Computing generalized inverses using LU factorization of matrix product

An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and T*(AT*)+, where R and T are rational matrices with appropriate dimensions and corresponding rank. The proposed algorithm is based on these general representations and the Cholesky factorization of symmetric positive matrices. The algorithm is implemented in programming languages MATHEMATICA and DELPHI, and illustrated via examples. Numerical results of the algorithm, corresponding to the Moore-Penrose inverse, are compared with corresponding results obtained by several known methods for computing the Moore-Penrose inverse

Effective partitioning method for computing weighted Moore-Penrose inverse

We introduce a method and an algorithm for computing the weighted Moore-Penrose inverse of multiple-variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices. These methods and algorithms are generalizations of algorithms developed in [M.B. Tasic, P.S. Stanimirovic, M.D. Petkovic, Symbolic computation of weighted Moore-Penrose inverse using partitioning method, Appl. Math. Comput. 189 (2007) 615-640] to multiple-variable rational and polynomial matrices and improvements of these algorithms on sparse matrices. Also, these methods are generalizations of the partitioning method for computing the Moore-Penrose inverse of rational and polynomial matrices introduced in [P.S. Stanimirovic, M.B. Tasic, Partitioning method for rational and polynomial matrices, Appl. Math. Comput. 155 (2004) 137-163; M.D. Petkovic, P.S. Stanimirovic, Symbolic computation of the Moore-Penrose inverse using partitioning method, Internat. J. Comput. Math. 82 (2005) 355-367] to the case of weighted Moore-Penrose inverse. Algorithms are implemented in the symbolic computational package MATHEMATICA

Compact HI clouds from the GALFA-HI survey

The Galactic Arecibo L-band Feed Array HI (GALFA-HI) survey is mapping the entire Arecibo sky at 21-cm, over a velocity range of -700 to +700 km/s (LSR), at a velocity resolution of 0.18 km/s and a spatial resolution of 3.5 arcmin. The unprecedented resolution and sensitivity of the GALFA-HI survey have resulted in the detection of numerous isolated, very compact HI clouds at low Galactic velocities, which are distinctly separated from the HI disk emission. In the limited area of ~4600 deg$^2$ surveyed so far, we have detected 96 of such compact clouds. The detected clouds are cold with a median T$_{k,max}$ (the kinetic temperature in the case in which there is no non-thermal broadening) of 300 K. Moreover, these clouds are quite compact and faint, with median values of 5 arcmin in angular size, 0.75 K in peak brightness temperature, and $5 \times 10^{18}$ cm$^{-2}$ in HI column density. Most of the clouds deviate from Galactic rotation at the 20-30 km/s level, and a significant fraction show evidence for a multiphase medium and velocity gradients. No counterparts for these clouds were found in other wavebands. From the modeling of spatial and velocity distributions of the whole compact cloud population, we find that the bulk of the compact clouds are related to the Galactic disk, and their distances are likely to be in the range of 0.1 to a few kpc. We discuss various possible scenarios for the formation and maintenance of this cloud population and its significance for Galactic ISM studies.Comment: Accepted for publication in the Astrophysical Journa

The Structure of a Low-Metallicity Giant Molecular Cloud Complex

To understand the impact of low metallicities on giant molecular cloud (GMC) structure, we compare far infrared dust emission, CO emission, and dynamics in the star-forming complex N83 in the Wing of the Small Magellanic Cloud. Dust emission (measured by Spitzer as part of the S3MC and SAGE-SMC surveys) probes the total gas column independent of molecular line emission and traces shielding from photodissociating radiation. We calibrate a method to estimate the dust column using only the high-resolution Spitzer data and verify that dust traces the ISM in the HI-dominated region around N83. This allows us to resolve the relative structures of H2, dust, and CO within a giant molecular cloud complex, one of the first times such a measurement has been made in a low-metallicity galaxy. Our results support the hypothesis that CO is photodissociated while H2 self-shields in the outer parts of low-metallicity GMCs, so that dust/self shielding is the primary factor determining the distribution of CO emission. Four pieces of evidence support this view. First, the CO-to-H2 conversion factor averaged over the whole cloud is very high 4-11 \times 10^21 cm^-2/(K km/s), or 20-55 times the Galactic value. Second, the CO-to-H2 conversion factor varies across the complex, with its lowest (most nearly Galactic) values near the CO peaks. Third, bright CO emission is largely confined to regions of relatively high line-of-sight extinction, A_V >~ 2 mag, in agreement with PDR models and Galactic observations. Fourth, a simple model in which CO emerges from a smaller sphere nested inside a larger cloud can roughly relate the H2 masses measured from CO kinematics and dust.Comment: 17 pages, 10 figures (including appendix), accepted for publication in the Astrophysical Journa

First Detection of HCO+^+ Absorption in the Magellanic System

We present the first detection of HCO$^+$ absorption in the Magellanic System. Using the Australia Telescope Compact Array (ATCA), we observed 9 extragalactic radio continuum sources behind the Magellanic System and detected HCO$^+$ absorption towards one source located behind the leading edge of the Magellanic Bridge. The detection is located at LSR velocity of $v=214.0 \pm 0.4\rm\,km\,s^{-1}$, with a full width at half maximum of $\Delta v=4.5\pm 1.0\rm\,km\,s^{-1}$ and optical depth of $\tau(\rm HCO^+)=0.10\pm 0.02$. Although there is abundant neutral hydrogen (HI) surrounding the sightline in position-velocity space, at the exact location of the absorber the HI column density is low, $<10^{20}\rm\,cm^{-2}$, and there is little evidence for dust or CO emission from Planck observations. While the origin and survival of molecules in such a diffuse environment remains unclear, dynamical events such as HI flows and cloud collisions in this interacting system likely play an important role.Comment: Accepted for publication in ApJ. 6 pages, 2 figures, 2 table

