Ordered Level Planarity, Geodesic Planarity and Bi-Monotonicity

We introduce and study the problem Ordered Level Planarity which asks for a planar drawing of a graph such that vertices are placed at prescribed positions in the plane and such that every edge is realized as a y-monotone curve. This can be interpreted as a variant of Level Planarity in which the vertices on each level appear in a prescribed total order. We establish a complexity dichotomy with respect to both the maximum degree and the level-width, that is, the maximum number of vertices that share a level. Our study of Ordered Level Planarity is motivated by connections to several other graph drawing problems. Geodesic Planarity asks for a planar drawing of a graph such that vertices are placed at prescribed positions in the plane and such that every edge is realized as a polygonal path composed of line segments with two adjacent directions from a given set $S$ of directions symmetric with respect to the origin. Our results on Ordered Level Planarity imply $NP$-hardness for any $S$ with $|S|\ge 4$ even if the given graph is a matching. Katz, Krug, Rutter and Wolff claimed that for matchings Manhattan Geodesic Planarity, the case where $S$ contains precisely the horizontal and vertical directions, can be solved in polynomial time [GD'09]. Our results imply that this is incorrect unless $P=NP$. Our reduction extends to settle the complexity of the Bi-Monotonicity problem, which was proposed by Fulek, Pelsmajer, Schaefer and \v{S}tefankovi\v{c}. Ordered Level Planarity turns out to be a special case of T-Level Planarity, Clustered Level Planarity and Constrained Level Planarity. Thus, our results strengthen previous hardness results. In particular, our reduction to Clustered Level Planarity generates instances with only two non-trivial clusters. This answers a question posed by Angelini, Da Lozzo, Di Battista, Frati and Roselli.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Signals of Warped Extra Dimensions at the LHC

We discuss the signatures of the spin-2 graviton excitations predicted by the Randall-Sundrum model with one warped extra dimension, in dilepton and diphoton production at LHC. By using a specific angular analysis, we assess the ranges in mass and coupling constant where such gravitons can be discriminated against competitor spin-1 and spin-0 objects, that potentially could manifest themselves in these processes with the same mass and rate of events. Depending on the value of the coupling constant to quarks and leptons, the numerical results indicate graviton identification mass ranges up to 1.1-2.4 TeV and 1.6-3.2 TeV for LHC nominal energy of 14 TeV and time-integrated luminosity of 10 and 100~${\rm fb}^{-1}$, respectively.Comment: 8 pages, Talk given at QCD@Work - International Workshop on QCD - Theory and Experiment, 20 - 23 June, 2010, Martina Franca Ital

Neurosurgical implications of the Jugular Vein Nutcracker

In the last ten years, a new variant of Eagle Syndrome is emerging and being described: Styloid Jugular Nutcracker (SJN). In SJN, an elongated or vertically directed styloid process causes jugular vein stenosis by compressing the vein against the arch of C1. The clinical consequences appear to be various and misunderstood, ascribable mainly to venous flow impairment and consequent intracranial hypertension. The aim of this paper is to create an overview of Jugular Vein Nutcracker and to focus on its neurosurgical implications. A PRISMA-based literature search was performed to select the most relevant papers on the topic and to realize a mini-review. Future searches in the neurosurgical field should focus on collecting data about further causes of jugular stenosis compression and the association of SJN with cerebrovascular diseases. It would also be interesting to investigate the potential role of primary and secondary prevention, which is unknown so far

Superpatterns and Universal Point Sets

An old open problem in graph drawing asks for the size of a universal point set, a set of points that can be used as vertices for straight-line drawings of all n-vertex planar graphs. We connect this problem to the theory of permutation patterns, where another open problem concerns the size of superpatterns, permutations that contain all patterns of a given size. We generalize superpatterns to classes of permutations determined by forbidden patterns, and we construct superpatterns of size n^2/4 + Theta(n) for the 213-avoiding permutations, half the size of known superpatterns for unconstrained permutations. We use our superpatterns to construct universal point sets of size n^2/4 - Theta(n), smaller than the previous bound by a 9/16 factor. We prove that every proper subclass of the 213-avoiding permutations has superpatterns of size O(n log^O(1) n), which we use to prove that the planar graphs of bounded pathwidth have near-linear universal point sets.Comment: GD 2013 special issue of JGA

