Matroid and Knapsack Center Problems

In the classic $k$-center problem, we are given a metric graph, and the objective is to open $k$ nodes as centers such that the maximum distance from any vertex to its closest center is minimized. In this paper, we consider two important generalizations of $k$-center, the matroid center problem and the knapsack center problem. Both problems are motivated by recent content distribution network applications. Our contributions can be summarized as follows: 1. We consider the matroid center problem in which the centers are required to form an independent set of a given matroid. We show this problem is NP-hard even on a line. We present a 3-approximation algorithm for the problem on general metrics. We also consider the outlier version of the problem where a given number of vertices can be excluded as the outliers from the solution. We present a 7-approximation for the outlier version. 2. We consider the (multi-)knapsack center problem in which the centers are required to satisfy one (or more) knapsack constraint(s). It is known that the knapsack center problem with a single knapsack constraint admits a 3-approximation. However, when there are at least two knapsack constraints, we show this problem is not approximable at all. To complement the hardness result, we present a polynomial time algorithm that gives a 3-approximate solution such that one knapsack constraint is satisfied and the others may be violated by at most a factor of $1+\epsilon$. We also obtain a 3-approximation for the outlier version that may violate the knapsack constraint by $1+\epsilon$.Comment: A preliminary version of this paper is accepted to IPCO 201

Emergence of off-axis equilibria in a quantum vortex gas

We experimentally study the emergence of high-energy equilibrium states in a chiral vortex gas of like-circulation vortices realized within a disk-shaped atomic Bose-Einstein condensate. In contrast to the familiar triangular Abrikosov lattice, the lowest-energy state of the superfluid in a rotating frame, we observe the formation of rotating vortex equilibria that are highly disordered and have significant energy per vortex. Experimental stirring protocols realize equilibrium states at both positive and negative absolute temperatures of the vortex gas. At sufficiently high energies the system exhibits a symmetry breaking transition, resulting in an off-axis equilibrium phase that no longer shares the symmetry of the container. By initializing vortices in a non-equilibrium distribution with sufficient energy, relaxation to equilibrium is observed within experimental timescales and an off-axis equilibrium state emerges at negative absolute temperature. The observed equilibria are in close agreement with mean field theory of the microcanonical ensemble of the vortex gas.Comment: V1: 13 pages, 6 figures, 5 in main tex

Turbulent relaxation to equilibrium in a two-dimensional quantum vortex gas

We experimentally study emergence of microcanonical equilibrium states in the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. Same-sign vortices are injected into a quasi-two-dimensional disk-shaped atomic Bose-Einstein condensate using a range of mechanical stirring protocols. The resulting long-time vortex distributions are found to be in excellent agreement with the mean-field Poisson-Boltzmann equation for the system describing the microcanonical ensemble at fixed energy H and angular momentum M. The equilibrium states are characterized by the corresponding thermodynamic variables of inverse temperature β and rotation frequency ω. We are able to realize equilibria spanning the full phase diagram of the vortex gas, including on-axis states near zero-temperature, infinite temperature, and negative absolute temperatures. At sufficiently high energies the system exhibits a symmetry breaking transition, resulting in an off-axis equilibrium phase at negative absolute temperature that no longer shares the symmetry of the container. We introduce a point vortex model with phenomenological damping and noise that is able to quantitatively reproduce the equilibration dynamics.We experimentally study emergence of microcanonical equilibrium states in the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. Same-sign vortices are injected into a quasi-two-dimensional disk-shaped atomic Bose-Einstein condensate using a range of mechanical stirring protocols. The resulting long-time vortex distributions are found to be in excellent agreement with the mean-field Poisson-Boltzmann equation for the system describing the microcanonical ensemble at fixed energy H and angular momentum M. The equilibrium states are characterized by the corresponding thermodynamic variables of inverse temperature β and rotation frequency ω. We are able to realize equilibria spanning the full phase diagram of the vortex gas, including on-axis states near zero-temperature, infinite temperature, and negative absolute temperatures. At sufficiently high energies the system exhibits a symmetry breaking transition, resulting in an off-axis equilibrium phase at negative absolute temperature that no longer shares the symmetry of the container. We introduce a point vortex model with phenomenological damping and noise that is able to quantitatively reproduce the equilibration dynamics

