Static Analysis of Parity Games: Alternating Reachability Under Parity

It is well understood that solving parity games is equivalent, up to polynomial time, to model checking of the modal mu-calculus. It is a long-standing open problem whether solving parity games (or model checking modal mu-calculus formulas) can be done in polynomial time. A recent approach to studying this problem has been the design of partial solvers, algorithms that run in polynomial time and that may only solve parts of a parity game. Although it was shown that such partial solvers can completely solve many practical benchmarks, the design of such partial solvers was somewhat ad hoc, limiting a deeper understanding of the potential of that approach. We here mean to provide such robust foundations for deeper analysis through a new form of game, alternating reachability under parity. We prove the determinacy of these games and use this determinacy to define, for each player, a monotone fixed point over an ordered domain of height linear in the size of the parity game such that all nodes in its greatest fixed point are won by said player in the parity game. We show, through theoretical and experimental work, that such greatest fixed points and their computation leads to partial solvers that run in polynomial time. These partial solvers are based on established principles of static analysis and are more effective than partial solvers studied in extant work

Analyzing the Fierz Rearrangement Freedom for Local Chiral Two-Nucleon Potentials

Chiral effective field theory is a framework to derive systematic nuclear interactions. It is based on the symmetries of quantum chromodynamics and includes long-range pion physics explicitly, while shorter-range physics is expanded in a general operator basis. The number of low-energy couplings at a particular order in the expansion can be reduced by exploiting the fact that nucleons are fermions and therefore obey the Pauli exclusion principle. The antisymmetry permits the selection of a subset of the allowed contact operators at a given order. When local regulators are used for these short-range interactions, however, this "Fierz rearrangement freedom" is violated. In this paper, we investigate the impact of this violation at leading order (LO) in the chiral expansion. We construct LO and next-to-leading order (NLO) potentials for all possible LO-operator pairs and study their reproduction of phase shifts, the ${}^4$He ground-state energy, and the neutron-matter energy at different densities. We demonstrate that the Fierz rearrangement freedom is partially restored at NLO where subleading contact interactions enter. We also discuss implications for local chiral three-nucleon interactions.Comment: 11 pages, 5 figure

Relationships of surface air temperature anomalies over Europe to persistence of atmospheric circulation patterns conducive to heat waves

Heat waves are among natural hazards with the most severe consequences for human society, including pronounced mortality impacts in mid-latitudes. Recent studies have hypothesized that the enhanced persistence of atmospheric circulation may affect surface climatic extremes, mainly the frequency and severity of heat waves. In this paper we examine relationships between the persistence of the Hess-Brezowsky circulation types conducive to summer heat waves and air temperature anomalies at stations over most of the European continent. We also evaluate differences between temperature anomalies during late and early stages of warm circulation types in all seasons. Results show that more persistent circulation patterns tend to enhance the severity of heat waves and support more pronounced temperature anomalies. Recent sharply rising trends in positive temperature extremes over Europe may be related to the greater persistence of the circulation types, and if similar changes towards enhanced persistence affect other mid-latitudinal regions, analogous consequences and implications for temperature extremes may be expected

Factorization for generic jet production

Factorization is the central ingredient in any theoretical prediction for collider experiments. We introduce a factorization formalism that can be applied to any desired observable, like event shapes or jet observables, for any number of jets and a wide range of jet algorithms in leptonic or hadronic collisions. This is achieved by using soft-collinear effective theory to prove the formal factorization of a generic fully-differential cross section in terms of a hard coefficient, and generic jet and soft functions. In this formalism, whether a given observable factorizes in the usual sense, depends on whether it is inclusive enough, so the jet functions can be calculated perturbatively. The factorization formula for any such observable immediately follows from our general result, including the precise definition of the jet and soft functions appropriate for the observable in question. As examples of our formalism, we work out several results in two-jet production for both e+e- and pp collisions. For the latter, we also comment on how our formalism allows one to treat underlying events and beam remnants.Comment: 33 pages, v2: minor typos corrected, journal versio

Engineering evaluations and studies. Report for Ku-band studies, exhibit A

System performance aspects of the Ku band radar communication hardware and investigations into the Ku band/payload interfaces are discussed. The communications track problem caused by the excessive signal dynamic range at the servo input was investigated. The management/handover logic is discussed and a simplified description of the transmitter enable logic function is presented. Output noise produced by a voltage-controlled oscillator chip used in the SPA return-link channel 3 mid-bit detector is discussed. The deployed assembly (DA) and EA-2 critical design review data are evaluated. Cross coupling effects on antenna servo stability were examined. A series of meetings on the acceptance test specification for the deployed assembly is summarized