The Partial Visibility Representation Extension Problem

For a graph $G$, a function $\psi$ is called a \emph{bar visibility representation} of $G$ when for each vertex $v \in V(G)$, $\psi(v)$ is a horizontal line segment (\emph{bar}) and $uv \in E(G)$ iff there is an unobstructed, vertical, $\varepsilon$-wide line of sight between $\psi(u)$ and $\psi(v)$. Graphs admitting such representations are well understood (via simple characterizations) and recognizable in linear time. For a directed graph $G$, a bar visibility representation $\psi$ of $G$, additionally, puts the bar $\psi(u)$ strictly below the bar $\psi(v)$ for each directed edge $(u,v)$ of $G$. We study a generalization of the recognition problem where a function $\psi'$ defined on a subset $V'$ of $V(G)$ is given and the question is whether there is a bar visibility representation $\psi$ of $G$ with $\psi(v) = \psi'(v)$ for every $v \in V'$. We show that for undirected graphs this problem together with closely related problems are \NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Efficacy of oral hyposensitization in allergic contact dermatitis caused by nickel

Background. Nickel contact allergy remains common in Western countries, and the dermatitis may require prolonged treatment. The development of new strategies aimed at improving the quality of life of affected individuals is needed. Objectives. To investigate the efficacy of oral hyposensitization in nickel-allergic individuals and how this affects in vitro T cell responsiveness to the metal. Methods. Twenty-eight nickel-allergic patients received a daily dose of 50 μg of elemental nickel (given as NiSO 4·6H 2O) in cellulose capsules for 3 months. Severity of clinical manifestations, in vivo nickel responsiveness and in vitro T cell responses to the metal were assessed after 1 and 3 months. Results. Twenty-six patients finished the study. In these patients, oral hyposensitization ameliorated clinical manifestations despite continued nickel exposures, and increased the threshold of skin responsiveness to nickel. The 12 enrolled patients in the immunological study showed decreased in vitro T lymphocyte responsiveness to the metal, in terms of both cell proliferation and cytokine release. In the 1-year follow-up, 50% of the patients experienced relapses of the clinical manifestations at sites of topical exposure to nickel. Conclusions. Our study suggested therapeutic efficacy of oral hyposensitization in allergic individuals. Placebo-controlled studies are required to confirm the results and determine the optimal therapeutic regimen for prolonged beneficial effects

study of the aggregation properties of a novel amphiphilic C60 fullerene derivative

none7An amphiphilic C60-derivative, AFE, characterized by the presence of the chiral fragment of L-acetyl carnitine in its hydrophilic appendage has been synthesized. In binary (THF/H2O) and ternary (THF/MeOH/H2O) solutions, AFE exhibits a strong tendency to self-aggregation, provided that the Hildebrand polarity index, ä, of the solvent is higher than about 15. A stable aqueous solution of aggregated AFE was obtained. Partition experiments between n-octanol and water show that AFE cannot be spontaneously transferred from water into the organic solvent (and vice versa), although it is effectively “salted-out” by common electrolytes. Light scattering and reversed-phase liquid chromatography experiments carried out on the aqueous solution of AFE suggest for the aggregates an average diameter of 120 nm.openANGELINI G.; DE MARIA P.; FONTANA A.; PIERINI M.; MAGGINI M.; GASPARRINI F.; ZAPPIA G.Angelini, G.; DE MARIA, P.; Fontana, A.; Pierini, M.; Maggini, M.; Gasparrini, F.; Zappia, Giovann