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1. When interacting with a visualization of a bipartite graph, one of the most common tasks requires identifying the neighbors of a given vertex. In interactive visualizations, selecting a vertex of interest usually highlights the edges to its neighbors while hiding/shading the rest of the graph. If the graph is large, the highlighted subgraph may not fit in the display window. This motivates a natural optimization task: find an arrangement of the vertices along two layers that reduces the size of the window needed to see a selected vertex and all its neighbors. We consider two variants of the problem; for one we present an efficient algorithm, while for the other we show NP-hardness and give a 2-approximation.
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4. We initiate the study of Simultaneous Graph Embedding with Fixed Edges in the beyond planarity framework. In the QSEFE problem, we allow edge crossings, as long as each graph individually is drawn quasiplanar, that is, no three edges pairwise cross. %We call this problem the QSEFE problem. We show that a triple consisting of two planar graphs and a tree admit a QSEFE. This result also implies that a pair consisting of a 1-planar graph and a planar graph admits a QSEFE. We show several other positive results for triples of planar graphs, in which certain structural properties for their common subgraphs are fulfilled. For the case in which simplicity is also required, we give a triple consisting of two quasiplanar graphs and a star that does not admit a QSEFE. Moreover, in contrast to the planar SEFE problem, we show that it is not always possible to obtain a QSEFE for two matchings if the quasiplanar drawing of one matching is fixed.
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5. Abstract

Atomic oxygen (O) in the mesosphere and lower thermosphere (MLT) results from a balance between production via photo‐dissociation in the lower thermosphere and chemical loss by recombination in the upper mesosphere. The transport of O downward from the lower thermosphere into the mesosphere is preferentially driven by the eddy diffusion process that results from dissipating gravity waves and instabilities. The motivation here is to probe the intra‐annual variability of the eddy diffusion coefficient (kzz) and eddy velocity in the MLT based on the climatology of the region, initially accomplished by Garcia and Solomon (1985,https://doi.org/10.1029/JD090iD02p03850). In the current study, the intra‐annual cycle was divided into 26 two‐week periods for each of three zones: the northern hemisphere (NH), southern hemisphere (SH), and equatorial (EQ). Both 16 years of SABER (2002–2018) and 10 years of SCIAMACHY (2002–2012) O density measurements, along with NRLMSIS®2.0 were used for calculation of atomic oxygen eddy diffusion velocities and fluxes. Our prominent findings include a dominant annual oscillation below 87 km in the NH and SH zones, with a factor of 3–4 variation between winter and summer at 83 km, and a dominant semiannual oscillation at all altitudes in the EQ zone. The measured global average kzzat 96 km lacks the intra‐annual variability of upper atmosphere density data deduced by Qian et al. (2009,https://doi.org/10.1029/2008JA013643). The very large seasonal (and hemispherical) variations in kzzand O densities are important to separate and isolate in satellite analysis and to incorporate in MLT models.

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