Aligned Drawings of Planar Graphs

Let $G$ be a graph that is topologically embedded in the plane and let $\mathcal{A}$ be an arrangement of pseudolines intersecting the drawing of $G$. An aligned drawing of $G$ and $\mathcal{A}$ is a planar polyline drawing $\Gamma$ of $G$ with an arrangement $A$ of lines so that $\Gamma$ and $A$ are homeomorphic to $G$ and $\mathcal{A}$. We show that if $\mathcal{A}$ is stretchable and every edge $e$ either entirely lies on a pseudoline or it has at most one intersection with $\mathcal{A}$, then $G$ and $\mathcal{A}$ have a straight-line aligned drawing. In order to prove this result, we strengthen a result of Da Lozzo et al., and prove that a planar graph $G$ and a single pseudoline $\mathcal{L}$ have an aligned drawing with a prescribed convex drawing of the outer face. We also study the less restrictive version of the alignment problem with respect to one line, where only a set of vertices is given and we need to determine whether they can be collinear. We show that the problem is NP-complete but fixed-parameter tractable.Comment: Preliminary work appeared in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Drawing Graphs within Restricted Area

We study the problem of selecting a maximum-weight subgraph of a given graph such that the subgraph can be drawn within a prescribed drawing area subject to given non-uniform vertex sizes. We develop and analyze heuristics both for the general (undirected) case and for the use case of (directed) calculation graphs which are used to analyze the typical mistakes that high school students make when transforming mathematical expressions in the process of calculating, for example, sums of fractions

Algorithms and Bounds for Drawing Non-planar Graphs with Crossing-free Subgraphs

We initiate the study of the following problem: Given a non-planar graph G and a planar subgraph S of G, does there exist a straight-line drawing {\Gamma} of G in the plane such that the edges of S are not crossed in {\Gamma} by any edge of G? We give positive and negative results for different kinds of connected spanning subgraphs S of G. Moreover, in order to enlarge the subset of instances that admit a solution, we consider the possibility of bending the edges of G not in S; in this setting we discuss different trade-offs between the number of bends and the required drawing area.Comment: 21 pages, 9 figures, extended version of 'Drawing Non-planar Graphs with Crossing-free Subgraphs' (21st International Symposium on Graph Drawing, 2013

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

On the Area Requirements of Planar Greedy Drawings of Triconnected Planar Graphs

In this paper we study the area requirements of planar greedy drawings of triconnected planar graphs. Cao, Strelzoff, and Sun exhibited a family $\cal H$ of subdivisions of triconnected plane graphs and claimed that every planar greedy drawing of the graphs in $\mathcal H$ respecting the prescribed plane embedding requires exponential area. However, we show that every $n$-vertex graph in $\cal H$ actually has a planar greedy drawing respecting the prescribed plane embedding on an $O(n)\times O(n)$ grid. This reopens the question whether triconnected planar graphs admit planar greedy drawings on a polynomial-size grid. Further, we provide evidence for a positive answer to the above question by proving that every $n$-vertex Halin graph admits a planar greedy drawing on an $O(n)\times O(n)$ grid. Both such results are obtained by actually constructing drawings that are convex and angle-monotone. Finally, we consider $\alpha$-Schnyder drawings, which are angle-monotone and hence greedy if $\alpha\leq 30^\circ$, and show that there exist planar triangulations for which every $\alpha$-Schnyder drawing with a fixed $\alpha<60^\circ$ requires exponential area for any resolution rule

Extending Upward Planar Graph Drawings

In this paper we study the computational complexity of the Upward Planarity Extension problem, which takes in input an upward planar drawing $\Gamma_H$ of a subgraph $H$ of a directed graph $G$ and asks whether $\Gamma_H$ can be extended to an upward planar drawing of $G$. Our study fits into the line of research on the extensibility of partial representations, which has recently become a mainstream in Graph Drawing. We show the following results. First, we prove that the Upward Planarity Extension problem is NP-complete, even if $G$ has a prescribed upward embedding, the vertex set of $H$ coincides with the one of $G$, and $H$ contains no edge. Second, we show that the Upward Planarity Extension problem can be solved in $O(n \log n)$ time if $G$ is an $n$-vertex upward planar $st$-graph. This result improves upon a known $O(n^2)$-time algorithm, which however applies to all $n$-vertex single-source upward planar graphs. Finally, we show how to solve in polynomial time a surprisingly difficult version of the Upward Planarity Extension problem, in which $G$ is a directed path or cycle with a prescribed upward embedding, $H$ contains no edges, and no two vertices share the same $y$-coordinate in $\Gamma_H$

