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

Quantum Circuit Cosmology: The Expansion of the Universe Since the First Qubit

We consider cosmological evolution from the perspective of quantum information. We present a quantum circuit model for the expansion of a comoving region of space, in which initially-unentangled ancilla qubits become entangled as expansion proceeds. We apply this model to the comoving region that now coincides with our Hubble volume, taking the number of entangled degrees of freedom in this region to be proportional to the de Sitter entropy. The quantum circuit model is applicable for at most 140 $e$-folds of inflationary and post-inflationary expansion: we argue that no geometric description was possible before the time $t_1$ when our comoving region was one Planck length across, and contained one pair of entangled degrees of freedom. This approach could provide a framework for modeling the initial state of inflationary perturbations.Comment: v2, minor correction

Asteroid families classification: exploiting very large data sets

The number of asteroids with accurately determined orbits increases fast. The catalogs of asteroid physical observations have also increased, although the number of objects is still smaller than in the orbital catalogs. We developed a new approach to the asteroid family classification by combining the Hierarchical Clustering Method (HCM) with a method to add new members to existing families. This procedure makes use of the much larger amount of information contained in the proper elements catalogs, with respect to classifications using also physical observations for a smaller number of asteroids. Our work is based on the large catalog of the high accuracy synthetic proper elements (available from AstDyS). We first identify a number of core families; to these we attribute the next layer of smaller objects. Then, we remove all the family members from the catalog, and reapply the HCM to the rest. This gives both halo families which extend the core families and new independent families, consisting mainly of small asteroids. These two cases are discriminated by another step of attribution of new members and by merging intersecting families. By using information from absolute magnitudes, we take advantage of the larger size range in some families to analyze their shape in the proper semimajor axis vs. inverse diameter plane. This leads to a new method to estimate the family age (or ages). The results from the previous steps are then analyzed, using also auxiliary information on physical properties including WISE albedos and SDSS color indexes. This allows to solve some difficult cases of families overlapping in the proper elements space but generated by different collisional events. We analyze some examples of cratering families (Massalia, Vesta, Eunomia) which show internal structures, interpreted as multiple collisions. We also discuss why Ceres has no family

Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. Part III: Twist Number Method

We study the writhe, twist and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov--D\'emoulin equilibrium solution, non force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger--Prior formula that is suitable for arbitrary geometry and both force-free and non-force-free models. The magnetic helicity is estimated by the twist multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field.Comment: To be published in Ap