Planar Embeddings with Small and Uniform Faces

Motivated by finding planar embeddings that lead to drawings with favorable aesthetics, we study the problems MINMAXFACE and UNIFORMFACES of embedding a given biconnected multi-graph such that the largest face is as small as possible and such that all faces have the same size, respectively. We prove a complexity dichotomy for MINMAXFACE and show that deciding whether the maximum is at most $k$ is polynomial-time solvable for $k \leq 4$ and NP-complete for $k \geq 5$. Further, we give a 6-approximation for minimizing the maximum face in a planar embedding. For UNIFORMFACES, we show that the problem is NP-complete for odd $k \geq 7$ and even $k \geq 10$. Moreover, we characterize the biconnected planar multi-graphs admitting 3- and 4-uniform embeddings (in a $k$-uniform embedding all faces have size $k$) and give an efficient algorithm for testing the existence of a 6-uniform embedding.Comment: 23 pages, 5 figures, extended version of 'Planar Embeddings with Small and Uniform Faces' (The 25th International Symposium on Algorithms and Computation, 2014

Advances in C-Planarity Testing of Clustered Graphs

A clustered graph C=(G,T) consists of an undirected graph G and a rooted tree T in which the leaves of T correspond to the vertices of G=(V,E). Each vertex c in T corresponds to a subset of the vertices of the graph called ''cluster''. C-planarity is a natural extension of graph planarity for clustered graphs, and plays an important role in automatic graph drawing. The complexity status of c-planarity testing is unknown. It has been shown that c-planarity can be tested in linear time for c-connected graphs, i.e., graphs in which the cluster induced subgraphs are connected. In this paper, we provide a polynomial time algorithm for c-planarity testing for "almost" c-connected clustered graphs, i.e., graphs for which all c-vertices corresponding to the non-c-connected clusters lie on the same path in T starting at the root of T, or graphs in which for each non-connected cluster its super-cluster and all its siblings are connected. The algorithm uses ideas of the algorithm for subgraph induced planar connectivity augmentation. We regard it as a first step towards general c-planarity testing

Antioxidant activities in vitro of water and liposoluble extracts obtained by different species of edible insects and invertebrates

A new global interest in entomophagy, the practice of eating insects, and invertebrates, arise from the impellent necessity of preserving agriculture resources and to obtain a drastic reduction of the ecological impact of animal food on the planet. The composite nutritional content, direct consequences of a plant-based feeding, associated with the undoubtedly ecological properties, suggest for insects a role as sustainable and functional foods. We aim to investigate the ability of water and liposoluble extracts, obtained by 12 commercially available edible insects and two invertebrates, to display an antioxidant effect in vitro. Results show that water-soluble extracts of grasshoppers, silkworm, and crickets display the highest values of antioxidant capacity (TEAC), 5-fold higher than fresh orange juice, while evening cicada, giant water bugs, Thai zebra tarantula, and black scorpions have negligible values. Grasshoppers, African caterpillars, and crickets have the highest levels of reducing power (FRAP), double than fresh orange juice. Grasshoppers, black ants, and mealworms contain the highest levels of total polyphenols, while Thai zebra tarantula, black scorpions, and giant water bugs are positioned at the bottom of the ranking. The liposoluble fraction of silkworm, evening cicada, and African caterpillars shows highest level of TEAC, twice than olive oil, while Thai zebra tarantula, palm worm, and black ants are placed at the bottom of the ranking. Edible insects and invertebrates represent a potential source of antioxidant ingredients with an efficiency related to their taxonomy and eating habits. More evidences are needed in order to understand if the practice of eating insects and invertebrates might contribute to modulate oxidative stress in humans

The Potential of Mixtures of Pure Fluids in ORC-based Power Units fed by Exhaust Gases in Internal Combustion Engines

Abstract ORC represents an effective challenge in the waste heat recovery from ICEs. In spite of technological aspects, its thermodynamic design still deserves attention. Mixtures of pure fluids show interesting properties able to improve exergetic efficiency of the Rankine cycle, thanks to the positive slope of the phase changing. They can reduce also ODP and GWP, helping the replacement trends of working fluids. The paper optimizes cycle exergetic efficiency considering mixtures of pure fluids. The use of hydrocarbons in mixtures is particularly suitable and when used in limited fractions with other organic fluids they loses the limits related to the flammability.R245fa is a fluid that obtains a large net power increase when used in mixtures with hydrocarbons, compared to pure fluid an optimized R245fa/benzene mixture, for instance, attains an 11% net power increase

