A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem

The clustered planarity problem (c-planarity) asks whether a hierarchically clustered graph admits a planar drawing such that the clusters can be nicely represented by regions. We introduce the cd-tree data structure and give a new characterization of c-planarity. It leads to efficient algorithms for c-planarity testing in the following cases. (i) Every cluster and every co-cluster (complement of a cluster) has at most two connected components. (ii) Every cluster has at most five outgoing edges. Moreover, the cd-tree reveals interesting connections between c-planarity and planarity with constraints on the order of edges around vertices. On one hand, this gives rise to a bunch of new open problems related to c-planarity, on the other hand it provides a new perspective on previous results.Comment: 17 pages, 2 figure

Advances on Testing C-Planarity of Embedded Flat Clustered Graphs

We show a polynomial-time algorithm for testing c-planarity of embedded flat clustered graphs with at most two vertices per cluster on each face.Comment: Accepted at GD '1

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

Star-Forming, Rotating Spheroidal Galaxies in the GAMA and SAMI Surveys

The Galaxy And Mass Assembly (GAMA) survey has morphologically identified a class of ‘Little Blue Spheroid’ (LBS) galaxies whose relationship to other classes of galaxies we now examine in detail. Considering a sample of 868 LBSs, we find that such galaxies display similar but not identical colours, specific star formation rates, stellar population ages, mass-to-light ratios, and metallicities to Sd-Irr galaxies. We also find that LBSs typically occupy environments of even lower density than those of Sd-Irr galaxies, where ∼65 per cent of LBS galaxies live in isolation. Using deep, high-resolution imaging from VST KiDS and the new Bayesian, 2D galaxy profile modelling code PROFIT, we further examine the detailed structure of LBSs and find that their Sérsic indices, sizes, and axial ratios are compatible with those of low-mass elliptical galaxies. We then examine SAMI Galaxy survey integral field emission line kinematics for a subset of 62 LBSs and find that the majority (42) of these galaxies display ordered rotation with the remainder displaying disturbed/non-ordered dynamics. Finally, we consider potential evolutionary scenarios for a population with this unusual combination of properties, concluding that LBSs are likely formed by a mixture of merger and accretion processes still recently active in low-redshift dwarf populations. We also infer that if LBS-like galaxies were subjected to quenching in a rich environment, they would plausibly resemble cluster dwarf ellipticals

Search for anomalous Wtb couplings in single top quark production in ppbar collisions at sqrt(s) = 1.96 TeV

We present new direct constraints on a general $Wtb$ interaction using data corresponding to an integrated luminosity of 5.4 fb$^{-1}$ collected by the D0 detector at the Tevatron $p\bar{p}$ collider. The standard model provides a purely left-handed vector coupling at the $Wtb$ vertex, while the most general, lowest dimension Lagrangian allows right-handed vector and left- or right-handed tensor couplings as well. We obtain precise limits on these anomalous couplings by comparing the data to the expectations from different assumptions on the $Wtb$ coupling.Comment: Submitted to Phys. Lett.

Energy dependence of ϕ meson production at forward rapidity in pp collisions at the LHC

The production of $\phi$ mesons has been studied in pp collisions at LHC energies with the ALICE detector via the dimuon decay channel in the rapidity region $2.5< y < 4$. Measurements of the differential cross section $\mathrm{d}^2\sigma /\mathrm{d}y \mathrm{d}p_{\mathrm {T}}$ are presented as a function of the transverse momentum ($p_{\mathrm {T}}$) at the center-of-mass energies $\sqrt{s}=5.02$, 8 and 13 TeV and compared with the ALICE results at midrapidity. The differential cross sections at $\sqrt{s}=5.02$ and 13 TeV are also studied in several rapidity intervals as a function of $p_{\mathrm {T}}$, and as a function of rapidity in three $p_{\mathrm {T}}$ intervals. A hardening of the $p_{\mathrm {T}}$-differential cross section with the collision energy is observed, while, for a given energy, $p_{\mathrm {T}}$ spectra soften with increasing rapidity and, conversely, rapidity distributions get slightly narrower at increasing $p_{\mathrm {T}}$. The new results, complementing the published measurements at $\sqrt{s}=2.76$ and 7 TeV, allow one to establish the energy dependence of $\phi$ meson production and to compare the measured cross sections with phenomenological models. None of the considered models manages to describe the evolution of the cross section with $p_{\mathrm {T}}$ and rapidity at all the energies.publishedVersio

