Sales and Promotions: A More General Model

We embed the Varian (1980) model in a broader setting that considers how switcher/loyal customer segments are determined. Generally, customer acquisition is deterministic while pricing is randomized. The equilibrium outcome depends on the timing of customer acquisition relative to pricing. If sellers acquire customers before setting prices, the unique equilibrium is asymmetric. If sellers acquire customers and set prices simultaneously, the unique equilibrium is symmetric. Our results provide a fundamental justification for previous analyses that variously assumed the outcome to be asymmetric or symmetric. The comparative statics for the asymmetric and symmetric equilibria are identical.competition, pricing, customer acquisition

Three-dimensional general relativistic hydrodynamics II: long-term dynamics of single relativistic stars

This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The tests involve single non-rotating stars in stable equilibrium, non-rotating stars undergoing radial and quadrupolar oscillations, non-rotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, non-rotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasi-radial oscillations. The numerical evolutions have been carried out in full general relativity using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing (HRSC) treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.Comment: 19 pages, 17 figure

Sensitivity of global soil carbon stocks to combined nutrient enrichment

Soil stores approximately twice as much carbon as the atmosphere and fluctuations in the size of the soil carbon pool directly influence climate conditions. We used the Nutrient Network global change experiment to examine how anthropogenic nutrient enrichment might influence grassland soil carbon storage at a global scale. In isolation, enrichment of nitrogen and phosphorous had minimal impacts on soil carbon storage. However, when these nutrients were added in combination with potassium and micronutrients, soil carbon stocks changed considerably, with an average increase of 0.04 KgCm−2 year−1 (standard deviation 0.18 KgCm−2 year−1). These effects did not correlate with changes in primary productivity, suggesting that soil carbon decomposition may have been restricted. Although nutrient enrichment caused soil carbon gains most dry, sandy regions, considerable absolute losses of soil carbon may occur in high‐latitude regions that store the majority of the world's soil carbon. These mechanistic insights into the sensitivity of grassland carbon stocks to nutrient enrichment can facilitate biochemical modelling efforts to project carbon cycling under future climate scenarios

Associations of common breast cancer susceptibility alleles with risk of breast cancer subtypes in BRCA1 and BRCA2 mutation carriers

Introduction: More than 70 common alleles are known to be involved in breast cancer (BC) susceptibility, and several exhibit significant heterogeneity in their associations with different BC subtypes. Although there are differences in the association patterns between BRCA1 and BRCA2 mutation carriers and the general population for several loci, no study has comprehensively evaluated the associations of all known BC susceptibility alleles with risk of BC subtypes in BRCA1 and BRCA2 carriers. Methods: We used data from 15,252 BRCA1 and 8,211 BRCA2 carriers to analyze the associations between approximately 200,000 genetic variants on the iCOGS array and risk of BC subtypes defined by estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor 2 (HER2) and triple-negative- (TN) status; morphologic subtypes; histological grade; and nodal involvement. Results: The estimated BC hazard ratios (HRs) for the 74 known BC alleles in BRCA1 carriers exhibited moderate correlations with the corresponding odds ratios from the general population. However, their associations with ER-positive BC in BRCA1 carriers were more consistent with the ER-positive as

Assessing associations between the AURKAHMMR-TPX2-TUBG1 functional module and breast cancer risk in BRCA1/2 mutation carriers

While interplay between BRCA1 and AURKA-RHAMM-TPX2-TUBG1 regulates mammary epithelial polarization, common genetic variation in HMMR (gene product RHAMM) may be associated with risk of breast cancer in BRCA1 mutation carriers. Following on these observations, we further assessed the link between the AURKA-HMMR-TPX2-TUBG1 functional module and risk of breast cancer in BRCA1 or BRCA2 mutation carriers. Forty-one single nucleotide polymorphisms (SNPs) were genotyped in 15,252 BRCA1 and 8,211 BRCA2 mutation carriers and subsequently analyzed using a retrospective likelihood appr

Techniques for measuring aerosol attenuation using the Central Laser Facility at the Pierre Auger Observatory

The Pierre Auger Observatory in Malargüe, Argentina, is designed to study the properties of ultra-high energy cosmic rays with energies above 10(18) eV. It is a hybrid facility that employs a Fluorescence Detector to perform nearly calorimetric measurements of Extensive Air Shower energies. To obtain reliable calorimetric information from the FD, the atmospheric conditions at the observatory need to be continuously monitored during data acquisition. In particular, light attenuation due to aerosols is an important atmospheric correction. The aerosol concentration is highly variable, so that the aerosol attenuation needs to be evaluated hourly. We use light from the Central Laser Facility, located near the center of the observatory site, having an optical signature comparable to that of the highest energy showers detected by the FD. This paper presents two procedures developed to retrieve the aerosol attenuation of fluorescence light from CLF laser shots. Cross checks between the two methods demonstrate that results from both analyses are compatible, and that the uncertainties are well understood. The measurements of the aerosol attenuation provided by the two procedures are currently used at the Pierre Auger Observatory to reconstruct air shower data

