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Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number of particles greater than or equal to the three needed to define triangle shapes. The resulting shape complexity is a simple scale-invariant quantity that measures the extent to which a collection of particles has a uniform or clustered distribution. As a positive-definite number with an absolute minimum realised on the most uniform distribution the particles can have, it not only characterises all physical structures from crystals to the most complex that can exist but also determines for them a measure that makes richly structured shapes more probable than bland ones. Strikingly, the criterion employed to define the shape complexity forces it to be the product of the two functions that define Newtonian universal gravitation. This suggests both the form and solutions the law of a universe of such particles should have and leads to a theory that not only determines the complexity and probability of any individual shape but also its creation from the maximally uniform shape. It does this moreover in a manner which makes it probable that the cosmological principle, according to which on a sufficiently large scale the universe should have the same appearance everywhere, holds. Our theory relies on universal group-theoretical principles that may allow generalisation to include all forces and general relativity., Comment: 16 pages, Latex, 4 figures

We present the first large-scale, full radiative transfer simulations of the reionization of the intergalactic medium in the presence of Lyman-limit systems (LLSs). To illustrate the impact of LLS opacity, possibly missed by previous simulations, we add either a uniform or spatially-varying hydrogen bound-free opacity. This opacity, implemented as the mean free path (mfp) of the ionizing photons, extrapolates the observed, post-reionization redshift dependence into the epoch of reionization. In qualitative agreement with previous studies, we find that at late times the presence of LLSs slows down the ionization fronts, and alters the size distribution of H II regions. We quantitatively characterize the size distribution and morphological evolution of H II regions and examine the effects of the LLSs on the redshifted 21-cm signal from the patchy reionization. The presence of LLSs extends the ionization history by $\Delta z \sim 0.8$. The LLS absorbers significantly impede the late-time growth of the H II regions. The position dependent LLS distribution slows reionization further and additionally limits the late growth of the ionized regions. However, there is no "freeze out" of the H II regions and the largest regions grow to the size of the simulation volume. The 21-cm power spectra show that at large scales the power drops by a factor of 2 for 50% and 75% ionization stages (at $k = 0.1$ $\text{h} \, \text{Mpc}^{-1} $) reflecting the limiting effect of the LLSs on the growth of ionized patches. The statistical observables such as the RMS of the brightness temperature fluctuations and the peak amplitudes of the 21-cm power spectra at large-scales ($k = 0.05 - 0.1$ $\text{h} \, \text{Mpc}^{-1} $) are diminished by the presence of LLS.

We provide an overview of 21cm tomography of the Cosmic Dawn and Epoch of Reionization as possible with SKA-Low. We show why tomography is essential for studying CD/EoR and present the scales which can be imaged at different frequencies for the different phases of SKA- Low. Next we discuss the different ways in which tomographic data can be analyzed. We end with an overview of science questions which can only be answered by tomography, ranging from the characterization of individual objects to understanding the global processes shaping the Universe during the CD/EoR, Comment: 14 pages, 3 figures. Accepted for publication in the SKA Science Book 'Advancing Astrophysics with the Square Kilometre Array', to appear in 2015. PoS(AASKA14)010

Image subtraction in astronomy is a tool for transient object discovery such as asteroids, extra-solar planets and supernovae. To match point spread functions (PSFs) between images of the same field taken at different times a convolution technique is used. Particularly suitable for large-scale images is a computationally intensive spatially-varying kernel. The underlying algorithm is inherently massively parallel due to unique kernel generation at every pixel location. The spatially-varying kernel cannot be efficiently computed through the Convolution Theorem, and thus does not lend itself to acceleration by Fast Fourier Transform (FFT). This work presents results of accelerated implementation of the spatially-varying kernel image convolution in multi-cores with OpenMP and graphic processing units (GPUs). Typical speedups over ANSI-C were a factor of 50 and a factor of 1000 over the initial IDL implementation, demonstrating that the techniques are a practical and high impact path to terabyte-per-night image pipelines and petascale processing., Comment: 4 pages. Accepted to IEEE-ICIP 2012

We present high resolution H41a hydrogen recombination line observations of the 1.2' (3 pc) region surrounding Sgr A* at 92 GHz using the OVRO Millimeter Array with an angular resolution of 7" x 3" and velocity resolution of 13 km/s. New observations of H31a, H35a, H41a, and H44a lines were obtained using the NRAO 12-m telescope, and their relative line strengths are interpreted in terms of various emission mechanisms. These are the most extensive and most sensitive observations of recombination line to date. Observations of HCO+ (1 - 0) transition at 89 GHz are also obtained simultaneously with a 40% improved angular resolution and 4-15 times improved sensitivity over previous observations, and the distribution and kinematics of the dense molecular gas in the circumnuclear disk (CND) are mapped and compared with those of the ionized gas. The line brightness ratios of the hydrogen recombination lines are consistent with purely spontaneous emission from 7000 K gas with n_e = 20,000 cm$^{-3}$ near LTE condition. A virial analysis suggests that the most prominent molecular gas clumps in the CND have mean densities of 10^7 cm^{-3}, sufficient to withstand the tidal shear in the Galactic Center region. Therefore, these clumps may survive over several dynamical times, and the CND may be a dynamically stable structure. We estimate a total gas mass of 3 x 10^5 solar mass for the CND. \, Comment: 34 pages including 11 figures (4 jpgs), Latex, uses aastex. The full pdf format file including high resolution figures is available at http://www.astro.umass.edu/~myun/papers/SgrA.pdf . To appear in the 20 November 2004 (V616) issue of the Astrophysical Journal

We have made observations of the \ion{H}{1} in the southern ringed barred spiral galaxies NGC~1433 and NGC~6300 with the Australia Telescope Compact Array (ATCA), the main goal being to test the resonance theory for the origin of these rings. NGC~1433 is the prototypical ringed barred spiral, and displays distinct \ion{H}{1}~counterparts to its nuclear ring, inner ring, outer pseudoring, and plume-like features. The $L_{4}$ and $L_{5}$ regions at corotation, as well as the bar itself, are relatively devoid of neutral atomic hydrogen. By associating the inner ring of NGC~1433 with the inner second harmonic resonance, and its outer pseudoring with the outer Lindblad resonance, we are able to infer a bar pattern speed for NGC~1433 of $26\pm5$~km~s$^{-1}$~kpc$^{-1}$. By way of contrast, NGC~6300 possesses a much more extended \ion{H}{1}~disk than NGC~1433. There is a gas ring underlying the inner pseudoring, but it is both broader and slightly larger in diameter than the optical feature. By again linking this inner ring feature to the inner second harmonic resonance, we derive a bar pattern speed for NGC~6300 of $27\pm8$~km~s$^{-1}$~kpc$^{-1}$, but in this case, neither the outer pseudoring nor the nuclear ring predicted by the resonance-ring theory can be identified in NGC~6300. Although it may be the case that the ring in NGC~6300 is not related to a resonance with the bar at all, we postulate instead that NGC~6300 is merely a less well-developed example of a resonance-ring galaxy than is NGC~1433., Comment: 21 pages, aas2pp4 LaTeX, no figures included. Accepted for April 1 1996 ApJ. Full paper (with figures) available from http://www.phys.unsw.edu.au/~sdr/prep.html