Infall near clusters of galaxies: comparing gas and dark matter velocity profiles

We consider the dynamics in and near galaxy clusters. Gas, dark matter and galaxies are presently falling into the clusters between approximately 1 and 5 virial radii. At very large distances, beyond 10 virial radii, all matter is following the Hubble flow, and inside the virial radius the matter particles have on average zero radial velocity. The cosmological parameters are imprinted on the infall profile of the gas, however, no method exists, which allows a measurement of it. We consider the results of two cosmological simulations (using the numerical codes RAMSES and Gadget) and find that the gas and dark matter radial velocities are very similar. We derive the relevant dynamical equations, in particular the generalized hydrostatic equilibrium equation, including both the expansion of the Universe and the cosmological background. This generalized gas equation is the main new contribution of this paper. We combine these generalized equations with the results of the numerical simulations to estimate the contribution to the measured cluster masses from the radial velocity: inside the virial radius it is negligible, and inside two virial radii the effect is below 40%, in agreement the earlier analyses for DM. We point out how the infall velocity in principle may be observable, by measuring the gas properties to distance of about two virial radii, however, this is practically not possible today.Comment: 7 pages, 3 figures, to appear in MNRA

Price vs Quantity in Duopoly Supergames with Close Substitutes

We model the non-cooperative choice between quantity and price in order to stabilize collusion, through two meta-games where each firm alternatively considers its payoff in the market supergame as directly related to its own or the rival's ability to collude. In the first setting, (i) if cartel profits are evenly split, firms collude in prices irrespective of the degree of differentiation, so that initially a Prisoners' Dilemma is observed, while for very close substitutes the outcome is Pareto-efficient; (ii) if Nash bargaining is adopted, price setting is dominant when substitutability is low, while no dominant strategy exists when substitutability is high, and the game has two asymmetric equilibria. In the second setting, the Nash equilibrium is unique and Pareto-e±cient for the most part of the substitutability range, while again two asymmetric equilibria obtain when products are very close substitutes

Validity of Inflammatory Bowel Disease Diagnoses in the Danish National Patient Registry:A Population-Based Study from the North Denmark Region

PURPOSE: The Danish National Patient Registry (DNPR) is recognized for providing high-quality data. However, only a few minor studies have validated inflammatory bowel disease (IBD) diagnoses in the DNPR, reporting various degrees of validity. To pave the way for large-scale studies of IBD in Denmark, we aimed to investigate the validity of IBD among >8000 patients registered in the DNPR between 2002 and 2020 in the North Denmark Region. PATIENTS AND METHODS: To evaluate the reliability of the diagnoses in the DNPR, we initially compared all patients registered with one IBD diagnosis during 2002–2020 to a list of already verified patients in the regional IBD database GASTROBIO. Medical records on all DNPR registered patients not on the list were manually reviewed by a gastroenterologist to verify or dismiss the IBD diagnosis. Positive predictive values (PPV) were calculated. RESULTS: Of 8040 patients with at least one IBD diagnosis in DNPR, 5263 were already confirmed cases, leaving 2777 for medical record evaluation, of whom 849 had IBD. In total, 6112 were correctly registered with IBD based on one diagnosis, and 1343 were incorrectly registered, resulting in a PPV of 0.82 (95% CI, 0.81–0.83). For patients registered with at least two diagnoses, the PPV was 0.95 (95% CI, 0.95–0.96), and with at least three diagnoses, the PPV was 0.98 (95% CI, 0.98–0.99). Results were similar for UC and CD separately. Of note, the completeness of valid cases went from 6112 to 4606 (75%; 95% CI, 74%-76%) when demanding at least two registered diagnoses and to 3320 (54%; 95% CI, 53%-56%) when demanding at least three registered diagnoses. CONCLUSION: Reassuringly, the validity of IBD diagnoses in DNPR is high, especially for patients registered more than once. However, the reduced completeness when applying a true case definition of at least two registered diagnoses should be considered