Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise

This paper is concerned with exponentially ill-posed operator equations with additive impulsive noise on the right hand side, i.e. the noise is large on a small part of the domain and small or zero outside. It is well known that Tikhonov regularization with an $L^1$ data fidelity term outperforms Tikhonov regularization with an $L^2$ fidelity term in this case. This effect has recently been explained and quantified for the case of finitely smoothing operators. Here we extend this analysis to the case of infinitely smoothing forward operators under standard Sobolev smoothness assumptions on the solution, i.e. exponentially ill-posed inverse problems. It turns out that high order polynomial rates of convergence in the size of the support of large noise can be achieved rather than the poor logarithmic convergence rates typical for exponentially ill-posed problems. The main tools of our analysis are Banach spaces of analytic functions and interpolation-type inequalities for such spaces. We discuss two examples, the (periodic) backwards heat equation and an inverse problem in gradiometry.Comment: to appear in SIAM J. Numer. Ana

Silicon isotopes as a tracer for silicate utilization in the Peruvian upwelling

EGU2011-6081 Natural stable isotopes are a powerful tool in marine sciences to investigate biological processes, such as present and past nutrient utilization. In this study we present the first dissolved silicon isotope data in the upwelling area off Peru, where one of the world’s largest Oxygen Minimum Zones (OMZ) is located. Silicon is the most important component required for phytoplankton (diatom) growth, which dominates primary productivity in this region. Stable Si isotopes are fractionated during diatom growth in that the lighter Si isotopes are preferentially incorporated into diatoms with a fractionation factor of -1.1 promille. The Si isotope composition of dissolved silicic acid of the corresponding surface waters is therefore left isotopically heavier. The Si isotope composition, 30Si/28Si, is expressed as δ30Si values, which stand forh deviations from a given standard (NBS28). Investigation of the dissolved seawater Si isotope composition thus provides a measure for the utilization and, combined with information on the Si isotope composition of the water masses upwelling off Peru, it is a measure for the supply pathways of Si to the coastal upwelling centres. Surface waters on the shelf off Peru are mainly fed by the Equatorial Undercurrent, which mainly consists of waters originating from the western and Central Pacific and which has a characteristic δ30Si of +1.5 promille. In areas and during phases of intense upwelling the fractionation of Si isotopes was observed to be weaker due to upwelling-driven supply of less fractionated Si (δ30Si = 1.7 promille, from water depths of around 100-150 m, whereas under weak upwelling conditions fractionation is higher (δ30Si ~3 promille due to a more complete utilization of the available dissolved silicate. The distribution of dissolved δ30Si correlates strongly with particulate biogenic silicate (opal) concentrations in that highest opal concentrations in the surface waters show the lowest δ30Si values thus strongest upwelling intensity. The most extreme δ30Si values in surface waters (δ30Si = 4.5 promille are observed offshore where silicic acid concentrations are nearly zero. Furthermore we compare the δ30Si data with the dissolved nitrogen isotope distribution, which in addition to nitrate utilization is mainly influenced by denitrification and annamox processes in the OMZ. Combined silicon and nitrogen isotope compositions can thus help to disentangle different fractionation processes within the nitrogen cycle

Expression of Cartilage Developmental Genes in Hoxc8- and Hoxd4-Transgenic Mice

Hox genes encode transcription factors, which regulate skeletal patterning and chondrocyte differentiation during the development of cartilage, the precursor to mature bone. Overexpression of the homeobox transcription factors Hoxc8 and Hoxd4 causes severe cartilage defects due to delay in cartilage maturation. Matrix metalloproteinases (MMPs), bone morphogenetic proteins (BMPs) and fibroblastic growth factors (FGFs) are known to play important roles in skeletal development and endochondral bone formation and remodeling. In order to investigate whether these molecules are aberrantly expressed in Hoxc8- and/or Hoxd4-transgenic cartilage, we performed quantitative RT-PCR on chondrocytes from Hox-transgenic mice. Gene expression levels of Bmp4, Fgf8, Fgf10, Mmp9, Mmp13, Nos3, Timp3, Wnt3a and Wnt5a were altered in Hoxc8-transgenic chondrocytes, and Fgfr3, Ihh, Mmp8, and Wnt3a expression levels were altered in Hoxd4-transgenic chondrocytes, respectively. Notably, Wnt3a expression was elevated in Hoxc8- and reduced in Hoxd4-transgenic cartilage. These results suggest that both transcription factors affect cartilage maturation through different molecular mechanisms, and provide the basis for future studies into the role of these genes and possible interactions in pathogenesis of cartilage defects in Hoxc8- and Hoxd4-transgenic mice

Plio-Pleistocene changes in water mass exchange and erosional inputs in the Fram Strait

