On distribution formulas for complex and ℓ\ell-adic polylogarithms

We study an $\ell$-adic Galois analogue of the distribution formulas for polylogarithms with special emphasis on path dependency and arithmetic behaviors. As a goal, we obtain a notion of certain universal Kummer-Heisenberg measures that enable interpolating the $\ell$-adic polylogarithmic distribution relations for all degrees.Comment: This article has appeared in the proceedings volume "Periods in Quantum Field Theory and Arithmetic" (J.~Burgos Gil, K.~Ebrahimi-Fard, H.~Gangl eds), [Conference proceedings ICMAT-MZV 2014] Springer Proceedings in Mathematics \& Statistics {\bf 314} (2020), pp.593--61

A unified approach to shape and topological sensitivity analysis of discretized optimal design problems

We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is represented by a piecewise linear and globally continuous level set function on a fixed finite element mesh and relate perturbations of the level set function to perturbations of the shape or topology of the corresponding design. We illustrate the sensitivity analysis for a problem that is constrained by a reaction-diffusion equation and draw connections between our discrete sensitivities and the well-established continuous concepts of shape and topological derivatives. Finally, we verify our sensitivities and illustrate their application in a level-set-based design optimization algorithm where no distinction between shape and topological updates has to be made

Creating an artificial wine taster: Inferring the influence of must and yeast from the aroma profile of wines using artificial intelligence

The human brain is able to compute information from very complex olfactorical impressions. The special pattern of the concentrations of hundreds of aroma constituents allows an experienced wine taster to determine special features of the wine, for instance grape variety or vintage.Artificial Neural Networks are often used to recognize shapes and patterns like faces or finger prints. Here we use Artificial Neural Networks to mimic the abilities of a wine taster to deal with very complex olfactorical patterns. We produced 120 unique wines combining twelve different grape musts and ten yeast strains and determined the aroma profile (83 aroma constituents) of all wines. We analyzed the ability of a well trained neural network to recognize the used must variety and the fermenting yeast strain from unknown aroma profiles. Furthermore we investigated the capability to predict the aroma profile of a wine with a must variety/yeast strain combination that is new to the neural network.In 96 % of all trials the neural network identified the must that was used for wine production correctly (expected random propability: 8 %). An accurate identification of the yeast strain, used for fermentation, occurred in 67 % of all trials (propability by chance: 10 %).The aroma profiles of the must/yeast combinations new to the neural network were forecasted with a divergence of only 2.1 % compared to the actual wine of this production characterization. Thus we conclude that a comprehensive description of wines using neural networks is possible.

Micro-mechanical oscillator ground state cooling via intracavity optical atomic excitations

We predict ground state cooling of a micro-mechanical oscillator, i.e. a vibrating end-mirror of an optical cavity, by resonant coupling of mirror vibrations to a narrow internal optical transition of an ensemble of two level systems. The particles represented by a collective mesoscopic spin model implement, together with the cavity, an efficient, frequency tailorable zero temperature loss channel which can be turned to a gain channel of pump. As opposed to the case of resolved-sideband cavity cooling requiring a small cavity linewidth, one can work here with low finesses and very small cavity volumes to enhance the light mirror and light atom coupling. The tailored loss and gain channels provide for efficient removal of vibrational quanta and suppress reheating. In a simple physical picture of sideband cooling, the atoms shape the cavity profile to enhance/inhibit scattering into higher/lower energy sidebands. The method should be applicable to other cavity based cooling schemes for atomic and molecular gases as for molecular ensembles coupled to stripline cavities

Auswirkung verschiedener Bodenpflegesysteme auf rebenparasitäre und rehvirenübertragende Nematoden

Research NoteEffects of different types of soil cultivation to grape parasitical and grape virus vector nematodesWithin the research project "Soil management in selected locations around Lake Neusiedl" soil samples were taken from Donnerskirchen and Rust for the analysis of the nematode-pedofauna during summer 1999. At Rust (planted with cv. Blauburgunder) the type of soil management had a highly significant effect on the nematode population. After five years of soil covering with straw, permanent green cover or green cover in winter the nematode population on average was twice as high as in bare soil and green cover during spring. The latter variants were clean cultivated in spring. Distribution of nematodes in the sloping site of Donnerskirchen (planted with cvs Gruner Veltliner and Welschriesling) turned out to be inhomogenous, depending on the site of the slope. Here soil cultivation had no significant influence on the nematode fauna

Genetic variability and incidence of systemic diseases in wild vines (Vitis vinifera ssp. silvestris) along the Danube

In the riparian woods of Danube and March east of Vienna 87 wild specimens of Vitis vinifera ssp. silvestris were genetically analysed and compared. The silvestris population can be split into 6 distinct groups, but this clustering cannot be explained solely by the geographical distance. The unique genetic variability observed represents a strong case for preservation of wild grapevines.The incidence of bacterioses, viroses and nematodes transmitting nepoviruses to these vines were registered. None of the analysed specimens suffered from Agrobacterium vitis-induced crown gall. Only some vines were infected by viral pathogens such as GLRaV I and SLRV. Thus the wild vines do not constitute a risk for the surrounding commercial vineyards. On the other hand, diseases spread from cultivated grapevines may seriously harm the wild vine population. Four species of nematodes transmitting nepoviruses were registered. Samples of Xiphinema vuittenezi and Longidorus attenuatus from the Lobau (natural forests, north of the Danube in the area of Vienna) differ morphometrically from others found on arable soils or isolated from the research area.

Restricted sum formula of alternating Euler sums

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Scaling properties of cavity-enhanced atom cooling

We extend an earlier semiclassical model to describe the dissipative motion of N atoms coupled to M modes inside a coherently driven high-finesse cavity. The description includes momentum diffusion via spontaneous emission and cavity decay. Simple analytical formulas for the steady-state temperature and the cooling time for a single atom are derived and show surprisingly good agreement with direct stochastic simulations of the semiclassical equations for N atoms with properly scaled parameters. A thorough comparison with standard free-space Doppler cooling is performed and yields a lower temperature and a cooling time enhancement by a factor of M times the square of the ratio of the atom-field coupling constant to the cavity decay rate. Finally it is shown that laser cooling with negligible spontaneous emission should indeed be possible, especially for relatively light particles in a strongly coupled field configuration.Comment: 7 pages, 5 figure

Ultra-cold atoms in an optical cavity: two-mode laser locking to the cavity avoiding radiation pressure

The combination of ultra-cold atomic clouds with the light fields of optical cavities provides a powerful model system for the development of new types of laser cooling and for studying cooperative phenomena. These experiments critically depend on the precise tuning of an incident pump laser with respect to a cavity resonance. Here, we present a simple and reliable experimental tuning scheme based on a two-mode laser spectrometer. The scheme uses a first laser for probing higher-order transversal modes of the cavity having an intensity minimum near the cavity's optical axis, where the atoms are confined by a magnetic trap. In this way the cavity resonance is observed without exposing the atoms to unwanted radiation pressure. A second laser, which is phase-locked to the first one and tuned close to a fundamental cavity mode drives the coherent atom-field dynamics.Comment: 7 pages, 7 figure