Identification of the byproducts of the oxygen evolution reaction on rutile-type oxides under dynamic conditions

Peer reviewedPostprin

Combinatorial Properties of Triangle-Free Rectangle Arrangements and the Squarability Problem

We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of rectangles intersects. First, we investigate combinatorial contact arrangements, i.e., arrangements of interior-disjoint rectangles, with a triangle-free intersection graph. We show that such rectangle arrangements are in bijection with the 4-orientations of an underlying planar multigraph and prove that there is a corresponding geometric rectangle contact arrangement. Moreover, we prove that every triangle-free planar graph is the contact graph of such an arrangement. Secondly, we introduce the question whether a given rectangle arrangement has a combinatorially equivalent square arrangement. In addition to some necessary conditions and counterexamples, we show that rectangle arrangements pierced by a horizontal line are squarable under certain sufficient conditions.Comment: 15 pages, 13 figures, extended version of a paper to appear at the International Symposium on Graph Drawing and Network Visualization (GD) 201

Low body temperature associated with severe ischemic stroke within 6 hours of onset: The Bergen NORSTROKE Study

Christopher E Kvistad, Lars Thomassen, Ulrike Waje-Andreassen, Halvor NaessDepartment of Neurology, Haukeland University Hospital, University of Bergen, Bergen, NorwayBackground: Hypothermia is considered neuroprotective and a potential treatment in cerebral ischemia. Some studies suggest that hyperthermia may promote clot lysis. We hypothesized that low body temperature would prolong time to spontaneous clot lysis resulting in an association between low body temperature and severe neurological deficits in the early phase of ischemic stroke.Methods: In this prospective study, patients (n = 516) exhibiting ischemic stroke with symptom onset within 6 hours were included. Body temperature and National Institute of Health Stroke Scale (NIHSS) score were registered on admission. Because low body temperature on admission may be secondary to immobilization due to large stroke, separate analyses were performed on patients with cerebral hemorrhage admitted within 6 hours (n = 85).Results: Linear regression showed that low body temperature on admission was independently associated with a high NIHSS score within 6 hours of stroke onset in patients with ischemic stroke (P < 0.001). The association persisted when NIHSS was measured at 24 hours after admission. No such associations were found in patients with cerebral hemorrhage admitted within 6 hours of stroke onset.Conclusion: Our study suggests that low body temperature within 6 hours of symptom onset is associated with severe ischemic stroke. This is in support of our hypothesis, although other contributing mechanisms cannot be excluded.Keywords: body temperature, cerebral infarction, cerebral hemorrhage, clot lysi

On a Tree and a Path with no Geometric Simultaneous Embedding

Two graphs $G_1=(V,E_1)$ and $G_2=(V,E_2)$ admit a geometric simultaneous embedding if there exists a set of points P and a bijection M: P -> V that induce planar straight-line embeddings both for $G_1$ and for $G_2$. While it is known that two caterpillars always admit a geometric simultaneous embedding and that two trees not always admit one, the question about a tree and a path is still open and is often regarded as the most prominent open problem in this area. We answer this question in the negative by providing a counterexample. Additionally, since the counterexample uses disjoint edge sets for the two graphs, we also negatively answer another open question, that is, whether it is possible to simultaneously embed two edge-disjoint trees. As a final result, we study the same problem when some constraints on the tree are imposed. Namely, we show that a tree of depth 2 and a path always admit a geometric simultaneous embedding. In fact, such a strong constraint is not so far from closing the gap with the instances not admitting any solution, as the tree used in our counterexample has depth 4.Comment: 42 pages, 33 figure

III-V-on-silicon anti-colliding pulse-type mode-locked laser

An anti-colliding pulse-type III–V-on-silicon passively mode-locked laser is presented for the first time based on a III–V-on-silicon distributed Bragg reflector as outcoupling mirror implemented partially underneath the III–V saturable absorber. Passive mode-locking at 4.83 GHz repetition rate generating 3 ps pulses is demonstrated. The generated fundamental RF tone shows a 1.7 kHz 3 dB linewidth. Over 9 mW waveguide coupled output power is demonstrated

Extending a perfect matching to a Hamiltonian cycle

Graph TheoryInternational audienceRuskey and Savage conjectured that in the d-dimensional hypercube, every matching M can be extended to a Hamiltonian cycle. Fink verified this for every perfect matching M, remarkably even if M contains external edges. We prove that this property also holds for sparse spanning regular subgraphs of the cubes: for every d ≥7 and every k, where 7 ≤k ≤d, the d-dimensional hypercube contains a k-regular spanning subgraph such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle. We do not know if this result can be extended to k=4,5,6. It cannot be extended to k=3. Indeed, there are only three 3-regular graphs such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle, namely the complete graph on 4 vertices, the complete bipartite 3-regular graph on 6 vertices and the 3-cube on 8 vertices. Also, we do not know if there are graphs of girth at least 5 with this matching-extendability property

Contact Representations of Graphs in 3D

We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there exists a simultaneous representation of the graph and its dual with 3D boxes. We give a linear-time algorithm for constructing such a representation. This result extends the existing primal-dual contact representations of planar graphs in 2D using circles and triangles. While contact graphs in 2D directly correspond to planar graphs, we next study representations of non-planar graphs in 3D. In particular we consider representations of optimal 1-planar graphs. A graph is 1-planar if there exists a drawing in the plane where each edge is crossed at most once, and an optimal n-vertex 1-planar graph has the maximum (4n - 8) number of edges. We describe a linear-time algorithm for representing optimal 1-planar graphs without separating 4-cycles with 3D boxes. However, not every optimal 1-planar graph admits a representation with boxes. Hence, we consider contact representations with the next simplest axis-aligned 3D object, L-shaped polyhedra. We provide a quadratic-time algorithm for representing optimal 1-planar graph with L-shaped polyhedra