Relatively Complete Verification of Probabilistic Programs: An Expressive Language for Expectation-Based Reasoning

We study a syntax for specifying quantitative “assertions” - functions mapping program states to numbers - for probabilistic program verification. We prove that our syntax is expressive in the following sense: Given any probabilistic program C, if a function f is expressible in our syntax, then the function mapping each initial state σ to the expected value of f evaluated in the final states reached after termination C on σ (also called the weakest preexpectation wp[C](f)) is also expressible in our syntax. As a consequence, we obtain a relatively complete verification system for verifying expected values and probabilities in the sense of Cook: Apart from a single reasoning step about the inequality of two functions given as syntactic expressions in our language, given f, g, and C, we can check whether g ≤ wp[C](f)

Bounded Model Checking for Probabilistic Programs

In this paper we investigate the applicability of standard model checking approaches to verifying properties in probabilistic programming. As the operational model for a standard probabilistic program is a potentially infinite parametric Markov decision process, no direct adaption of existing techniques is possible. Therefore, we propose an on-the-fly approach where the operational model is successively created and verified via a step-wise execution of the program. This approach enables to take key features of many probabilistic programs into account: nondeterminism and conditioning. We discuss the restrictions and demonstrate the scalability on several benchmarks

Nanometer Scale Mapping of the Density of States in an Inhomogeneous Superconductor

Using high speed scanning tunneling spectroscopy, we perform a full mapping of the quasiparticle density of states (DOS) in single crystals of BiPbSrCaCuO(2212). The measurements carried out at 5 K showed a complex spatial pattern of important variations of the local DOS on the nanometer scale. Superconducting areas are co-existing with regions of a smooth and larger gap-like DOS structure. The superconducting regions are found to have a minimum size of about 3 nm. The role of Pb-introduced substitutional disorder in the observed spatial variations of the local DOS is discussed.Comment: 4 page Letter with 3 figures (2 color figures

Dust-forming molecules in VY Canis Majoris (and Betelgeuse)

The formation of inorganic dust in circumstellar environments of evolved stars is poorly understood. Spectra of molecules thought to be most important for the nucleation, i.e. AlO, TiO, and TiO2, have been recently detected in the red supergiant VY CMa. These molecules are effectively formed in VY CMa and the observations suggest that non-equilibrium chemistry must be involved in their formation and nucleation into dust. In addition to exploring the recent observations of VY CMa, we briefly discuss the possibility of detecting these molecules in the dust-poor circumstellar environment of Betelgeuse.Comment: contribution to Betelgeuse Workshop 2012: "The physics of Red Supergiants: recent advances and open questions", 26-29 Nov 2012 Paris (France

Temperature dependence of the collective mode and its influence on the band splitting in bilayer cuprates

The recently observed bilayer splitting in high-T$_c$ cuprates is analyzed within a model where the charge carriers are coupled to a phenomenological bosonic spectrum which interpolates between the marginal Fermi liquid structure and collective mode type behavior as a function of temperature. We argue that the origin of the collective mode is probably associated with dynamic incommensurate charge density waves. Moreover it is shown that the resulting temperature dependence of the self-energy $\Sigma$ is in good agreement with $\Sigma$ as extracted from angle-resolved photoemission data.Comment: 6 pages, 4 figures, accepted for PR

Pure rotational spectra of TiO and TiO_2 in VY Canis Majoris

We report the first detection of pure rotational transitions of TiO and TiO_2 at (sub-)millimeter wavelengths towards the red supergiant VY CMa. A rotational temperature, T_rot, of about 250 K was derived for TiO_2. Although T_rot was not well constrained for TiO, it is likely somewhat higher than that of TiO_2. The detection of the Ti oxides confirms that they are formed in the circumstellar envelopes of cool oxygen-rich stars and may be the "seeds" of inorganic-dust formation, but alternative explanations for our observation of TiO and TiO_2 in the cooler regions of the envelope cannot be ruled out at this time. The observations suggest that a significant fraction of the oxides is not converted to dust, but instead remains in the gas phase throughout the outflow.Comment: to appear in Astronomy and Astrophysic

Performance of a GridPix detector based on the Timepix3 chip

A GridPix readout for a TPC based on the Timepix3 chip is developed for future applications at a linear collider. The GridPix detector consists of a gaseous drift volume read out by a single Timepix3 chip with an integrated amplification grid. Its performance is studied in a test beam with 2.5 GeV electrons. The GridPix detector detects single ionization electrons with high efficiency. The Timepix3 chip allowed for high sample rates and time walk corrections. Diffusion is found to be the dominating error on the track position measurement both in the pixel plane and in the drift direction, and systematic distortions in the pixel plane are below 10 $\mu$m. Using a truncated sum, an energy loss (dE/dx) resolution of 4.1% is found for an effective track length of 1 m.Comment: To be published in Nuclear Instruments and Methods in Physics Research Section