Simultaneous Embeddings with Few Bends and Crossings

A simultaneous embedding with fixed edges (SEFE) of two planar graphs $R$ and $B$ is a pair of plane drawings of $R$ and $B$ that coincide when restricted to the common vertices and edges of $R$ and $B$. We show that whenever $R$ and $B$ admit a SEFE, they also admit a SEFE in which every edge is a polygonal curve with few bends and every pair of edges has few crossings. Specifically: (1) if $R$ and $B$ are trees then one bend per edge and four crossings per edge pair suffice (and one bend per edge is sometimes necessary), (2) if $R$ is a planar graph and $B$ is a tree then six bends per edge and eight crossings per edge pair suffice, and (3) if $R$ and $B$ are planar graphs then six bends per edge and sixteen crossings per edge pair suffice. Our results improve on a paper by Grilli et al. (GD'14), which proves that nine bends per edge suffice, and on a paper by Chan et al. (GD'14), which proves that twenty-four crossings per edge pair suffice.Comment: Full version of the paper "Simultaneous Embeddings with Few Bends and Crossings" accepted at GD '1

Regression based polynomial chaos expansion for crop phenology estimation coupled with polsar imagery

Crop phenology monitoring using Synthetic Aperture Radar(SAR) data is gaining popularity within the remote sensing community due to SAR’s all weather and large coverage imaging capability. This paper introduces a polynomial chaos expansion (PCE) based regression algorithm to retrieve BBCH scale of crops, which identifies the phenology of crops in a standardized system. The impact and applicability of the proposed methodology is successfully illustrated using the TerraSAR-X dual-pol imagery that was acquired over the cultivation period of paddy-rice fields located in Turkey. To assess the applicability of the methodology, root mean square and correlation analysis were performed under different amount of training data and number of inputs

Does symmetry preclude the evolution of senescence? A comment on Pen and Flatt 2021

Funding Information: C.d.V. and H.K. were supported by Swiss National Science Foundation grant no. 310030B_182836. C.d.V. was also supported by an Academy of Finland grant (no. 340130, awarded to Jussi Lehtonen). E.Y.E. was supported by the National Institutes of Health (NIH) grant no. U54 CA217376 (awarded to Hanna Kokko) and Swiss National Science Foundation grant no. P500PB_203022.Peer reviewe

Evaluation of the biocompatibility of experimentally manufactured portland cement: an animal study

Objectives: The purpose of this study was to evaluate the biocompatibility of MTA and the experimentally manufactured portland cement (EMPC). Study design: Twenty one Sprague Dawley (SD) rats were allocated to testing of three groups. Group I and Group II included ProRoot MTA and the EMPC. The materials were mixed with distilled water and placed in polyethylene tubes. The tubes were implanted subcutaneously in the dorsal region of the animals. Group III served as control; the implanted polyethylene tubes remained empty. At 7, 14, and 28 days after the implantation, the animals were sacrificed and the implants were removed with the surrounding tissues. The specimens were prepared for histological examination to evaluate the inflammatory response. Results: No significant difference was found between tissue reactions against the tested materials (p>0.05). Also, control group showed similar results(p>0.05). Conclusions: Results suggest that the EMPC has the potential to be used in clinical conditions in which ProRoot MTA is indicated. MTA and the EMPC show comparable biocompatibility when evaluated in vivo. Although the results are supportive for the EMPC, more studies are required before the safe clinical use of the EMPC

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

Design and synthesis of soluble dibenzosuberane-substituted fullerene derivatives for bulk-heterojunction polymer solar cells

Cataloged from PDF version of article.Two new dibenzosuberane-substituted fullerene derivatives, dibenzosuberane-C60 monoadduct (DBSCMA) and bis-adduct (DBSCBA) were synthesized using a classical cyclopropanation reaction via a tosylhydrazone route for application as acceptor materials in polymer solar cells (PSCs). DBSCBA shows good solubility in common organic solvents and both derivatives were characterized by 1HNMR, 13C NMR, MALD-TOF, elemental analysis and UV-vis absorption measurements. The shift of fullerene energy levels induced by the dibenzosuberane substitution was investigated by using theoretical simulations and ultraviolet photoelectron spectroscopy. Bulk-heterojunction PSCs based on poly (3-hexylthiophene) (P3HT) and dibenzosuberane-C60 derivatives were fabricated and optimized by adjusting the donor/acceptor ratio and using thermal annealing and solvent additive. The morphologies of the active layers processed under different conditions were also examined by atomic force microscopy. When tested under an illumination of AM 1.5 G at 100 mW/ cm2, the highest power conversion efficiency of the devices using DBSCBA is 3.70% which is superior to that of conventional P3HT:PCBM devices. © 2013 Elsevier B.V