Bayesian Analysis of Two Stellar Populations in Galactic Globular Clusters II: NGC 5024, NGC 5272, and NGC 6352

We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACS Treasury observations of Galactic Globular Clusters to find and characterize two stellar populations in NGC 5024 (M53), NGC 5272 (M3), and NGC 6352. For these three clusters, both single and double-population analyses are used to determine a best fit isochrone(s). We employ a sophisticated Bayesian analysis technique to simultaneously fit the cluster parameters (age, distance, absorption, and metallicity) that characterize each cluster. For the two-population analysis, unique population level helium values are also fit to each distinct population of the cluster and the relative proportions of the populations are determined. We find differences in helium ranging from $\sim$0.05 to 0.11 for these three clusters. Model grids with solar $\alpha$-element abundances ([$\alpha$/Fe] =0.0) and enhanced $\alpha$-elements ([$\alpha$/Fe]=0.4) are adopted.Comment: ApJ, 21 pages, 14 figures, 7 table

BAYESIAN ANALYSIS OF TWO STELLAR POPULATIONS IN GALACTIC GLOBULAR CLUSTERS I: STATISTICAL AND COMPUTATIONAL METHODS

We develop a Bayesian model for globular clusters composed of multiple stellar populations, extending earlier statistical models for open clusters composed of simple (single) stellar populations (e.g., van Dyk et al. 2009; Stein et al. 2013). Specifically, we model globular clusters with two populations that differ in helium abundance. Our model assumes a hierarchical structuring of the parameters in which physical properties—age, metallicity, helium abundance, distance, absorption, and initial mass—are common to (i) the cluster as a whole or to (ii) individual populations within a cluster, or are unique to (iii) individual stars. An adaptive Markov chain Monte Carlo (MCMC) algorithm is devised for model fitting that greatly improves convergence relative to its precursor non-adaptive MCMC algorithm. Our model and computational tools are incorporated into an open-source software suite known as BASE-9. We use numerical studies to demonstrate that our method can recover parameters of two-population clusters, and also show model misspecification can potentially be identified. As a proof of concept, we analyze the two stellar populations of globular cluster NGC 5272 using our model and methods. (BASE-9 is available from GitHub: https://github.com/argiopetech/base/releases)

Визначення правового статусу садівницьких, городницьких та дачних товариств

Розкриваються особливості правового статусу садівницьких, городницьких та дач­них товариств, досліджується їх організаційно-правова форма та ті специфічні пра­вові ознаки, що знаходяться в її основі. У зв’язку з відсутністю правової бази діяль­ності цих товариств, робиться спроба сформувати основні теоретико-правові кон­цептуальні підходи до розуміння їх природи та змоделювати законодавчу схему регулювання їх діяльності.Раскрываются особенности правового статуса садоводческих, огороднических и дачных товариществ, исследуются их организационно-правовая форма и правовые особенности, составляющие ее основание. В связи с отсутствием правовых обоснований деятельности этих товариществ автор стремится сформировать основные теоре­тико-правовые концептуальные подходы к раскрытию их сущности и смоделировать законодательную схему регулирования деятельности рассматриваемых товариществ.In article features of legal status of garden, vegetable-garden and country companies reveal, their organizational legal form and those specific features that are in its basis are investigated. In connection with absence of legal base of activity of these communities is attempted to generate the basic theoretical-legal conceptual approaches to understanding of their nature and model legislative sphere of regulation of their activity becomes

The Escape Problem for Irreversible Systems

The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When this assumption fails many of the results of classical transition-rate theory no longer apply, and no general method exists for computing the weak-noise asymptotics of fundamental quantities such as the mean escape time. In this paper we present a general technique for analysing the weak-noise limit of a wide range of stochastically perturbed continuous-time nonlinear dynamical systems. We simplify the original problem, which involves solving a partial differential equation, into one in which only ordinary differential equations need be solved. This allows us to resolve some old issues for the case when detailed balance holds. When it does not hold, we show how the formula for the mean escape time asymptotics depends on the dynamics of the system along the most probable escape path. We also present new results on short-time behavior and discuss the possibility of focusing along the escape path.Comment: 24 pages, APS revtex macros (version 2.1) now available from PBB via `get oldrevtex.sty

Constraint-based runtime prediction of SLA violations in service orchestrations

Service compositions put together loosely-coupled component services to perform more complex, higher level, or cross-organizational tasks in a platform-independent manner. Quality-of-Service (QoS) properties, such as execution time, availability, or cost, are critical for their usability, and permissible boundaries for their values are defined in Service Level Agreements (SLAs). We propose a method whereby constraints that model SLA conformance and violation are derived at any given point of the execution of a service composition. These constraints are generated using the structure of the composition and properties of the component services, which can be either known or empirically measured. Violation of these constraints means that the corresponding scenario is unfeasible, while satisfaction gives values for the constrained variables (start / end times for activities, or number of loop iterations) which make the scenario possible. These results can be used to perform optimized service matching or trigger preventive adaptation or healing

Simplicity of State and Overlap Structure in Finite-Volume Realistic Spin Glasses

We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent boundary conditions, such as periodic, at most a pair of flip-related (or the appropriate number of symmetry-related in the non-Ising case) states appear, and the Parisi overlap distribution correspondingly exhibits at most a pair of delta-functions at plus/minus the self-overlap. This rules out the nonstandard SK picture introduced by us earlier, and when combined with our previous elimination of more standard versions of the mean field picture, argues against the possibility of even limited versions of mean field ordering in realistic spin glasses. If broken spin flip symmetry should occur, this leaves open two main possibilities for ordering in the spin glass phase: the droplet/scaling two-state picture, and the chaotic pairs many-state picture introduced by us earlier. We present scaling arguments which provide a possible physical basis for the latter picture, and discuss possible reasons behind numerical observations of more complicated overlap structures in finite volumes.Comment: 22 pages (LaTeX; needs revtex), 1 figure (PostScript); to appear in Physical Review

Heat kernel estimates and spectral properties of a pseudorelativistic operator with magnetic field

Based on the Mehler heat kernel of the Schroedinger operator for a free electron in a constant magnetic field an estimate for the kernel of E_A is derived, where E_A represents the kinetic energy of a Dirac electron within the pseudorelativistic no-pair Brown-Ravenhall model. This estimate is used to provide the bottom of the essential spectrum for the two-particle Brown-Ravenhall operator, describing the motion of the electrons in a central Coulomb field and a constant magnetic field, if the central charge is restricted to Z below or equal 86