Streaming Algorithms for Submodular Function Maximization

We consider the problem of maximizing a nonnegative submodular set function $f:2^{\mathcal{N}} \rightarrow \mathbb{R}^+$ subject to a $p$-matchoid constraint in the single-pass streaming setting. Previous work in this context has considered streaming algorithms for modular functions and monotone submodular functions. The main result is for submodular functions that are {\em non-monotone}. We describe deterministic and randomized algorithms that obtain a $\Omega(\frac{1}{p})$-approximation using $O(k \log k)$-space, where $k$ is an upper bound on the cardinality of the desired set. The model assumes value oracle access to $f$ and membership oracles for the matroids defining the $p$-matchoid constraint.Comment: 29 pages, 7 figures, extended abstract to appear in ICALP 201

Report of the IAU/IAG Joint Working Group on Theory of Earth Rotation and Validation

This report focuses on some selected scientific outcomes of the activities developed by the IAU/IAG Joint Working Group on Theory of Earth rotation and validation along the term 2015–2019. It is based on its end-of-term report to the IAG Commission 3 published in the Travaux de l’IAG 2015–2019, which in its turn updates previous reports to the IAG and IAU, particularly the triennial report 2015–2018 to the IAU Commission A2, and the medium term report to the IAG Commission 3 (2015–2017). The content of the report has served as a basis for the IAG General Assembly to adopt Resolution 5 on Improvement of Earth rotation theories and models.JMF, AE, and JG were partially supported by Spanish Project AYA2016-79775-P (AEI/FEDER, UE). The work of RSG described in this paper was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Support for that work was provided by the Earth Surface and Interior Focus Area of NASA’s Science Mission Directorate

Astrometric Control of the Inertiality of the Hipparcos Catalog

Based on the most complete list of the results of an individual comparison of the proper motions for stars of various programs common to the Hipparcos catalog, each of which is an independent realization of the inertial reference frame with regard to stellar proper motions, we redetermined the vector $\omega$ of residual rotation of the ICRS system relative to the extragalactic reference frame. The equatorial components of this vector were found to be the following: $\omega_x = +0.04\pm 0.15$ mas yr$^{-1}$, $\omega_y = +0.18\pm 0.12$ mas yr$^{-1}$, and $\omega_z = -0.35\pm 0.09$ mas yr$^{-1}$.Comment: 8 pages, 1 figur

A Calanais myth and an alignment of the east stone-row with both the rising of the Pleiades and crossovers of Venus at sunrise on the summer solstices

Acknowledgements My thanks to Stefan Sagrott of Historic Environment Scotland for his help in obtaining Patrick Ashmore’s data and to David Forrest, School of Geographical and Earth Sciences, University of Glasgow, for providing a copy of David Tait’s map of Calanais.Peer reviewedPublisher PD

New precession expressions, valid for long time intervals ( Corrigendum )

International audienc

Carbonea in Ukraine

Carbonea (Lecanoraceae, Ascomycota) genus contains about 20 species of lichenized and lichenicolous fungi. Four species among them are known in Ukraine: Carbonea assimilis (Körb.) Hafellner et Hertel, C. vitellinaria (Nyl.) Hertel, C. invadens (H. Magn.) M.P. Andreev, and C. vorticosa (Flörke) Hertel. We report about five taxa of Carbonea in Ukraine in the Carpathians and the Crimean peninsula: C. aggregantula (Müll. Arg.) Diederich & Triebel, C. supersparsa (Nyl.) Hertel (both new to Ukraine), C. assimilis (identification not confirmed by us), C. vitellinaria and C. vorticosa. We provide a description of the genus and characterize the Ukrainian taxa. We also present the key for determination of Carbonea involving species known in Ukraine and also those that might eventually be found in Ukraine. Morphologically, species similar to Carbonea from other genera are also included in the determination key. Carbonea invadens was incorrectly recorded from Ukraine, the respective voucher specimen is Scoliciosporum intrusum (Th. Fr.) Hafellner, poorly known taxon similar to Carbonea that is new for Ukraine. We also provide a characterization of Scoliciosporum intrusum and included it into the key

New precession expressions, valid for long time intervals ( Corrigendum )

International audienc

New precession expressions, valid for long time intervals

Context. The present IAU model of precession, like its predecessors, is given as a set of polynomial approximations of various precession parameters intended for high-accuracy applications over a limited time span. Earlier comparisons with numerical integrations have shown that this model is valid only for a few centuries around the basic epoch, J2000.0, while for more distant epochs it rapidly diverges from the numerical solution. In our preceding studies we also obtained preliminary developments for the precessional contribution to the motion of the equator: coordinates X,Y of the precessing pole and precession parameters ψA,ωA, suitable for use over long time intervals. Aims. The goal of the present paper is to obtain upgraded developments for various sets of precession angles that would fit modern observations near J2000.0 and at the same time fit numerical integration of the motions of solar system bodies on scales of several thousand centuries. Methods. We used the IAU 2006 solutions to represent the precession of the ecliptic and of the equator close to J2000.0 and, for more distant epochs, a numerical integration using the Mercury 6 package and solutions by Laskar et al. (1993, A&A, 270, 522) with upgraded initial conditions and constants to represent the ecliptic, and general precession and obliquity, respectively. From them, different precession parameters were calculated in the interval  ± 200 millennia from J2000.0, and analytical expressions are found that provide a good fit for the whole interval. Results. Series for the various precessional parameters, comprising a cubic polynomial plus from 8 to 14 periodic terms, are derived that allow precession to be computed with an accuracy comparable to IAU 2006 around the central epoch J2000.0, a few arcseconds throughout the historical period, and a few tenths of a degree at the ends of the  ± 200 millennia time span. Computer algorithms are provided that compute the ecliptic and mean equator poles and the precession matrix