Reconstructing a Simple Polytope from its Graph

Blind and Mani (1987) proved that the entire combinatorial structure (the vertex-facet incidences) of a simple convex polytope is determined by its abstract graph. Their proof is not constructive. Kalai (1988) found a short, elegant, and algorithmic proof of that result. However, his algorithm has always exponential running time. We show that the problem to reconstruct the vertex-facet incidences of a simple polytope P from its graph can be formulated as a combinatorial optimization problem that is strongly dual to the problem of finding an abstract objective function on P (i.e., a shelling order of the facets of the dual polytope of P). Thereby, we derive polynomial certificates for both the vertex-facet incidences as well as for the abstract objective functions in terms of the graph of P. The paper is a variation on joint work with Michael Joswig and Friederike Koerner (2001).Comment: 14 page

Current Results of the EC-sponsored Catchment Modelling (CatchMod) Cluster

To support the Water Framework Directive implementation, much research has been commissioned at both national and European levels. CatchMod is a cluster of these projects, which is focusing on the development of computational catchment models and related tools. This paper presents an overview of the results of the CatchMod cluster to dat

The Influence of Strategic Patenting on Companies’ Patent Portfolios

This paper analyses whether strategic motives for patenting influence the characteristics of companies’ patent portfolios. We use the number of citations and oppositions to represent these characteristics. The investigation is based on survey and patent data from German companies. We find clear evidence that the companies’ patenting strategies explain the characteristics of their patent portfolios. First, companies using patents to protect their technological knowledge base receive a higher number of citations for their patents. Second, the motive of offensive – but not of defensive – blocking is related to a higher incidence of oppositions, whereas companies using patents as bartering chips in collaborations receive fewer oppositions to their patents

Polytopality and Cartesian products of graphs

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes. Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.Comment: 21 pages, 10 figure

GRAVITY: the Calibration Unit

We present in this paper the design and characterisation of a new sub-system of the VLTI 2nd generation instrument GRAVITY: the Calibration Unit. The Calibration Unit provides all functions to test and calibrate the beam combiner instrument: it creates two artificial stars on four beams, and dispose of four delay lines with an internal metrology. It also includes artificial stars for the tip-tilt and pupil guiding systems, as well as four metrology pick-up diodes, for tests and calibration of the corresponding sub-systems. The calibration unit also hosts the reference targets to align GRAVITY to the VLTI, and the safety shutters to avoid the metrology light to propagate in the VLTI-lab. We present the results of the characterisation and validtion of these differrent sub-units.Comment: 12 pages, 11 figures. Proceeding of SPIE 9146 "Optical and Infrared Interferometry IV

The GRAVITY metrology system: modeling a metrology in optical fibers

GRAVITY is the second generation VLT Interferometer (VLTI) instrument for high-precision narrow-angle astrometry and phase-referenced interferometric imaging. The laser metrology system of GRAVITY is at the heart of its astrometric mode, which must measure the distance of 2 stars with a precision of 10 micro-arcseconds. This means the metrology has to measure the optical path difference between the two beam combiners of GRAVITY to a level of 5 nm. The metrology design presents some non-common paths that have consequently to be stable at a level of 1 nm. Otherwise they would impact the performance of GRAVITY. The various tests we made in the past on the prototype give us hints on the components responsible for this error, and on their respective contribution to the total error. It is however difficult to assess their exact origin from only OPD measurements, and therefore, to propose a solution to this problem. In this paper, we present the results of a semi-empirical modeling of the fibered metrology system, relying on theoretical basis, as well as on characterisations of key components. The modeling of the metrology system regarding various effects, e.g., temperature, waveguide heating or mechanical stress, will help us to understand how the metrology behave. The goals of this modeling are to 1) model the test set-ups and reproduce the measurements (as a validation of the modeling), 2) determine the origin of the non-common path errors, and 3) propose modifications to the current metrology design to reach the required 1nm stability.Comment: 20 pages, 19 figures. Proceeding of SPIE 9146 "Optical and Infrared Interferometry IV

PIONIER: a visitor instrument for the VLTI

PIONIER is a 4-telescope visitor instrument for the VLTI, planned to see its first fringes in 2010. It combines four ATs or four UTs using a pairwise ABCD integrated optics combiner that can also be used in scanning mode. It provides low spectral resolution in H and K band. PIONIER is designed for imaging with a specific emphasis on fast fringe recording to allow closure-phases and visibilities to be precisely measured. In this work we provide the detailed description of the instrument and present its updated status.Comment: Proceedings of SPIE conference Optical and Infrared Interferometry II (Conference 7734) San Diego 201

Mass Transfer by Stellar Wind

I review the process of mass transfer in a binary system through a stellar wind, with an emphasis on systems containing a red giant. I show how wind accretion in a binary system is different from the usually assumed Bondi-Hoyle approximation, first as far as the flow's structure is concerned, but most importantly, also for the mass accretion and specific angular momentum loss. This has important implications on the evolution of the orbital parameters. I also discuss the impact of wind accretion, on the chemical pollution and change in spin of the accreting star. The last section deals with observations and covers systems that most likely went through wind mass transfer: barium and related stars, symbiotic stars and central stars of planetary nebulae (CSPN). The most recent observations of cool CSPN progenitors of barium stars, as well as of carbon-rich post-common envelope systems, are providing unique constraints on the mass transfer processes.Comment: Chapter 7, in Ecology of Blue Straggler Stars, H.M.J. Boffin, G. Carraro & G. Beccari (Eds), Astrophysics and Space Science Library, Springe

The fiber coupler and beam stabilization system of the GRAVITY interferometer

We present the installed and fully operational beam stabilization and fiber injection subsystem feeding the 2nd generation VLTI instrument GRAVITY. The interferometer GRAVITY requires an unprecedented stability of the VLTI optical train to achieve micro-arcsecond astrometry. For this purpose, GRAVITY contains four fiber coupler units, one per telescope. Each unit is equipped with actuators to stabilize the telescope beam in terms of tilt and lateral pupil displacement, to rotate the field, to adjust the polarization and to compensate atmospheric piston. A special roof-prism offers the possibility of on-axis as well as off-axis fringe tracking without changing the optical train. We describe the assembly, integration and alignment and the resulting optical quality and performance of the individual units. Finally, we present the closed-loop performance of the tip-tilt and pupil tracking achieved with the final systems in the lab.Comment: 14 pages, 13 figures. Proceedings of the SPIE 9146 "Optical and Infrared Interferometry IV