Algorithms for Stable Matching and Clustering in a Grid

We study a discrete version of a geometric stable marriage problem originally proposed in a continuous setting by Hoffman, Holroyd, and Peres, in which points in the plane are stably matched to cluster centers, as prioritized by their distances, so that each cluster center is apportioned a set of points of equal area. We show that, for a discretization of the problem to an $n\times n$ grid of pixels with $k$ centers, the problem can be solved in time $O(n^2 \log^5 n)$, and we experiment with two slower but more practical algorithms and a hybrid method that switches from one of these algorithms to the other to gain greater efficiency than either algorithm alone. We also show how to combine geometric stable matchings with a $k$-means clustering algorithm, so as to provide a geometric political-districting algorithm that views distance in economic terms, and we experiment with weighted versions of stable $k$-means in order to improve the connectivity of the resulting clusters.Comment: 23 pages, 12 figures. To appear (without the appendices) at the 18th International Workshop on Combinatorial Image Analysis, June 19-21, 2017, Plovdiv, Bulgari

Slit and integral-field optical spectroscopy of the enigmatic quasar HE0450-2958

Interest in the quasar HE0450-2958 arose following the publication of the non-detection of its expected massive host, leading to various interpretations. This article investigates the gaseous and stellar contents of the system through additional VLT/FORS slit spectra and integral field spectroscopy from VLT/VIMOS. We apply our MCS deconvolution algorithm on slit spectra for the separation of the QSO and diffuse components, and develop a new method to remove the point sources in Integral Field Spectra, allowing extraction of velocity maps, narrow-line images, spatially resolved spectra or ionization diagrams of the surroundings of HE0450-2958. The whole system is embedded in gas, mostly ionized by the QSO radiation field and shocks associated with radio jets. The observed gas and star dynamics are unrelated, revealing a strongly perturbed system. Despite longer spectroscopic observations, the host galaxy remains undetected.Comment: 9 pages, 13 figures, in press in A&

The use of neural network algorithms for the classification of undifferentiated arthritis by synovial histopathology

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The diagnostic value of synovial histopathology in undifferentiated inflammatory arthritis: a prospective study in 154 consecutive patients

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Dark Sector from Interacting Canonical and Non-Canonical Scalar Fields

In this work it is investigated general models with interactions between two canonical scalar fields and between one non-canonical (tachyon-type) and one canonical scalar field. The potentials and couplings to the gravity are selected through the Noether symmetry approach. These general models are employed to describe interactions between dark energy and dark matter, with the fields being constrained by the astronomical data. The cosmological solutions of some cases are compared with the observed evolution of the late Universe.Comment: 20 pages, 13 figures, correction of misprints in eqs. (4), (5), (43), (44

ZOBOV: a parameter-free void-finding algorithm

ZOBOV (ZOnes Bordering On Voidness) is an algorithm that finds density depressions in a set of points, without any free parameters, or assumptions about shape. It uses the Voronoi tessellation to estimate densities, which it uses to find both voids and subvoids. It also measures probabilities that each void or subvoid arises from Poisson fluctuations. This paper describes the ZOBOV algorithm, and the results from its application to the dark-matter particles in a region of the Millennium Simulation. Additionally, the paper points out an interesting high-density peak in the probability distribution of dark-matter particle densities.Comment: 10 pages, 8 figures, MNRAS, accepted. Added explanatory figures, and better edge-detection methods. ZOBOV code available at http://www.ifa.hawaii.edu/~neyrinck/vobo