Data challenges of time domain astronomy

Astronomy has been at the forefront of the development of the techniques and methodologies of data intensive science for over a decade with large sky surveys and distributed efforts such as the Virtual Observatory. However, it faces a new data deluge with the next generation of synoptic sky surveys which are opening up the time domain for discovery and exploration. This brings both new scientific opportunities and fresh challenges, in terms of data rates from robotic telescopes and exponential complexity in linked data, but also for data mining algorithms used in classification and decision making. In this paper, we describe how an informatics-based approach-part of the so-called "fourth paradigm" of scientific discovery-is emerging to deal with these. We review our experiences with the Palomar-Quest and Catalina Real-Time Transient Sky Surveys; in particular, addressing the issue of the heterogeneity of data associated with transient astronomical events (and other sensor networks) and how to manage and analyze it.Comment: 15 pages, 3 figures, to appear in special issue of Distributed and Parallel Databases on Data Intensive eScienc

A Computation of the Maximal Order Type of the Term Ordering on Finite Multisets

We give a sharpening of a recent result of Aschenbrenner and Pong about the maximal order type of the term ordering on the finite multisets over a wpo. Moreover we discuss an approach to compute maximal order types of well-partial orders which are related to tree embeddings

A serendipitous all sky survey for bright objects in the outer solar system

We use seven yearʼs worth of observations from the Catalina Sky Survey and the Siding Spring Survey covering most of the northern and southern hemisphere at galactic latitudes higher than 20° to search for serendipitously imaged moving objects in the outer solar system. These slowly moving objects would appear as stationary transients in these fast cadence asteroids surveys, so we develop methods to discover objects in the outer solar system using individual observations spaced by months, rather than spaced by hours, as is typically done. While we independently discover eight known bright objects in the outer solar system, the faintest having $V=19.8\pm 0.1,$ no new objects are discovered. We find that the survey is nearly 100% efficient at detecting objects beyond 25 AU for $V\lesssim 19.1$ ($V\lesssim 18.6$ in the southern hemisphere) and that the probability that there is one or more remaining outer solar system object of this brightness left to be discovered in the unsurveyed regions of the galactic plane is approximately 32%

Local SU(5) Unification from the Heterotic String

We construct a 6D supergravity theory which emerges as intermediate step in the compactification of the heterotic string to the supersymmetric standard model in four dimensions. The theory has N=2 supersymmetry and a gravitational sector with one tensor and two hypermultiplets in addition to the supergravity multiplet. Compactification to four dimensions occurs on a T^2/Z_2 orbifold which has two inequivalent pairs of fixed points with unbroken SU(5) and SU(2)xSU(4) symmetry, respectively. All gauge, gravitational and mixed anomalies are cancelled by the Green-Schwarz mechanism. The model has partial 6D gauge-Higgs unification. Two quark-lepton generations are localized at the SU(5) branes, the third family is composed of split bulk hypermultiplets. The top Yukawa coupling is given by the 6D gauge coupling, all other Yukawa couplings are generated by higher-dimensional operators at the SU(5) branes. The presence of the SU(2)xSU(4) brane breaks SU(5) and generates split gauge and Higgs multiplets with N=1 supersymmetry in four dimensions. The third generation is obtained from two split \bar{5}-plets and two split 10-plets, which together have the quantum numbers of one \bar{5}-plet and one 10-plet. This avoids unsuccessful SU(5) predictions for Yukawa couplings of ordinary 4D SU(5) grand unified theories.Comment: 38 pages. v2: Typos correcte

Ultrametric Logarithm Laws, II

We prove positive characteristic versions of the logarithm laws of Sullivan and Kleinbock-Margulis and obtain related results in Metric Diophantine Approximation.Comment: submitted to Montasefte Fur Mathemati

The reporting of studies conducted using observational routinely collected health data statement for pharmacoepidemiology (RECORD-PE).

In pharmacoepidemiology, routinely collected data from electronic health records (including primary care databases, registries, and administrative healthcare claims) are a resource for research evaluating the real world effectiveness and safety of medicines. Currently available guidelines for the reporting of research using non-randomised, routinely collected data—specifically the REporting of studies Conducted using Observational Routinely collected health Data (RECORD) and the Strengthening the Reporting of OBservational studies in Epidemiology (STROBE) statements—do not capture the complexity of pharmacoepidemiological research. We have therefore extended the RECORD statement to include reporting guidelines specific to pharmacoepidemiological research (RECORD-PE). This article includes the RECORD-PE checklist (also available on www.record-statement.org) and explains each checklist item with examples of good reporting. We anticipate that increasing use of the RECORD-PE guidelines by researchers and endorsement and adherence by journal editors will improve the standards of reporting of pharmacoepidemiological research undertaken using routinely collected data. This improved transparency will benefit the research community, patient care, and ultimately improve public health

Nearest Neighbor Distances on a Circle: Multidimensional Case

We study the distances, called spacings, between pairs of neighboring energy levels for the quantum harmonic oscillator. Specifically, we consider all energy levels falling between E and E+1, and study how the spacings between these levels change for various choices of E, particularly when E goes to infinity. Primarily, we study the case in which the spring constant is a badly approximable vector. We first give the proof by Boshernitzan-Dyson that the number of distinct spacings has a uniform bound independent of E. Then, if the spring constant has components forming a basis of an algebraic number field, we show that, when normalized up to a unit, the spacings are from a finite set. Moreover, in the specific case that the field has one fundamental unit, the probability distribution of these spacings behaves quasiperiodically in log E. We conclude by studying the spacings in the case that the spring constant is not badly approximable, providing examples for which the number of distinct spacings is unbounded.Comment: Version 2 is updated to include more discussion of previous works. 17 pages with five figures. To appear in the Journal of Statistical Physic

Naked Singularity Formation In f(R) Gravity

We study the gravitational collapse of a star with barotropic equation of state $p=w\rho$ in the context of $f({\mathcal R})$ theories of gravity. Utilizing the metric formalism, we rewrite the field equations as those of Brans-Dicke theory with vanishing coupling parameter. By choosing the functionality of Ricci scalar as $f({\mathcal R})=\alpha{\mathcal R}^{m}$, we show that for an appropriate initial value of the energy density, if $\alpha$ and $m$ satisfy certain conditions, the resulting singularity would be naked, violating the cosmic censorship conjecture. These conditions are the ratio of the mass function to the area radius of the collapsing ball, negativity of the effective pressure, and the time behavior of the Kretschmann scalar. Also, as long as parameter $\alpha$ obeys certain conditions, the satisfaction of the weak energy condition is guaranteed by the collapsing configuration.Comment: 15 pages, 4 figures, to appear in GR