scholarly journals Understanding biases when fitting disk truncations

2016 ◽  
Vol 11 (S321) ◽  
pp. 303-303
Author(s):  
Nicolás Cardiel ◽  
Raffaella A. Marino ◽  
Sergio Pascual ◽  
M. Teresa Ceballos ◽  
Armando Gil de Paz ◽  
...  
Keyword(s):  
Ordinary Least Squares ◽  
Disk Galaxies ◽  
Relevant Parameter ◽  
Imaging Data ◽  
Intermediate Point ◽  
Least Squares Fit ◽  
Fitting Procedures ◽  
Noise Limit ◽  
Normal Standard ◽  
Exponential Disk

AbstractTruncations in the stellar population at the edges of disk galaxies are thought to be a common morphological feature (e.g., Erwin et al. 2005; and more recently Marino et al. 2016). In fact, using imaging data from the SDSS, Pohlen & Trujillo (2006) showed that only ~ 10% of face-on to intermediate inclined, nearby, late-type (Sb-Sdm) spiral galaxies have a normal/standard purely exponential disk down to the noise limit. In situations like these, the simultaneous fit of two lines, joined or not at an intermediate point (the break radius), constitutes a natural step towards the modelling of radial variation in surface brightness, metallicity, or any other relevant parameter. This work shows the results of simple simulations in which the simultaneous fit to two joined lines is compared to the simultaneous fit of two independent lines (i.e., two lines that do not necessarily coincide at an intermediate point), and also to the traditional single ordinary least squares fit. These simulations reveal some biases that should be taken into account when facing these kind of fitting procedures.

scholarly journals Disk Galaxies: The Global Properties of Star Formation and the Chemical Abundance Gradients

1987 ◽  
Vol 115 ◽  
pp. 621-621
Author(s):  
Michael A. Dopita ◽  
Ian R. Evans
Keyword(s):  
Star Formation ◽  
Radial Variation ◽  
Disk Galaxies ◽  
Chemical Abundance ◽  
Global Properties ◽  
Exponential Disk ◽  
Scale Length

In the relatively gas-rich, pure exponential disk galaxies, available data is accumulating which suggests that the distribution of starformation in the disk either shows no radial variation, or else has a scale-length which is much longer than that of the stars.

scholarly journals Nonlinear (MARS) modeling of long-term variations of surface UV-B radiation as revealed from the analysis of Belsk, Poland data for the period 1976–2000

2003 ◽  
Vol 21 (8) ◽  
pp. 1887-1896 ◽  
Author(s):  
J. W. Krzyścin
Keyword(s):  
Ordinary Least Squares ◽  
Statistical Technique ◽  
Multivariate Adaptive Regression Splines ◽  
Atmospheric Composition ◽  
Total Solar Radiation ◽  
Long Distance ◽  
Least Squares Fit ◽  
Non Local ◽  
Global Atmospheric Circulation ◽  
High Level

Abstract. A new, powerful statistical technique, multivariate adaptive regression splines (MARS), is applied to reproduce monthly fractional deviations of UV-B doses over Belsk, Poland, during the snowless (May–October) part of the year in the period 1976–2000. Two kinds of regressors were used: local ones (total ozone, percentage of sky covered by low-, mid-, high-level clouds or total solar radiation over Belsk) and non-local ones, i.e. those describing the long-distance forcings on the surface UV-B due to changes in the global atmospheric circulation. Standard indices of the Quasi-Biennial, North Atlantic, El Niño-Southern Oscillations, and the 11-year solar activity were used as non-local regressors. The results there indicate that the MARS procedure is able to reproduce the observed year-to-year and decadal oscillations in the UV data. The MARS model yields better model-observation agreement than an ordinary least-squares fit based on the same set of regressors. It is found that MARS is capable of handling interactions between the local and non-local regressors, suggesting a possible nonlinear nature of connections between variables characterizing the atmospheric transparency over Belsk and the long-distance forcings. MARS enables a reconstruction of the surface UV-B variations over any site based on the cloud and ozone data presently stored on web pages.Key words. Atmospheric composition and structure (aerosols and particles; biosphere-atmosphere interactions)

scholarly journals The Formation of Exponential Disk Galaxies in MOND

2020 ◽  
Vol 890 (2) ◽  
pp. 173 ◽  
Author(s):  
Nils Wittenburg ◽  
Pavel Kroupa ◽  
Benoit Famaey
Keyword(s):  
Disk Galaxies ◽  
Exponential Disk

scholarly journals Efficient Position Estimation of 3D Fluorescent Spherical Beads in Confocal Microscopy via Poisson Denoising

