Differential Characters and Geometric Chains

We study Cheeger-Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit formula for any natural transformation between a differential cohomology theory and the model given by differential characters. Fiber integration for fibers with boundary is treated in the context of relative differential characters. As applications we treat higher-dimensional holonomy, parallel transport, and transgression.Comment: references adde

Relative differential cohomology

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.Comment: 60 page

Cheeger-Chern-Simons theory and differential String classes

We introduce certain relative differential characters which we call Cheeger-Chern-Simons characters. These combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as the Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, the Cheeger-Chern-Simons characters generalize Chern-Simons invariants of oriented manifolds with boundary. Using Cheeger-Chern-Simons characters, we introduce the notion of differential trivializations of universal characteristic classes. Specializing to the class 1/2 $p_1 \in H^4(B\mathrm{Spin}_n;\mathbb Z)$ this yields a notion of differential String classes. Differential String classes turn out to be stable isomorphism classes of geometric String structures.Comment: v3: enlarged version; references adde

Theoretical study of ionization profiles of molecular clouds near supernova remnants: Tracing the hadronic origin of GeV gamma radiation

Context: Since a few years, signatures of supernova remnants associated with molecular clouds have been detected in gamma rays. Whether these gamma rays are generated by cosmic ray electrons or by cosmic ray protons is usually not known. The detection of hadronic ionization signatures in spatial coincidence with gamma ray signatures can help to unambiguously identify supernova remnants as sources of cosmic ray protons. Methods: In order to calculate hadronic signatures from cosmic ray-induced ionization for an examination of the origin of the observed gamma rays, the transport equation for cosmic ray protons propagating in a molecular cloud, including the relevant momentum loss processes, is solved analytically and the proton flux at any position in the cloud is determined. Results: Since the solution of the transport equation is obtained for arbitrary source functions, it can be used for a variety of supernova remnants. The corresponding theoretical ionization rate, as a function of the penetration depth, is derived and compared to photoinduced ionization profiles in a case study with four supernova remnants associated with molecular clouds. Three of the remnants show a clear dominance of the hadronically induced ionization rate, while for one remnant, X-ray emission seems to dominate by a factor of 10. Conclusions: This is the first derivation of position-dependent profiles for cosmic ray-induced ionization with an analytic solution for arbitrary cosmic ray source spectra. The cosmic ray-induced ionization has to be compared to X-ray ionization for strong X-ray sources. For sources dominated by cosmic ray-induced ionization (e.g., W49B), the ionization profiles can be used in the future to map the spatial structure of hadronic gamma rays and rotation-vibrational lines induced by cosmic ray protons, helping to identify sources of hadronic cosmic rays.Comment: published in Astronomy and Astrophysics, 20 pages, 17 figure

Is there a Superior Distance Function for Matching in Small Samples?

The study contributes to the development of ’standards’ for the application of matching algorithms in empirical evaluation studies. The focus is on the first step of the matching procedure, the choice of an appropriate distance function. Supplementary o most former studies, the simulation is strongly based on empirical evaluation ituations. This reality orientation induces the focus on small samples. Furthermore, ariables with different scale levels must be considered explicitly in the matching rocess. The choice of the analysed distance functions is determined by the results of former theoretical studies and recommendations in the empirical literature. Thus, in the simulation, two balancing scores (the propensity score and the index score) and the Mahalanobis distance are considered. Additionally, aggregated statistical distance functions not yet used for empirical evaluation are included. The matching outcomes are compared using non-parametrical scale-specific tests for identical distributions of the characteristics in the treatment and the control groups. The simulation results show that, in small samples, aggregated statistical distance functions are the better choice for summarising similarities in differently scaled variables compared to the commonly used measures.distance functions, matching, microeconometric evaluation, propensity score, simulation

Which One is Me?: Identifying Oneself on Public Displays

While user representations are extensively used on public displays, it remains unclear how well users can recognize their own representation among those of surrounding users. We study the most widely used representations: abstract objects, skeletons, silhouettes and mirrors. In a prestudy (N=12), we identify five strategies that users follow to recognize themselves on public displays. In a second study (N=19), we quantify the users' recognition time and accuracy with respect to each representation type. Our findings suggest that there is a significant effect of (1) the representation type, (2) the strategies performed by users, and (3) the combination of both on recognition time and accuracy. We discuss the suitability of each representation for different settings and provide specific recommendations as to how user representations should be applied in multi-user scenarios. These recommendations guide practitioners and researchers in selecting the representation that optimizes the most for the deployment's requirements, and for the user strategies that are feasible in that environment