Predicting crop yields and soil‐plant nitrogen dynamics in the US Corn Belt

We used the Agricultural Production Systems sIMulator (APSIM) to predict and explain maize and soybean yields, phenology, and soil water and nitrogen (N) dynamics during the growing season in Iowa, USA. Historical, current and forecasted weather data were used to drive simulations, which were released in public four weeks after planting. In this paper, we (1) describe the methodology used to perform forecasts; (2) evaluate model prediction accuracy against data collected from 10 locations over four years; and (3) identify inputs that are key in forecasting yields and soil N dynamics. We found that the predicted median yield at planting was a very good indicator of end‐of‐season yields (relative root mean square error [RRMSE] of ∼20%). For reference, the prediction at maturity, when all the weather was known, had a RRMSE of 14%. The good prediction at planting time was explained by the existence of shallow water tables, which decreased model sensitivity to unknown summer precipitation by 50–64%. Model initial conditions and management information accounted for one‐fourth of the variation in maize yield. End of season model evaluations indicated that the model simulated well crop phenology (R2 = 0.88), root depth (R2 = 0.83), biomass production (R2 = 0.93), grain yield (R2 = 0.90), plant N uptake (R2 = 0.87), soil moisture (R2 = 0.42), soil temperature (R2 = 0.93), soil nitrate (R2 = 0.77), and water table depth (R2 = 0.41). We concluded that model set‐up by the user (e.g. inclusion of water table), initial conditions, and early season measurements are very important for accurate predictions of soil water, N and crop yields in this environment

Geology, sulfide geochemistry and supercritical venting at the Beebe Hydrothermal Vent Field, Cayman Trough

The Beebe Vent Field (BVF) is the world's deepest known hydrothermal system, at 4960m below sea level. Located on the Mid-Cayman Spreading Centre, Caribbean, the BVF hosts high temperature (∼401°C) ‘black smoker' vents that build Cu, Zn and Au-rich sulphide mounds and chimneys. The BVF is highly gold-rich, with Au values up to 93 ppm and an average Au:Ag ratio of 0.15. Gold precipitation is directly associated with diffuse flow through ‘beehive' chimneys. Significant mass-wasting of sulphide material at the BVF, accompanied by changes in metal content, results in metaliferous talus and sediment deposits. Situated on very thin (2-3km thick) oceanic crust, at an ultraslow spreading centre, the hydrothermal system circulates fluids to a depth of ∼1.8km in a basement that is likely to include a mixture of both mafic and ultramafic lithologies. We suggest hydrothermal interaction with chalcophile-bearing sulphides in the mantle rocks, together with precipitation of Au in beehive chimney structures, has resulted in the formation of a Au-rich volcanogenic massive sulphide (VMS) deposit. With its spatial distribution of deposit materials and metal contents, the BVF represents a modern day analogue for basalt hosted, Au-rich VMS systems. This article is protected by copyright. All rights reserved

Enamel thickness variation in the deciduous dentition of extant large-bodied hominoids

Objectives: Enamel thickness features prominently in hominoid evolutionary studies. To date, however, studies of enamel thickness in humans, great apes, and their fossil relatives have focused on the permanent molar row. Comparatively little research effort has been devoted to tissue proportions within deciduous teeth. Here we attempt to fill this gap by documenting enamel thickness variation in the deciduous dentition of extant large‐bodied hominoids. Materials and methods: We used microcomputed tomography to image dental tissues in 80 maxillary and 78 mandibular deciduous premolars of Homo sapiens, Pan troglodytes, Gorilla, and Pongo. Two‐dimensional virtual sections were created from the image volumes to quantify average (AET) and relative (RET) enamel thickness, as well as its distribution across the crown. Results: Our results reveal no significant differences in enamel thickness among the great apes. Unlike the pattern present in permanent molars, Pongo does not stand out as having relatively thicker‐enameled deciduous premolars than P. troglodytes and Gorilla. Humans, on the other hand, possess significantly thicker deciduous premolar enamel in comparison to great apes. Following expectations from masticatory biomechanics, we also find that the “functional” side (protocone, protoconid) of deciduous premolars generally possesses thicker enamel than the “nonfunctional” side. Discussion: Our study lends empirical support to anecdotal observations that patterns of AET and RET observed for permanent molars of large‐bodied apes do not apply to deciduous premolars. By documenting enamel thickness variation in hominoid deciduous teeth, this study provides the comparative context to interpret rates and patterns of wear of deciduous teeth and their utility in life history reconstructions

Melanesian mtDNA Complexity

Melanesian populations are known for their diversity, but it has been hard to grasp the pattern of the variation or its underlying dynamic. Using 1,223 mitochondrial DNA (mtDNA) sequences from hypervariable regions 1 and 2 (HVR1 and HVR2) from 32 populations, we found the among-group variation is structured by island, island size, and also by language affiliation. The more isolated inland Papuan-speaking groups on the largest islands have the greatest distinctions, while shore dwelling populations are considerably less diverse (at the same time, within-group haplotype diversity is less in the most isolated groups). Persistent differences between shore and inland groups in effective population sizes and marital migration rates probably cause these differences. We also add 16 whole sequences to the Melanesian mtDNA phylogenies. We identify the likely origins of a number of the haplogroups and ancient branches in specific islands, point to some ancient mtDNA connections between Near Oceania and Australia, and show additional Holocene connections between Island Southeast Asia/Taiwan and Island Melanesia with branches of haplogroup E. Coalescence estimates based on synonymous transitions in the coding region suggest an initial settlement and expansion in the region at ∼30–50,000 years before present (YBP), and a second important expansion from Island Southeast Asia/Taiwan during the interval ∼3,500–8,000 YBP. However, there are some important variance components in molecular dating that have been overlooked, and the specific nature of ancestral (maternal) Austronesian influence in this region remains unresolved

