A new approach to multi-frequency synthesis in radio interferometry

We present a new approach to multi-frequency synthesis in radio astronomy. Using Bayesian inference techniques, the new technique estimates the sky brightness and the spectral index simultaneously. In principle, the bandwidth of a wide-band observation can be fully exploited for sensitivity and resolution, currently only limited by higher order effects like spectral curvature. Employing this new approach, we further present a multi-frequency extension to the imaging algorithm RESOLVE. In simulations, this new algorithm outperforms current multi-frequency imaging techniques like MS-MF-CLEAN.Comment: 13 pages, 5 fugures, submitted to Astronomy and Astrophysic

Artifacts in incomplete data tomography - with applications to photoacoustic tomography and sonar

We develop a paradigm using microlocal analysis that allows one to characterize the visible and added singularities in a broad range of incomplete data tomography problems. We give precise characterizations for photo- and thermoacoustic tomography and Sonar, and provide artifact reduction strategies. In particular, our theorems show that it is better to arrange Sonar detectors so that the boundary of the set of detectors does not have corners and is smooth. To illustrate our results, we provide reconstructions from synthetic spherical mean data as well as from experimental photoacoustic data

Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

Solar total and spectral irradiance reconstruction over the last 9000 years

Changes in solar irradiance and in its spectral distribution are among the main natural drivers of the climate on Earth. However, irradiance measurements are only available for less than four decades, while assessment of solar influence on Earth requires much longer records. The aim of this work is to provide the most up-to-date physics-based reconstruction of the solar total and spectral irradiance (TSI/SSI) over the last nine millennia. The concentrations of the cosmogenic isotopes 14C and 10Be in natural archives have been converted to decadally averaged sunspot numbers through a chain of physics-based models. TSI and SSI are reconstructed with an updated SATIRE model. Reconstructions are carried out for each isotope record separately, as well as for their composite. We present the first ever SSI reconstruction over the last 9000 years from the individual 14C and 10Be records as well as from their newest composite. The reconstruction employs physics-based models to describe the involved processes at each step of the procedure. Irradiance reconstructions based on two different cosmogenic isotope records, those of 14C and 10Be, agree well with each other in their long-term trends despite their different geochemical paths in the atmosphere of Earth. Over the last 9000 years, the reconstructed secular variability in TSI is of the order of 0.11%, or 1.5 W/m2. After the Maunder minimum, the reconstruction from the cosmogenic isotopes is consistent with that from the direct sunspot number observation. Furthermore, over the nineteenth century, the agreement of irradiance reconstructions using isotope records with the reconstruction from the sunspot number by Chatzistergos et al. (2017) is better than that with the reconstruction from the WDC-SILSO series (Clette et al. 2014), with a lower chi-square-value

The Uses of Argument in Mathematics

Stephen Toulmin once observed that `it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate'. Might the application of Toulmin's layout of arguments to mathematics remedy this oversight? Toulmin's critics fault the layout as requiring so much abstraction as to permit incompatible reconstructions. Mathematical proofs may indeed be represented by fundamentally distinct layouts. However, cases of genuine conflict characteristically reflect an underlying disagreement about the nature of the proof in question.Comment: 10 pages, 5 figures. To be presented at the Ontario Society for the Study of Argumentation Conference, McMaster University, May 2005 and LOGICA 2005, Hejnice, Czech Republic, June 200

What determines large scale galaxy clustering: halo mass or local density?

Using dark matter simulations we show how halo bias is determined by local density and not by halo mass. This is not totally surprising, as according to the peak-background split model, local density is the property that constraints bias at large scales. Massive haloes have a high clustering because they reside in high density regions. Small haloes can be found in a wide range of environments which determine their clustering amplitudes differently. This contradicts the assumption of standard Halo Occupation Distribution (HOD) models that the bias and occupation of haloes is determined solely by their mass. We show that the bias of central galaxies from semi-analytic models of galaxy formation as a function of luminosity and colour is not correctly predicted by the standard HOD model. Using local density instead of halo mass the HOD model correctly predicts galaxy bias. These results indicate the need to include information about local density and not only mass in order to correctly apply HOD analysis in these galaxy samples. This new model can be readily applied to observations and has the advantage that the galaxy density can be directly observed, in contrast with the dark matter halo mass.Comment: 11 pages, 9 figure

Lithium enrichment on the single active K1-giant DI Piscium -- Possible joint origin of differential rotation and Li enrichment

We investigate the surface spot activity of the rapidly rotating, lithium-rich active single K-giant DI Psc to measure the surface differential rotation and understand the mechanisms behind the Li-enrichment. Doppler imaging was applied to recover the surface temperature distribution of DI Psc in two subsequent rotational cycles using the individual mapping lines Ca I 6439, Fe I 6430, Fe I 6421 and Li I 6708. Surface differential rotation was derived by cross-correlation of the subsequent maps. Difference maps are produced to study the uniformity of Li-enrichment on the surface. These maps are compared with the rotational modulation of the Li I 6708 line equivalent width. Doppler images obtained for the Ca and Fe mapping lines agree well and reveal strong polar spottedness, as well as cool features at lower latitudes. Cross-correlating the consecutive maps yields antisolar differential rotation with shear coefficient -0.083 +- 0.021. The difference of the average and the Li maps indicates that the lithium abundance is non-activity related. There is also a significant rotational modulation of the Li equivalent width.Comment: 8 pages, 7 figures, accepted in A&