Generalizing Boolean Satisfiability I: Background and Survey of Existing Work

This is the first of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper is a survey of the work underlying ZAP, and discusses previous attempts to improve the performance of the Davis-Putnam-Logemann-Loveland algorithm by exploiting the structure of the problem being solved. We examine existing ideas including extensions of the Boolean language to allow cardinality constraints, pseudo-Boolean representations, symmetry, and a limited form of quantification. While this paper is intended as a survey, our research results are contained in the two subsequent articles, with the theoretical structure of ZAP described in the second paper in this series, and ZAP's implementation described in the third

Generalizing Boolean Satisfiability II: Theory

This is the second of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper presents the theoretical basis for the ideas underlying ZAP, arguing that existing ideas in this area exploit a single, recurring structure in that multiple database axioms can be obtained by operating on a single axiom using a subgroup of the group of permutations on the literals in the problem. We argue that the group structure precisely captures the general structure at which earlier approaches hinted, and give numerous examples of its use. We go on to extend the Davis-Putnam-Logemann-Loveland inference procedure to this broader setting, and show that earlier computational improvements are either subsumed or left intact by the new method. The third paper in this series discusses ZAPs implementation and presents experimental performance results

Spin-Dependent Antenna Splitting Functions

We consider parton showers based on radiation from QCD dipoles or `antennae'. These showers are built from 2->3 parton splitting processes. The question then arises of what functions replace the Altarelli-Parisi splitting functions in this approach. We give a detailed answer to this question, applicable to antenna showers in which partons carry definite helicity, and to both initial- and final-state emissions.Comment: 31 pages, 12 figure

Simulating the Impact of X-ray Heating during the Cosmic Dawn

Upcoming observations of the 21-cm signal from the Epoch of Reionization will soon provide the first direct detection of this era. This signal is influenced by many astrophysical effects, including long range X-ray heating of the intergalactic gas. During the preceding Cosmic Dawn era the impact of this heating on the 21-cm signal is particularly prominent, especially before spin temperature saturation. We present the largest-volume (349\,Mpc comoving=244~$h^{-1}$Mpc) full numerical radiative transfer simulations to date of this epoch that include the effects of helium and multi-frequency heating, both with and without X-ray sources. We show that X-ray sources contribute significantly to early heating of the neutral intergalactic medium and, hence, to the corresponding 21-cm signal. The inclusion of hard, energetic radiation yields an earlier, extended transition from absorption to emission compared to the stellar-only case. The presence of X-ray sources decreases the absolute value of the mean 21-cm differential brightness temperature. These hard sources also significantly increase the 21-cm fluctuations compared the common assumption of temperature saturation. The 21-cm differential brightness temperature power spectrum is initially boosted on large scales, before decreasing on all scales. Compared to the case of the cold, unheated intergalactic medium, the signal has lower rms fluctuations and increased non-Gaussianity, as measured by the skewness and kurtosis of the 21-cm probability distribution functions. Images of the 21-cm signal with resolution around 11~arcmin still show fluctuations well above the expected noise for deep integrations with the SKA1-Low, indicating that direct imaging of the X-ray heating epoch could be feasible.Comment: 13 pages, 8 figure

Seasonal changes in microbial dissolved organic sulfur transformations in coastal waters

The marine trace gas dimethylsulfide (DMS) is the single most important biogenic source of atmospheric sulfur, accounting for up to 80% of global biogenic sulfur emissions. Approximately 300 million tons of DMS are produced annually, but the majority is degraded by microbes in seawater. The DMS precursor dimethylsulfoniopropionate (DMSP) and oxidation product dimethylsulphoxide (DMSO) are also important organic sulfur reservoirs. However, the marine sinks of dissolved DMSO remain unknown. We used a novel combination of stable and radiotracers to determine seasonal changes in multiple dissolved organic sulfur transformation rates to ascertain whether microbial uptake of dissolved DMSO was a significant loss pathway. Surface concentrations of DMS ranged from 0.5 to 17.0 nM with biological consumption rates between 2.4 and 40.8 nM·d−1. DMS produced from the reduction of DMSO was not a significant process. Surface concentrations of total DMSO ranged from 2.3 to 102 nM with biological consumption of dissolved DMSO between 2.9 and 111 nM·d−1. Comparisons between 14C2-DMSO assimilation and dissimilation rates suggest that the majority of dissolved DMSO was respired (>94%). Radiotracer microbial consumption rates suggest that dissimilation of dissolved DMSO to CO2 can be a significant loss pathway in coastal waters, illustrating the significance of bacteria in controlling organic sulfur seawater concentrations

Generalizing Boolean Satisfiability III: Implementation

This is the third of three papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal has been to define a representation in which this structure is apparent and can be exploited to improve computational performance. The first paper surveyed existing work that (knowingly or not) exploited problem structure to improve the performance of satisfiability engines, and the second paper showed that this structure could be understood in terms of groups of permutations acting on individual clauses in any particular Boolean theory. We conclude the series by discussing the techniques needed to implement our ideas, and by reporting on their performance on a variety of problem instances

The Last of the Finite Loop Amplitudes in QCD

We use on-shell recursion relations to determine the one-loop QCD scattering amplitudes with a massless external quark pair and an arbitrary number (n-2) of positive-helicity gluons. These amplitudes are the last of the unknown infrared- and ultraviolet-finite loop amplitudes of QCD. The recursion relations are similar to ones applied at tree level, but contain new non-trivial features corresponding to poles present for complex momentum arguments but absent for real momenta. We present the relations and the compact solutions to them, valid for all n. We also present compact forms for the previously-computed one-loop n-gluon amplitudes with a single negative helicity and the rest positive helicity.Comment: 45 pages, revtex, 7 figures, v2 minor correction

Swimming in curved space or The Baron and the cat

We study the swimming of non-relativistic deformable bodies in (empty) static curved spaces. We focus on the case where the ambient geometry allows for rigid body motions. In this case the swimming equations turn out to be geometric. For a small swimmer, the swimming distance in one stroke is determined by the Riemann curvature times certain moments of the swimmer.Comment: 19 pages 6 figure