Developments on drug discovery and on new therapeutics: highly diluted tinctures act as biological response modifiers

<p>Abstract</p> <p>Background</p> <p>In the search for new therapies novel drugs and medications are being discovered, developed and tested in laboratories. Highly diluted substances are intended to enhance immune system responses resulting in reduced frequency of various diseases, and often present no risk of serious side-effects due to its low toxicity. Over the past years our research group has been investigating the action of highly diluted substances and tinctures on cells from the immune system.</p> <p>Methods</p> <p>We have developed and tested several highly diluted tinctures and here we describe the biological activity of M1, M2, and M8 both <it>in vitro </it>in immune cells from mice and human, and <it>in vivo </it>in mice. Cytotoxicity, cytokines released and NF-κB activation were determined after <it>in vitro </it>treatment. Cell viability, oxidative response, lipid peroxidation, bone marrow and lymph node cells immunophenotyping were accessed after mice <it>in vivo </it>treatment.</p> <p>Results</p> <p>None of the highly diluted tinctures tested were cytotoxic to macrophages or K562. Lipopolysaccharide (LPS)-stimulated macrophages treated with all highly diluted tinctures decreased tumour necrosis factor alpha (TNF-α) release and M1, and M8 decreased IFN-<it>γ </it>production. M1 has decreased NF-κB activity on TNF-α stimulated reporter cell line. <it>In vivo </it>treatment lead to a decrease in reactive oxygen species (ROS), nitric oxide (NO) production was increased by M1, and M8, and lipid peroxidation was induced by M1, and M2. All compounds enhanced the innate immunity, but M1 also augmented acquired immunity and M2 diminished B lymphocytes, responsible to acquired immunity.</p> <p>Conclusions</p> <p>Based on the results presented here, these highly diluted tinctures were shown to modulate immune responses. Even though further investigation is needed there is an indication that these highly diluted tinctures could be used as therapeutic interventions in disorders where the immune system is compromised.</p

Toksikološka svojstva citrinina

Citrinin (CTN) is a nephrotoxic mycotoxin produced by several fungal strains belonging to the genera Penicillium, Aspergillus, and Monascus. It contaminates various commodities of plant origin, cereals in particular, and is usually found together with another nephrotoxic mycotoxin, ochratoxin A (OTA). These two mycotoxins are believed to be involved in the aetiology of endemic nephropathy. In addition to nephrotoxicity, CTN is also embryocidal and fetotoxic. The genotoxic properties of CTN have been demonstrated with the micronuleus test (MN), but not with single-cell gel electrophoresis. The mechanism of CTN toxicity is not fully understood, especially not whether CTN toxicity and genotoxicity are the consequence of oxidative stress or of increased permeability of mitochondrial membranes. CTN requires complex cellular biotransformation to exert mutagenicity. Compared with other mycotoxins, CTN contamination of food and feed is rather scarce. However, it is reasonable to believe that humans are much more frequently exposed to CTN than generally accepted, because it is produced by the same moulds as OTA, which is a common contaminant of human food all over the world. At present, there are no specifi c regulations either in Croatia or in the European Union concerning CTN in any kind of commodity.Citrinin (CTN) nefrotoksičan je mikotoksin koji proizvode različiti sojevi plijesni iz rodova Penicillium, Aspergillus i Monascus. CTN se može naći u različitim namirnicama biljnog podrijetla, osobito u žitaricama i obično se nalazi zajedno s drugim nefrotoksičnim mikotoksinom, okratoksinom A (OTA). Pretpostavlja se da je izloženost ovim mikotoksinima povezana s nastankom endemske nefropatije. Osim što je nefrotoksičan, CTN je još i embricidan i fetotoksičan. Na genotoksičnost citrinina upućuje pozitivan mikronukleusni test na različitim vrstama staničnih kultura, iako je kometski test negativan. Mutagenost CTN-a očituje se na različitim vrstama stanica samo ako se pridodaju stanični aktivatori kao npr. S9-mix. Mehanizam toksičnosti CTN-a nije potpuno razjašnjen pa još uvijek traje znanstvena rasprava je li njegova toksičnost i genotoksičnost posljedica oksidacijskog stresa ili povećane permeabilnosti mitohondrijskih membrana. U dostupnoj literaturi podaci o kontaminiranosti hrane i krmiva ovim mikotoksinom mnogo su rjeđi od onih za druge mikotoksine. Može se pretpostaviti da su ljudi često izloženi ovom mikotoksinu zato što ga proizvode iste plijesni koje proizvode i OTA, a one kontaminiraju hranu po cijelom svijetu. U Hrvatskoj i u zemljama Europske Unije ne postoje zakonske odredbe o dopuštenim granicama CTN-a u bilo kojoj vrsti hrane