We determined the isotopic composition of neodymium (Nd) and lead (Pb) of past seawater to reconstruct water mass exchange and erosional input between the Arctic Ocean and the Norwegian-Greenland Seas over the past 5 Ma. For this purpose, sediments of ODP site 911 (leg 151) located at 900 m water depth on the Yermak Plateau in the Fram Strait were used. The paleo-seawater variability of Nd and Pb isotopes was extracted from the sea water-derived metal oxide coatings on the sediment particles following the leaching method of Gutjahr et al. (2007). All radiogenic isotope data were acquired by Multi-Collector (MC) ICP-MS. The site 911 stratigraphy of Knies et al. (2009) was applied. Surface sediment Sr and Nd isotope data, as well as downcore Sr isotope data obtained on the same leaches are close to seawater and confirm the seawater origin of the Nd and Pb isotope signatures. The deep water Nd isotope time series extracted from site 911 was in general more radiogenic ("Nd = -7.5 to -10) than present day deep water ("Nd = -9.8 to -11.8) in the area of the Fram Strait (Andersson et al., 2008) and does not show a systematic trend with time. In contrast, the radiogenic isotope composition of Pb evolved from 206Pb/204Pb ratios around 18.7 to more radiogenic values around 19.2 between 2 Ma and today. The data indicate that mixing of water masses from the Arctic Ocean and the Norwegian-Greenland Seas has controlled the Nd isotope signatures of deep waters on the Yermak Plateau over the past 5 Ma. Prior to 1.7 Ma the Nd isotope signatures on the Yermak Plateau were less radiogenic than waters from the same depth in the central Arctic Ocean (Haley et al., 2008) pointing to a greater influence from the Norwegian-Greenland Seas. After 1.7 Ma the central Arctic and Yermak Plateau data have varied around similar values indicating water mass mixing overall similar to today. In contrast, the Pb isotope composition of deep waters in the Fram Strait appears to have been dominated by weathering inputs from glacially weathering old continental landmasses, such as Greenland or parts of Svalbard since 2 Ma. A similar control over the Pb isotope evolution of seawater since the onset of Northern Hemisphere Glaciation was recorded by ferromanganese crusts that grew from North Atlantic DeepWater in the western North Atlantic. References: Gutjahr, M., Frank, M., Stirling, C.H., Klemm, V., van de Flierdt, T. and Halliday, A.N. (2007): Reliable extraction of a deepwater trace metal isotope signal from Fe-Mn oxyhydroxide coatings of marine sediments.- Chemical Geology 242, 351-370 Haley B. A., M. Frank, R.F. Spielhagen and A. Eisenhauer (2008): Influence of brine formation on Arctic Ocean circulation over the past 15 million years. Nature Geoscience 1, 68–72 Andersson, P.S., Porcelli, D., Frank, M., Björk, G., Dahlqvist, R. and Gustafsson, Ö. (2008): Neodymium isotopes in seawater from the Barents Sea and Fram Strait Arctic- Atlantic gateways.- Geochim. Cosmochim. Acta 72, 2854-2867 Knies, J., J. Matthiessen, C. Vogt, J.S. Laberg, B.O. Hjelstuen, M.Smelror, E. Larsen, K. Andreassen, T. Eidvin and T.O. Vorren (2009): The Plio-Pleistocene glaciation of the Barents Sea–Svalbard region: a new model based on revised chronostratigraphy - Quaternary Science Reviews 28, 9-10, 812-82

Holocene fluctuations of neodymium isotope ratios in eastern Fram Strait sediments - An indication for deepwater variability?

EGU2012-11739 The Fram Strait as the only deep water connection of the world’s oceans to the Arctic plays a substantial role for the heat influx to the Arctic Ocean and controls freshening of the Nordic Seas through Arctic sea ice export. Large amounts of warm and saline Atlantic Water derived from the North Atlantic Drift transport most of the heat through eastern Fram Strait to the Arctic basin, resulting in year-round ice-free conditions. Arctic sea ice and cold and fresh waters exit the western part of the strait southward along the Greenland shelf. However, little is still known about the water mass transport at intermediate and bottom water depths in the Fram Strait. High-resolution Holocene sediment sequences from the Western Svalbard margin have been investigated for its neodymium isotope ratios stored in ferromanganese oxyhydroxide coatings of the sediment to derive information on the source of bottom seawater passing the site. The radiogenic isotope data are compared to a multitude of proxy indicators for the climatic and oceanographic variability in the eastern Fram Strait during the past 8,500 years. In order to obtain a calibration of the Nd isotope compositions extracted from sediments to modern bottom water mass signatures in the area, a set of core top and water samples from different water depths in the Fram Strait was additionally investigated for its present-day Nd isotope signatures. A significantly higher inflow of deepwater produced in the Nordic Seas to the core site is inferred for the earlier periods of the Holocene. Cooler surface water conditions and increased sea ice abundances during the late Holocene coincide with more radiogenic Nd isotope ratios likely resembling the neoglacial trend of the northern North Atlantic

The Economic Cost of the American Civil War: Estimates and Implications

Economic

Medizinbibliotheken: Inter:disziplinär – Inter:national – Inter:aktiv an der Veterinärmedizinschen Universität Wien (Wien, 25.–27. September 2017)

Report on the annual conference of the Working Committee for Medical Librarianship/Arbeitsgemeinschaft für Medizinisches Bibliothekswesen (AGMB)