Information Structures in Optimal Auctions

A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. These properties imply that the optimal selling strategy of a seller can be implemented by a sequence of exclusive take-it or leave-it offers.Optimal Auction, Private Values, Information Structures, Partitions

Global detection and analysis of coastline associated rainfall using an objective pattern recognition technique

Coastally associated rainfall is a common feature especially in tropical and subtropical regions. However, it has been difficult to quantify the contribution of coastal rainfall features to the overall local rainfall. We develop a novel technique to objectively identify precipitation associated with land-sea interaction and apply it to satellite based rainfall estimates. The Maritime Continent, the Bight of Panama, Madagascar and the Mediterranean are found to be regions where land-sea interactions plays a crucial role in the formation of precipitation. In these regions $\approx$ 40% to 60% of the total rainfall can be related to coastline effects. Due to its importance for the climate system, the Maritime Continent is a particular region of interest with high overall amounts of rainfall and large fractions resulting from land-sea interactions throughout the year. To demonstrate the utility of our identification method we investigate the influence of several modes of variability, such as the Madden-Julian-Oscillation and the El Ni\~no Southern Oscillation, on coastal rainfall behavior. The results suggest that during large scale suppressed convective conditions coastal effects tend modulate the rainfall over the Maritime Continent leading to enhanced rainfall over land regions compared to the surrounding oceans. We propose that the novel objective dataset of coastally influenced precipitation can be used in a variety of ways, such as to inform cumulus parametrization or as an additional tool for evaluating the simulation of coastal precipitation within weather and climate models

Model simulations and comparison with pollen-based reconstructions

This study is concerned with vegetation modelling in northern Asia and its comparison with pollen-based vegetation and climate reconstructions. With the help of BIOME1, a global biogeographic equilibrium vegetation model, vegetation dynamics during the last interglacial (LI) period in the northern Asian region can be simulated. In the study, an alternative algorithm to calculate a moisture index (α) is implemented, and the vegetation is modelled for the optimum phase (125 ka BP) and the end of the LI period (115 ka BP). The simulations show an approximately 28% increase in the area occupied by forest biomes for the 125 ka BP time-slice and an approximately 14% decrease in forest-dominated areas around 115 ka BP in comparison to today. Compared to the present day, the tree-line for the 125 ka BP time-slice was located on average 4.05 ± 2.03° further north. Comparison of the modelled results with available pollen-based reconstructions shows that the simulated and reconstructed results for the optimum of the LI period are consistent. With both algorithms calculating the moisture index α, i.e. α1 and α2, the tree line shifts back (∼10 ± 4.4°) between the optimum and the end of the LI period. The area occupied by forest in both simulations had declined by an average of ∼42%. Furthermore, the data-model comparison shows that the modelling results obtained with the newly implemented moisture index are in slightly better agreement with the climate reconstructions

Information Structures in Optimal Auctions

A seller wishes to sell an object to one of multiple bidders. The valuations of the bidders are privately known. We consider the joint design problem in which the seller can decide the accuracy by which bidders learn their valuation and to whom to sell at what price. We establish that optimal information structures in an optimal auction exhibit a number of properties: (i) information structures can be represented by monotone partitions, (ii) the cardinality of each partition is finite, (iii) the partitions are asymmetric across agents. These properties imply that the optimal selling strategy of a seller can be implemented by a sequence of exclusive take-it or leave-it offers

The elemental composition of the Sun II. The iron group elements Sc to Ni

We redetermine the abundances of all iron group nuclei in the Sun, based on neutral and singly-ionised lines of Sc, Ti, V, Mn, Fe, Co and Ni in the solar spectrum. We employ a realistic 3D hydrodynamic model solar atmosphere, corrections for departures from local thermodynamic equilibrium (NLTE), stringent line selection procedures and high quality observational data. We have scoured the literature for the best quality oscillator strengths, hyperfine constants and isotopic separations available for our chosen lines. We find $\log \epsilon_\mathrm{Sc}=3.16\pm0.04$, $\log \epsilon_\mathrm{Ti}=4.93\pm0.04$, $\log \epsilon_\mathrm{V}=3.89\pm0.08$, $\log \epsilon_\mathrm{Cr}=5.62\pm0.04$, $\log \epsilon_\mathrm{Mn}=5.42\pm0.04$, $\log \epsilon_\mathrm{Fe}=7.47\pm0.04$, $\log \epsilon_\mathrm{Co}=4.93\pm0.05$ and $\log \epsilon_\mathrm{Ni}=6.20\pm0.04$. Our uncertainties factor in both statistical and systematic errors (the latter estimated for possible errors in the model atmospheres and NLTE line formation). The new abundances are generally in good agreement with the CI meteoritic abundances but with some notable exceptions. This analysis constitutes both a full exposition and a slight update of the preliminary results we presented in Asplund, Grevesse, Sauval & Scott (arXiv:0909.0948), including full line lists and details of all input data we employed.Comment: 10 figures, 24 pages + 10 online-only pages of tables. v2. Matches version accepted by A&

