On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings

We study two variants of the well-known orthogonal drawing model: (i) the smooth orthogonal, and (ii) the octilinear. Both models form an extension of the orthogonal, by supporting one additional type of edge segments (circular arcs and diagonal segments, respectively). For planar graphs of max-degree 4, we analyze relationships between the graph classes that can be drawn bendless in the two models and we also prove NP-hardness for a restricted version of the bendless drawing problem for both models. For planar graphs of higher degree, we present an algorithm that produces bi-monotone smooth orthogonal drawings with at most two segments per edge, which also guarantees a linear number of edges with exactly one segment.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Planar Drawings of Fixed-Mobile Bigraphs

A fixed-mobile bigraph G is a bipartite graph such that the vertices of one partition set are given with fixed positions in the plane and the mobile vertices of the other part, together with the edges, must be added to the drawing. We assume that G is planar and study the problem of finding, for a given k >= 0, a planar poly-line drawing of G with at most k bends per edge. In the most general case, we show NP-hardness. For k=0 and under additional constraints on the positions of the fixed or mobile vertices, we either prove that the problem is polynomial-time solvable or prove that it belongs to NP. Finally, we present a polynomial-time testing algorithm for a certain type of "layered" 1-bend drawings

Pixel and Voxel Representations of Graphs

We study contact representations for graphs, which we call pixel representations in 2D and voxel representations in 3D. Our representations are based on the unit square grid whose cells we call pixels in 2D and voxels in 3D. Two pixels are adjacent if they share an edge, two voxels if they share a face. We call a connected set of pixels or voxels a blob. Given a graph, we represent its vertices by disjoint blobs such that two blobs contain adjacent pixels or voxels if and only if the corresponding vertices are adjacent. We are interested in the size of a representation, which is the number of pixels or voxels it consists of. We first show that finding minimum-size representations is NP-complete. Then, we bound representation sizes needed for certain graph classes. In 2D, we show that, for $k$-outerplanar graphs with $n$ vertices, $\Theta(kn)$ pixels are always sufficient and sometimes necessary. In particular, outerplanar graphs can be represented with a linear number of pixels, whereas general planar graphs sometimes need a quadratic number. In 3D, $\Theta(n^2)$ voxels are always sufficient and sometimes necessary for any $n$-vertex graph. We improve this bound to $\Theta(n\cdot \tau)$ for graphs of treewidth $\tau$ and to $O((g+1)^2n\log^2n)$ for graphs of genus $g$. In particular, planar graphs admit representations with $O(n\log^2n)$ voxels

Anandamide Capacitates Bull Spermatozoa through CB1 and TRPV1 Activation

Anandamide (AEA), a major endocannabinoid, binds to cannabinoid and vanilloid receptors (CB1, CB2 and TRPV1) and affects many reproductive functions. Nanomolar levels of anandamide are found in reproductive fluids including mid-cycle oviductal fluid. Previously, we found that R(+)-methanandamide, an anandamide analogue, induces sperm releasing from bovine oviductal epithelium and the CB1 antagonist, SR141716A, reversed this effect. Since sperm detachment may be due to surface remodeling brought about by capacitation, the aim of this paper was to investigate whether anandamide at physiological concentrations could act as a capacitating agent in bull spermatozoa. We demonstrated that at nanomolar concentrations R(+)-methanandamide or anandamide induced bull sperm capacitation, whereas SR141716A and capsazepine (a TRPV1 antagonist) inhibited this induction. Previous studies indicate that mammalian spermatozoa possess the enzymatic machinery to produce and degrade their own AEA via the actions of the AEA-synthesizing phospholipase D and the fatty acid amide hydrolase (FAAH) respectively. Our results indicated that, URB597, a potent inhibitor of the FAAH, produced effects on bovine sperm capacitation similar to those elicited by exogenous AEA suggesting that this process is normally regulated by an endogenous tone. We also investigated whether anandamide is involved in bovine heparin-capacitated spermatozoa, since heparin is a known capacitating agent of bovine sperm. When the spermatozoa were incubated in the presence of R(+)-methanandamide and heparin, the percentage of capacitated spermatozoa was similar to that in the presence of R(+)-methanandamide alone. The pre-incubation with CB1 or TRPV1 antagonists inhibited heparin-induced sperm capacitation; moreover the activity of FAAH was 30% lower in heparin-capacitated spermatozoa as compared to control conditions. This suggests that heparin may increase endogenous anandamide levels. Our findings indicate that anandamide induces sperm capacitation through the activation of CB1 and TRPV1 receptors and could be involved in the same molecular pathway as heparin in bovines

Observation of B(s)0→J/ψpp¯ decays and precision measurements of the B(s)0 masses

