Vertical structures induced by embedded moonlets in Saturn's rings: the gap region

We study the vertical extent of propeller structures in Saturn's rings. Our focus lies on the gap region of the propeller and on non-inclined propeller moonlets. In order to describe the vertical structure of propellers we extend the model of Spahn and Sremcevic (2000) to include the vertical direction. We find that the gravitational interaction of ring particles with the non-inclined moonlet does not induce considerable vertical excursions of ring particles, but causes a considerable thermal motion in the ring plane. We expect ring particle collisions to partly convert the lateral induced thermal motion into vertical excursions of ring particles. For the gap region of the propeller, we calculate gap averaged propeller heights on the order of 0.7 Hill radii, which is of the order of the moonlet radius. In our model the propeller height decreases exponentially until viscous heating and collisional cooling balance. We estimate Hill radii of 370m and 615m for the propellers Earhart and Bleriot. Our model predicts about 120km for the azimuthal extent of the Earhart propeller at Saturn's 2009 equinox, being consistent with values determined from Cassini images

Online Exploration of Polygons with Holes

We study online strategies for autonomous mobile robots with vision to explore unknown polygons with at most h holes. Our main contribution is an (h+c_0)!-competitive strategy for such polygons under the assumption that each hole is marked with a special color, where c_0 is a universal constant. The strategy is based on a new hybrid approach. Furthermore, we give a new lower bound construction for small h.Comment: 16 pages, 9 figures, submitted to WAOA 201

On Temporal Graph Exploration

A temporal graph is a graph in which the edge set can change from step to step. The temporal graph exploration problem TEXP is the problem of computing a foremost exploration schedule for a temporal graph, i.e., a temporal walk that starts at a given start node, visits all nodes of the graph, and has the smallest arrival time. In the first part of the paper, we consider only temporal graphs that are connected at each step. For such temporal graphs with $n$ nodes, we show that it is NP-hard to approximate TEXP with ratio $O(n^{1-\epsilon})$ for any $\epsilon>0$. We also provide an explicit construction of temporal graphs that require $\Theta(n^2)$ steps to be explored. We then consider TEXP under the assumption that the underlying graph (i.e. the graph that contains all edges that are present in the temporal graph in at least one step) belongs to a specific class of graphs. Among other results, we show that temporal graphs can be explored in $O(n^{1.5} k^2 \log n)$ steps if the underlying graph has treewidth $k$ and in $O(n \log^3 n)$ steps if the underlying graph is a $2\times n$ grid. In the second part of the paper, we replace the connectedness assumption by a weaker assumption and show that $m$-edge temporal graphs with regularly present edges and with random edges can always be explored in $O(m)$ steps and $O(m \log n)$ steps with high probability, respectively. We finally show that the latter result can be used to obtain a distributed algorithm for the gossiping problem.Comment: This is an extended version of an ICALP 2015 pape

Carbonyl Reductases and Pluripotent HydroxysteroidDehydrogenases of the Short-Chain Dehydrogenase/ReductaseSuperfamily:Structural Aspects of Oligomerization in 3alpha-HydroxysteroidDehydrogenase /Carbonyl Reductase from Comamonas testosteroni:New Approaches for efficient Protein Design

Carbonyl reduction of aldehydes, ketones and quinones to their corresponding hydroxy de-rivatives plays an important role in the phase-I metabolism of many endogenous (biogenic aldehydes, steroids, prostaglandins, reactive lipid peroxidation products) and xenobiotic (pharmacologic drugs, carcinogens, toxicants) compounds. Carbonyl-reducing enzymes are grouped into two large protein superfamilies, the aldo-keto reductases (AKR) and the short-chain dehydrogenases/reductases (SDR). Whereas aldehyde reductase and aldose reductase are AKRs, several forms of carbonyl reductase belong to the SDRs. In addition, there exist a variety of pluripotent hydroxysteroid dehydrogenases (HSDs) of both superfamilies which specifically catalyze the oxidoreduction at different positions of the steroid nucleus, and which also catalyze rather non-specifically the reductive metabolism of a great number of non-steroidal carbonyl compounds. The present review summarizes recent findings on car-bonyl reductases and pluripotent HSDs of the SDR protein superfamily