The elemental composition of the Sun III. The heavy elements Cu to Th

We re-evaluate the abundances of the elements in the Sun from copper ($Z=29$) to thorium ($Z=90$). Our results are mostly based on neutral and singly-ionised lines in the solar spectrum. We use the latest 3D hydrodynamic solar model atmosphere, and in a few cases also correct for departures from local thermodynamic equilibrium (LTE) using non-LTE (NLTE) calculations performed in 1D. In order to minimise statistical and systematic uncertainties, we make stringent line selections, employ the highest-quality observational data and carefully assess oscillator strengths, hyperfine constants and isotopic separations available in the literature, for every line included in our analysis. Our results are typically in good agreement with the abundances in the most pristine meteorites, but there are some interesting exceptions. This analysis constitutes both a full exposition and a slight update of the relevant parts of the preliminary results we presented in Asplund, Grevesse, Sauval & Scott (arXiv:0909.0948), including full line lists and details of all input data that we have employed.Comment: 5 figures, 18 pages + 6 online-only pages of tables. v2. Matches version accepted by A&

The elemental composition of the Sun II. The iron group elements Sc to Ni

We redetermine the abundances of all iron group nuclei in the Sun, based on neutral and singly-ionised lines of Sc, Ti, V, Mn, Fe, Co and Ni in the solar spectrum. We employ a realistic 3D hydrodynamic model solar atmosphere, corrections for departures from local thermodynamic equilibrium (NLTE), stringent line selection procedures and high quality observational data. We have scoured the literature for the best quality oscillator strengths, hyperfine constants and isotopic separations available for our chosen lines. We find log ϵSc = 3.16 ± 0.04, log ϵTi = 4.93 ± 0.04, log ϵV = 3.89 ± 0.08, log ϵCr = 5.62 ± 0.04, log ϵMn = 5.42 ± 0.04, log ϵFe = 7.47 ± 0.04, log ϵCo = 4.93 ± 0.05 and log ϵNi = 6.20 ± 0.04. Our uncertainties factor in both statistical and systematic errors (the latter estimated for possible errors in the model atmospheres and NLTE line formation). The new abundances are generally in good agreement with the CI meteoritic abundances but with some notable exceptions. This analysis constitutes both a full exposition and a slight update of the preliminary results we presented in Asplund et al. (2009, ARA&A, 47, 481), including full line lists and details of all input data we employed

NLTE effects on Fe I/II in the atmospheres of FGK stars and application to abundance analysis of their spectra

We describe the first results from our project aimed at large-scale calculations of NLTE abundance corrections for important astrophysical atoms and ions. In this paper, the focus is on Fe which is a proxy of stellar metallicity and is commonly used to derive effective temperature and gravity. We present a small grid of NLTE abundance corrections for Fe I lines and discuss how NLTE effects influence determination of effective temperature, surface gravity, and metallicity for late-type stars.Comment: 6 pages, to be published in IOP The Journal of Physics: Conference Series, proceedings of the Workshop: 'Stellar Atmospheres in the Gaia Era: Quantitative Spectroscopy and Comparative Spectrum Modelling', Brussels, June 201

Ionization balance of Ti in the photospheres of the Sun and four late-type stars

In this paper we investigate statistical equilibrium of Ti in the atmospheres of late-type stars. The Ti I/Ti II level populations are computed with available experimental atomic data, except for photoionization and collision induced transition rates, for which we have to rely on theoretical approximations. For the Sun, the NLTE line formation with adjusted H I inelastic collision rates and MAFAGS-OS model atmosphere solve the long-standing discrepancy between Ti I and Ti II lines. The NLTE abundances determined from both ionization stages agree within $0.01$ dex with each other and with the Ti abundance in C I meteorites. The Ti NLTE model does not perform similarly well for the metal-poor stars, overestimating NLTE effects in the atmospheres of dwarfs, but underestimating overionization for giants. Investigating different sources of errors, we find that only [Ti/Fe] ratios based on Ti II and Fe II lines can be safely used in studies of Galactic chemical evolution. To avoid spurious abundance trends with metallicity and dwarf/giant discrepancies, it is strongly recommended to disregard Ti I lines in abundance analyses, as well as in determination of surface gravities.Comment: 16 pages, accepted for publication in MNRA