Besov regularity for operator equations on patchwise smooth manifolds

We study regularity properties of solutions to operator equations on patchwise smooth manifolds $\partial\Omega$ such as, e.g., boundaries of polyhedral domains $\Omega \subset \mathbb{R}^3$. Using suitable biorthogonal wavelet bases $\Psi$, we introduce a new class of Besov-type spaces $B_{\Psi,q}^\alpha(L_p(\partial \Omega))$ of functions $u\colon\partial\Omega\rightarrow\mathbb{C}$. Special attention is paid on the rate of convergence for best $n$-term wavelet approximation to functions in these scales since this determines the performance of adaptive numerical schemes. We show embeddings of (weighted) Sobolev spaces on $\partial\Omega$ into $B_{\Psi,\tau}^\alpha(L_\tau(\partial \Omega))$, $1/\tau=\alpha/2 + 1/2$, which lead us to regularity assertions for the equations under consideration. Finally, we apply our results to a boundary integral equation of the second kind which arises from the double layer ansatz for Dirichlet problems for Laplace's equation in $\Omega$.Comment: 42 pages, 3 figures, updated after peer review. Preprint: Bericht Mathematik Nr. 2013-03 des Fachbereichs Mathematik und Informatik, Universit\"at Marburg. To appear in J. Found. Comput. Mat

Besov regularity of solutions to the p-Poisson equation

In this paper, we study the regularity of solutions to the $p$-Poisson equation for all $1<p<\infty$. In particular, we are interested in smoothness estimates in the adaptivity scale $B^\sigma_{\tau}(L_{\tau}(\Omega))$, $1/\tau = \sigma/d+1/p$, of Besov spaces. The regularity in this scale determines the order of approximation that can be achieved by adaptive and other nonlinear approximation methods. It turns out that, especially for solutions to $p$-Poisson equations with homogeneous Dirichlet boundary conditions on bounded polygonal domains, the Besov regularity is significantly higher than the Sobolev regularity which justifies the use of adaptive algorithms. This type of results is obtained by combining local H\"older with global Sobolev estimates. In particular, we prove that intersections of locally weighted H\"older spaces and Sobolev spaces can be continuously embedded into the specific scale of Besov spaces we are interested in. The proof of this embedding result is based on wavelet characterizations of Besov spaces.Comment: 45 pages, 2 figure

Adaptive Wavelet BEM for boundary integral equations. Theory and numerical experiments

We are concerned with the numerical treatment of boundary integral equations by the adaptive wavelet boundary element method. In particular, we consider the second kind Fredholm integral equation for the double layer potential operator on patchwise smooth manifolds contained in ℝ 3 . The corresponding operator equations are treated by adaptive implementations that are in complete accordance with the underlying theory. The numerical experiments demonstrate that adaptive methods really pay off in this setting. The observed convergence rates fit together very well with the theoretical predictions based on the Besov regularity of the exact solution

Adaptive Wavelet BEM for boundary integral equations. Theory and numerical experiments

In this paper, we are concerned with the numerical treatment of boundary integral equations by means of the adaptive wavelet boundary element method (BEM). In particular, we consider the second kind Fredholm integral equation for the double layer potential operator on patchwise smooth manifolds contained in $\mathbb{R}^3$. The corresponding operator equations are treated by means of adaptive implementations that are in complete accordance with the underlying theory. The numerical experiments demonstrate that adaptive methods really pay off in this setting. The observed convergence rates fit together very well with the theoretical predictions that can be made on the basis of a systematic investigation of the Besov regularity of the exact solution

