Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras

We study a special sort of 2-dimensional extended Topological Quantum Field Theories (TQFTs) which we call open-closed TQFTs. These are defined on open-closed cobordisms by which we mean smooth compact oriented 2-manifolds with corners that have a particular global structure in order to model the smooth topology of open and closed string worldsheets. We show that the category of open-closed TQFTs is equivalent to the category of knowledgeable Frobenius algebras. A knowledgeable Frobenius algebra (A,C,i,i^*) consists of a symmetric Frobenius algebra A, a commutative Frobenius algebra C, and an algebra homomorphism i:C->A with dual i^*:A->C, subject to some conditions. This result is achieved by providing a generators and relations description of the category of open-closed cobordisms. In order to prove the sufficiency of our relations, we provide a normal form for such cobordisms which is characterized by topological invariants. Starting from an arbitrary such cobordism, we construct a sequence of moves (generalized handle slides and handle cancellations) which transforms the given cobordism into the normal form. Using the generators and relations description of the category of open-closed cobordisms, we show that it is equivalent to the symmetric monoidal category freely generated by a knowledgeable Frobenius algebra. Our formalism is then generalized to the context of open-closed cobordisms with labeled free boundary components, i.e. to open-closed string worldsheets with D-brane labels at their free boundaries.Comment: 47 pages; LaTeX2e with xypic and pstricks macros; corrected typo

An evaluation framework for stereo-based driver assistance

This is the post-print version of the Article - Copyright @ 2012 Springer VerlagThe accuracy of stereo algorithms or optical flow methods is commonly assessed by comparing the results against the Middlebury database. However, equivalent data for automotive or robotics applications rarely exist as they are difficult to obtain. As our main contribution, we introduce an evaluation framework tailored for stereo-based driver assistance able to deliver excellent performance measures while circumventing manual label effort. Within this framework one can combine several ways of ground-truthing, different comparison metrics, and use large image databases. Using our framework we show examples on several types of ground truthing techniques: implicit ground truthing (e.g. sequence recorded without a crash occurred), robotic vehicles with high precision sensors, and to a small extent, manual labeling. To show the effectiveness of our evaluation framework we compare three different stereo algorithms on pixel and object level. In more detail we evaluate an intermediate representation called the Stixel World. Besides evaluating the accuracy of the Stixels, we investigate the completeness (equivalent to the detection rate) of the StixelWorld vs. the number of phantom Stixels. Among many findings, using this framework enables us to reduce the number of phantom Stixels by a factor of three compared to the base parametrization. This base parametrization has already been optimized by test driving vehicles for distances exceeding 10000 km

Actively Tuned and Spatially Trapped Polaritons

We report active tuning of the polariton resonance of quantum well excitons in a semiconductor microcavity using applied stress. Starting with the quantum well exciton energy higher than the cavity photon mode, we use stress to reduce the exciton energy and bring it into resonance with the photon mode. At the point of zero detuning, line narrowing and strong increase of the photoluminescence are seen. By the same means, we create an in-plane harmonic potential for the polaritons, which allows trapping, potentially making Bose-Einstein condensation of polaritons analogous to trapped atoms possible. We demonstrate drift of the polaritons into this trap.Comment: 10 pages, 5 figure