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We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C∗-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fréchet–Lie group structure on differential cohomology groups.
We report on the formation of wrinkle-patterned surface morphologies in cesium formamidinium-based Cs(x)FA(1-y)Pb(I1-yBry)(3) perovskite compositions with x = 0-0.3 and y = 0-0.3 under various spin-coating conditions. By varying the Cs and Br contents, the perovskite precursor solution concentration and the spin-coating procedure, the occurrence and characteristics of the wrinkle-shaped morphology can be tailored systematically. Cs(0.17)FA(0.83)Pb(I0.83Br0.17)(3) perovskite layers were analyzed regarding their surface roughness, microscopic structure, local and overall composition, and optoelectronic properties. Application of these films in p-i-n perovskite solar cells (PSCs) with indium-doped tin oxide/NiOx/perovskite/C-60/bathocuproine/Cu architecture resulted in up to 15.3 and 17.0% power conversion efficiency for the flat and wrinkled morphology, respectively. Interestingly, we find slightly red-shifted photoluminescence (PL) peaks for wrinkled areas and we are able to directly correlate surface topography with PL peak mapping. This is attributed to differences in the local grain size, whereas there is no indication for compositional demixing in the films. We show that the perovskite composition, crystallization kinetics, and layer thickness strongly influence the formation of wrinkles which is proposed to be related to the release of compressive strain during perovskite crystallization. Our work helps us to better understand film formation and to further improve the efficiency of PSCs with widely used mixed-perovskite compositions.
By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology and differential forms with compact support, in full analogy to ordinary differential cohomology. We prove an excision theorem for differential cohomology using a suitable relative version. Furthermore, we use our model to give an independent proof of Pontryagin duality for differential cohomology recovering a result of [Harvey, Lawson, Zweck - Amer. J. Math. 125 (2003), 791]: On any oriented manifold, ordinary differential cohomology is isomorphic to the smooth Pontryagin dual of compactly supported differential cohomology. For manifolds of finite-type, a similar result is obtained interchanging ordinary with compactly supported differential cohomology.
Background: Functional abdominal pain (FAP) is not only a highly prevalent disease but also poses a considerable burden on children and their families. Untreated, FAP is highly persistent until adulthood, also leading to an increased risk of psychiatric disorders. Intervention studies underscore the efficacy of cognitive behavioral treatment approaches but are limited in terms of sample size, long-term follow-up data, controls and inclusion of psychosocial outcome data.
Methods/Design: In a multicenter randomized controlled trial, 112 children aged 7 to 12 years who fulfill the Rome III criteria for FAP will be allocated to an established cognitive behavioral training program for children with FAP (n = 56) or to an active control group (focusing on age-appropriate information delivery; n = 56). Randomization occurs centrally, blockwise and is stratified by center. This study is performed in five pediatric gastroenterology outpatient departments. Observer-blind assessments of outcome variables take place four times: pre-, post-, 3- and 12-months post-treatment. Primary outcome is the course of pain intensity and frequency. Secondary endpoints are health-related quality of life, pain-related coping and cognitions, as well as selfefficacy.
Discussion: This confirmatory randomized controlled clinical trial evaluates the efficacy of a cognitive behavioral intervention for children with FAP. By applying an active control group, time and attention processes can be controlled, and long-term follow-up data over the course of one year can be explored.
We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomology to each other. We discuss long exact sequences for both notions, thereby clarifying their relation to absolute differential cohomology. We construct the external and internal product of relative and absolute characters and show that relative differential cohomology is a right module over the absolute differential cohomology ring. Finally we construct fiber integration and transgression for relative differential characters.
