Assortment optimisation under a general discrete choice model: A tight analysis of revenue-ordered assortments

The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are constructed by fixing a threshold revenue $\pi$ and then choosing all products with revenue at least $\pi$. This is known as the revenue-ordered assortments strategy. In this paper we study the approximation guarantees provided by revenue-ordered assortments when customers are rational in the following sense: the probability of selecting a specific product from the set being offered cannot increase if the set is enlarged. This rationality assumption, known as regularity, is satisfied by almost all discrete choice models considered in the revenue management and choice theory literature, and in particular by random utility models. The bounds we obtain are tight and improve on recent results in that direction, such as for the Mixed Multinomial Logit model by Rusmevichientong et al. (2014). An appealing feature of our analysis is its simplicity, as it relies only on the regularity condition. We also draw a connection between assortment optimisation and two pricing problems called unit demand envy-free pricing and Stackelberg minimum spanning tree: These problems can be restated as assortment problems under discrete choice models satisfying the regularity condition, and moreover revenue-ordered assortments correspond then to the well-studied uniform pricing heuristic. When specialised to that setting, the general bounds we establish for revenue-ordered assortments match and unify the best known results on uniform pricing.Comment: Minor changes following referees' comment

Combination of searches for Higgs boson pairs in pp collisions at s=13TeV with the ATLAS detector

This letter presents a combination of searches for Higgs boson pair production using up to 36.1 fb−1 of proton–proton collision data at a centre-of-mass energy s=13 TeV recorded with the ATLAS detector at the LHC. The combination is performed using six analyses searching for Higgs boson pairs decaying into the bb¯bb¯, bb¯W+W−, bb¯τ+τ−, W+W−W+W−, bb¯γγ and W+W−γγ final states. Results are presented for non-resonant and resonant Higgs boson pair production modes. No statistically significant excess in data above the Standard Model predictions is found. The combined observed (expected) limit at 95% confidence level on the non-resonant Higgs boson pair production cross-section is 6.9 (10) times the predicted Standard Model cross-section. Limits are also set on the ratio (κλ) of the Higgs boson self-coupling to its Standard Model value. This ratio is constrained at 95% confidence level in observation (expectation) to −5.0<κλ<12.0 (−5.8<κλ<12.0). In addition, limits are set on the production of narrow scalar resonances and spin-2 Kaluza–Klein Randall–Sundrum gravitons. Exclusion regions are also provided in the parameter space of the habemus Minimal Supersymmetric Standard Model and the Electroweak Singlet Model

Multiplicity Distributions and Charged-neutral Fluctuations

Results from the multiplicity distributions of inclusive photons and charged particles, scaling of particle multiplicities, event-by-event multiplicity fluctuations, and charged-neutral fluctuations in 158$\cdot A$ GeV Pb+Pb collisions are presented and discussed. A scaling of charged particle multiplicity as $N_{part}^{1.07\pm 0.05}$ and photons as $N_{part}^{1.12\pm 0.03}$ have been observed, indicating violation of naive wounded nucleon model. The analysis of localized charged-neutral fluctuation indicates a model-independent demonstration of non-statistical fluctuations in both charged particles and photons in limited azimuthal regions. However, no correlated charged-neutral fluctuations are observed.Comment: Talk given at the International Symposium on Nuclear Physics (ISNP-2000), Mumbai, India, 18-22 Dec 2000, Proceedings to be published in Pramana, Journal of Physic

Search for flavour-changing neutral currents in processes with one top quark and a photon using 81 fb−1 of pp collisions at s=13TeV with the ATLAS experiment

A search for flavour-changing neutral current (FCNC) events via the coupling of a top quark, a photon, and an up or charm quark is presented using 81 fb−1 of proton–proton collision data taken at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC. Events with a photon, an electron or muon, a b-tagged jet, and missing transverse momentum are selected. A neural network based on kinematic variables differentiates between events from signal and background processes. The data are consistent with the background-only hypothesis, and limits are set on the strength of the tqγ coupling in an effective field theory. These are also interpreted as 95% CL upper limits on the cross section for FCNC tγ production via a left-handed (right-handed) tuγ coupling of 36 fb (78 fb) and on the branching ratio for t→γu of 2.8×10−5 (6.1×10−5). In addition, they are interpreted as 95% CL upper limits on the cross section for FCNC tγ production via a left-handed (right-handed) tcγ coupling of 40 fb (33 fb) and on the branching ratio for t→γc of 22×10−5 (18×10−5)

Measurement of the Z(→ ℓ + ℓ −)γ production cross-section in pp collisions at √s = 13 TeV with the ATLAS detector

The production of a prompt photon in association with a Z boson is studied in proton-proton collisions at a centre-of-mass energy s = 13 TeV. The analysis uses a data sample with an integrated luminosity of 139 fb−1 collected by the ATLAS detector at the LHC from 2015 to 2018. The production cross-section for the process pp → ℓ+ℓ−γ + X (ℓ = e, μ) is measured within a fiducial phase-space region defined by kinematic requirements on the photon and the leptons, and by isolation requirements on the photon. An experimental precision of 2.9% is achieved for the fiducial cross-section. Differential cross-sections are measured as a function of each of six kinematic variables characterising the ℓ+ℓ−γ system. The data are compared with theoretical predictions based on next-to-leading-order and next-to-next-to-leading-order perturbative QCD calculations. The impact of next-to-leading-order electroweak corrections is also considered. [Figure not available: see fulltext.]

