400 research outputs found

    Interactive Learning-Based Realizability for Heyting Arithmetic with EM1

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    We apply to the semantics of Arithmetic the idea of ``finite approximation'' used to provide computational interpretations of Herbrand's Theorem, and we interpret classical proofs as constructive proofs (with constructive rules for √,∃\vee, \exists) over a suitable structure \StructureN for the language of natural numbers and maps of G\"odel's system \SystemT. We introduce a new Realizability semantics we call ``Interactive learning-based Realizability'', for Heyting Arithmetic plus \EM_1 (Excluded middle axiom restricted to Σ10\Sigma^0_1 formulas). Individuals of \StructureN evolve with time, and realizers may ``interact'' with them, by influencing their evolution. We build our semantics over Avigad's fixed point result, but the same semantics may be defined over different constructive interpretations of classical arithmetic (Berardi and de' Liguoro use continuations). Our notion of realizability extends intuitionistic realizability and differs from it only in the atomic case: we interpret atomic realizers as ``learning agents''

    Evidence for Neutrino Oscillations from Muon Decay at Rest

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    A search for nu_bar_mu to nu_bar_e oscillations has been conducted at the Los Alamos Meson Physics Facility using nu_bar_mu from mu+ decay at rest. The nu_bar_e are detected via the reaction (nu_bar_e,p) -> (e+,n), correlated with the 2.2 MeV gamma from (n,p) -> (d,gamma). The use of tight cuts to identify e+ events with correlated gamma rays yields 22 events with e+ energy between 36 and 60 MeV and only 4.6 (+/- 0.6) background events. The probability that this excess is due entirely to a statistical fluctuation is 4.1E-08. A chi^2 fit to the entire e+ sample results in a total excess of 51.8 (+18.7) (-16.9) (+/- 8.0) events with e+ energy between 20 and 60 MeV. If attributed to nu_bar_mu -> nu_bar_e oscillations, this corresponds to an oscillation probability (averaged over the experimental energy and spatial acceptance) of 0.0031 (+0.0011) (-0.0010) (+/- 0.0005).Comment: 57 pages, 34 figures, revtex, additional information available at http://nu1.lampf.lanl.gov/~lsnd

    Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE) Conceptual Design Report Volume 2: The Physics Program for DUNE at LBNF

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    The Physics Program for the Deep Underground Neutrino Experiment (DUNE) at the Fermilab Long-Baseline Neutrino Facility (LBNF) is described
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