The charge ratio, $R_\mu = N_{\mu^+}/N_{\mu^-}$, for cosmogenic multiple-muon events observed at an under- ground depth of 2070 mwe has been measured using the magnetized MINOS Far Detector. The multiple-muon events, recorded nearly continuously from August 2003 until April 2012, comprise two independent data sets imaged with opposite magnetic field polarities, the comparison of which allows the systematic uncertainties of the measurement to be minimized. The multiple-muon charge ratio is determined to be $R_\mu = 1.104 \pm 0.006 {\rm \,(stat.)} ^{+0.009}_{-0.010} {\rm \,(syst.)} $. This measurement complements previous determinations of single-muon and multiple-muon charge ratios at underground sites and serves to constrain models of cosmic ray interactions at TeV energies.
A new algorithm is presented to discriminate reconstructed hadronic decays of tau leptons ($\tau_\mathrm{h}$) that originate from genuine tau leptons in the CMS detector against $\tau_\mathrm{h}$ candidates that originate from quark or gluon jets, electrons, or muons. The algorithm inputs information from all reconstructed particles in the vicinity of a $\tau_\mathrm{h}$ candidate and employs a deep neural network with convolutional layers to efficiently process the inputs. This algorithm leads to a significantly improved performance compared with the previously used one. For example, the efficiency for a genuine $\tau_\mathrm{h}$ to pass the discriminator against jets increases by 10-30% for a given efficiency for quark and gluon jets. Furthermore, a more efficient $\tau_\mathrm{h}$ reconstruction is introduced that incorporates additional hadronic decay modes. The superior performance of the new algorithm to discriminate against jets, electrons, and muons and the improved $\tau_\mathrm{h}$ reconstruction method are validated with LHC proton-proton collision data at $\sqrt{s} =$ 13 TeV.