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    Capacity of Sum-networks for Different Message Alphabets

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    A sum-network is a directed acyclic network in which all terminal nodes demand the `sum' of the independent information observed at the source nodes. Many characteristics of the well-studied multiple-unicast network communication problem also hold for sum-networks due to a known reduction between instances of these two problems. Our main result is that unlike a multiple unicast network, the coding capacity of a sum-network is dependent on the message alphabet. We demonstrate this using a construction procedure and show that the choice of a message alphabet can reduce the coding capacity of a sum-network from 11 to close to 00

    Energy dependence of ϕ\phi(1020) production at mid-rapidity in pp collisions with ALICE at the LHC

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    Hadronic resonances are unique tools to investigate the interplay of re-scattering and regeneration effects during the hadronization phase in heavy-ion collisions. Measurements in small collision systems provide a necessary baseline for heavy-ion data, help to tune pQCD inspired event generators and give insight into the search for the onset of collective effects. As the ϕ\phi meson has a longer lifetime compared to other resonances, it is expected that its production would be much less affected by regeneration and re-scattering processes. We report on measurements of ϕ\phi meson production in minimum bias pp collisions at different beam energies and as a function of charged particle multiplicity with the ALICE detector at the LHC. The results include the transverse momentum (pT)(p_{\mathrm{T}}) distributions of ϕ\phi as well as the particle yield ratios. Finally, we have also studied the ϕ\phi effective strangeness content by comparing our results to theoretical calculations.Comment: 3 pages, 2 figures, Presented in XXVIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2018
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