Exotic clouds in the local interstellar medium

The neutral interstellar medium (ISM) inside the Local Bubble (LB) has been known to have properties typical of the warm neutral medium (WNM). However, several recent neutral hydrogen (HI) absorption experiments show evidence for the existence of at least several cold diffuse clouds inside or at the boundary of the LB, with properties highly unusual relative to the traditional cold neutral medium. These cold clouds have a low HI column density, and AU-scale sizes. As the kinematics of cold and warm gas inside the LB are similar, this suggests a possibility of all these different flavors of the local ISM belonging to the same interstellar flow. The co-existence of warm and cold phases inside the LB is exciting as it can be used to probe the thermal pressure inside the LB. In addition to cold clouds, several discrete screens of ionized scattering material are clearly located inside the LB. The cold exotic clouds inside the LB are most likely long-lived, and we expect many more clouds with similar properties to be discovered in the future with more sensitive radio observations. While physical mechanisms responsible for the production of such clouds are still poorly understood, dynamical triggering of phase conversion and/or interstellar turbulence are likely to play an important role.Comment: 10 pages, refereed, accepted for publication in the proceedings of the "From the Outer Heliosphere to the Local Bubble: Comparisons of New Observations with Theory" conference, Space Science Review

The role of feedback in shaping the structure of the interstellar medium

We present an analysis of the role of feedback in shaping the neutral hydrogen (H I) content of simulated disc galaxies. For our analysis, we have used two realizations of two separate Milky Way-like (similar to L star) discs - one employing a conservative feedback scheme (McMaster Unbiased Galaxy Survey), the other significantly more energetic [Making Galaxies In a Cosmological Context (MaGICC)]. To quantify the impact of these schemes, we generate zeroth moment (surface density) maps of the inferred H I distribution; construct power spectra associated with the underlying structure of the simulated cold interstellar medium, in addition to their radial surface density and velocity dispersion profiles. Our results are compared with a parallel, self-consistent, analysis of empirical data from The H I Nearby Galaxy Survey (THINGS). Single power-law fits (P proportional to k(gamma)) to the power spectra of the stronger feedback (MaGICC) runs (over spatial scales corresponding to similar to 0.5 to similar to 20 kpc) result in slopes consistent with those seen in the THINGS sample (gamma similar to -2.5). The weaker feedback (MUGS) runs exhibit shallower power-law slopes (gamma similar to -1.2). The power spectra of the MaGICC simulations are more consistent though with a two-component fit, with a flatter distribution of power on larger scales (i.e. gamma similar to -1.4 for scales in excess of similar to 2 kpc) and a steeper slope on scales below similar to 1 kpc (gamma similar to -5), qualitatively consistent with empirical claims, as well as our earlier work on dwarf discs. The radial H I surface density profiles of the MaGICC discs show a clear exponential behaviour, while those of the MUGS suite are essentially flat; both behaviours are encountered in nature, although the THINGS sample is more consistent with our stronger (MaGICC) feedback runs

Design and analysis of recurrent neural network models with non‐linear activation functions for solving time‐varying quadratic programming problems

A special recurrent neural network (RNN), that is the zeroing neural network (ZNN), is adopted to find solutions to time‐varying quadratic programming (TVQP) problems with equality and inequality constraints. However, there are some weaknesses in activation functions of traditional ZNN models, including convex restriction and redundant formulation. With the aid of different activation functions, modified ZNN models are obtained to overcome the drawbacks for solving TVQP problems. Theoretical and experimental research indicate that the proposed models are better and more effective at solving such TVQP problems

A Radio and Optical Polarization Study of the Magnetic Field in the Small Magellanic Cloud

We present a study of the magnetic field of the Small Magellanic Cloud (SMC), carried out using radio Faraday rotation and optical starlight polarization data. Consistent negative rotation measures (RMs) across the SMC indicate that the line-of-sight magnetic field is directed uniformly away from us with a strength 0.19 +/- 0.06 microGauss. Applying the Chandrasekhar-Fermi method to starlight polarization data yields an ordered magnetic field in the plane of the sky of strength 1.6 +/- 0.4 microGauss oriented at a position angle 4 +/- 12 degs, measured counter-clockwise from the great circle on the sky joining the SMC to the Large Magellanic Cloud (LMC). We construct a three-dimensional magnetic field model of the SMC, under the assumption that the RMs and starlight polarization probe the same underlying large-scale field. The vector defining the overall orientation of the SMC magnetic field shows a potential alignment with the vector joining the center of the SMC to the center of the LMC, suggesting the possibility of a "pan-Magellanic'' magnetic field. A cosmic-ray driven dynamo is the most viable explanation of the observed field geometry, but has difficulties accounting for the observed uni-directional field lines. A study of Faraday rotation through the Magellanic Bridge is needed to further test the pan-Magellanic field hypothesis.Comment: 28 pages, 6 figures, accepted for publication in Ap