Linear Estimating Equations for Exponential Families with Application to Gaussian Linear Concentration Models

In many families of distributions, maximum likelihood estimation is intractable because the normalization constant for the density which enters into the likelihood function is not easily available. The score matching estimator of Hyv\"arinen (2005) provides an alternative where this normalization constant is not required. The corresponding estimating equations become linear for an exponential family. The score matching estimator is shown to be consistent and asymptotically normally distributed for such models, although not necessarily efficient. Gaussian linear concentration models are examples of such families. For linear concentration models that are also linear in the covariance we show that the score matching estimator is identical to the maximum likelihood estimator, hence in such cases it is also efficient. Gaussian graphical models and graphical models with symmetries form particularly interesting subclasses of linear concentration models and we investigate the potential use of the score matching estimator for this case

PEPSI deep spectra. I. The Sun-as-a-star

As part of the first Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) key-science project, we aim to provide well-exposed (viz. deep) high-resolution spectra of representative stellar targets. These spectra will be made available in form of (electronic) atlases. The first star in this series of papers is our Sun. It also acts as a system-performance cornerstone. The deep spectra in this paper are the results of combining up to 100 consecutive exposures per wavelength setting and are compared with other solar flux atlases. Our software for the optimal data extraction and reduction of PEPSI spectra is described and verified with the solar data. Three deep solar flux spectra with a spectral resolution of up to 270,000, a continuous wavelength coverage from 383 nm to 914 nm, and a photon signal to noise ratio (S/N) of between 2,000-8,000:1 depending on wavelength are presented. Additionally, a time-series of 996 high-cadence spectra in one cross disperser is used to search for intrinsic solar modulations. The wavelength calibration based on Th-Ar exposures and simultaneous Fabry-Perot combs enables an absolute wavelength solution within 10 m/s (rms) with respect to the HARPS laser-comb solar atlas and a relative rms of 1.2 m/s for one day. For science demonstration, we redetermined the disk-average solar Li abundance to 1.09+/-0.04 dex on the basis of 3D NLTE model atmospheres. We detected disk-averaged p-mode RV oscillations with a full amplitude of 47 cm/s at 5.5 min. Comparisons with two solar FTS atlases, as well as with the HARPS solar atlas, validate the PEPSI data product. Now, PEPSI/SDI solar-flux spectra are being taken with a sampling of one deep spectrum per day, and are supposed to continue a full magnetic cycle of the Sun.Comment: in press, 13 pages, 8 figures, data available from pepsi.aip.d

3D Simulation of Convection and Spectral Line Formation in A-type Stars

We present first realistic numerical simulations of 3D radiative convection in the surface layers of main sequence A-type stars with Teff = 8000 K and 8500 K, log g = 4.4 and 4.0, recently performed with the CO5BOLD radiation hydrodynamics code. The resulting models are used to investigate the structure of the H+HeI and the HeII convection zones in comparison with the predictions of local and non-local convection theories, and to determine the amount of "overshoot" into the stable layers below the HeII convection zone. The simulations also predict how the topology of the photospheric granulation pattern changes from solar to A-type star convection. The influence of the photospheric temperature fluctuations and velocity fields on the shape of spectral lines is demonstrated by computing synthetic line profiles and line bisectors for some representative examples, allowing us to confront the 3D model results with observations.Comment: 5 pages, 6 figures (17 figure files), 1 Tabl

Kinetic induced phase transition

An Ising model with local Glauber dynamics is studied under the influence of additional kinetic restrictions for the spin-flip rates depending on the orientation of neighboring spins. Even when the static interaction between the spins is completely eliminated and only an external field is taken into account the system offers a phase transition at a finite value of the applied field. The transition is realized due to a competition between the activation processes driven by the field and the dynamical rules for the spin-flips. The result is based on a master equation approach in a quantum formulation.Comment: 13 page

Fingerprint Analysis with Marked Point Processes

We present a framework for fingerprint matching based on marked point process models. An efficient Monte Carlo algorithm is developed to calculate the marginal likelihood ratio for the hypothesis that two observed prints originate from the same finger against the hypothesis that they originate from different fingers. Our model achieves good performance on an NIST-FBI fingerprint database of 258 matched fingerprint pairs