Capacity of Sum-networks for Different Message Alphabets

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 $1$ to close to $0$

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

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 $\phi$ 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 $\phi$ 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 $(p_{\mathrm{T}})$ distributions of $\phi$ as well as the particle yield ratios. Finally, we have also studied the $\phi$ 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