Queues with random back-offs

We consider a broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation periods may be initiated after each service completion, and can be randomly terminated with certain probabilities that depend on the queue length. We examine the scaled queue length and delay in a heavy-traffic regime, and demonstrate a sharp trichotomy, depending on how the activation rate and vacation probability behave as function of the queue length. In particular, the effect of the vacation periods may either (i) completely vanish in heavy-traffic conditions, (ii) contribute an additional term to the queue lengths and delays of similar magnitude, or even (iii) give rise to an order-of-magnitude increase. The heavy-traffic asymptotics are obtained by combining stochastic lower and upper bounds with exact results for some specific cases. The heavy-traffic trichotomy provides valuable insight in the impact of the back-off algorithms on the delay performance in wireless random-access networks

The Size, Shape, and Scattering of Sagittarius A* at 86 GHz: First VLBI with ALMA

The Galactic center supermassive black hole Sagittarius A* (Sgr A*) is one of the most promising targets to study the dynamics of black hole accretion and outflow via direct imaging with very long baseline interferometry (VLBI). At 3.5 mm (86 GHz), the emission from Sgr A* is resolvable with the Global Millimeter VLBI Array (GMVA). We present the first observations of Sgr A* with the phased Atacama Large Millimeter/submillimeter Array (ALMA) joining the GMVA. Our observations achieve an angular resolution of ~87 μas, improving upon previous experiments by a factor of two. We reconstruct a first image of the unscattered source structure of Sgr A* at 3.5 mm, mitigating the effects of interstellar scattering. The unscattered source has a major-axis size of 120 ± 34 μas (12 ± 3.4 Schwarzschild radii) and a symmetrical morphology (axial ratio of 1.2_(-0.2)^(+0.3)), which is further supported by closure phases consistent with zero within 3σ. We show that multiple disk-dominated models of Sgr A* match our observational constraints, while the two jet-dominated models considered are constrained to small viewing angles. Our long-baseline detections to ALMA also provide new constraints on the scattering of Sgr A*, and we show that refractive scattering effects are likely to be weak for images of Sgr A* at 1.3 mm with the Event Horizon Telescope. Our results provide the most stringent constraints to date for the intrinsic morphology and refractive scattering of Sgr A*, demonstrating the exceptional contribution of ALMA to millimeter VLBI

Size Class Dependent Relationships between Temperature and Phytoplankton Photosynthesis-Irradiance Parameters in the Atlantic Ocean

Over the past decade, a number of methods have been developed to estimate size-class primary production from either in situ phytoplankton pigment data or remotely-sensed data. In this context, the first objective of this study was to compare two methods of estimating size class specific (micro-, nano-, and pico-phytoplankton) photosynthesis-irradiance (PE) parameters from pigment data. The second objective was to analyse the relationship between environmental variables (temperature, nitrate and PAR) and PE parameters in the different size-classes. A large dataset was used of simultaneous measurements of the PE parameters (n = 1,260) and phytoplankton pigment markers (n = 2,326), from 3 different institutes. There were no significant differences in mean PE parameters of the different size classes between the chemotaxonomic method of Uitz et al. (2008) and the pigment markers and carbon-to-Chl a ratios method of Sathyendranath et al. (2009). For both methods, mean maximum photosynthetic rates (PBm ) for micro-phytoplankton were significantly lower than those for pico-phytoplankton and nano-phytoplankton. The mean light limited slope (�B) for nano-phytoplankton were significantly higher than for the other size taxa. For micro-phytoplankton dominated samples identified using the Sathyendranath et al. (2009) method, both PBm and �B exhibited a significant, positive linear relationship with temperature, whereas for pico-phytoplankton the correlation with temperature was negative. Nano-phytoplankton dominated samples showed a positive correlation between PBm and temperature, whereas for �B and the light saturation parameter (Ek) the correlations were not significant. For the Uitz et al. (2008) method, only micro-phytoplankton PBm , pico-phytoplankton �B, nano- and pico-phytoplankton Ek exhibited significant relationships with temperature. The temperature ranges occupied by the size classes derived using these methods differed. The Uitz et al. (2008) method exhibited a wider temperature range compared to those derived from the Sathyendranath et al. (2009) method. The differences arise from the classification of mixed populations. Based on these patterns, we therefore recommend using the Sathyendranath et al. (2009) method to derive micro-phytoplankton PE parameters at sea water temperatures up to 8◦C during monospecific blooms and the Uitz et al. (2008) method to derive PE parameters of mixed populations over the temperature range from 8 to 18◦C. Both methods exhibited similar relationships between pico-phytoplankton PE parameters and temperatures >18◦C