2020 ◽  
Author(s):  
Alessandro Benfenati ◽  
Francesco Bonacci ◽  
Tarik Bourouina ◽  
Hugues Talbot
Keyword(s):  
Image Denoising ◽  
3D Imaging ◽  
Weighted Least Squares ◽  
Classical Problem ◽  
Position Estimation ◽  
Spherical Particles ◽  
Imaging Data ◽  
Geometrical Properties ◽  
Least Squares Fit

AbstractParticle estimation is a classical problem arising in many science fields, such as biophysics, fluid mechanics and biomedical imaging. Many interesting applications in these areas involve 3D imaging data: This work presents a technique to estimate the 3D coordinates of the center of spherical particles. This procedure has its core in the processing of the images of the scanned volume: It firstly applies denoising techniques to each frame of the scanned volume and then provides an estimation of both the center and the profile of the 2D intersections of the particles with the frames, by coupling the usage of Total Variation functional and of a regularized weighted Least Squares fit. Then, the 2D information is used to retrieve the 3D coordinates using geometrical properties. The experiments provide evidence that image denoising has a large impact on the performance of the particle tracking procedures, since they strongly depend on the quality of the initial acquisition. This work shows that the choice of tailored image denoising technique for Poisson noise leads to a better estimation of the particle positions.

scholarly journals The long-solved problem of the best-fit straight line: Application to isotopic mixing lines

2016 ◽  
Author(s):  
Richard Wehr ◽  
Scott R . Saleska
Keyword(s):  
Least Squares ◽  
Geometric Mean ◽  
Ordinary Least Squares ◽  
Interesting Case ◽  
Least Squares Regression ◽  
Straight Line ◽  
Least Squares Fit ◽  
Special Cases ◽  
Isotopic Mixing ◽  
Best Fit

Abstract. It has been almost 50 years since York published an exact and general solution for the best-fit straight line to independent points with normally distributed errors in both x and y. York’s solution is highly cited in the geophysical literature but almost unknown outside of it, so that there has been no ebb in the tide of books and papers wrestling with the problem. Much of the post-1969 literature on straight-line fitting has sown confusion not merely by its content but by its very existence. The optimal least-squares fit is already known; the problem is already solved. Here we introduce the non-specialist reader to York’s solution, and demonstrate its application in the interesting case of the isotopic mixing line, an analytical tool widely used to determine the isotopic signature of trace gas sources for the study of biogeochemical cycles. The most commonly known linear regression methods — ordinary least squares regression (OLS), geometric mean regression (GMR), and orthogonal distance regression (ODR) — have each been recommended as the best method for fitting isotopic mixing lines. In fact, OLS, GMR, and ODR are all special cases of York’s solution that are valid only under particular measurement conditions, and those conditions do not hold in general for isotopic mixing lines. Using Monte Carlo simulations, we quantify the biases in OLS, GMR, and ODR under various conditions and show that York’s general — and convenient — solution is always the least biased.

scholarly journals The long-solved problem of the best-fit straight line: application to isotopic mixing lines

2017 ◽  
Vol 14 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Richard Wehr ◽  
Scott R. Saleska
Keyword(s):  
Least Squares ◽  
Geometric Mean ◽  
Ordinary Least Squares ◽  
Interesting Case ◽  
Least Squares Regression ◽  
Straight Line ◽  
Least Squares Fit ◽  
Special Cases ◽  
Isotopic Mixing ◽  
Best Fit

Abstract. It has been almost 50 years since York published an exact and general solution for the best-fit straight line to independent points with normally distributed errors in both x and y. York's solution is highly cited in the geophysical literature but almost unknown outside of it, so that there has been no ebb in the tide of books and papers wrestling with the problem. Much of the post-1969 literature on straight-line fitting has sown confusion not merely by its content but by its very existence. The optimal least-squares fit is already known; the problem is already solved. Here we introduce the non-specialist reader to York's solution and demonstrate its application in the interesting case of the isotopic mixing line, an analytical tool widely used to determine the isotopic signature of trace gas sources for the study of biogeochemical cycles. The most commonly known linear regression methods – ordinary least-squares regression (OLS), geometric mean regression (GMR), and orthogonal distance regression (ODR) – have each been recommended as the best method for fitting isotopic mixing lines. In fact, OLS, GMR, and ODR are all special cases of York's solution that are valid only under particular measurement conditions, and those conditions do not hold in general for isotopic mixing lines. Using Monte Carlo simulations, we quantify the biases in OLS, GMR, and ODR under various conditions and show that York's general – and convenient – solution is always the least biased.

