Multiple scattering effects on heavy meson production in p+A collisions at backward rapidity

We study the incoherent multiple scattering effects on heavy meson production in the backward rapidity region of p+A collisions within the generalized high-twist factorization formalism. We calculate explicitly the double scattering contributions to the heavy meson differential cross sections by taking into account both initial-state and final-state interactions, and find that these corrections are positive. We further evaluate the nuclear modification factor for muons that come form the semi-leptonic decays of heavy flavor mesons. Phenomenological applications in d+Au collisions at a center-of-mass energy $\sqrt{s}=200$ GeV at RHIC and in p+Pb collisions at $\sqrt{s}=5.02$ TeV at the LHC are presented. We find that incoherent multiple scattering can describe rather well the observed nuclear enhancement in the intermediate $p_T$ region for such reactions.Comment: 10 pages, 6 figures, published version in PL

Can Gradient Descent Provably Learn Linear Dynamic Systems?

We study the learning ability of linear recurrent neural networks with gradient descent. We prove the first theoretical guarantee on linear RNNs with Gradient Descent to learn any stable linear dynamic system. We show that despite the non-convexity of the optimization loss if the width of the RNN is large enough (and the required width in hidden layers does not rely on the length of the input sequence), a linear RNN can provably learn any stable linear dynamic system with the sample and time complexity polynomial in $\frac{1}{1-\rho_C}$ where $\rho_C$ is roughly the spectral radius of the stable system. Our results provide the first theoretical guarantee to learn a linear RNN and demonstrate how can the recurrent structure help to learn a dynamic system.Comment: 29 page