High Resolution Linear Polarimetric Imaging for the Event Horizon Telescope

Images of the linear polarization of synchrotron radiation around Active Galactic Nuclei (AGN) identify their projected magnetic field lines and provide key data for understanding the physics of accretion and outflow from supermassive black holes. The highest resolution polarimetric images of AGN are produced with Very Long Baseline Interferometry (VLBI). Because VLBI incompletely samples the Fourier transform of the source image, any image reconstruction that fills in unmeasured spatial frequencies will not be unique and reconstruction algorithms are required. In this paper, we explore extensions of the Maximum Entropy Method (MEM) to linear polarimetric VLBI imaging. In contrast to previous work, our polarimetric MEM algorithm combines a Stokes I imager that uses only bispectrum measurements that are immune to atmospheric phase corruption with a joint Stokes Q and U imager that operates on robust polarimetric ratios. We demonstrate the effectiveness of our technique on 7- and 3-mm wavelength quasar observations from the VLBA and simulated 1.3-mm Event Horizon Telescope observations of Sgr A* and M87. Consistent with past studies, we find that polarimetric MEM can produce superior resolution compared to the standard CLEAN algorithm when imaging smooth and compact source distributions. As an imaging framework, MEM is highly adaptable, allowing a range of constraints on polarization structure. Polarimetric MEM is thus an attractive choice for image reconstruction with the EHT.Comment: 19 pages, 9 figures. Accepted for publication in ApJ. Imaging code available at https://github.com/achael/eht-imaging

Primary Production: Sensitivity to Surface Irradiance and Implications for Archiving Data

An equation is derived to express the sensitivity of daily, watercolumn production by phytoplankton in the ocean to variations in irradiance at the sea surface. Assuming no spectral effects, and a vertically uniform chlorophyll profile, the sensitivity is a function only of the dimensionless irradiance. Spectral effects can be accounted for as a function of the chlorophyll concentration. At the global scale, the relative reduction in daily production consequent on halving the surface irradiance (representing the expected scope for variation in surface irradiance under natural conditions) is found to be from 30 to 40%. Choice of data source for irradiance may incur a further systematic error of up to 15%. Given that local irradiance (the principal forcing for primary production) may vary from day to day, the issue of how to archive production data for the most generality is discussed and recommendations made in this regard

Dynamical Imaging with Interferometry

By linking widely separated radio dishes, the technique of very long baseline interferometry (VLBI) can greatly enhance angular resolution in radio astronomy. However, at any given moment, a VLBI array only sparsely samples the information necessary to form an image. Conventional imaging techniques partially overcome this limitation by making the assumption that the observed cosmic source structure does not evolve over the duration of an observation, which enables VLBI networks to accumulate information as the Earth rotates and changes the projected array geometry. Although this assumption is appropriate for nearly all VLBI, it is almost certainly violated for submillimeter observations of the Galactic Center supermassive black hole, Sagittarius A* (Sgr A*), which has a gravitational timescale of only ~20 seconds and exhibits intra-hour variability. To address this challenge, we develop several techniques to reconstruct dynamical images ("movies") from interferometric data. Our techniques are applicable to both single-epoch and multi-epoch variability studies, and they are suitable for exploring many different physical processes including flaring regions, stable images with small time-dependent perturbations, steady accretion dynamics, or kinematics of relativistic jets. Moreover, dynamical imaging can be used to estimate time-averaged images from time-variable data, eliminating many spurious image artifacts that arise when using standard imaging methods. We demonstrate the effectiveness of our techniques using synthetic observations of simulated black hole systems and 7mm Very Long Baseline Array observations of M87, and we show that dynamical imaging is feasible for Event Horizon Telescope observations of Sgr A*.Comment: 16 Pages, 12 Figures, Accepted for publication in Ap

Scratching beneath the surface: a model to predict the vertical distribution of Prochlorococcus using remote sensing.

The unicellular cyanobacterium Prochlorococcus is the most dominant resident of the subtropical gyres, which are considered to be the largest biomes on Earth. In this study, the spatial and temporal variability in the global distribution of Prochlorococcus was estimated in the Atlantic Ocean using an empirical model based on data from 13 Atlantic Meridional Transect cruises. Our model uses satellite-derived sea surface temperature (SST), remote-sensing reflectance at 443 and 488 nm, and the water temperature at a depth of 200 m from Argo data. The model divides the population of Prochlorococcus into two groups: ProI, which dominates under high-light conditions associated with the surface, and ProII, which favors low-light found near the deep chlorophyll maximum. ProI and ProII are then summed to provide vertical profiles of the concentration of Prochlorococcus cells. This model predicts that Prochlorococcus cells contribute 32 Mt of carbon biomass (7.4×1026 cells) to the Atlantic Ocean, concentrated mainly within the subtropical gyres (35%) and areas near the Equatorial Convergence Zone (30%). When projected globally, 3.4×1027 Prochlorococcus cells represent 171 Mt of carbon biomass, with 43% of this global biomass allocated to the upper ocean (0-45 m depth). Annual cell standing stocks were relatively stable between the years 2003 and 2014, and the contribution of the gyres varies seasonally as gyres expand and contract, tracking changes in light and temperature, with lowest cell abundances during the boreal and austral winter (1.4×1013 cells m-2), when surface cell concentrations were highest (9.8×104 cells ml-1), whereas the opposite scenario was observed in spring-summer (2×1013 cells m-2). This model provides a three-dimensional view of the abundance of Prochlorococcus cells, revealing that Prochlorococcus contributes significantly to total phytoplankton biomass in the Atlantic Ocean, and can be applied using either in-situ measurements at the sea surface (r2=0.83) or remote-sensing observables (r2=0.58)