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Register a new userMaximum Entropy Reconstruction of the Interstellar Medium: I. Theory
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We have developed a technique to map the three-dimensional structure of the local interstellar medium using a maximum entropy reconstruction technique. A set of column densities N to stars of known distance can in principle be used to recover a three-dimensional density field n, since the two quantities are related by simple geometry through the equation N = C n, where C is a matrix characterizing the stellar spatial distribution. In practice, however, there is an infinte number of solutions to this equation. We use a maximum entropy reconstruction algorithm to find the density field containing the least information which is consistent with the observations. The solution obtained with this technique is, in some sense, the model containing the minimum structure. We apply the algorithm to several simulated data sets to demonstrate its feasibility and success at recovering ``real density contrasts. This technique can be applied to any set of column densities whose end points are specified. In a subsequent paper we shall describe the application of this method to a set of stellar color excesses to derive a map of the dust distribution, and to soft X-ray absorption columns to hot stars to derive a map of the total density of the interstellar medium.
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We present a study of the HII region Sh2-205 and its environs, based on data obtained from the CGPS, 12CO observations, and MSX data. We find that Sh2-205 can be separated in three independent optical structures: SH 149.25-0.0, SH 148.83-0.67, and LBN 148.11-0.45. The derived spectral indices show the thermal nature of SH 148.83-0.67 and LBN 148.11-0.45. The morphology of SH 148.83-0.67, both in the optical and radio data, along with the energetic requ irements indicate that this feature is an interstellar bubble powered by the UV photons of HD 24431 (O9 III). LBN 148.11-0.45 has the morphology of a classic al HII region and their ionizing sources remain uncertain. Dust and molecular gas are found related to LBN 148.11-0.45.Particularly, a photodissociation region is detected at the interface between the ionized and molecular regions. If the proposed exciting star HD 24094 were an O8--O9 type star, as suggested by its near-infrared colors, its UV photon flux would be enough to explain the ionization of the nebula. The optical, radio continuum, and 21-cm line data allow us to conclude that SH 148.83-0.67 is an interstellar bubble powered by the energetic action of HD 24431. The associated neutral atomic and ionized masses are 180 Mo and 300 Mo, respectively. The emission of SH 149.25-0.0 is too faint to derive the dust and gas parameters. An HI shell centered at (l,b) = (149.0, 1.5) was also identified. It correlates morphologically with molecular gas emission. The neutral atomic and molecular masses are 1600 Mo and 2.6 x 10^4 Mo, respectively. The open cluster NGC 1444 is the most probable responsible for shaping this HI structure.
The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region where the main part of probability mass is located.
Dwarf spheroidal galaxies are among the most numerous galaxy population in the Universe, but their main formation and evolution channels are still not well understood. The three dwarf spheroidal satellites (NGC147, NGC185, and NGC205) of the Andromeda galaxy are characterised by very different interstellar medium (ISM) properties, which might suggest them being at different galaxy evolutionary stages. While the dust content of NGC205 has been studied in detail by De Looze et al. (2012), we present new Herschel dust continuum observations of NGC147 and NGC185. The non-detection of NGC147 in Herschel SPIRE maps puts a strong constraint on its dust mass (< 128 Msun). For NGC185, we derive a total dust mass M_d = 5.1 x 10^3 Msun, which is a factor of ~2-3 higher than that derived from ISO and Spitzer observations and confirms the need for longer wavelength observations to trace more massive cold dust reservoirs. We, furthermore, estimate the dust production by asymptotic giant branch (AGB) stars and supernovae (SNe). For NGC147, the upper limit on the dust mass is consistent with expectations of the material injected by the evolved stellar population. In NGC185 and NGC205, the observed dust content is one order of magnitude higher compared to the estimated dust production by AGBs and SNe. Efficient grain growth, and potentially longer dust survival times (3-6 Gyr) are required to account for their current dust content. Our study confirms the importance of grain growth in the gas phase to account for the current dust reservoir in galaxies.
We demonstrate that the maximum-entropy method for gravitational lens reconstruction presented in Bridle et al. (1998) may be applied even when only shear emph{or} magnification information is present. We also demonstrate that the method can easily handle irregularly shaped observing fields and, because shear is a non-local function of the lensing mass, reconstructions that use shear information can successfully bridge small gaps in observations. For our simulations we use a mass density distribution that is realistic for a z=0.4 cluster of total mass around 10^15 h^-1 M_solar. Using HST-quality shear data alone, covering the area of four WFPC2 observations, we detect 60 per cent of the mass of the cluster within the area observed, despite the mass sheet degeneracy. This is qualitatively because the shear provides information about the variations in the mass distribution, and our prior includes a positivity constraint. We investigate the effect of using various sizes of observing field and find that 50 to 100 per cent of the cluster mass is detected, depending on the observing strategy and cluster shape. Finally we demonstrate how this method can cope with strong lensing regions of a mass distribution.
Recent years have seen the rise of convolutional neural network techniques in exemplar-based image synthesis. These methods often rely on the minimization of some variational formulation on the image space for which the minimizers are assumed to be the solutions of the synthesis problem. In this paper we investigate, both theoretically and experimentally, another framework to deal with this problem using an alternate sampling/minimization scheme. First, we use results from information geometry to assess that our method yields a probability measure which has maximum entropy under some constraints in expectation. Then, we turn to the analysis of our method and we show, using recent results from the Markov chain literature, that its error can be explicitly bounded with constants which depend polynomially in the dimension even in the non-convex setting. This includes the case where the constraints are defined via a differentiable neural network. Finally, we present an extensive experimental study of the model, including a comparison with state-of-the-art methods and an extension to style transfer.
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