Primal-dual variable neighborhood search for the simple plant-location problem

Copyright @ 2007 INFORMSThe variable neighborhood search metaheuristic is applied to the primal simple plant-location problem and to a reduced dual obtained by exploiting the complementary slackness conditions. This leads to (i) heuristic resolution of (metric) instances with uniform fixed costs, up to n = 15,000 users, and m = n potential locations for facilities with an error not exceeding 0.04%; (ii) exact solution of such instances with up to m = n = 7,000; and (iii) exact solutions of instances with variable fixed costs and up to m = n = 15, 000.This work is supported by NSERC Grant 105574-02; NSERC Grant OGP205041; and partly by the Serbian Ministry of Science, Project 1583

Radio Planetary Nebulae in the Large Magellanic Cloud

We present 21 new radio-continuum detections at catalogued planetary nebula (PN) positions in the Large Magellanic Cloud (LMC) using all presently available data from the Australia Telescope Online Archive at 3, 6, 13 and 20 cm. Additionally, 11 previously detected LMC radio PNe are re-examined with $7$ detections confirmed and reported here. An additional three PNe from our previous surveys are also studied. The last of the 11 previous detections is now classified as a compact \HII\ region which makes for a total sample of 31 radio PNe in the LMC. The radio-surface brightness to diameter ($\Sigma$-D) relation is parametrised as $\Sigma \propto {D^{ - \beta }}$. With the available 6~cm $\Sigma$-$D$ data we construct $\Sigma$-$D$ samples from 28 LMC PNe and 9 Small Magellanic Cloud (SMC) radio detected PNe. The results of our sampled PNe in the Magellanic Clouds (MCs) are comparable to previous measurements of the Galactic PNe. We obtain $\beta=2.9\pm0.4$ for the MC PNe compared to $\beta = 3.1\pm0.4$ for the Galaxy. For a better insight into sample completeness and evolutionary features we reconstruct the $\Sigma$-$D$ data probability density function (PDF). The PDF analysis implies that PNe are not likely to follow linear evolutionary paths. To estimate the significance of sensitivity selection effects we perform a Monte Carlo sensitivity simulation on the $\Sigma$-$D$ data. The results suggest that selection effects are significant for values larger than $\beta \sim 2.6$ and that a measured slope of $\beta=2.9$ should correspond to a sensitivity-free value of $\sim 3.4$.Comment: 19 pages, 9 figures, 6 table

Radio-continuum study of Large Magellanic Cloud Supernova Remnant J0509-6731

We present a detailed study of Australia Telescope Compact Array (ATCA) observations ($\lambda$ = 20, 13, 6 & 3~cm) of supernova remnant (SNR) J0509--6731 in the Large Magellanic Cloud (LMC). The remnant has a ring morphology with brightened regions towards the south-western limb. We also find a second brightened inner ring which is only seen in the radio-continuum. The SNR is almost circular, with a diameter ranging from 7 to 8~pc, and a steep radio spectral index between 36 and 3~cm of $\alpha=-0.73\pm0.02$, which is characteristic of younger SNRs. We also report detection of radially orientated polarisation across the remnant at 6~cm, with a mean fractional polarisation level of $P\cong$~(26~$\pm$~13)%. We find the magnetic field ($\sim$168~$\mu$G) and $\Sigma - D$ ($\Sigma =$ $1.1\times 10^{-19}$~W m$^{-2}$~Hz$^{-1}$~sr$^{-1}$ , $D=$ 7.35~pc) to be consistent with other young remnants

The Sigma-D Analysis of Recently Detected Radio Planetary Nebulae in the Magellanic Clouds

Our aim is to investigate and analyze the radio surface brightness to diameter ($\Sigma-D$) relation for recently detected, bright radio-continuum planetary nebulae (PNe) in the Magellanic Clouds (MC). We apply a Monte Carlo analysis in order to account for sensitivity selection effects on measured $\Sigma-D$ relation slopes for bright radio PNe in the MCs. In the $\Sigma-D$ plane these radio MCs PNe are positioned among the brightest of the nearby Galactic PNe, and are close to the $D^{-2}$ sensitivity line of the MCs radio maps. The fitted Large Magellanic Cloud (LMC) data slope appears to be influenced with survey sensitivity. This suggests the MCs radio PN sample represents just the "tip of the iceberg" of the actual luminosity function. Specifically, our results imply that sensitivity selection tends to flatten the slope of the $\Sigma-D$ relation. Although MCs PNe appear to share the similar evolution properties as Galactic PNe, small number of data points prevented us to further constrain their evolution properties.Comment: 5 pages, 2 figures, updated references, Astronomy and Astrophysics, in pres

Bankruptcy risk model and empirical tests

We analyze the size dependence and temporal stability of firm bankruptcy risk in the US economy by applying Zipf scaling techniques. We focus on a single risk factor-the debt-to-asset ratio R-in order to study the stability of the Zipf distribution of R over time. We find that the Zipf exponent increases during market crashes, implying that firms go bankrupt with larger values of R. Based on the Zipf analysis, we employ Bayes's theorem and relate the conditional probability that a bankrupt firm has a ratio R with the conditional probability of bankruptcy for a firm with a given R value. For 2,737 bankrupt firms, we demonstrate size dependence in assets change during the bankruptcy proceedings. Prepetition firm assets and petition firm assets follow Zipf distributions but with different exponents, meaning that firms with smaller assets adjust their assets more than firms with larger assets during the bankruptcy process. We compare bankrupt firms with nonbankrupt firms by analyzing the assets and liabilities of two large subsets of the US economy: 2,545 Nasdaq members and 1,680 New York Stock Exchange (NYSE) members. We find that both assets and liabilities follow a Pareto distribution. The finding is not a trivial consequence of the Zipf scaling relationship of firm size quantified by employees-although the market capitalization of Nasdaq stocks follows a Pareto distribution, the same distribution does not describe NYSE stocks. We propose a coupled Simon model that simultaneously evolves both assets and debt with the possibility of bankruptcy, and we also consider the possibility of firm mergers.Comment: 8 pages, 8 figure