A network-based view of regional growth

The need to better understand the mechanisms underlying regional growth patterns is widely recognised. This paper argues that regional growth is partly a function of the value created through inter-organisational flows of knowledge within and across regions. It is proposed that investment in calculative networks by organisations to access knowledge is a form of capital, termed network capital, which should be incorporated into regional growth models. The paper seeks to develop a framework to capture the value of network capital within these models based on the spatial configuration and the nature of the knowledge flowing through networks

The Formation of Globules in Planetary Nebulae

We discuss the formation of globules in planetary nebulae, typified by those observed in the Helix Nebula. We show that the properties of the globules, their number, mass, separation, and overall geometry strongly support a scenario in which globules are formed by the fragmentation of a swept-up shell as opposed to models in which the knots form in the AGB wind. We show that the RT or other instabilities which lead to the break-up of shells formed in the nebulae by fast winds or ionization fronts can produce arrays of globules with the overall geometry and within the mass range observed. We also show that the presence of a magnetic field in the circumstellar gas may play an important role in controlling the fragmentation process. Using field strengths measured in the precursor AGB envelopes, we find that close to the central star where the fields are relatively strong, the wavelengths of unstable MRT modes are larger than the shell dimensions, and the fragmentation of the shell is suppressed. The wavelength of the most unstable MRT mode decreases with increasing distance from the star, and when it becomes comparable to the shell thickness, it can lead to the sudden, rapid break-up of an accelerating shell. For typical nebula parameters, the model results in numerous fragments with a mass scale and a separation scale similar to those observed. Our results provide a link between global models of PN shaping in which shells form via winds and ionization fronts, and the formation of small scale structures in the nebulae.Comment: 4 pages, 2 figures, to appear in IAU Symp. 234, Planetary Nebulae in Our Galaxy and Beyond, eds. M. J. Barlow, R. H. Mende

Deep optical imaging of AGB circumstellar envelopes

We report results of a program to image the extended circumstellar envelopes of asymptotic giant branch (AGB) stars in dust-scattered Galactic light. The goal is to characterize the shapes of the envelopes to probe the mass-loss geometry and the presence of hidden binary companions. The observations consist of deep optical imaging of 22 AGB stars with high mass loss rates: 16 with the ESO 3.5 m NTT telescope, and the remainder with other telescopes. The circumstellar envelopes are detected in 15 objects, with mass loss rates > 2E-6 Msun/year. The surface brightness of the envelopes shows a strong decrease with Galactic radius, which indicates a steep radial gradient in the interstellar radiation field. The envelopes range from circular to elliptical in shape, and we characterize them by the ellipticity (E = major/minor axis) of iso-intensity contours. We find that about 50 percent of the envelopes are close to circular with E 1.2. We interpret the shapes in terms of populations of single stars and binaries whose envelopes are flattened by a companion. The distribution of E is qualitatively consistent with expectations based on population synthesis models of binary AGB stars. We also find that about 50 percent of the sample exhibit small-scale, elongated features in the central regions. We interpret these as the escape of light from the central star through polar holes, which are also likely produced by companions. Our observations of envelope flattening and polar holes point to a hidden population of companions within the circumstellar envelopes of AGB stars. These companions are expected to play an important role in the transition to post-AGB stars and the formation of planetary nebulae.Comment: 19 pages, 13 figures, color pictures in Appendix, accepted by A&

PASS-GLM: polynomial approximate sufficient statistics for scalable Bayesian GLM inference

Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent estimates of uncertainty, incorporation of prior information, and sharing of power across experiments via hierarchical models. In practice, however, the approximate Bayesian methods necessary for inference have either failed to scale to large data sets or failed to provide theoretical guarantees on the quality of inference. We propose a new approach based on constructing polynomial approximate sufficient statistics for GLMs (PASS-GLM). We demonstrate that our method admits a simple algorithm as well as trivial streaming and distributed extensions that do not compound error across computations. We provide theoretical guarantees on the quality of point (MAP) estimates, the approximate posterior, and posterior mean and uncertainty estimates. We validate our approach empirically in the case of logistic regression using a quadratic approximation and show competitive performance with stochastic gradient descent, MCMC, and the Laplace approximation in terms of speed and multiple measures of accuracy -- including on an advertising data set with 40 million data points and 20,000 covariates.Comment: In Proceedings of the 31st Annual Conference on Neural Information Processing Systems (NIPS 2017). v3: corrected typos in Appendix

Neutral atomic carbon in the globules of the Helix

We report detection of the 609u line of neutral atomic carbon in globules of the Helix nebula. The measurements were made towards the position of peak CO emission. At the same position, we obtained high-quality CO(2-1) and 13CO(2-1) spectra and a 135" x 135" map in CO(2-1). The velocity distribution of CI shows six narrow (1 -> 2 km/sec) components which are associated with individual globules traced in CO. The CI column densities are 0.5 -> 1.2 x 10^16/cm^2. CI is found to be a factor of ~6 more abundant than CO. Our estimate for the mass of the neutral envelope is an order of magnitude larger than previous estimates. The large abundance of CI in the Helix can be understood as a result of the gradual photoionisation of the molecular envelope by the central star's radiation field.Comment: 5 pages, Latex, AAS macros, 3 EPS figures, to appear in Astrophysical Journal Letter

The Shapes of AGB Envelopes as Probes of Binary Companions

We describe how the large scale geometry of the circumstellar envelopes of asymptotic giant branch stars can be used to probe the presence of unseen stellar companions. A nearby companion modifies the mass loss by gravitationally focusing the wind towards the orbital plane, and thereby determines the shape of the envelope at large distances from the star. Using available simulations, we develop a prescription for the observed shapes of envelopes in terms of the binary parameters, envelope orientation, and type of observation. The prescription provides a tool for the analysis of envelope images at optical, infrared, and millimetre wavelengths, which can be used to constrain the presence of companions in well observed cases. We illustrate this approach by examining the possible role of binary companions in triggering the onset of axi-symmetry in planetary nebula formation. If interaction with the primary leads to axi-symmetry, the spherical halos widely seen around newly formed nebulae set limits on the companion mass. Only low mass objects may orbit close to the primary without observable shaping effects: they remain invisible until the interaction causes a sudden change in the mass loss geometry.Comment: 11 pages, 7 figures, to appear in MNRA