Measurement of W± boson production in Pb+Pb collisions at √sNN=5.02Te with the ATLAS detector

A measurement of W± boson production in Pb+Pb collisions at sNN=5.02Te is reported using data recorded by the ATLAS experiment at the LHC in 2015, corresponding to a total integrated luminosity of 0.49nb-1. The W± bosons are reconstructed in the electron or muon leptonic decay channels. Production yields of leptonically decaying W± bosons, normalised by the total number of minimum-bias events and the nuclear thickness function, are measured within a fiducial region defined by the detector acceptance and the main kinematic requirements. These normalised yields are measured separately for W+ and W- bosons, and are presented as a function of the absolute value of pseudorapidity of the charged lepton and of the collision centrality. The lepton charge asymmetry is also measured as a function of the absolute value of lepton pseudorapidity. In addition, nuclear modification factors are calculated using the W± boson production cross-sections measured in pp collisions. The results are compared with predictions based on next-to-leading-order calculations with CT14 parton distribution functions as well as with predictions obtained with the EPPS16 and nCTEQ15 nuclear parton distribution functions. No dependence of normalised production yields on centrality and a good agreement with predictions are observed for mid-central and central collisions. For peripheral collisions, the data agree with predictions within 1.7 (0.9) standard deviations for W- (W+) bosons

Measurement of Λ (1520) production in pp collisions at √s=7TeV and p–Pb collisions at √sNN=5.02TeV

The production of the Λ (1520) baryonic resonance has been measured at midrapidity in inelastic pp collisions at s=7TeV and in p–Pb collisions at sNN=5.02TeV for non-single diffractive events and in multiplicity classes. The resonance is reconstructed through its hadronic decay channel Λ (1520) → pK - and the charge conjugate with the ALICE detector. The integrated yields and mean transverse momenta are calculated from the measured transverse momentum distributions in pp and p–Pb collisions. The mean transverse momenta follow mass ordering as previously observed for other hyperons in the same collision systems. A Blast-Wave function constrained by other light hadrons (π, K, KS0, p, Λ) describes the shape of the Λ (1520) transverse momentum distribution up to 3.5GeV/c in p–Pb collisions. In the framework of this model, this observation suggests that the Λ (1520) resonance participates in the same collective radial flow as other light hadrons. The ratio of the yield of Λ (1520) to the yield of the ground state particle Λ remains constant as a function of charged-particle multiplicity, suggesting that there is no net effect of the hadronic phase in p–Pb collisions on the Λ (1520) yield

Measurement of prompt D0, D+, D*+, and DS+ production in p–Pb collisions at √sNN = 5.02 TeV

The measurement of the production of prompt D0, D+, D*+, and DS+ mesons in proton–lead (p–Pb) collisions at the centre-of-mass energy per nucleon pair of sNN = 5.02 TeV, with an integrated luminosity of 292 ± 11 μb−1, are reported. Differential production cross sections are measured at mid-rapidity (−0.96 < ycms< 0.04) as a function of transverse momentum (pT) in the intervals 0 < pT< 36 GeV/c for D0, 1 < pT< 36 GeV/c for D+ and D*+, and 2 < pT< 24 GeV/c for D+ mesons. For each species, the nuclear modification factor RpPb is calculated as a function of pT using a proton-proton (pp) ref- erence measured at the same collision energy. The results are compatible with unity in the whole pT range. The average of the non-strange D mesons RpPb is compared with theoretical model predictions that include initial-state effects and parton transport model predictions. The pT dependence of the D0, D+, and D*+ nuclear modification factors is also reported in the interval 1 < pT< 36 GeV/c as a function of the collision centrality, and the central-to-peripheral ratios are computed from the D-meson yields measured in different centrality classes. The results are further compared with charged-particle measurements and a similar trend is observed in all the centrality classes. The ratios of the pT-differential cross sections of D0, D+, D*+, and DS+ mesons are also reported. The DS+ and D+ yields are compared as a function of the charged-particle multiplicity for several pT intervals. No modification in the relative abundances of the four species is observed with respect to pp collisions within the statistical and systematic uncertainties. [Figure not available: see fulltext.]

Measurement of electrons from heavy-flavour hadron decays as a function of multiplicity in p-Pb collisions at √sNN = 5.02 TeV

The multiplicity dependence of electron production from heavy-flavour hadron decays as a function of transverse momentum was measured in p-Pb collisions at sNN = 5.02 TeV using the ALICE detector at the LHC. The measurement was performed in the centre-of-mass rapidity interval −1.07 < ycms< 0.14 and transverse momentum interval 2 < pT< 16 GeV/c. The multiplicity dependence of the production of electrons from heavy-flavour hadron decays was studied by comparing the pT spectra measured for different multiplicity classes with those measured in pp collisions (QpPb) and in peripheral p-Pb collisions (Qcp). The QpPb results obtained are consistent with unity within uncertainties in the measured pT interval and event classes. This indicates that heavy-flavour decay electron production is consistent with binary scaling and independent of the geometry of the collision system. Additionally, the results suggest that cold nuclear matter effects are negligible within uncertainties, in the production of heavy-flavour decay electrons at midrapidity in p-Pb collisions. [Figure not available: see fulltext.