Hierarchical Partial Planarity

In this paper we consider graphs whose edges are associated with a degree of {\em importance}, which may depend on the type of connections they represent or on how recently they appeared in the scene, in a streaming setting. The goal is to construct layouts of these graphs in which the readability of an edge is proportional to its importance, that is, more important edges have fewer crossings. We formalize this problem and study the case in which there exist three different degrees of importance. We give a polynomial-time testing algorithm when the graph induced by the two most important sets of edges is biconnected. We also discuss interesting relationships with other constrained-planarity problems.Comment: Conference version appeared in WG201

Functional properties of edible insects: a systematic review

: Consumption of edible insects has been widely suggested as an environmentally sustainable substitute for meat to reduce GHG emissions. However, the novel research field for edible insects rely on the content of bioactive ingredients and on the ability to induce a functional effect in humans. The goal of this manuscript was to review the available body of evidence on the properties of edible insects in modulating oxidative and inflammatory stress, platelet aggregation, lipid and glucose metabolism and weight control. A search for literature investigating the functional role of edible insects was carried out in the PUBMED database using specific keywords. A total of 55 studies, meeting inclusion criteria after screening, were divided on the basis of the experimental approach: in vitro studies, cellular models/ex vivo studies or in vivo studies. In the majority of the studies, insects demonstrated the ability to reduce oxidative stress, modulate antioxidant status, restore the impaired activity of antioxidant enzymes and reduce markers of oxidative damage. Edible insects displayed anti-inflammatory activity reducing cytokines and modulating specific transcription factors. Results from animal studies suggest that edible insects can modulate lipid and glucose metabolism. The limited number of studies focused on the assessment of anticoagulation activity of edible insects make it difficult to draw conclusions. More evidence from dietary intervention studies in humans is needed to support the promising evidence from in vitro and animal models about the functional role of edible insects consumption

Convex drawings of graphs with non-convex boundary

Abstract. In this paper, we study a new problem of finding a convex drawing of graphs with a non-convex boundary. It is proved that every triconnected plane graph whose boundary is fixed with a star-shaped polygon admits a drawing in which every inner facial cycle is drawn as a convex polygon. Such a drawing, called an inner-convex drawing, can be obtained in linear time.

Food-borne Lactiplantibacillus plantarum protect normal intestinal cells against inflammation by modulating reactive oxygen species and IL-23/IL-17 axis

Food-associated Lactiplantibacillus plantarum (Lpb. plantarum) strains, previously classified as Lactobacillus plantarum, are a promising strategy to face intestinal inflammatory diseases. Our study was aimed at clarifying the protective role of food-borne Lpb. plantarum against inflammatory damage by testing the scavenging microbial ability both in selected strains and in co-incubation with normal mucosa intestinal cells (NCM460). Here, we show that Lpb. plantarum endure high levels of induced oxidative stress through partially neutralizing reactive oxygen species (ROS), whereas they elicit their production when co-cultured with NCM460. Moreover, pre-treatment with food-borne Lpb. plantarum significantly reduce pro-inflammatory cytokines IL-17F and IL-23 levels in inflamed NCM460 cells. Our results suggest that food-vehicled Lpb. plantarum strains might reduce inflammatory response in intestinal cells by directly modulating local ROS production and by triggering the IL-23/IL-17 axis with future perspectives on health benefits in the gut derived by the consumption of functional foods enriched with selected strains

Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time

Thomassen characterized some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph is drawable in straight-lines if and only if it does not contain the configuration [C. Thomassen, Rectilinear drawings of graphs, J. Graph Theory, 10(3), 335-341, 1988]. In this paper, we characterize some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph can be re-embedded into a straight-line drawable 1-plane embedding of the same graph if and only if it does not contain the configuration. Re-embedding of a 1-plane embedding preserves the same set of pairs of crossing edges. We give a linear-time algorithm for finding a straight-line drawable 1-plane re-embedding or the forbidden configuration.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016). This is an extended abstract. For a full version of this paper, see Hong S-H, Nagamochi H.: Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time, Technical Report TR 2016-002, Department of Applied Mathematics and Physics, Kyoto University (2016

Splitting Clusters To Get C-Planarity

In this paper we introduce a generalization of the c-planarity testing problem for clustered graphs. Namely, given a clustered graph, the goal of the S PLIT-C-P LANARITY problem is to split as few clusters as possible in order to make the graph c-planar. Determining whether zero splits are enough coincides with testing c-planarity. We show that S PLIT-C-P LANARITY is NP-complete for c-connected clustered triangulations and for non-c-connected clustered paths and cycles. On the other hand, we present a polynomial-time algorithm for flat c-connected clustered graphs whose underlying graph is a biconnected seriesparallel graph, both in the fixed and in the variable embedding setting, when the splits are assumed to maintain the c-connectivity of the clusters