Optimal static pricing for a tree network

We study the static pricing problem for a network service provider in a loss system with a tree structure. In the network, multiple classes share a common inbound link and then have dedicated outbound links. The motivation is from a company that sells phone cards and needs to price calls to different destinations. We characterize the optimal static prices in order to maximize the steady-state revenue. We report new structural findings as well as alternative proofs for some known results. We compare the optimal static prices versus prices that are asymptotically optimal, and through a set of illustrative numerical examples we show that in certain cases the loss in revenue can be significant. Finally, we show that static prices obtained using the reduced load approximation of the blocking probabilities can be easily obtained and have near-optimal performance, which makes them more attractive for applications.Massachusetts Institute of Technology. Center for Digital BusinessUnited States. Office of Naval Research (Contract N00014-95-1-0232)United States. Office of Naval Research (Contract N00014-01-1-0146)National Science Foundation (U.S.) (Contract DMI-9732795)National Science Foundation (U.S.) (Contract DMI-0085683)National Science Foundation (U.S.) (Contract DMI-0245352

Constraint propagation equations of the 3+1 decomposition of f(R) gravity

Theories of gravity other than general relativity (GR) can explain the observed cosmic acceleration without a cosmological constant. One such class of theories of gravity is f(R). Metric f(R) theories have been proven to be equivalent to Brans-Dicke (BD) scalar-tensor gravity without a kinetic term. Using this equivalence and a 3+1 decomposition of the theory it has been shown that metric f(R) gravity admits a well-posed initial value problem. However, it has not been proven that the 3+1 evolution equations of metric f(R) gravity preserve the (hamiltonian and momentum) constraints. In this paper we show that this is indeed the case. In addition, we show that the mathematical form of the constraint propagation equations in BD-equilavent f(R) gravity and in f(R) gravity in both the Jordan and Einstein frames, is exactly the same as in the standard ADM 3+1 decomposition of GR. Finally, we point out that current numerical relativity codes can incorporate the 3+1 evolution equations of metric f(R) gravity by modifying the stress-energy tensor and adding an additional scalar field evolution equation. We hope that this work will serve as a starting point for relativists to develop fully dynamical codes for valid f(R) models.Comment: 25 pages, matches published version in CQG, references update

Massage-like stroking boosts the immune system in mice

Recent clinical evidence suggests that the therapeutic effect of massage involves the immune system and that this can be exploited as an adjunct therapy together with standard drug-based approaches. In this study, we investigated the mechanisms behind these effects exploring the immunomodulatory function of stroking as a surrogate of massage-like therapy in mice. C57/BL6 mice were stroked daily for 8 days either with a soft brush or directly with a gloved hand and then analysed for differences in their immune repertoire compared to control non-stroked mice. Our results show that hand-but not brush-stroked mice demonstrated a significant increase in thymic and splenic T cell number (p lt 0.05; p lt 0.01). These effects were not associated with significant changes in CD4/CD8 lineage commitment or activation profile. The boosting effects on T cell repertoire of massage-like therapy were associated with a decreased noradrenergic innervation of lymphoid organs and counteracted the immunosuppressive effect of hydrocortisone in vivo. Together our results in mice support the hypothesis that massage-like therapies might be of therapeutic value in the treatment of immunodeficiencies and related disorders and suggest a reduction of the inhibitory noradrenergic tone in lymphoid organs as one of the possible explanations for their immunomodulatory function

The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity waveforms for non-precessing black-hole binaries The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity waveforms for non-precessing black-hole binaries (Addendum to vol 29, 124001, 2012)

This is an Addendum for the article 2012 Class. Quantum Grav. 29 124001 A recent paper (Ajith et al 2012 Class. Quantum Grav. 29 124001) described a catalog of 56 hybrid post-Newtonian/numerical-relativity waveforms modeling the inspiral, merger and ringdown of binary black hole systems spanning a range of mass ratios and spins. This catalog has been created and validated for use in the NINJA-2 project to study the sensitivity of gravitational-wave search and parameter-estimation algorithms. The contents of this catalog are being made available for public use. This addendum describes the public release

The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity waveforms for non-precessing black-hole binaries