Symptoms of Arctic Amplification observed in Ny-Ålesund

Over the recent decades, temperature increase in the Arctic has been almost twice as large as the global average. This amplification of global warming is attributed to various feedback mechanisms present in the Arctic environment. Some processes are locally confined to the diminishing sea ice cover of the Arctic ocean, particularly the sea ice – albedo effect during polar day. Other amplifying processes related to the increasing open water surface of the Arctic ocean include e.g. the increasing heat flux from the ocean to the atmosphere. The resulting latent heat flux and augmenting evaporation contribute to an increasing atmospheric moisture content, which affects the longwave downward radiation directly or via changing cloud microphysics. Furthermore, atmospheric moisture and heat are more frequently advected from lower latitudes into the Arctic in relation to changes in the atmospheric circulation. During the dark period of polar night, the Arctic warming trend is not homogenously distributed over the polar cap, but occurs strongest at the surface in the Barents / Kara Seas and in the free troposphere of the Arctic North Atlantic sector. Thus, Svalbard is located in a key region of climate change. Observations from Ny-Ålesund at the west coast of the Svalbard archipelago show an annual temperature increase of 1.4 K per decade since the 1990s, with an average temperature that by now exceeds those observed during the early Arctic warming period in the 1920 to 1940s. The recent winter warming is even twice as high, and is accompanied by an increase in atmospheric moisture. Surface radiation observations in winter further indicate a change in cloudiness along with an increase in net longwave radiation. Although the winter warming is bottom-amplified, radiosonde observations show that the increasing temperature signal occurs over the entire troposphere. Indeed, part of the Svalbard winter warming is associated with enhanced warm and moist air advection in the free troposphere caused by increased cyclonic activity related to changes in atmospheric circulation patterns. The various processes contributing to Arctic amplification of climate warming link the local observations from Ny-Ålesund with processes occurring both in the Arctic and in the northern hemispheric mid-latitudes

Macrophage Migration Inhibitory Factor (MIF) Drives Murine Psoriasiform Dermatitis

The immunomodulator Macrophage Migration Inhibitory Factor (MIF) exerts pleiotropic immunomodulatory activities and has been implicated in the pathogenesis of diverse inflammatory diseases. Expression levels of MIF are also significantly elevated in the skin and serum of psoriasis patients, but the pathogenic significance of MIF in psoriasis is unknown. We have therefore addressed the role of MIF in two mouse models of psoriasis, namely in the imiquimod-induced psoriasiform dermatitis (IIPD) and the IL-23-induced dermatitis model. Daily treatment with Aldara™ cream, containing imiquimod, markedly increased the abundance of MIF in the skin and generated a cellular skin expression pattern of MIF closely resembling that in human plaque psoriasis. Deficiency in MIF significantly alleviated IIPD. On the clinical level, all hallmarks of psoriasiform dermatitis, including erythema, skin infiltration, and desquamation were reduced in Mif−/− mice. On the histopathological level, MIF deficiency decreased keratinocyte hyperproliferation, inflammatory cell infiltration, specifically with respect to monocyte-derived cells, and dermal angiogenesis, suggesting that MIF may be involved in the pathogenesis of psoriasiform dermatitis through several mechanisms. Similarly, MIF deficiency also significantly reduced disease in the IL-23-induced dermatitis model, suggesting that MIF is involved in the pathogenic pathways activated by IL-23 and required to achieve full-blown psoriasiform dermatitis. Collectively, our results lend support to a possible disease-promoting role of MIF in psoriasis, which should be further investigated

The clinical global impression scale and the influence of patient or staff perspective on outcome

<p>Abstract</p> <p>Background</p> <p>Since its first publication, the Clinical Global Impression Scale (CGI) has become one of the most widely used assessment instruments in psychiatry. Although some conflicting data has been presented, studies investigating the CGI's validity have only rarely been conducted so far. It is unclear whether the improvement index CGI-I or a difference score of the severity index CGI-S_difis more valid in depicting clinical change. The current study examined the validity of these two measures and investigated whether therapists' CGI ratings correspond to the view the patients themselves have on their condition.</p> <p>Methods</p> <p>Thirty-one inpatients of a German psychotherapeutic hospital suffering from a major depressive disorder (age M = 45.3, SD = 17.2; 58.1% women) participated. Patients filled in the Beck Depression Inventory (BDI). CGI-S and CGI-I were rated from three perspectives: the treating therapist (THER), the team of therapists involved in the patient's treatment (TEAM), and the patient (PAT). BDI and CGI-S were filled in at admission and discharge, CGI-I at discharge only. Data was analysed using effect sizes, Spearman's <it>ρ </it>and intra-class correlations (ICC).</p> <p>Results</p> <p>Effect sizes between CGI-I and CGI-S _difratings were large for all three perspectives with substantially higher change scores on CGI-I than on CGI-S _dif. BDI_difcorrelated moderately with PAT ratings, but did not correlate significantly with TEAM or THER ratings. Congruence between CGI-ratings from the three perspectives was low for CGI-S _dif(ICC = .37; Confidence Interval [CI] .15 to .59; <it>F</it>_30,60= 2.77, <it>p </it>< .001; mean <it>ρ </it>= 0.36) and moderate for CGI-I (ICC = .65 (CI .47 to .80; <it>F</it>_30,60= 6.61, <it>p </it>< .001; mean <it>ρ </it>= 0.59).</p> <p>Conclusions</p> <p>Results do not suggest a definite recommendation for whether CGI-I or CGI-S _difshould be used since no strong evidence for the validity of neither of them could be found. As congruence between CGI ratings from patients' and staff's perspective was not convincing it cannot be assumed that CGI THER or TEAM ratings fully represent the view of the patient on the severity of his impairment. Thus, we advocate for the incorporation of multiple self- and clinician-reported scales into the design of clinical trials in addition to CGI in order to gain further insight into CGI's relation to the patients' perspective.</p

