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

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

Incorporating high-resolution demand and techno-economic optimization to evaluate micro-grids into the Open Source Spatial Electrification Tool (OnSSET)

For decades, electrification planning in the developing world has often focused on extending the national grid to increase electricity access. This article draws attention to the potential complementary role of decentralized alternatives – primarily micro-grids – to address universal electricity access targets. To this aim, we propose a methodology consisting of three steps to estimate the LCOE and to size micro-grids for large-scale geo-spatial electrification modelling. In the first step, stochastic load demand profiles are generated for a wide range of settlement archetypes using the open-source RAMP model. In the second step, stochastic optimization is carried by the open-source MicroGridsPy model for combinations of settlement size, load demand profiles and other important techno-economic parameters influencing the LCOE. In the third step, surrogate models are generated to automatically evaluate the LCOE using a multivariate regression of micro-grid optimization results as a function of influencing parameters defining each scenario instance. Our developments coupled to the OnSSET electrification tool reveal an important increase in the cost-competitiveness of micro-grids compared to previous analyses

From the development of an open-source energy modelling tool to its application and the creation of communities of practice: The example of OSeMOSYS

In the last decades, energy modelling has supported energy planning by offering insights into the dynamics between energy access, resource use, and sustainable development. Especially in recent years, there has been an attempt to strengthen the science-policy interface and increase the involvement of society in energy planning processes. This has, both in the EU and worldwide, led to the development of open-source and transparent energy modelling practices. This paper describes the role of an open-source energy modelling tool in the energy planning process and highlights its importance for society. Specifically, it describes the existence and characteristics of the relationship between developing an open-source, freely available tool and its application, dissemination and use for policy making. Using the example of the Open Source energy Modelling System (OSeMOSYS), this work focuses on practices that were established within the community and that made the framework's development and application both relevant and scientifically grounded

The Climate, Land, Energy, and Water systems (CLEWs) framework: a retrospective of activities and advances to 2019

Population growth, urbanization and economic development drive the use of resources. Securing access to essential services such as energy, water, and food, while achieving sustainable development, require that policy and planning processes follow an integrated approach. The 'Climate-, Land-, Energy- and Water-systems' (CLEWs) framework assists the exploration of interactions between (and within) CLEW systems via quantitative means. The approach was first introduced by the International Atomic Energy Agency to conduct an integrated systems analysis of a biofuel chain. The framework assists the exploration of interactions between (and within) CLEW systems via quantitative means. Its multi-institutional application to the case of Mauritius in 2012 initiated the deployment of the framework. A vast number of completed and ongoing applications of CLEWs span different spatial and temporal scales, discussing two or more resource interactions under different political contexts. Also, the studies vary in purpose. This shapes the methods that support CLEWs-type analyses. In this paper, we detail the main steps of the CLEWs framework in perspective to its application over the years. We summarise and compare key applications, both published in the scientific literature, as working papers and reports by international organizations. We discuss differences in terms of geographic scope, purpose, interactions represented, analytical approach and stakeholder involvement. In addition, we review other assessments, which contributed to the advancement of the CLEWs framework. The paper delivers recommendations for the future development of the framework, as well as keys to success in this type of evaluations

Intraocular Formation of Heavy Oil in the Subretinal Space

Background: Heavy oil formation was found in the subretinal space in three patients with repeated vitreoretinal surgery. Cases: These patients had received perfluorocarbon liquid ( PFL) and silicone oil injection for retinal detachment in a previous surgery. Observations: A transparent " heavy density" oil bubble was found in the subretinal space in these patients. The heavy oil bubble was eventually removed by manual aspiration with a blunt-tipped 21-gauge needle. The retinas were reattached in all three cases. Conclusions: Silicone oil may mix with incompletely removed PFL to form heavy oil. During reoperation for persistent retinal detachment, these substances should be specifically sought and removed. (C ) Japanese Ophthalmological Society 2004

Column Planarity and Partial Simultaneous Geometric Embedding

We introduce the notion of column planarity of a subset R of the vertices of a graph G. Informally, we say that R is column planar in G if we can assign x-coordinates to the vertices in R such that any assignment of y-coordinates to them produces a partial embedding that can be completed to a plane straight-line drawing of G. Column planarity is both a relaxation and a strengthening of unlabeled level planarity. We prove near tight bounds for column planar subsets of trees: any tree on n vertices contains a column planar set of size at least 14n/17 and for any ε > 0 and any sufficiently large n, there exists an n-vertex tree in which every column planar subset has size at most (5/6 + ε)n. We also consider a relaxation of simultaneous geometric embedding (SGE), which we call partial SGE (PSGE). A PSGE of two graphs G 1 and G 2 allows some of their vertices to map to two different points in the plane. We show how to use column planar subsets to construct k-PSGEs in which k vertices are still mapped to the same point. In particular, we show that any two trees on n vertices admit an 11n/17-PSGE, two outerpaths admit an n/4-PSGE, and an outerpath and a tree admit a 11n/34-PSGE

Geometric Simultaneous Embeddings of a Graph and a Matching

The geometric simultaneous embedding problem asks whether two planar graphs on the same set of vertices in the plane can be drawn using straight lines, such that each graph is plane. Geometric simultaneous embedding is a current topic in graph drawing and positive and negative results are known for various classes of graphs. So far only connected graphs have been considered. In this paper we present the first results for the setting where one of the graphs is a matching. In particular, we show that there exists a planar graph and a matching which do not admit a geometric simultaneous embedding. This generalizes the same result for a planar graph and a path. On the positive side, we describe algorithms that compute a geometric simultaneous embedding of a matching and a wheel, outerpath, or tree. Our proof for a matching and a tree sheds new light on a major open question: do a tree and a path always admit a geometric simultaneous embedding? Our drawing algorithms minimize the number of orientations used to draw the edges of the matching. Specifically, when embedding a matching and a tree, we can draw all matching edges horizontally. When embedding a matching and a wheel or an outerpath, we use only two orientations