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search and parameter-estimation algorithms using numerically generated waveforms, and to foster closer collaboration between the numerical relativity and data analysis communities. The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions. The goal of the NINJA-2 project is to overcome these limitations with long post-Newtonian - numerical relativity hybrid waveforms, large numbers of injections, and the use of real detector data. We report on the submission requirements for the NINJA-2 project and the construction of the waveform catalog. Eight numerical relativity groups have contributed 63 hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. We summarize the techniques used by each group in constructing their submissions. We also report on the procedures used to validate these submissions, including examination in the time and frequency domains and comparisons of waveforms from different groups against each other. These procedures have so far considered only the $(\ell,m)=(2,2)$ mode. Based on these studies we judge that the hybrid waveforms are suitable for NINJA-2 studies. We note some of the plans for these investigations

Menus for Feeding Black Holes

Black holes are the ultimate prisons of the Universe, regions of spacetime where the enormous gravity prohibits matter or even light to escape to infinity. Yet, matter falling toward the black holes may shine spectacularly, generating the strongest source of radiation. These sources provide us with astrophysical laboratories of extreme physical conditions that cannot be realized on Earth. This chapter offers a review of the basic menus for feeding matter onto black holes and discusses their observational implications.Comment: 27 pages. Accepted for publication in Space Science Reviews. Also to appear in hard cover in the Space Sciences Series of ISSI "The Physics of Accretion onto Black Holes" (Springer Publisher

Searches After Gravitational-waves Using ARizona Observatories (SAGUARO): System Overview and First Results from Advanced LIGO/Virgo's Third Observing Run

We present Searches After Gravitational-waves Using ARizona Observatories (SAGUARO), a comprehensive effort dedicated to the discovery and characterization of optical counterparts to gravitational wave (GW) events. SAGUARO utilizes ground-based facilities ranging from 1.5m to 10m in diameter, located primarily in the Northern Hemisphere. We provide an overview of SAGUARO's telescopic resources, pipeline for transient detection, and database for candidate visualization. We describe SAGUARO's discovery component, which utilizes the $5$~deg$^2$ field-of-view optical imager on the Mt. Lemmon 1.5m telescope, reaching limits of $\approx 21.3$~AB mag while rapidly tiling large areas. We also describe the follow-up component of SAGUARO, used for rapid vetting and monitoring of optical candidates. With the onset of Advanced LIGO/Virgo's third observing run, we present results from the first three SAGUARO searches following the GW events S190408an, S190425z and S190426c, which serve as a valuable proof-of-concept of SAGUARO. We triggered and searched 15, 60 and 60 deg$^{2}$ respectively, 17.6, 1.4 and 41.8 hrs after the initial GW alerts. We covered 7.8, 3.0 and 5.1\% of the total probability within the GW event localizations, reaching 3$\sigma$ limits of 19.8, 21.3 and 20.8 AB mag, respectively. Although no viable counterparts associated with these events were found, we recovered 6 known transients and ruled out 5 potential candidates. We also present Large Binocular Telescope spectroscopy of PS19eq/SN2019ebq, a promising kilonova candidate that was later determined to be a supernova. With the ability to tile large areas and conduct detailed follow-up, SAGUARO represents a significant addition to GW counterpart searches.Comment: 16 pages, 7 figures, 1 table. Accepted to ApJ

Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration

The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ~100-200 solar masses, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios <= 4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters

SERENA:Particle Instrument Suite for Determining the Sun-Mercury Interaction from BepiColombo

International audienceThe ESA-JAXA BepiColombo mission to Mercury will provide simultaneous measurements from two spacecraft, offering an unprecedented opportunity to investigate magnetospheric and exospheric particle dynamics at Mercury as well as their interactions with solar wind, solar radiation, and interplanetary dust. The particle instrument suite SERENA (Search for Exospheric Refilling and Emitted Natural Abundances) is flying in space on-board the BepiColombo Mercury Planetary Orbiter (MPO) and is the only instrument for ion and neutral particle detection aboard the MPO. It comprises four independent sensors: ELENA for neutral particle flow detection, Strofio for neutral gas detection, PICAM for planetary ions observations, and MIPA, mostly for solar wind ion measurements. SERENA is managed by a System Control Unit located inside the ELENA box. In the present paper the scientific goals of this suite are described, and then the four units are detailed, as well as their major features and calibration results. Finally, the SERENA operational activities are shown during the orbital path around Mercury, with also some reference to the activities planned during the long cruise phase

Correction to: SERENA: Particle Instrument Suite for Determining the Sun-Mercury Interaction from BepiColombo

International audienc