An algebraic formula for the index of a vector field on an isolated complete intersection singularity

Let (V,0) be a germ of a complete intersection variety in \CC^{n+k}, n>0, having an isolated singularity at 0 and X be the germ of a holomorphic vector field on \CC^{n+k} tangent to V and having on V an isolated zero at 0. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient space \CC^{n+k} we give a formula for the homological index in terms of local linear algebra.Comment: 18 pages; added an example which is not quasi homogeneous. A script calculating this example can be found at http://www.iag.uni-hannover.de/~bothmer/gobelin/ or at the and of the source file of this articl

Optimization and optimality test for the Max-Cut Problem

We show that the following two problems are polynomially equivalent:\ud 1. Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not.\ud 2. Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not, and in case it is not, find a better solutionC′.\ud \ud As a consequence, an optimality testing oracle may be used to design a polynomial time algorithm for approximately solving the (weighted) Max-Cut Problem.\ud This in turn implies that recognizing optimal cuts in an unweighted graph is NP-hard

Design and Performance of the CMS Pixel Detector Readout Chip

The readout chip for the CMS pixel detector has to deal with an enormous data rate. On-chip zero suppression is inevitable and hit data must be buffered locally during the latency of the first level trigger. Dead-time must be kept at a minimum. It is dominated by contributions coming from the readout. To keep it low an analog readout scheme has been adopted where pixel addresses are analog coded. We present the architecture of the final CMS pixel detector readout chip with special emphasis on the analog readout chain. Measurements of its performance are discussed.Comment: 8 pages, 11 figures. Contribution to the Proceedings of the Pixel2005 Workshop, Bonn, German

A relaxationless demonstration of the Quantum Zeno Paradox on an individual atom

The driven evolution of the spin of an individual atomic ion on the ground-state hyperfine resonance is impeded by the observation of the ion in one of the pertaining eigenstates. Detection of resonantly scattered light identifies the ion in its upper ``bright'' state. The lower ``dark'' ion state is free of relaxation and correlated with the detector by a null signal. Null events represent the straightforward demonstration of the quantum Zeno paradox. Also, high probability of survival was demonstrated when the ion, driven by a fractionated $\pi$ pulse, was probed {\em and monitored} during the intermissions of the drive, such that the ion's evolution is completely documented.Comment: 7 page