, Grant No.8022-00137B. The experimental data (DOI:10.11583/DTU.16739449, active upon pub791 lication) can be downloaded from https://figshare.com/s/accc92bad9fe629c943cPeer reviewedPublisher PD

Orchestrators of coordination:Towards a new role of the state in coordinated capitalism?

Liberalization poses significant challenges for the continued provision of collective goods within coordinated market economies (CME). Extant scholarship suggests two dominant sets of responses. Either CMEs continue to rely on employer coordination, but only for a privileged core, leading to dualization. Or, in cases where the state enjoys high capacity, the state instead compensates for liberalization but ends up crowding out employer coordination. In both cases, the result is decreasing employer coordination. We argue that in CMEs, the state may also play the role of “orchestrator” by supporting the revitalization of employer coordination. It does so through the deployment of ideational and institutional resources that mobilize employers’ associations on a voluntary basis. Applying our framework to a core area of coordinated capitalism, vocational education and training, we show that in both Germany and Switzerland, this indirect and soft form of state intervention was instrumental for turning around their crisis-stricken vocational training systems.publishe

Multivariate Hawkes process models of the occurrence of regulatory elements

<p>Abstract</p> <p>Background</p> <p>A central question in molecular biology is how transcriptional regulatory elements (TREs) act in combination. Recent high-throughput data provide us with the location of multiple regulatory regions for multiple regulators, and thus with the possibility of analyzing the multivariate distribution of the occurrences of these TREs along the genome.</p> <p>Results</p> <p>We present a model of TRE occurrences known as the Hawkes process. We illustrate the use of this model by analyzing two different publically available data sets. We are able to model, in detail, how the occurrence of one TRE is affected by the occurrences of others, and we can test a range of natural hypotheses about the dependencies among the TRE occurrences. In contrast to earlier efforts, pre-processing steps such as clustering or binning are not needed, and we thus retain information about the dependencies among the TREs that is otherwise lost. For each of the two data sets we provide two results: first, a qualitative description of the dependencies among the occurrences of the TREs, and second, quantitative results on the favored or avoided distances between the different TREs.</p> <p>Conclusions</p> <p>The Hawkes process is a novel way of modeling the joint occurrences of multiple TREs along the genome that is capable of providing new insights into dependencies among elements involved in transcriptional regulation. The method is available as an R package from <url>http://www.math.ku.dk/~richard/ppstat/</url>.</p

Direct Detection of Products from the Pyrolysis of 2-Phenethyl Phenyl Ether

The pyrolysis of 2-phenethyl phenyl ether (PPE, C_6H_5C_2H_4OC_6H_5) in a hyperthermal nozzle (300-1350 °C) was studied to determine the importance of concerted and homolytic unimolecular decomposition pathways. Short residence times (<100 μs) and low concentrations in this reactor allowed the direct detection of the initial reaction products from thermolysis. Reactants, radicals, and most products were detected with photoionization (10.5 eV) time-of-flight mass spectrometry (PIMS). Detection of phenoxy radical, cyclopentadienyl radical, benzyl radical, and benzene suggest the formation of product by the homolytic scission of the C_6H_5C_2H_4-OC_6H_5 and C_6H_5CH_2-CH_2OC_6H_5 bonds. The detection of phenol and styrene suggests decomposition by a concerted reaction mechanism. Phenyl ethyl ether (PEE, C_6H_5OC_2H_5) pyrolysis was also studied using PIMS and using cryogenic matrix-isolated infrared spectroscopy (matrix-IR). The results for PEE also indicate the presence of both homolytic bond breaking and concerted decomposition reactions. Quantum mechanical calculations using CBS-QB3 were conducted, and the results were used with transition state theory (TST) to estimate the rate constants for the different reaction pathways. The results are consistent with the experimental measurements and suggest that the concerted retro-ene and Maccoll reactions are dominant at low temperatures (below 1000 °C), whereas the contribution of the C_6H_5C_2H_4-OC_6H_5 homolytic bond scission reaction increases at higher temperatures (above 1000 °C)

Demonstration of PLOTs from the EuroPLOT project

The EuroPLOT project (2010-2013) has been funded to explore the concept of persuasive design for learning and teaching. It has developed Persuasive Learn-ing Objects and Technologies (PLOTs), manifested in two tools and a set of learning objects that have been tested and evaluated in four different case studies. These PLOTs will be shown in this demonstration, and the participants can try them out and experience for themselves the impact of persuasive technology that is embedded in these PLOTs. This will be one authoring tool (PLOTMaker) and one delivery tool (PLOTLearner). Furthermore, there will be learning objects shown which have been developed for those four different case studies. All of these PLOTs have already been tested and evaluated during case studies with real learners

The heart of a convex body

We investigate some basic properties of the {\it heart} $\heartsuit(\mathcal{K})$ of a convex set $\mathcal{K}.$ It is a subset of $\mathcal{K},$ whose definition is based on mirror reflections of euclidean space, and is a non-local object. The main motivation of our interest for $\heartsuit(\mathcal{K})$ is that this gives an estimate of the location of the hot spot in a convex heat conductor with boundary temperature grounded at zero. Here, we investigate on the relation between $\heartsuit(\mathcal{K})$ and the mirror symmetries of $\mathcal{K};$ we show that $\heartsuit(\mathcal{K})$ contains many (geometrically and phisically) relevant points of $\mathcal{K};$ we prove a simple geometrical lower estimate for the diameter of $\heartsuit(\mathcal{K});$ we also prove an upper estimate for the area of $\heartsuit(\mathcal{K}),$ when $\mathcal{K}$ is a triangle.Comment: 15 pages, 3 figures. appears as "Geometric Properties for Parabolic and Elliptic PDE's", Springer INdAM Series Volume 2, 2013, pp 49-6