Minimally disproportional representation: generalized entropy and Stolarsky Mean-Divisor Methods of Apportionment

We study divisor methods, the primary class to solve apportionment problems, based upon Stolarsky means Saß. These encompass the five traditional methods. We disclose a one-to-one relation between methods of the form Sa1 and aggregate measures of seat/vote disproportionality of the generalized entropy family: using a divisor method based upon such a generalized logarithmic mean coincides with minimizing a generalized entropy inequality measure. The Balinski-Young ‘favoring small states’.-ordering ranks the generalized entropy methods. This framework improves upon an inconsistency in the traditional inequality approach to apportionment problems, which we illustrate by showing that the major rationale of the ‘method of equal proportions’.is consistently preserved by a non-traditional method.

Measurement of differential cross sections for top quark pair production using the lepton plus jets final state in proton-proton collisions at 13 TeV

National Science Foundation (U.S.

Particle-flow reconstruction and global event description with the CMS detector

The CMS apparatus was identified, a few years before the start of the LHC operation at CERN, to feature properties well suited to particle-flow (PF) reconstruction: a highly-segmented tracker, a fine-grained electromagnetic calorimeter, a hermetic hadron calorimeter, a strong magnetic field, and an excellent muon spectrometer. A fully-fledged PF reconstruction algorithm tuned to the CMS detector was therefore developed and has been consistently used in physics analyses for the first time at a hadron collider. For each collision, the comprehensive list of final-state particles identified and reconstructed by the algorithm provides a global event description that leads to unprecedented CMS performance for jet and hadronic tau decay reconstruction, missing transverse momentum determination, and electron and muon identification. This approach also allows particles from pileup interactions to be identified and enables efficient pileup mitigation methods. The data collected by CMS at a centre-of-mass energy of 8 TeV show excellent agreement with the simulation and confirm the superior PF performance at least up to an average of 20 pileup interactions

Identification of heavy-flavour jets with the CMS detector in pp collisions at 13 TeV

Many measurements and searches for physics beyond the standard model at the LHC rely on the efficient identification of heavy-flavour jets, i.e. jets originating from bottom or charm quarks. In this paper, the discriminating variables and the algorithms used for heavy-flavour jet identification during the first years of operation of the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13 TeV, are presented. Heavy-flavour jet identification algorithms have been improved compared to those used previously at centre-of-mass energies of 7 and 8 TeV. For jets with transverse momenta in the range expected in simulated $\mathrm{t}\overline{\mathrm{t}}$ events, these new developments result in an efficiency of 68% for the correct identification of a b jet for a probability of 1% of misidentifying a light-flavour jet. The improvement in relative efficiency at this misidentification probability is about 15%, compared to previous CMS algorithms. In addition, for the first time algorithms have been developed to identify jets containing two b hadrons in Lorentz-boosted event topologies, as well as to tag c jets. The large data sample recorded in 2016 at a centre-of-mass energy of 13 TeV has also allowed the development of new methods to measure the efficiency and misidentification probability of heavy-flavour jet identification algorithms. The heavy-flavour jet identification efficiency is measured with a precision of a few per cent at moderate jet transverse momenta (between 30 and 300 GeV) and about 5% at the highest jet transverse momenta (between 500 and 1000 GeV)

Search for heavy resonances decaying to a top quark and a bottom quark in the lepton+jets final state in proton–proton collisions at 13 TeV

info:eu-repo/semantics/publishe

Evidence for the Higgs boson decay to a bottom quark–antiquark pair

info:eu-repo/semantics/publishe

Pseudorapidity and transverse momentum dependence of flow harmonics in pPb and PbPb collisions

info:eu-repo/semantics/publishe