Planarity of streamed graphs

In this paper we introduce a notion of planarity for graphs that are presented in a streaming fashion. A streamed graph is a stream of edges e1,e2,…,em on a vertex set V. A streamed graph is ω-stream planar with respect to a positive integer window size ω if there exists a sequence of planar topological drawings Γi of the graphs Gi=(V,ej|i≤

What is the work-load during training sessions in rugby union?

There is a great interest in coaches and fitness trainers to define the physical demands of training, in order to optimize the training process, to evaluate the players\u2019 performance and provide suitable recovery time and nutrition. The determination of training load can be particularly challenging in Rugby Union, a team sport played by 15 players of highly variable build, that is characterized by short, high intensity efforts (struggle, impacts, sprinting) and longer, low intensity activities (standing still, walking, jogging).Our study aimed at applying a heart rate based approach to measure absolute and relative workloads in two typologies of training, typically used in rugby union: team session (TS) and unit training (UT).Methods15 forwards (FW) and 15 backs (BK) from Venezia Mestre Rugby (elite Italian senior championship) undertook one incremental test to exhaustion on the treadmill to determine individual VO2max, heart rate (HR) at max and HR/VO2 relationship. Furthermore, within the following month, HR was continuously monitored during 12 training sessions (6 TS and 6 UT).For each training session, we determined absolute (Kcal*kg-1*min-1) and relative intensity (%HRmax, %VO2max,). Mean and standard deviation were calculated in FW and BK for TS and UT sessions and compared by t test (p< 0.05).Results & DiscussionThe athletes were 24\ub13 years old, a 12\ub13 years playing experience and a VO2max of 47\ub15 ml*kg-1*min-1. FW and BK weight and height were: 108\ub18 and 92\ub112 Kg; 187\ub11 and 181\ub11 cm respectively. Workload data are reported in the table. Team session training (TS) Unit training (UT) min %HRmax %VO2max Kcal*kg-1*min-1 min %HRmax %VO2max Kcal*kg-1*min-1FW 59\ub112 72\ub18 58\ub112 0.13\ub10.03 73\ub17\ua7 67\ub16\ua7 52\ub111\ua7 0.12\ub1 0.03\ua7BK 59\ub112 74\ub16* 59\ub19 0.14\ub10.02* 71\ub17\ua7 73\ub14* 58\ub18* 0.14\ub1 0.02** and \ua7 indicate, respectively, a significant difference vs FW and vs TS.ConclusionOur study successfully determined absolute and relative workload during specific training sessions in rugby union players. For BK, absolute and relative workload was similar for the two training modes and higher compared to FW. For FW, TS was performed at a higher absolute and relative intensity compared to UT. In this group of senior players of a national level, the overall workload of both TS and UT was within the moderate intensity domain