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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<sc>bstract</sc> An angular analysis ofB⁰→ K^*0e⁺e⁻decays is presented using proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of 9 fb⁻¹. The analysis is performed in the region of the dilepton invariant mass squared of 1.1–6.0 GeV²/c⁴. In addition, a test of lepton flavour universality is performed by comparing the obtained angular observables with those measured inB⁰→ K^*0μ⁺μ⁻decays. In general, the angular observables are found to be consistent with the Standard Model expectations as well as with global analyses of otherb → sℓ⁺ℓ⁻processes, whereℓis either a muon or an electron. No sign of lepton-flavour-violating effects is observed. 

A<sc>bstract</sc> A search for the decay$$ {B}_c^{+} $$ $B_c^{+}$→ χ_c1(3872)π⁺is reported using proton-proton collision data collected with the LHCb detector between 2011 and 2018 at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb⁻¹. No significant signal is observed. Using the decay$$ {B}_c^{+} $$ $B_c^{+}$→ψ(2S)π⁺as a normalisation channel, an upper limit for the ratio of branching fractions$$ {\mathcal{R}}_{\psi (2S)}^{\chi_{c1}(3872)}=\frac{{\mathcal{B}}_{B_c^{+}\to {\chi}_{c1}(3872){\pi}^{+}}}{{\mathcal{B}}_{B_c^{+}\to \psi (2S){\pi}^{+}}}\times \frac{{\mathcal{B}}_{\chi_{c1}(3872)\to J/\psi {\pi}^{+}{\pi}^{-}}}{{\mathcal{B}}_{\psi (2S)\to J/\psi {\pi}^{+}{\pi}^{-}}}<0.05(0.06), $$ $R_{\psi \left(2S\right)}^{{\chi }_{c1}\left(3872\right)}=\frac{B_{B_c^{+}\to {\chi }_{c1}\left(3872\right){\pi }^{+}}}{B_{B_c^{+}\to \psi \left(2S\right){\pi }^{+}}}\times \frac{B_{{\chi }_{c1}\left(3872\right)\to J/\psi {\pi }^{+}{\pi }^{-}}}{B_{\psi \left(2S\right)\to J/\psi {\pi }^{+}{\pi }^{-}}}<0.05\left(0.06\right),$ is set at the 90 (95)% confidence level. 

The branching fraction of the decay $B^{+}\to \psi \left(2S\right)\varphi \left(1020\right)K^{+}$, relative to the topologically similar decay $B^{+}\to J/\psi \varphi \left(1020\right)K^{+}$, is measured using proton-proton collision data collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. The ratio is found to be $0.061\pm 0.004\pm 0.009$, where the first uncertainty is statistical and the second systematic. Using the world-average branching fraction for $B^{+}\to J/\psi \varphi \left(1020\right)K^{+}$, the branching fraction for the decay $B^{+}\to \psi \left(2S\right)\varphi \left(1020\right)K^{+}$is found to be $(3.0\pm 0.2\pm 0.5\pm 0.2)\times {10}^{-6}$, where the first uncertainty is statistical, the second systematic, and the third is due to the branching fraction of the normalization channel. © 2025 CERN, for the LHCb Collaboration2025CERN 

A search for $CP$violation in ${\mathrm{\Lambda }}_b^0\to p{K}^{-}$and ${\mathrm{\Lambda }}_b^0\to p{\pi }^{-}$decays is presented using the full Run 1 and Run 2 data samples of $pp$collisions collected with the LHCb detector, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$at center-of-mass energies of 7, 8, and 13 TeV. For the Run 2 data sample, the $CP$-violating asymmetries are measured to be $A_{CP}^{p{K}^{-}}=(-1.4\pm 0.7\pm 0.4)\%$and $A_{CP}^{p{\pi }^{-}}=(0.4\pm 0.9\pm 0.4)\%$, where the first uncertainty is statistical and the second is systematic. Following significant improvements in the evaluation of systematic uncertainties compared to the previous LHCb measurement, the Run 1 dataset is reanalyzed to update the corresponding results. When combining the Run 2 and updated Run 1 measurements, the final results are found to be $A_{CP}^{p{K}^{-}}=(-1.1\pm 0.7\pm 0.4)\%$and $A_{CP}^{p{\pi }^{-}}=(0.2\pm 0.8\pm 0.4)\%$, constituting the most precise measurements of these asymmetries to date. © 2025 CERN, for the LHCb Collaboration2025CERN 

A<sc>bstract</sc> TheΥ(2S) andΥ(3S) production cross-sections are measured relative to that of theΥ(1S) meson, as a function of charged-particle multiplicity in proton-proton collisions at a centre-of-mass energy of 13 TeV. The measurement uses data collected by the LHCb experiment in 2018 corresponding to an integrated luminosity of 2 fb⁻¹. Both theΥ(2S)-to-Υ(1S) andΥ(3S)-to-Υ(1S) cross-section ratios are found to decrease significantly as a function of event multiplicity, with theΥ(3S)-to-Υ(1S) ratio showing a steeper decline towards high multiplicity. This hierarchy is qualitatively consistent with the comover model predictions, indicating that final-state interactions play an important role in bottomonia production in high-multiplicity events. 

A study is presented of $B^{+}\to K_{\mathrm{S}}^0{K}^{-}{\pi }^{+}{K}^{+}$and $B^{+}\to K_{\mathrm{S}}^0{K}^{+}{\pi }^{-}{K}^{+}$decays based on the analysis of proton-proton collision data collected with the LHCb detector at center-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. The $K_{\mathrm{S}}^{0}K\pi$invariant-mass distributions of both $B^{+}$decay modes show, in the $m\left(K_{\mathrm{S}}^{0}K\pi \right)<1.85\mathrm{GeV}$mass region, large activity which is resolved using an amplitude analysis. A simple model, where $J^{PC}$amplitudes are described by multiple Breit-Wigner functions with appropriate angular distributions, provides a good description of the experimental data. In this approach a complex mixture of $J^{PC}=0^{-+}$, $1^{++}$and $1^{+-}$amplitudes is observed that is dominated by $\eta \left(1405\right)$, $\eta \left(1470\right)$, $\eta \left(1760\right)$, $f_1\left(1285\right)$, $f_1\left(1420\right)$and $h_1\left(1405\right)$resonances. The $K_{\mathrm{S}}^{0}K\pi$Dalitz plots are dominated by asymmetric crossing $K^{*}\overline{K}$bands which are different for the two $B^{+}$decay modes. This is due to a different interference pattern between the $1^{++}$and $1^{+-}$amplitudes in the two channels. Branching fractions are measured for each resonant contribution. © 2025 CERN, for the LHCb Collaboration2025CERN 

The first test of lepton flavor universality between muons and electrons using $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$( $\ell =e$, $\mu$) decays is presented. The measurement is performed with data from proton-proton collisions collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. The ratio of branching fractions between $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$and $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$decays is measured in the dilepton invariant-mass-squared range $1.1<q^2<7.0{\mathrm{GeV}}^2/c^4$and is found to be $R_{K\pi \pi }^{-1}=1.31_{-0.17}^{+0.18}\left(\mathrm{stat}){}_{-0.09}^{+0.12}\right(\mathrm{syst})$, in agreement with the standard model prediction. The first observation of the $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$decay is also reported. © 2025 CERN, for the LHCb Collaboration2025CERN