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In this work, we give a new parallel algorithm for the problem of maximizing a non-monotone diminishing returns submodular function subject to a cardinality constraint. For any desired accuracy epsilon, our algorithm achieves a 1/e−epsilon approximation using O(logn*log(1/epsilon)/epsilon^3) parallel rounds of function evaluations. The approximation guarantee nearly matches the best approximation guarantee known for the problem in the sequential setting and the number of parallel rounds is nearly-optimal for any constant epsilon. Previous algorithms achieve worse approximation guarantees using Ω(log^2 n) parallel rounds. Our experimental evaluation suggests that our algorithm obtains solutions whose objective value nearly matches the value obtained by the state of the art sequential algorithms, and it outperforms previous parallel algorithms in number of parallel rounds, iterations, and solution quality. 

A bstract We report on a measurement of the $$ {\Lambda}_c^{+} $$ Λ c + to D 0 production ratio in peripheral PbPb collisions at $$ \sqrt{s_{\textrm{NN}}} $$ s NN = 5 . 02 TeV with the LHCb detector in the forward rapidity region 2 < y < 4 . 5. The $$ {\Lambda}_c^{+} $$ Λ c + ( D 0 ) hadrons are reconstructed via the decay channel $$ {\Lambda}_c^{+} $$ Λ c + → pK − π + ( D 0 → K − π + ) for 2 < p T < 8 GeV/ c and in the centrality range of about 65–90%. The results show no significant dependence on p T , y or the mean number of participating nucleons. They are also consistent with similar measurements obtained by the LHCb collaboration in pPb and Pbp collisions at $$ \sqrt{s_{\textrm{NN}}} $$ s NN = 5 . 02 TeV. The data agree well with predictions from PYTHIA in pp collisions at $$ \sqrt{s} $$ s = 5 TeV but are in tension with predictions of the Statistical Hadronization model. 

A bstract A search for the lepton-flavour violating decays B 0 → K *0 μ ± e ∓ and $$ {B}_s^0 $$ B s 0 → ϕμ ± e ∓ is presented, using proton-proton collision data collected by the LHCb detector at the LHC, corresponding to an integrated luminosity of 9 fb − 1 . No significant signals are observed and upper limits of $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({B}^0\to {K}^{\ast 0}{\mu}^{+}{e}^{-}\right)<5.7\times {10}^{-9}\left(6.9\times {10}^{-9}\right),\\ {}\mathcal{B}\left({B}^0\to {K}^{\ast 0}{\mu}^{-}{e}^{+}\right)<6.8\times {10}^{-9}\left(7.9\times {10}^{-9}\right),\\ {}\mathcal{B}\left({B}^0\to {K}^{\ast 0}{\mu}^{\pm }{e}^{\mp}\right)<10.1\times {10}^{-9}\left(11.7\times {10}^{-9}\right),\\ {}\mathcal{B}\left({B}_s^0\to \phi {\mu}^{\pm }{e}^{\mp}\right)<16.0\times {10}^{-9}\left(19.8\times {10}^{-9}\right)\end{array}} $$ B B 0 → K ∗ 0 μ + e − < 5.7 × 10 − 9 6.9 × 10 − 9 , B B 0 → K ∗ 0 μ − e + < 6.8 × 10 − 9 7.9 × 10 − 9 , B B 0 → K ∗ 0 μ ± e ∓ < 10.1 × 10 − 9 11.7 × 10 − 9 , B B s 0 → ϕ μ ± e ∓ < 16.0 × 10 − 9 19.8 × 10 − 9 are set at 90% (95%) confidence level. These results constitute the world’s most stringent limits to date, with the limit on the decay $$ {B}_s^0 $$ B s 0 → ϕμ ± e ∓ the first being set. In addition, limits are reported for scalar and left-handed lepton-flavour violating New Physics scenarios. 

A bstract A first search for the lepton-flavour violating decays B 0 → K *0 τ ± μ ∓ is presented. The analysis is performed using a sample of proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV between 2011 and 2018, corresponding to an integrated luminosity of 9 fb − 1 . No significant signal is observed, and upper limits on the branching fractions are determined to be $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}{\tau}^{+}{\mu}^{-}\right)<1.0(1.2)\times {10}^{-5} $$ B B 0 → K ∗ 0 τ + μ − < 1.0 1.2 × 10 − 5 and $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}{\tau}^{-}{\mu}^{+}\right)<8.2(9.8)\times {10}^{-6} $$ B B 0 → K ∗ 0 τ − μ + < 8.2 9.8 × 10 − 6 at the 90% (95%) confidence level. 

A bstract An amplitude analysis of the D + → π − π + π + decay is performed with a sample corresponding to 1.5 fb − 1 of integrated luminosity of pp collisions at a centre-of-mass energy $$ \sqrt{s} $$ s = 8 TeV collected by the LHCb detector in 2012. The sample contains approximately six hundred thousand candidates with a signal purity of 95%. The resonant structure is studied through a fit to the Dalitz plot where the π − π + S-wave amplitude is extracted as a function of π − π + mass, and spin-1 and spin-2 resonances are included coherently through an isobar model. The S-wave component is found to be dominant, followed by the ρ (770) 0 π + and f 2 (1270) π + components. A small contribution from the ω (782) → π − π + decay is seen for the first time in the D + → π − π + π + decay.