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

Atmospheric nitrogen deposition in terrestrial ecosystems:Its impact on plant communities and consequences across trophic levels

The global nitrogen cycle has been greatly perturbed by human activities resulting in elevated nitrogen deposition in many parts of the world. The threat nitrogen deposition poses to ecosystem function and biodiversity is increasingly recognised. In terrestrial systems, impacts on the plant community are mainly through eutrophication and soil acidification. Interactions with secondary environmental drivers such as extreme weather and disease are also key mechanisms. Impacts on consumers can be caused by changes in the quality or quantity of food as a result of changes in food plant chemistry or species composition, changes in vegetation structure leading to a change in the availability of prey species, nesting sites or cooled microclimates or changes in the phenology of plants leading to causing phenological asynchrony. Primary consumers have received considerably less research attention than plants but negative impacts have been observed for both folivorous insects and pollinators. Mammal herbivores have received little research attention. New analysis of changes in plant traits along a gradient of nitrogen deposition in the UK shows that plants pollinated by large bees were negatively associated with N deposition whilst low pH was associated with lower nectar production, reduced occurrence of plants pollinated by long-tongued insects and a reduction in plants with larger floral units. Very few studies have investigated the effects on secondary consumers, but those that have suggest that there are likely to be negative impacts. This review identifies considerable knowledge gaps in the impacts of N deposition on higher tropic levels and highlights that for many groups, knowledge of N deposition impacts is patchy at best. Evidence that has been collected suggests that there are likely to be impacts on primary and secondary consumers making this a priority area for investigation

Architectural/Environmental Handbook for Extraterrestrial Design

Handbook on environmental and space utilization criteria for design of extraterrestrial manned spacecraft and shelter

Efeitos de tratamentos pré-germinativos e germinativos em sementes de Liquidambar styraciflua l. coletadas em Quedas do Iguaçu, PR.

Resumo

Long-term safety and efficacy of trifarotene 50 μg/g cream, a first-in-class RAR-γ selective topical retinoid, in patients with moderate facial and truncal acne.

BackgroundTreatment for both facial and truncal acne has not sufficiently been studied.ObjectivesTo evaluate the long-term safety and efficacy of trifarotene in both facial and truncal acne.MethodsIn a multicentre, open-label, 52-week study, patients with moderate facial and truncal acne received trifarotene 50 μg/g cream (trifarotene). Assessments included local tolerability, safety, investigator and physician's global assessments (IGA, PGA) and quality of life (QOL). A validated QOL questionnaire was completed by the patient at Baseline, Week 12, 26 and 52/ET.ResultsOf 453 patients enrolled, 342 (75.5%) completed the study. Trifarotene-related treatment-emergent adverse events (TEAEs) were reported in 12.6% of patients, and none was serious. Most related TEAEs were cutaneous and occurred during the first 3 months. Signs and symptoms of local tolerability were mostly mild or moderate and severe signs, and symptoms were reported for 2.2% to 7.1% of patients for the face and 2.5% to 5.4% for the trunk. Local irritation increased during the first week of treatment on the face and up to Weeks 2 to 4 on the trunk with both decreasing thereafter. At Week 12, IGA and PGA success rates were 26.6% and 38.6%, respectively. Success rates increased to 65.1% and 66.9%, respectively at Week 52. Overall success (both IGA and PGA success in the same patient) was 57.9% at Week 52. At Week 52 visit, 92/171 (53.8%) patients who had completed their assessments had scores from 0 to 1 (i.e. no effect of acne on their QOL) vs. 47/208 (22.6%) patients at Baseline visit.ConclusionIn this 52-week study, trifarotene was safe, well tolerated and effective in moderate facial and truncal acne

Data compression in the presence of observational error correlations

Numerical weather prediction (NWP) models are moving towards km-scale (and smaller) resolutions in order to forecast high-impact weather. As the resolution of NWP models increase the need for high-resolution observations to constrain these models also increases. A major hurdle to the assimilation of dense observations in NWP is the presence of non-negligible observation error correlations (OECs). Despite the difficulty in estimating these error correlations, progress is being made, with centres around the world now explicitly accounting for OECs in a variety of observation types. This paper explores how to make efficient use of this potentially dramatic increase in the amount of data available for assimilation. In an idealised framework it is illustrated that as the length-scales of the OECs increase the scales that the analysis is most sensitive to the observations become smaller. This implies that a denser network of observations is more beneficial with increasing OEC length-scales. However, the computational and storage burden associated with such a dense network may not be feasible. To reduce the amount of data, a compression technique based on retaining the maximum information content of the observations can be used. When the OEC length-scales are large (in comparison to the prior error correlations), the data compression will select observations of the smaller scales for assimilation whilst throwing out the larger scale information. In this case it is shown that there is a discrepancy between the observations with the maximum information and those that minimise the analysis error variances. Experiments are performed using the Ensemble Kalman Filter and the Lorenz-1996 model, comparing different forms of data reduction. It is found that as the OEC length-scales increase the assimilation becomes more sensitive to the choice of data reduction technique

Remote sensing applications to resource problems in South Dakota

There are no author-identified significant results in this report