The Geometry of Interaction of Differential Interaction Nets

The Geometry of Interaction purpose is to give a semantic of proofs or programs accounting for their dynamics. The initial presentation, translated as an algebraic weighting of paths in proofnets, led to a better characterization of the lambda-calculus optimal reduction. Recently Ehrhard and Regnier have introduced an extension of the Multiplicative Exponential fragment of Linear Logic (MELL) that is able to express non-deterministic behaviour of programs and a proofnet-like calculus: Differential Interaction Nets. This paper constructs a proper Geometry of Interaction (GoI) for this extension. We consider it both as an algebraic theory and as a concrete reversible computation. We draw links between this GoI and the one of MELL. As a by-product we give for the first time an equational theory suitable for the GoI of the Multiplicative Additive fragment of Linear Logic.Comment: 20 pagee, to be published in the proceedings of LICS0

An Explicit Framework for Interaction Nets

Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on elementary properties of graph theory. We give here a more explicit presentation based on notions borrowed from Girard's Geometry of Interaction: interaction nets are presented as partial permutations and a composition of nets, the gluing, is derived from the execution formula. We then define contexts and reduction as the context closure of rules. We prove strong confluence of the reduction within our framework and show how interaction nets can be viewed as the quotient of some generalized proof-nets

Alternative view of oxygen reduction on porous carbon electrocatalysts: the substance of complex oxygen-surface interactions

Electrochemical oxygen reduction reaction (ORR) is an important energy-related process requiring alternative catalysts to expensive platinum-based ones. Although recently some advancements in carbon catalysts have been reported, there is still a lack of understanding which surface features might enhance their efficiency for ORR. Through a detailed study of oxygen adsorption on carbon molecular sieves and using inelastic neutron scattering, we demonstrated here that the extent of oxygen adsorption/interactions with surface is an important parameter affecting ORR. It was found that both the strength of O2 physical adsorption in small pores and its specific interactions with surface ether functionalities in the proximity of pores positively influence the ORR efficiency. We have shown that ultramicropores and hydrophobic surface rich in ether-based groups and/or electrons enhance ORR on carbon electrocatalysts and the performance parameters are similar to those measured on Pt/C with the number of electron transfer equal to 4

Scaling of charged particle multiplicity in Pb-Pb collisions at SPS energies

The charged particle multiplicity distribution $dN_{ch}/d\eta$ has been measured by the NA50 experiment in Pb--Pb collisions at the CERN SPS. Measurements were done at incident energies of 40 and 158 GeV per nucleon over a broad impact parameter range. The multiplicity distributions are studied as a function of centrality using the number of participating nucleons ($N_{part}$), or the number of binary nucleon--nucleon collisions ($N_{coll}$). Their values at midrapidity exhibit a power law scaling behaviour given by $N_{part}^{1.00}$ and $N_{coll}^{0.75}$ at 158 GeV. Compatible results are found for the scaling behaviour at 40 GeV. The width of the $dN_{ch}/d\eta$ distributions is larger at 158 than at 40 GeV/nucleon and decreases slightly with centrality at both energies. Our results are compared to similar studies performed by other experiments both at the CERN SPS and at RHIC.

Results on Charmonium States in Pb-Pb Interactions

We present cross-sections for J/$\psi$, $\psi^{\prime}$ and Drell-Yan production in lead-lead interactions at 158 GeV/nucleon. The Pb-Pb data, when compared with previous results obtained with lighter target or projectiles, show a similar behaviour for Drell-Yan, but exhibit an anomalous J/$\psi$ suppression, which increases with centrality

Intermediate mass dimuons in NA38/NA50

The NA38/NA50 experiments have measured, at the CERN SPS, the dimuon production in proton-nucleus and nucleus-nucleus collisions. In this paper it is shown that the mass continuum between the $\phi$ and the $J/{\psi}$ can be satisfactorily described, after having removed the combinatorial background due to uncorrelated $\pi$ and $K$ decays, as a sum of two contributions, namely the Drell-Yan process and the semi-leptonic decay of pairs of charmed mesons, whose mass shape in the acceptance of the experiment has been evaluated using PYTHIA. However, in order to describe the A - B (namely S - U and Pb - Pb) mass spectra, the dimuon yield from open charm decays, which in $p$ - A collisions is found to be consistent with direct open charm measurements from other CERN and FNAL experiments, has to be enhanced with respect to a linear extrapolation of $p$ - A results. The size of the enhancement smoothly increases from peripheral S - U to central Pb - Pb interactions, reaching a factor $\sim$ 3 in central Pb - Pb collisions. The $P_{T}$ distributions of the events in the mass continuum are also compatible with the hypothesis of open charm enhancement in A - B collisions

Transverse momentum distributions of J/ψ\psi, ψ′\psi^{\prime}, Drell-Yan and continuum dimuons produced in Pb-Pb interactions at the SPS

Muon pairs produced in Pb-Pb interactions at 158~GeV/$c$ per nucleon are used to study the transverse momentum distributions of the J/$\psi$, $\psi^{\prime}$ and dimuons in the mass continuum. In particular, the dependence of these distributions on the centrality of the Pb-Pb collision is investigated in detail

Low mass dimuon production in proton and ion induced interactions at SPS

The low mass dimuon spectra collected in $p$-U collisions by the NA38 experiment significantly exceeds the total cross section expected from previous analysis, done by other experiments. The 'excess' events have a harder $p_{T}$ distribution than the muon pairs from $\eta$ and $\omega$ Dalitz decays, expected to dominate the mass window 0.4—0.65~GeV/$c^2$. We conjecture that the excess events might be due to $q\bar{q}$ annihilations, negligible at low $p_{T}$ but made visible by the $m_{T}$ cut applied in the NA38 data. Taking this assumption to parametrise the $p$-U spectra, we proceed with the analysis of the S-Cu, S-U and Pb-Pb data, collected by the NA38 and NA50 experiments, where we find that the measured mass spectra does not seem to exceed the expected low mass `cocktail' by more than 20%

Copernicus Ocean State Report, issue 6

The 6th issue of the Copernicus OSR incorporates a large range of topics for the blue, white and green ocean for all European regional seas, and the global ocean over 1993–2020 with a special focus on 2020