Sensor Array: Impedimetric Label‐Free Sensing of DNA Hybridization in Real Time for Rapid,PCR‐Based Detection of Microorganisms

A novel, impedance‐based electronic sensor format was used for label‐free, real‐time detection of microbial DNA on oligonucleotide probe arrays. Detection limits of 5–10 nM were achieved for single‐stranded, PCR‐amplified DNA targets. Hybridization selectivity yielded 9‐ to 12‐fold signal increases for specific targets, and the sensor arrays were re‐used multiple times without significant signal degradation. These and other features of the SHARP Laboratories of America (SLA) sensor array, such as its ability to acquire continuous measurements of DNA as it accumulates on the array surface, make it an attractive biosensor platform for field detection and monitoring of sentinel and/or pathogenic microorganisms.     

Area-preserving approximations of polygonal paths

Let P be an x-monotone polygonal path in the plane. For a path Q that approximates P let W_A(Q) be the area above P and below Q, and let W_B(Q) be the area above Q and below P. Given P and an integer k, we show how to compute a path Q with at most k edges that minimizes W_A(Q)+W_B(Q). Given P and a cost C, we show how to find a path Q with the smallest possible number of edges such that W_A(Q)+W_B(Q)C. However, given P, an integer k, and a cost C, it is NP-hard to determine if a path Q with at most k edges exists such that max{W_A(Q),W_B(Q)}C. We describe an approximation algorithm for this setting. Finally, it is also NP-hard to decide whether a path Q exists such that |W_A(Q)−W_B(Q)|=0. Nevertheless, in this error measure we provide an algorithm for computing an optimal approximation up to an additive error.     

The Voronoi Diagram of Curved Objects

Voronoi diagrams of curved objects can show certain phenomena that are often considered artifacts: The Voronoi diagram is not connected; there are pairs of objects whose bisector is a closed curve or even a two-dimensional object; there are Voronoi edges between different parts of the same site (so-called self-Voronoi-edges); these self-Voronoi-edges may end at seemingly arbitrary points not on a site, and, in the case of a circular site, even degenerate to a single isolated point. We give a systematic study of these phenomena, characterizing their differential-geometric and topological properties. We show how a given set of curves can be refined such that the resulting curves define a “well-behaved” Voronoi diagram. We also give a randomized incremental algorithm to compute this diagram. The expected running time of this algorithm is O(n log n).     

Finding a Guard that Sees Most and a Shop that Sells Most

We present a near-quadratic time algorithm that computes a point inside a simple polygon P in the plane having approximately the largest visibility polygon inside P, and a near-linear time algorithm for finding the point that will have approximately the largest Voronoi region when added to an n-point set in the plane. We apply the same technique to find the translation that approximately maximizes the area of intersection of two polygonal regions in near-quadratic time, and the rigid motion doing so in near-cubic time.     

Investigating Three Qubit Entanglement with Local Measurements

In this paper we describe how three qubit entanglement can be analyzed with local measurements. For this purpose we decompose entanglement witnesses into operators that can be measured locally. Our decompositions are optimized in the number of measurement settings needed for the measurement of one witness. Our method allows to detect true threepartite entanglement and especially GHZ-states with only four measurement settings.     

Imaging spatial correlations of Rydberg excitations in cold atom clouds

We use direct spatial imaging of cold 85Rb Rydberg atom clouds to measure the Rydberg-Rydberg correlation function. The results are in qualitative agreement with theoretical predictions [F. Robicheaux and J.?V. Hernández, Phys. Rev. A 72, 063403 (2005)]. We determine the blockade radius for states 44D(5/2), 60D(5/2), and 70D(5/2) and investigate the dependence of the correlation behavior on excitation conditions and detection delay. Experimental data hint at the existence of long-range order.     

Experimental observation of an entire family of four-photon entangled states

A single linear-optical setup is used to observe an entire family of four-photon entangled states. This approach breaks with the inflexibility of present linear-optical setups usually designed for the observation of a particular multipartite entangled state only. The family includes several prominent entangled states that are known to be highly relevant for quantum information applications.