The Kuratowski convergence of medial axes and conflict sets

This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed, definable (in some o-minimal structure) sets in {\Rz}^n under deformations. The second one is devoted to a similar study of conflict sets in definable families. We apply a new approach to the deformation process. Instead of seeing it as a `jump' from the initial to the final state, we perceive it as a continuous process, expressed using the Kuratowski convergence of sets (hence, unlike other authors, we do not require any regularity of the deformation). Our main `medial axis inner semi-continuity' result has already proved useful, as it was used to compute the tangent cone of the medial axis with application in singularity theory.Comment: The preprint has been extended to include also the study of the behaviour of the conflict set of a continuous family of definable sets performed with a new co-author. Therefore the title has slightly been changed, too. Besides that, the references have also been updated and in the last version we strengthened the statement of Theorem 5.1

From actinides to zinc: Using the full abundance pattern of the brightest star in Reticulum II to distinguish between different r-process sites

The ultra-faint dwarf galaxy Reticulum II was enriched by a rare and prolific r-process event, such as a neutron star merger. To investigate the nature of this event, we present high-resolution Magellan/MIKE spectroscopy of the brightest star in this galaxy. The high signal-to-noise allows us to determine the abundances of 41 elements, including the radioactive actinide element Th and first ever detections of third r-process peak elements (Os and Ir) in a star outside the Milky Way. The observed neutron-capture element abundances closely match the solar r-process component, except for the first r-process peak which is significantly lower than solar but matches other r-process enhanced stars. The ratio of first peak to heavier r-process elements implies the r-process site produces roughly equal masses of high and low electron fraction ejecta, within a factor of 2. We compare the detailed abundance pattern to predictions from nucleosynthesis calculations of neutron star mergers and magneto-rotationally driven jet supernovae, finding that nuclear physics uncertainties dominate over astrophysical uncertainties. We measure \log\mbox{Th/Eu} = -0.84 \pm 0.06\,\text{(stat)} \pm 0.22\,\text{(sys)}, somewhat lower than all previous Th/Eu observations. The youngest age we derive from this ratio is $21.7 \pm 2.8\,\text{(stat)} \pm 10.3\,\text{(sys)}$ Gyr, indicating that current initial production ratios do not well describe the r-process event in Reticulum II. The abundance of light elements up to Zn are consistent with extremely metal-poor Milky Way halo stars. They may eventually provide a way to distinguish between neutron star mergers and magneto-rotationally driven jet supernovae, but this would require more detailed knowledge of the chemical evolution of Reticulum II.Comment: 23 pages, 7 figures, accepted to Ap

A Presheaf Interpretation of the Generalized Freyd Conjecture

We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new results, but at least one known example drops out quite trivially.Comment: 8 pages; formerly titled "Thinking about the Freyd conjecture

Policy analysis for self-administrated role-based access control

Current techniques for security analysis of administrative role-based access control (ARBAC) policies restrict themselves to the separate administration assumption that essentially separates administrative roles from regular ones. The naive algorithm of tracking all users is all that is known for the security analysis of ARBAC policies without separate administration, and the state space explosion that this results in precludes building effective tools. In contrast, the separate administration assumption greatly simplifies the analysis since it makes it sufficient to track only one user at a time. However, separation limits the expressiveness of the models and restricts modeling distributed administrative control. In this paper, we undertake a fundamental study of analysis of ARBAC policies without the separate administration restriction, and show that analysis algorithms can be built that track only a bounded number of users, where the bound depends only on the number of administrative roles in the system. Using this fundamental insight paves the way for us to design an involved heuristic to further tame the state space explosion in practical systems. Our results are also very effective when applied on policies designed under the separate administration restriction. We implement our techniques and report on experiments conducted on several realistic case studies

Online Sorting via Searching and Selection

In this paper, we present a framework based on a simple data structure and parameterized algorithms for the problems of finding items in an unsorted list of linearly ordered items based on their rank (selection) or value (search). As a side-effect of answering these online selection and search queries, we progressively sort the list. Our algorithms are based on Hoare's Quickselect, and are parameterized based on the pivot selection method. For example, if we choose the pivot as the last item in a subinterval, our framework yields algorithms that will answer q<=n unique selection and/or search queries in a total of O(n log q) average time. After q=\Omega(n) queries the list is sorted. Each repeated selection query takes constant time, and each repeated search query takes O(log n) time. The two query types can be interleaved freely. By plugging different pivot selection methods into our framework, these results can, for example, become randomized expected time or deterministic worst-case time. Our methods are easy to implement, and we show they perform well in practice

Anisotropic multiple bounce models

We analyze the Galileon ghost condensate implementation of a bouncing cosmological model in the presence of a non negligible anisotropic stress. We exhibit its structure, which we find to be far richer than previously thought. In particular, even restricting attention to a single set of underlying microscopic parameters, we obtain, numerically, many qualitatively different regimes: depending on the initial conditions on the scalar field leading the dynamics of the universe, the contraction phase can evolve directly towards a singularity, avoid it by bouncing once, or even bounce many times before settling into an ever-expanding phase. We clarify the behavior of the anisotropies in these various situations.Comment: 11 pages, 9 figures, minor correction

Merging KK-means with hierarchical clustering for identifying general-shaped groups

Clustering partitions a dataset such that observations placed together in a group are similar but different from those in other groups. Hierarchical and $K$-means clustering are two approaches but have different strengths and weaknesses. For instance, hierarchical clustering identifies groups in a tree-like structure but suffers from computational complexity in large datasets while $K$-means clustering is efficient but designed to identify homogeneous spherically-shaped clusters. We present a hybrid non-parametric clustering approach that amalgamates the two methods to identify general-shaped clusters and that can be applied to larger datasets. Specifically, we first partition the dataset into spherical groups using $K$-means. We next merge these groups using hierarchical methods with a data-driven distance measure as a stopping criterion. Our proposal has the potential to reveal groups with general shapes and structure in a dataset. We demonstrate good performance on several simulated and real datasets.Comment: 16 pages, 1 table, 9 figures; accepted for publication in Sta