Hitting sets when the VC-dimension is small

We present an approximation algorithm for the hitting set problem when the VC-dimension of the set system is small. Our algorithm uses a linear programming relaxation to compute a probability measure for which ?-nets are always hitting sets (see Corollary 15.6 in Pach and Agarwal [Combinatorial Geometry, J. Wiley, New York, 1995]). The comparable algorithm of Brönnimann and Goodrich [Almost optimal set covers in finite VC-dimension, Discrete Comput. Geom. 14 (1995) 463] computes such a probability measure by an iterative reweighting technique. The running time of our algorithm is comparable with theirs, and the approximation ratio is smaller by a constant factor. We also show how our algorithm can be parallelized and extended to the minimum cost hitting set problem.     

Visualizing and analyzing the Mona Lisa.

Size and scale issues present a complexity problem in visualizing detailed 3D models built from sensor data. A model of Leonardo da Vinci's Mona Lisa, with its thin pictorial layer, illustrates the need for intuitive real-time processing tools that are seamlessly integrated with a multiresolution visualization environment.     

Local-search Extraction of MUSes

SAT is probably one of the most-studied constraint satisfaction problems. In this paper, a new hybrid technique based on local search is introduced in order to approximate and extract minimally unsatisfiable subformulas (in short, MUSes) of unsatisfiable SAT instances. It is based on an original counting heuristic grafted to a local search algorithm, which explores the neighborhood of the current interpretation in an original manner, making use of a critical clause concept. Intuitively, a critical clause is a falsified clause that becomes true thanks to a local search flip only when some other clauses become false at the same time. In the paper, the critical clause concept is investigated. It is shown to be the cornerstone of the efficiency of our approach, which outperforms competing ones to compute MUSes, inconsistent covers and sets of MUSes, most of the time.     

Shape analysis and injection molding optimization

Shape analysis is presented as a new approach towards optimization of polymer injection molding. Taking in consideration shape parameters such as optimal centering and skeleton transformation, the objective is to estimate the best location of the injection points to obtain lowest injection pressure and balanced filling of the mold. This paper concerns recent progress in the formulation of this problem.     

Investigation by laser Doppler velocimetry of the effects of liquid flow rates and feed positions on the flow patterns induced in a stirred tank by an axial-flow impeller

The flow patterns established in a continuously-fed stirred tank, equipped with a Mixel TT axial-flow impeller, have been investigated by laser Doppler velocimetry, for a high and a low value of mean residence time—mixing time ratio. The pseudo-two-dimensional axial-radial-velocity vector plots, as well as the spatial distributions of the tangential velocity component and the velocity profiles around the impeller, show that the interaction between the incoming liquid and the liquid entrained by the agitator rotation cause the flow pattern in the vessel to become strongly three-dimensional, especially in the region between the plane, where the feeding tube lies, and the 180°-downstream plane. The increase in the liquid flow rate and the location of the feed entry both affect the flow pattern, with the latter having a more pronounced effect. The overall process, in this mode of operation, depends upon the appropriate configuration and choice of parameters: for conditions corresponding to high liquid flow rates, the flow patterns indicate the possibility of short-circuiting, when the liquid is fed into the stream being drawn by the agitator and when the outlet is located at the bottom of the vessel.     

Ultra-fast quantum-well saturable absorber devices and their application to all-optical regeneration of telecommunication optical signals

We review recent advances in the investigation of vertical cavity saturable absorber devices and their use for the all-optical regeneration of telecommunication signals in ultra-long-haul transmission systems. Such devices are polarization-insensitive and operate as fully passive nonlinear optical elements. Two approaches for obtaining fast recovery absorber materials are described, relying upon ion irradiation or upon iron doping. The vertical micro-cavity devices are designed so as to optimize the switching contrast and the operating power. Their functional behaviour as extinction ratio amplifiers has been characterized and their optimal operating conditions have been determined. The potential application of these devices to all-optical regeneration has been investigated through numerical simulations and fully demonstrated in several long-distance transmission loop experiments, with results obtained at 10, 20 and 40 Gbit/s, showing significant improvements in system haul or operational margins. A four-channel fibered module has also been fabricated, as a perspective towards the development of wavelength division multiplexing (WDM) saturable absorber modules.