National identity predicts public health support during a global pandemic

Changing collective behaviour and supporting non-pharmaceutical interventions is an important component in mitigating virus transmission during a pandemic. In a large international collaboration (Study 1, N = 49,968 across 67 countries), we investigated self-reported factors associated with public health behaviours (e.g., spatial distancing and stricter hygiene) and endorsed public policy interventions (e.g., closing bars and restaurants) during the early stage of the COVID-19 pandemic (April-May 2020). Respondents who reported identifying more strongly with their nation consistently reported greater engagement in public health behaviours and support for public health policies. Results were similar for representative and non-representative national samples. Study 2 (N = 42 countries) conceptually replicated the central finding using aggregate indices of national identity (obtained using the World Values Survey) and a measure of actual behaviour change during the pandemic (obtained from Google mobility reports). Higher levels of national identification prior to the pandemic predicted lower mobility during the early stage of the pandemic (r = −0.40). We discuss the potential implications of links between national identity, leadership, and public health for managing COVID-19 and future pandemics.publishedVersio

Expanding the clinical phenotype of individuals with a 3-bp in-frame deletion of the NF1 gene (c.2970_2972del): an update of genotype–phenotype correlation

Purpose: Neurofibromatosis type 1 (NF1) is characterized by a highly variable clinical presentation, but almost all NF1-affected adults present with cutaneous and/or subcutaneous neurofibromas. Exceptions are individuals heterozygous for the NF1 in-frame deletion, c.2970_2972del (p.Met992del), associated with a mild phenotype without any externally visible tumors. Methods: A total of 135 individuals from 103 unrelated families, all carrying the constitutional NF1 p.Met992del pathogenic variant and clinically assessed using the same standardized phenotypic checklist form, were included in this study. Results: None of the individuals had externally visible plexiform or histopathologically confirmed cutaneous or subcutaneous neurofibromas. We did not identify any complications, such as symptomatic optic pathway gliomas (OPGs) or symptomatic spinal neurofibromas; however, 4.8% of individuals had nonoptic brain tumors, mostly low-grade and asymptomatic, and 38.8% had cognitive impairment/learning disabilities. In an individual with the NF1 constitutional c.2970_2972del and three astrocytomas, we provided proof that all were NF1-associated tumors given loss of heterozygosity at three intragenic NF1 microsatellite markers and c.2970_297

An Indication of Anisotropy in Arrival Directions of Ultra-high-energy Cosmic Rays through Comparison to the Flux Pattern of Extragalactic Gamma-Ray Sources

A new analysis of the data set from the Pierre Auger Observatory provides evidence for anisotropy in the arrival directions of ultra-high-energy cosmic rays on an intermediate angular scale, which is indicative of excess arrivals from strong, nearby sources. The data consist of 5514 events above 20 EeV with zenith angles up to 80 degrees. recorded before 2017 April 30. Sky models have been created for two distinct populations of extragalactic gamma-ray emitters: active galactic nuclei from the second catalog of hard Fermi-LAT sources (2FHL) and starburst galaxies from a sample that was examined with Fermi-LAT. Flux-limited samples, which include all types of galaxies from the Swift-BAT and 2MASS surveys, have been investigated for comparison. The sky model of cosmic-ray density constructed using each catalog has two free parameters, the fraction of events correlating with astrophysical objects, and an angular scale characterizing the clustering of cosmic rays around extragalactic sources. A maximum-likelihood ratio test is used to evaluate the best values of these parameters and to quantify the strength of each model by contrast with isotropy. It is found that the starburst model fits the data better than the hypothesis of isotropy with a statistical significance of 4.0 sigma, the highest value of the test statistic being for energies above 39 EeV. The three alternative models are favored against isotropy with 2.7 sigma-3.2 sigma significance. The origin of the indicated deviation from isotropy is examined and prospects for more sensitive future studies are discussed

Inferences on mass composition and tests of hadronic interactions from 0.3 to 100 EeV using the water-Cherenkov detectors of the Pierre Auger Observatory

We present a new method for probing the hadronic interaction models at ultrahigh energy and extracting details about mass composition. This is done using the time profiles of the signals recorded with the water-Cherenkov detectors of the Pierre Auger Observatory. The profiles arise from a mix of the muon and electromagnetic components of air showers. Using the risetimes of the recorded signals, we define a new parameter, which we use to compare our observations with predictions from simulations. We find, first, inconsistencies between our data and predictions over a greater energy range and with substantially more events than in previous studies. Second, by calibrating the new parameter with fluorescence measurements from observations made at the Auger Observatory, we can infer the depth of shower maximum Xmax for a sample of over 81,000 events extending from 0.3 to over 100 EeV. Above 30 EeV, the sample is nearly 14 times larger than what is currently available from fluorescence measurements and extending the covered energy range by half a decade. The energy dependence of ?Xmaxcopyright is compared to simulations and interpreted in terms of the mean of the logarithmic mass. We find good agreement with previous work and extend the measurement of the mean depth of shower maximum to greater energies than before, reducing significantly the statistical uncertainty associated with the inferences about mass composition