On the relationship between NLC-width and linear NLC-width

AbstractIn this paper, we consider NLC-width, NLCT-width, and linear NLC-width bounded graphs. We show that the set of all complete binary trees has unbounded linear NLC-width and that the set of all co-graphs has unbounded NLCT-width. Since trees have NLCT-width 3 and co-graphs have NLC-width 1, it follows that the family of linear NLC-width bounded graph classes is a proper subfamily of the family of NLCT-width bounded graph classes and that the family of NLCT-width bounded graph classes is a proper subfamily of the family of NLC-width bounded graph classes

On microphysical processes of noctilucent clouds (NLC): Observations and modeling of mean and width of the particle size-distribution

Noctilucent clouds (NLC) in the polar summer mesopause region have been observed in Norway (69° N, 16° E) between 1998 and 2009 by 3-color lidar technique. Assuming a mono-modal Gaussian size distribution we deduce mean and width of the particle sizes throughout the clouds. We observe a quasi linear relationship between distribution width and mean of the particle size at the top of the clouds and a deviation from this behavior for particle sizes larger than 40 nm, most often in the lower part of the layer. The vertically integrated particle properties show that 65% of the data follows the linear relationship with a slope of 0.42±0.02 for mean particle sizes up to 40 nm. For the vertically resolved particle properties (Δz = Combining double low line 0.15 km) the slope is comparable and about 0.39±0.03. For particles larger than 40 nm the distribution width becomes nearly independent of particle size and even decreases in the lower part of the layer. We compare our observations to microphysical modeling of noctilucent clouds and find that the distribution width depends on turbulence, the time that turbulence can act (cloud age), and the sampling volume/time (atmospheric variability). The model results nicely reproduce the measurements and show that the observed slope can be explained by eddy diffusion profiles as observed from rocket measurements. © 2010 Author(s)

Entangled-photon Fourier optics

Entangled photons, generated by spontaneous parametric down-conversion from a second-order nonlinear crystal, present a rich potential for imaging and image-processing applications. Since this source is an example of a three-wave mixing process, there is more flexibility in the choices of illumination and detection wavelengths and in the placement of object(s) to be imaged. Moreover, this source is entangled, a fact that allows for imaging configurations and capabilities that cannot be achieved using classical sources of light. In this paper we examine a number of imaging and image-processing configurations that can be realized using this source. The formalism that we utilize facilitates the determination of the dependence of imaging resolution on the physical parameters of the optical arrangement.Comment: 41 pages, 12 figures, accepted for publication in J. Opt. Soc. Am.

Line graphs of bounded clique-width

AbstractWe show that a set of graphs has bounded tree-width or bounded path-width if and only if the corresponding set of line graphs has bounded clique-width or bounded linear clique-width, respectively. This relationship implies some interesting algorithmic properties and re-proves already known results in a very simple way. It also shows that the minimization problem for NLC-width is NP-complete