Centroidal bases in graphs

We introduce the notion of a centroidal locating set of a graph $G$, that is, a set $L$ of vertices such that all vertices in $G$ are uniquely determined by their relative distances to the vertices of $L$. A centroidal locating set of $G$ of minimum size is called a centroidal basis, and its size is the centroidal dimension $CD(G)$. This notion, which is related to previous concepts, gives a new way of identifying the vertices of a graph. The centroidal dimension of a graph $G$ is lower- and upper-bounded by the metric dimension and twice the location-domination number of $G$, respectively. The latter two parameters are standard and well-studied notions in the field of graph identification. We show that for any graph $G$ with $n$ vertices and maximum degree at least~2, $(1+o(1))\frac{\ln n}{\ln\ln n}\leq CD(G) \leq n-1$. We discuss the tightness of these bounds and in particular, we characterize the set of graphs reaching the upper bound. We then show that for graphs in which every pair of vertices is connected via a bounded number of paths, $CD(G)=\Omega\left(\sqrt{|E(G)|}\right)$, the bound being tight for paths and cycles. We finally investigate the computational complexity of determining $CD(G)$ for an input graph $G$, showing that the problem is hard and cannot even be approximated efficiently up to a factor of $o(\log n)$. We also give an $O\left(\sqrt{n\ln n}\right)$-approximation algorithm

Breaking down the link between luminous and dark matter in massive galaxies

We present a study on the clustering of a stellar mass selected sample of galaxies with stellar masses M*>10^10Msol at redshifts 0.4<z<2.0, taken from the Palomar Observatory Wide-field Infrared Survey. We examine the clustering properties of these stellar mass selected samples as a function of redshift and stellar mass, and find that galaxies with high stellar masses have a progressively higher clustering strength than galaxies with lower stellar masses. We also find that galaxies within a fixed stellar mass range have a higher clustering strength at higher redshifts. We further estimate the average total masses of the dark matter haloes hosting these stellar-mass selected galaxies. For all galaxies in our sample the stellar-mass-to-total-mass ratio is always lower than the universal baryonic mass fraction and the stellar-mass-to-total-mass ratio is strongly correlated with the halo masses for central galaxies, such that more massive haloes contain a lower fraction of their mass in the form of stars. The remaining baryonic mass is included partially in stars within satellite galaxies in these haloes, and as diffuse hot and warm gas. We also find that, at a fixed stellar mass, the stellar-to-total-mass ratio increases at lower redshifts. This suggests that galaxies at a fixed stellar mass form later in lower mass dark matter haloes, and earlier in massive haloes. We interpret this as a `halo downsizing' effect.Comment: Proceedings of the IAU Symposium No. 277, 2010 "Tracing the Ancestry of Galaxies on the Land of our Ancestors"; Eds. Carignan, Freeman and Combe

Perturbative expansions from Monte Carlo simulations at weak coupling: Wilson loops and the static-quark self-energy

Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative. Twisted boundary conditions are used to eliminate the effects of lattice zero modes and to suppress nonperturbative finite-volume effects due to Z(3) phases. Simulations of the Wilson gluon action are done with both periodic and twisted boundary conditions, and over a wide range of lattice volumes (from $3^4$ to $16^4$) and couplings (from $\beta \approx 9$ to $\beta \approx 60$). A high precision comparison is made between the simulation data and results from finite-volume lattice perturbation theory. The Monte Carlo results are shown to be in excellent agreement with perturbation theory through second order. New results for third-order coefficients for a number of Wilson loops and the static-quark self-energy are reported.Comment: 36 pages, 15 figures, REVTEX documen

PLoS One

Objective Immune checkpoint inhibitors (ICIs) have recently shown tremendous promise in the treatment of diverse cancers. The available data suggests that ICIs are well tolerated in terms of health-related quality of life (HRQOL) compared to other anticancer therapies. However, it appears that instruments currently used to evaluate HRQOL in this context may fail to capture important symptomatology unique to ICIs. This systematic review was designed to assess the adequacy of methods used to report HRQOL in cancer patients treated with ICIs and to identify the quality of life scales used. Method A systematic review was performed (systematic registration number: PROSPERO: CRD42019121427). A search of the PubMed, PsycINFO, PsycARTICLES, Psychology and Behavioral Sciences collection, and SocINDEX databases was carried out for publications in English and in French. Relevant databases were searched from the earliest records through to March 2019. Publications were selected if they reported on HRQOL in patients with cancer treated by ICIs. Risk of bias was scored using the Cochrane Collaboration bias assessment tool. Results Our search identified 144 publications between 2012 and 2019, of which 15 RCTs met the inclusion criteria. The results suggest that even though the overall reporting of HRQOL was deemed to be of good quality, the data available was marred by methodological aspects such as the lack of HRQOL research hypotheses and the lack of questionnaires validated for cancer patients treated with immunotherapy. Conclusion This study provides a comprehensive analysis of the current state of the art and identifies gaps in knowledge on HRQOL analysis with respect to ICIs. It also suggests avenues for further research

Galactic conformity and central/satellite quenching, from the satellite profiles of M* galaxies at 0.4 < z < 1.9 in the UKIDSS UDS

We explore the redshift evolution of a curious correlation between the star formation properties of central galaxies and their satellites (‘galactic conformity') at intermediate to high redshift (0.4 9.7, around central galaxies at the characteristic Schechter function mass, M ∼ M*. We fit the radial profiles of satellite number densities with simple power laws, finding slopes in the range −1.1 to −1.4 for mass-selected satellites, and −1.3 to −1.6 for passive satellites. We confirm the tendency for passive satellites to be preferentially located around passive central galaxies at 3σ significance and show that it exists to at least z ∼ 2. Meanwhile, the quenched fraction of satellites around star-forming galaxies is consistent with field galaxies of equal stellar masses. We find no convincing evidence for a redshift-dependent evolution of these trends. One simple interpretation of these results is that only passive central galaxies occupy an environment that is capable of independently shutting off star formation in satellite galaxies. By examining the satellites of higher stellar mass star-forming galaxies (log(M*/M⊙) > 11), we conclude that the origin of galactic conformity is unlikely to be exclusively due to the host dark matter halo mass. A halo-mass-independent correlation could be established by either formation bias or a more physical connection between central and satellite star formation histories. For the latter, we argue that a star formation (or active galactic nucleus) related outburst event from the central galaxy could establish a hot halo environment which is then capable of quenching both central and satellite galaxie

Number counts and clustering properties of bright Distant Red Galaxies in the UKIDSS Ultra Deep Survey Early Data Release

We describe the number counts and spatial distribution of 239 Distant Red Galaxies (DRGs), selected from the Early Data Release of the UKIDSS Ultra Deep Survey. The DRGs are identified by their very red infrared colours with (J-K)AB>1.3, selected over 0.62 sq degree to a 90% completeness limit of KAB~20.7. This is the first time a large sample of bright DRGs has been studied within a contiguous area, and we provide the first measurements of their number counts and clustering. The population shows strong angular clustering, intermediate between those of K-selected field galaxies and optical/infrared-selected Extremely Red Galaxies. Adopting the redshift distributions determined from other recent studies, we infer a high correlation length of r0~11 h-1 Mpc. Such strong clustering could imply that our galaxies are hosted by very massive dark matter halos, consistent with the progenitors of present-day L>L* elliptical galaxies.Comment: 5 pages, 4 figures, revised version accepted to MNRAS. Higher-resolution figures available from the authors on reques