The first observation of the decays B 0 ( s ) → J / ψ p ¯ p is reported, using proton-proton collision data corresponding to an integrated luminosity of 5.2     fb − 1 , collected with the LHCb detector. These decays are suppressed due to limited available phase space, as well as due to Okubo-Zweig-Iizuka or Cabibbo suppression. The measured branching fractions are B ( B 0 → J / ψ p ¯ p ) = [ 4.51 ± 0.40 ( stat ) ± 0.44 ( syst ) ] × 10 − 7 , B ( B 0 s → J / ψ p ¯ p ) = [ 3.58 ± 0.19 ( stat ) ± 0.39 ( syst ) ] × 10 − 6 . For the B 0 s meson, the result is much higher than the expected value of O ( 10 − 9 ) . The small available phase space in these decays also allows for the most precise single measurement of both the B 0 mass as 5279.74 ± 0.30 ( stat ) ± 0.10 ( syst )     MeV and the B 0 s mass as 5366.85 ± 0.19 ( stat ) ± 0.13 ( syst )     MeV

Observation of the decay Λ _b ⁰ → ψ(2S)pπ⁻

International audienceThe Cabibbo-suppressed decay Λ$_{b}^{0}$  → ψ(2S)pπ$^{−}$ is observed for the first time using a data sample collected by the LHCb experiment in proton-proton collisions corresponding to 1.0, 2.0 and 1.9 fb$^{−1}$ of integrated luminosity at centre-of-mass energies of 7, 8 and 13 TeV, respectively. The ψ(2S) mesons are reconstructed in the μ$^{+}$μ$^{−}$ final state. The branching fraction with respect to that of the Λ$_{b}^{0}$  → ψ(2S)pK$^{−}$ decay mode is measured to b

Search for CP violation in Λb0→pK− and Λb0→pπ− decays

A search for CP violation in Λb0→pK− and Λb0→pπ− decays is presented using a sample of pp collisions collected with the LHCb detector and corresponding to an integrated luminosity of 3.0fb−1. The CP -violating asymmetries are measured to be ACPpK−=−0.020±0.013±0.019 and ACPpπ−=−0.035±0.017±0.020, and their difference ACPpK−−ACPpπ−=0.014±0.022±0.010, where the first uncertainties are statistical and the second systematic. These are the most precise measurements of such asymmetries to date

Evidence for an nc(1S)ff- resonance in B0 yc(1S)K+ decays

A Dalitz plot analysis of B0→ηc(1S)K+π- decays is performed using data samples of pp collisions collected with the LHCb detector at centre-of-mass energies of s=7,8 and 13TeV , corresponding to a total integrated luminosity of 4.7fb-1 . A satisfactory description of the data is obtained when including a contribution representing an exotic ηc(1S)π- resonant state. The significance of this exotic resonance is more than three standard deviations, while its mass and width are 4096±20-22+18MeV and 152±58-35+60MeV , respectively. The spin-parity assignments JP=0+ and JP=1- are both consistent with the data. In addition, the first measurement of the B0→ηc(1S)K+π- branching fraction is performed and gives B(B0→ηc(1S)K+π-)=(5.73±0.24±0.13±0.66)×10-4, where the first uncertainty is statistical, the second systematic, and the third is due to limited knowledge of external branching fractions

Model-independent measurement of mixing parameters in D0 → K S 0 π+π− decays

The first model-independent measurement of the charm mixing parameters in the decay D 0 → K S 0 π + π − is reported, using a sample of pp collision data recorded by the LHCb experiment, corresponding to an integrated luminosity of 1.0 fb−1 at a centre-of-mass energy of 7 TeV. The measured values are x=(−0.86±0.53±0.17)×10−2,y=(+0.03±0.46±0.13)×10−2, x=(−0.86±0.53±0.17)×10−2,y=(+0.03±0.46±0.13)×10−2, where the first uncertainties are statistical and include small contributions due to the external input for the strong phase measured by the CLEO collaboration, and the second uncertainties are systematic

Measurement of the electron reconstruction efficiency at LHCb

The single electron track-reconstruction efficiency is calibrated using a sample corresponding to 1.3 fb−1 of pp collision data recorded with the LHCb detector in 2017. This measurement exploits B+→ J/ψ(e+e−)K+ decays, where one of the electrons is fully reconstructed and paired with the kaon, while the other electron is reconstructed using only the information of the vertex detector. Despite this partial reconstruction, kinematic and geometric constraints allow the B meson mass to be reconstructed and the signal to be well separated from backgrounds. This in turn allows the electron reconstruction efficiency to be measured by matching the partial track segment found in the vertex detector to tracks found by LHCb's regular reconstruction algorithms. The agreement between data and simulation is evaluated, and corrections are derived for simulated electrons in bins of kinematics. These correction factors allow LHCb to measure branching fractions involving single electrons with a systematic uncertainty below 1%