Phase 1 Trials of rVSV Ebola Vaccine in Africa and Europe.

BACKGROUND: The replication-competent recombinant vesicular stomatitis virus (rVSV)-based vaccine expressing a Zaire ebolavirus (ZEBOV) glycoprotein was selected for rapid safety and immunogenicity testing before its use in West Africa. METHODS: We performed three open-label, dose-escalation phase 1 trials and one randomized, double-blind, controlled phase 1 trial to assess the safety, side-effect profile, and immunogenicity of rVSV-ZEBOV at various doses in 158 healthy adults in Europe and Africa. All participants were injected with doses of vaccine ranging from 300,000 to 50 million plaque-forming units (PFU) or placebo. RESULTS: No serious vaccine-related adverse events were reported. Mild-to-moderate early-onset reactogenicity was frequent but transient (median, 1 day). Fever was observed in up to 30% of vaccinees. Vaccine viremia was detected within 3 days in 123 of the 130 participants (95%) receiving 3 million PFU or more; rVSV was not detected in saliva or urine. In the second week after injection, arthritis affecting one to four joints developed in 11 of 51 participants (22%) in Geneva, with pain lasting a median of 8 days (interquartile range, 4 to 87); 2 self-limited cases occurred in 60 participants (3%) in Hamburg, Germany, and Kilifi, Kenya. The virus was identified in one synovial-fluid aspirate and in skin vesicles of 2 other vaccinees, showing peripheral viral replication in the second week after immunization. ZEBOV-glycoprotein-specific antibody responses were detected in all the participants, with similar glycoprotein-binding antibody titers but significantly higher neutralizing antibody titers at higher doses. Glycoprotein-binding antibody titers were sustained through 180 days in all participants. CONCLUSIONS: In these studies, rVSV-ZEBOV was reactogenic but immunogenic after a single dose and warrants further evaluation for safety and efficacy. (Funded by the Wellcome Trust and others; ClinicalTrials.gov numbers, NCT02283099, NCT02287480, and NCT02296983; Pan African Clinical Trials Registry number, PACTR201411000919191.)

Overview of the MOSAiC expedition - Atmosphere

With the Arctic rapidly changing, the needs to observe, understand, and model the changes are essential. To support these needs, an annual cycle of observations of atmospheric properties, processes, and interactions were made while drifting with the sea ice across the central Arctic during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition from October 2019 to September 2020. An international team designed and implemented the comprehensive program to document and characterize all aspects of the Arctic atmospheric system in unprecedented detail, using a variety of approaches, and across multiple scales. These measurements were coordinated with other observational teams to explore cross-cutting and coupled interactions with the Arctic Ocean, sea ice, and ecosystem through a variety of physical and biogeochemical processes. This overview outlines the breadth and complexity of the atmospheric research program, which was organized into 4 subgroups: atmospheric state, clouds and precipitation, gases and aerosols, and energy budgets. Atmospheric variability over the annual cycle revealed important influences from a persistent large-scale winter circulation pattern, leading to some storms with pressure and winds that were outside the interquartile range of past conditions suggested by long-term reanalysis. Similarly, the MOSAiC location was warmer and wetter in summer than the reanalysis climatology, in part due to its close proximity to the sea ice edge. The comprehensiveness of the observational program for characterizing and analyzing atmospheric phenomena is demonstrated via a winter case study examining air mass transitions and a summer case study examining vertical atmospheric evolution. Overall, the MOSAiC atmospheric program successfully met its objectives and was the most comprehensive atmospheric measurement program to date conducted over the Arctic sea ice. The obtained data will support a broad range of coupled-system scientific research and provide an important foundation for advancing multiscale modeling capabilities in the Arctic