A Population of Gamma-Ray Millisecond Pulsars Seen with the Fermi Large Area Telescope

Gamma-Ray Pulsar Bonanza Most of the pulsars we know about were detected through their radio emission; a few are known to pulse gamma rays but were first detected at other wavelengths (see the Perspective by Halpern ). Using the Fermi Gamma-Ray Space Telescope, Abdo et al. (p. 840 , published online 2 July; see the cover) report the detection of 16 previously unknown pulsars based on their gamma-ray emission alone. Thirteen of these coincide with previously unidentified gamma-ray sources, solving the 30-year-old mystery of their identities. Pulsars are fast-rotating neutron stars. With time they slow down and cease to radiate; however, if they are in a binary system, they can have their spin rates increased by mass transfer from their companion stars, starting a new life as millisecond pulsars. In another study, Abdo et al. (p. 845 ) report the detection of gamma-ray emission from the globular cluster 47 Tucanae, which is coming from an ensemble of millisecond pulsars in the cluster's core. The data imply that there are up to 60 millisecond pulsars in 47 Tucanae, twice as many as predicted by radio observations. In a further companion study, Abdo et al. (p. 848 , published online 2 July) searched Fermi Large Area Telescope data for pulsations from all known millisecond pulsars outside of stellar clusters, finding gamma-ray pulsations for eight of them. Their properties resemble those of other gamma-ray pulsars, suggesting that they share the same basic emission mechanism. Indeed, both sets of pulsars favor emission models in which the gamma rays are produced in the outer magnetosphere of the neutron star

Basic science232. Certolizumab pegol prevents pro-inflammatory alterations in endothelial cell function

Background: Cardiovascular disease is a major comorbidity of rheumatoid arthritis (RA) and a leading cause of death. Chronic systemic inflammation involving tumour necrosis factor alpha (TNF) could contribute to endothelial activation and atherogenesis. A number of anti-TNF therapies are in current use for the treatment of RA, including certolizumab pegol (CZP), (Cimzia ®; UCB, Belgium). Anti-TNF therapy has been associated with reduced clinical cardiovascular disease risk and ameliorated vascular function in RA patients. However, the specific effects of TNF inhibitors on endothelial cell function are largely unknown. Our aim was to investigate the mechanisms underpinning CZP effects on TNF-activated human endothelial cells. Methods: Human aortic endothelial cells (HAoECs) were cultured in vitro and exposed to a) TNF alone, b) TNF plus CZP, or c) neither agent. Microarray analysis was used to examine the transcriptional profile of cells treated for 6 hrs and quantitative polymerase chain reaction (qPCR) analysed gene expression at 1, 3, 6 and 24 hrs. NF-κB localization and IκB degradation were investigated using immunocytochemistry, high content analysis and western blotting. Flow cytometry was conducted to detect microparticle release from HAoECs. Results: Transcriptional profiling revealed that while TNF alone had strong effects on endothelial gene expression, TNF and CZP in combination produced a global gene expression pattern similar to untreated control. The two most highly up-regulated genes in response to TNF treatment were adhesion molecules E-selectin and VCAM-1 (q 0.2 compared to control; p > 0.05 compared to TNF alone). The NF-κB pathway was confirmed as a downstream target of TNF-induced HAoEC activation, via nuclear translocation of NF-κB and degradation of IκB, effects which were abolished by treatment with CZP. In addition, flow cytometry detected an increased production of endothelial microparticles in TNF-activated HAoECs, which was prevented by treatment with CZP. Conclusions: We have found at a cellular level that a clinically available TNF inhibitor, CZP reduces the expression of adhesion molecule expression, and prevents TNF-induced activation of the NF-κB pathway. Furthermore, CZP prevents the production of microparticles by activated endothelial cells. This could be central to the prevention of inflammatory environments underlying these conditions and measurement of microparticles has potential as a novel prognostic marker for future cardiovascular events in this patient group. Disclosure statement: Y.A. received a research grant from UCB. I.B. received a research grant from UCB. S.H. received a research grant from UCB. All other authors have declared no conflicts of interes