We construct new concrete examples of relative differential characters, which we call Cheeger-Chern-Simons characters. They combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, Cheeger-Chern-Simons characters generalize Chern-Simons invariants of oriented manifolds with boundary. We study the differential cohomology of compact Lie groups G and their classifying spaces BG. We show that the even degree differential cohomology of BG canonically splits into Cheeger-Simons characters and topologically trivial characters. We discuss the transgression in principal G-bundles and in the universal bundle. We introduce two methods to lift the universal transgression to a differential cohomology valued map. They generalize the Dijkgraaf-Witten correspondence between 3-dimensional Chern-Simons theories and Wess-Zumino-Witten terms to fully extended higher-order Chern-Simons theories. Using these lifts, we also prove two versions of a differential Hopf theorem. Using Cheeger-Chern-Simons characters and transgression, we introduce the notion of differential trivializations of universal characteristic classes. It generalizes well-established notions of differential String classes to arbitrary degree. Specializing to the class , we recover isomorphism classes of geometric string structures on Spin (n) -bundles with connection and the corresponding spin structures on the free loop space. The Cheeger-Chern-Simons character associated with the class together with its transgressions to loop space and higher mapping spaces defines a Chern-Simons theory, extended down to points. Differential String classes provide trivializations of this extended Chern-Simons theory. This setting immediately generalizes to arbitrary degree: for any universal characteristic class of principal G-bundles, we have an associated Cheeger-Chern-Simons character and extended Chern-Simons theory. Differential trivialization classes yield trivializations of this extended Chern-Simons theory.
Background: Functional abdominal pain (FAP) is not only a highly prevalent disease but also poses a considerable burden on children and their families. Untreated, FAP is highly persistent until adulthood, also leading to an increased risk of psychiatric disorders. Intervention studies underscore the efficacy of cognitive behavioral treatment approaches but are limited in terms of sample size, long-term follow-up data, controls and inclusion of psychosocial outcome data.
Methods/Design: In a multicenter randomized controlled trial, 112 children aged 7 to 12 years who fulfill the Rome III criteria for FAP will be allocated to an established cognitive behavioral training program for children with FAP (n = 56) or to an active control group (focusing on age-appropriate information delivery; n = 56). Randomization occurs centrally, blockwise and is stratified by center. This study is performed in five pediatric gastroenterology outpatient departments. Observer-blind assessments of outcome variables take place four times: pre-, post-, 3- and 12-months post-treatment. Primary outcome is the course of pain intensity and frequency. Secondary endpoints are health-related quality of life, pain-related coping and cognitions, as well as selfefficacy.
Discussion: This confirmatory randomized controlled clinical trial evaluates the efficacy of a cognitive behavioral intervention for children with FAP. By applying an active control group, time and attention processes can be controlled, and long-term follow-up data over the course of one year can be explored.
A hotspot at a position compatible with the BL. Lac object 1ES 2322-409 was serendipitously detected with H.E.S.S. during observations performed in 2004 and 2006 on the blazar PKS 2316-423. Additional data on 1ES 2322-409 were taken in 2011 and 2012, leading to a total live-time of 22.3 h. Point-like very-high-energy (VHE; E > 100 GeV) gamma-ray emission is detected from a source centred on the IFS 2322-409 position, with an excess of 116.7 events at a significance of 6.0 sigma. The average VHE gamma-ray spectrum is well described with a power law with a photon index Gamma = 3.40 +/- 0.66(stat) +/- 0.20(sys) and an integral flux Phi(E > 200 GeV) = (3.11 +/- 0.71(stat) 0.62(sys)) x 10(-2)cm(-2)s(-1), which corresponds to 1.1 per cent of the Crab nebula flux above 200 GeV. Multiwavelength data obtained with Fermi LAT, Swift XRT and UVOT, RXTE PCA, ATOM, and additional data from WISE, GROND, and Catalina are also used to characterize the broad-band non-thermal emission of lES 2322-409. The multiwavelength behaviour indicates day-scale variability. Swift UVOT and XRT data show strong variability at longer scales. A spectral energy distribution (SED) is built from contemporaneous observations obtained around a high state identified in Swift data. A modelling of the SED is performed with a stationary homogeneous one-zone synchrotronself-Compton leptonic model. The redshift of the source being unknown, two plausible values were tested for the modelling. A systematic scan of the model parameters space is performed, resulting in a well-constrained combination of values providing a good description of the broad-band behaviour of 1ES 2322-409.