Incremental and Modular Context-sensitive Analysis

Context-sensitive global analysis of large code bases can be expensive, which can make its use impractical during software development. However, there are many situations in which modifications are small and isolated within a few components, and it is desirable to reuse as much as possible previous analysis results. This has been achieved to date through incremental global analysis fixpoint algorithms that achieve cost reductions at fine levels of granularity, such as changes in program lines. However, these fine-grained techniques are not directly applicable to modular programs, nor are they designed to take advantage of modular structures. This paper describes, implements, and evaluates an algorithm that performs efficient context-sensitive analysis incrementally on modular partitions of programs. The experimental results show that the proposed modular algorithm shows significant improvements, in both time and memory consumption, when compared to existing non-modular, fine-grain incremental analysis techniques. Furthermore, thanks to the proposed inter-modular propagation of analysis information, our algorithm also outperforms traditional modular analysis even when analyzing from scratch.Comment: 56 pages, 27 figures. To be published in Theory and Practice of Logic Programming. v3 corresponds to the extended version of the ICLP2018 Technical Communication. v4 is the revised version submitted to Theory and Practice of Logic Programming. v5 (this one) is the final author version to be published in TPL

Coding Theory and Algebraic Combinatorics

This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings, kissing numbers, lattices, and association schemes. In particular, special interest is devoted to the relationship between codes and combinatorial designs. We describe and recapitulate important results in the development of the state of the art. In addition, we give illustrative examples and constructions, and highlight recent advances. Finally, we provide a collection of significant open problems and challenges concerning future research.Comment: 33 pages; handbook chapter, to appear in: "Selected Topics in Information and Coding Theory", ed. by I. Woungang et al., World Scientific, Singapore, 201

Primitive decompositions of Johnson graphs

A transitive decomposition of a graph is a partition of the edge set together with a group of automorphisms which transitively permutes the parts. In this paper we determine all transitive decompositions of the Johnson graphs such that the group preserving the partition is arc-transitive and acts primitively on the parts.Comment: 35 page

A GPU-Enabled, High-Resolution Cosmological Microlensing Parameter Survey

In the era of synoptic surveys, the number of known gravitationally lensed quasars is set to increase by over an order of magnitude. These new discoveries will enable a move from single-quasar studies to investigations of statistical samples, presenting new opportunities to test theoretical models for the structure of quasar accretion discs and broad emission line regions (BELRs). As one crucial step in preparing for this influx of new lensed systems, a large-scale exploration of microlensing convergence-shear parameter space is warranted, requiring the computation of O(10^5) high resolution magnification maps. Based on properties of known lensed quasars, and expectations from accretion disc/BELR modelling, we identify regions of convergence-shear parameter space, map sizes, smooth matter fractions, and pixel resolutions that should be covered. We describe how the computationally time-consuming task of producing ~290000 magnification maps with sufficient resolution (10000^2 pixel/map) to probe scales from the inner edge of the accretion disc to the BELR can be achieved in ~400 days on a 100 teraflop/s high performance computing facility, where the processing performance is achieved with graphics processing units. We illustrate a use-case for the parameter survey by investigating the effects of varying the lens macro-model on accretion disc constraints in the lensed quasar Q2237+0305. We find that although all constraints are consistent within their current error bars, models with more densely packed microlenses tend to predict shallower accretion disc radial temperature profiles. With a large parameter survey such as the one described here, such systematics on microlensing measurements could be fully explored.Comment: 30 pages, 3 figures, accepted for publication in Ap

The 3-Dimensional Distribution of Dust in NGC 891

We produce three-dimensional Monte-Carlo radiative transfer models of the edge-on spiral galaxy NGC 891, a fast-rotating galaxy thought to be an analogue to the Milky Way. The models contain realistic spiral arms and a fractal distribution of clumpy dust. We fit our models to Hubble Space Telescope images corresponding to the B and I bands, using shapelet analysis and a genetic algorithm to generate 30 statistically best-fitting models. These models have a strong preference for spirality and clumpiness, with average face-on attenuation decreasing from 0.24(0.16) to 0.03(0.03) mag in the B(I) band between 0.5 and 2 radial scale-lengths. Most of the attenuation comes from small high-density clumps with low (<10%) filling factors. The fraction of dust in clumps is broadly consistent with results from fitting NGC 891's spectral energy distribution. Because of scattering effects and the intermixed nature of the dust and starlight, attenuation is smaller and less wavelength-dependent than the integrated dust column-density. Our clumpy models typically have higher attenuation at low inclinations than previous radiative transfer models using smooth distributions of stars and dust, but similar attenuation at inclinations above 70 degrees. At all inclinations most clumpy models have less attenuation than expected from previous estimates based on minimizing scatter in the Tully-Fisher relation. Mass-to-light ratios are higher and the intrinsic scatter in the Tully-Fisher relation is larger than previously expected for galaxies similar to NGC 891. The attenuation curve changes as a function of inclination, with R_(B,B-I)=A_(B)/E(B-I) increasing by ~0.75 from face-on to near-edge-on orientations.Comment: 26 pages, 18 figures, accepted for publication in Ap