Near-optimal labeling schemes for nearest common ancestors

We consider NCA labeling schemes: given a rooted tree $T$, label the nodes of $T$ with binary strings such that, given the labels of any two nodes, one can determine, by looking only at the labels, the label of their nearest common ancestor. For trees with $n$ nodes we present upper and lower bounds establishing that labels of size $(2\pm \epsilon)\log n$, $\epsilon<1$ are both sufficient and necessary. (All logarithms in this paper are in base 2.) Alstrup, Bille, and Rauhe (SIDMA'05) showed that ancestor and NCA labeling schemes have labels of size $\log n +\Omega(\log \log n)$. Our lower bound increases this to $\log n + \Omega(\log n)$ for NCA labeling schemes. Since Fraigniaud and Korman (STOC'10) established that labels in ancestor labeling schemes have size $\log n +\Theta(\log \log n)$, our new lower bound separates ancestor and NCA labeling schemes. Our upper bound improves the $10 \log n$ upper bound by Alstrup, Gavoille, Kaplan and Rauhe (TOCS'04), and our theoretical result even outperforms some recent experimental studies by Fischer (ESA'09) where variants of the same NCA labeling scheme are shown to all have labels of size approximately $8 \log n$

Protein and cell patterning in closed polymer channels by photoimmobilizing proteins on photografted poly(ethylene glycol) diacrylate

Definable surface chemistry is essential for many applications of microfluidic polymer systems. However, small cross-section channels with a high surface to volume ratio enhance passive adsorption of molecules that depletes active molecules in solution and contaminates the channel surface. Here, we present a one-step photochemical process to coat the inner surfaces of closed microfluidic channels with a nanometer thick layer of poly(ethylene glycol) (PEG), well known to strongly reduce non-specific adsorption, using only commercially available reagents in an aqueous environment. The coating consists of PEG diacrylate (PEGDA) covalently grafted to polymer surfaces via UV light activation of the water soluble photoinitiator benzoyl benzylamine, a benzophenone derivative. The PEGDA coating was shown to efficiently limit the adsorption of antibodies and other proteins to <5% of the adsorbed amount on uncoated polymer surfaces. The coating could also efficiently suppress the adhesion of mammalian cells as demonstrated using the HT-29 cancer cell line. In a subsequent equivalent process step, protein in aqueous solution could be anchored onto the PEGDA coating in spatially defined patterns with a resolution of <15 μm using an inverted microscope as a projection lithography system. Surface patterns of the cell binding protein fibronectin were photochemically defined inside a closed microfluidic device that was initially homogeneously coated by PEGDA. The resulting fibronectin patterns were shown to greatly improve cell adhesion compared to unexposed areas. This method opens for easy surface modification of closed microfluidic systems through combining a low protein binding PEG-based coating with spatially defined protein patterns of interest

Photoemission electron microscopy of localized surface plasmons in silver nanostructures at telecommunication wavelengths

We image the field enhancement at Ag nanostructures using femtosecond laser pulses with a center wavelength of 1.55 micrometer. Imaging is based on non-linear photoemission observed in a photoemission electron microscope (PEEM). The images are directly compared to ultra violet PEEM and scanning electron microscopy (SEM) imaging of the same structures. Further, we have carried out atomic scale scanning tunneling microscopy (STM) on the same type of Ag nanostructures and on the Au substrate. Measuring the photoelectron spectrum from individual Ag particles shows a larger contribution from higher order photoemission process above the work function threshold than would be predicted by a fully perturbative model, consistent with recent results using shorter wavelengths. Investigating a wide selection of both Ag nanoparticles and nanowires, field enhancement is observed from 30% of the Ag nanoparticles and from none of the nanowires. No laser-induced damage is observed of the nanostructures neither during the PEEM experiments nor in subsequent SEM analysis. By direct comparison of SEM and PEEM images of the same nanostructures, we can conclude that the field enhancement is independent of the average nanostructure size and shape. Instead, we propose that the variations in observed field enhancement could originate from the wedge interface between the substrate and particles electrically connected to the substrate