Multiplicity dependence of inclusive J/psi production at midrapidity in pp collisions at root s=13 TeV

Measurements of the inclusive J/psi yield as a function of charged-particle pseudorapidity density dN(ch)/d eta in pp collisions at root s = 13 TeV with ALICE at the LHC are reported. The J/psi meson yield is measured at midrapidity (vertical bar y vertical bar <0.9) in the dielectron channel, for events selected based on the charged-particle multiplicity at midrapidity (vertical bar eta vertical bar <1) and at forward rapidity (-3.7 <eta <-1.7 and 2.8 <eta <5.1); both observables are normalized to their corresponding averages in minimum bias events. The increase of the normalized J/psi yield with normalized dN(ch)/d eta is significantly stronger than linear and dependent on the transverse momentum. The data are compared to theoretical predictions, which describe the observed trends well, albeit not always quantitatively. (C) 2020 European Organization for Nuclear Research. Published by Elsevier B.V.Peer reviewe

The SAMI Galaxy Survey: cubism and covariance, putting round pegs into square holes

We present a methodology for the regularization and combination of sparse sampled and irregularly gridded observations from fibre-optic multiobject integral field spectroscopy. The approach minimizes interpolation and retains image resolution on combining subpixel dithered data. We discuss the methodology in the context of the Sydney-AAO multiobject integral field spectrograph (SAMI) Galaxy Survey underway at the Anglo-Australian Telescope. The SAMI instrument uses 13 fibre bundles to perform high-multiplex integral field spectroscopy across a 1° diameter field of view. The SAMI Galaxy Survey is targeting ~3000 galaxies drawn from the full range of galaxy environments. We demonstrate the subcritical sampling of the seeing and incomplete fill factor for the integral field bundles results in only a 10 per cent degradation in the final image resolution recovered. We also implement a new methodology for tracking covariance between elements of the resulting data cubes which retains 90 per cent of the covariance information while incurring only a modest increase in the survey data volume

Constraints on the cosmic expansion history from GWTC–3

We use 47 gravitational wave sources from the Third LIGO–Virgo–Kamioka Gravitational Wave Detector Gravitational Wave Transient Catalog (GWTC–3) to estimate the Hubble parameter H(z), including its current value, the Hubble constant H0. Each gravitational wave (GW) signal provides the luminosity distance to the source, and we estimate the corresponding redshift using two methods: the redshifted masses and a galaxy catalog. Using the binary black hole (BBH) redshifted masses, we simultaneously infer the source mass distribution and H(z). The source mass distribution displays a peak around 34 M⊙, followed by a drop-off. Assuming this mass scale does not evolve with the redshift results in a H(z) measurement, yielding ${H}_{0}={68}_{-8}^{+12}\,\mathrm{km}\ \,\ {{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$ (68% credible interval) when combined with the H0 measurement from GW170817 and its electromagnetic counterpart. This represents an improvement of 17% with respect to the H0 estimate from GWTC–1. The second method associates each GW event with its probable host galaxy in the catalog GLADE+, statistically marginalizing over the redshifts of each event's potential hosts. Assuming a fixed BBH population, we estimate a value of ${H}_{0}={68}_{-6}^{+8}\,\mathrm{km}\ \,\ {{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$ with the galaxy catalog method, an improvement of 42% with respect to our GWTC–1 result and 20% with respect to recent H0 studies using GWTC–2 events. However, we show that this result is strongly impacted by assumptions about the BBH source mass distribution; the only event which is not strongly impacted by such assumptions (and is thus informative about H0) is the well-localized event GW190814

Efficient c-planarity testing for embedded flat clustered graphs with small faces

Let C be a clustered graph and suppose that the planar embedding of its underlying graph is fixed. Is testing the c-planarity of C easier than in the variable embedding setting? In this paper we give a first contribution towards answering the above question. Namely, we characterize c-planar embedded flat clustered graphs with at most five vertices per face and give an efficient testing algorithm for such graphs. The results are based on a more general methodology that sheds new light on the c-planarity testing problem