scholarly journals Lenses and Low Surface Brightness Disks

1983 ◽  
Vol 100 ◽  
pp. 253-254
Author(s):  
A. Bosma
Keyword(s):  
Surface Brightness ◽  
Disk Galaxies ◽  
Selection Effects ◽  
Central Surface ◽  
Low Surface Brightness ◽  
The Galaxy ◽  
Intrinsic Scatter ◽  
Limiting Surface ◽  
Disk Component ◽  
Exponential Disk

The 21.65-“law” for disk galaxies has been debated ever since Freeman's (1970) paper in which he found that for 28 out of 36 galaxies the extrapolated central surface brightness of the exponential disk component I0, follows this rule with little intrinsic scatter. Some people think it significant, while others invoke selection effects. Bosma and Freeman (1982) made a new attempt to clarify this problem by studying ratios of diameters of disk galaxies on the various Sky Surveys in a region of overlap. The limiting surface brightness levels were calibrated to be 24.6 and 25.6 magn/arcsec2 for the Palomar blue prints and the SRC J films, resp. The distribution of the ratio Γ = diameter (SRC) / diameter (PAL) gives a measure of the true distribution of Io if the galaxy has an exponential disk in the brightness interval 24.6 to 25.6; e.g. Io = 21.6 corresponds to Γ = 1.32, Io = 22.6 to Γ = 1.50 and Io = 23.6 to Γ = 1.90, etc.

scholarly journals The Fate of Ultraluminous Mergers

1999 ◽  
Vol 186 ◽  
pp. 349-349
Author(s):  
A.C. Baker ◽  
D.L. Clements
Keyword(s):  
Star Formation ◽  
Galaxy Formation ◽  
Elliptical Galaxies ◽  
Infrared Emission ◽  
Disk Galaxies ◽  
Merging Galaxies ◽  
Diverse Range ◽  
Good Spatial Resolution ◽  
Pass Through ◽  
Exponential Disk

Galaxy formation is a diverse range of ongoing processes. Numerical simulations suggest that disk galaxies in collision pass through a massive burst of star formation, and produce ‘elliptical–like’ remnants similar to bone fide elliptical galaxies. The observed relative numbers of merging systems and elliptical galaxies are consistent with this picture (Toomre 1977). We here investigate further by studying the distribution of old stars in a sample of merging galaxies : the ultraluminous IR galaxies (ULIRGs). We selected ten ULIRGs from the literature (Clements & Baker 1996; Leech et al. 1994; Zhenglong et al. 1991; Melnick & Mirabel 1990) by two criteria: proximity (redshifts z < 0.15), for good spatial resolution; and confirmed signs of merging. We obtained deep K–band images (tint ~ 1000 - 2700s) in good seeing using MAGIC on the Calar Alto 3.5m telescope. Our data have a field–of–view roughly equivalent to 10 - 20 effective radii for the galaxies. We have fitted analytic surface brightness profiles to the data for the exponential disk and the de Vaucouleurs r1/4 elliptical descriptions. We strongly favour the elliptical-like description in 8 out of 10 cases, supporting the picture that collision and merger of classical spiral galaxies can produce classical elliptical galaxies, through tidal disruption, violent star formation accompanied by prodigious infrared emission, and gravitational relaxation. These data can also constrain the properties of the ULIRG (double) nuclei and hence the lifetime of the ULIRG phase (Baker & Clements 1998).

Density waves in disk galaxies

1967 ◽  
Vol 31 ◽  
pp. 313-317 ◽  
Author(s):  
C. C. Lin ◽  
F. H. Shu
Keyword(s):  
Mathematical Analysis ◽  
Spiral Structure ◽  
Stellar System ◽  
Collective Modes ◽  
Disk Galaxies ◽  
Spiral Pattern ◽  
Density Waves ◽  
The Galaxy ◽  
Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

Background subtraction in STEM energy-loss mapping

1984 ◽  
Vol 42 ◽  
pp. 568-569
Author(s):  
R.D. Leapman ◽  
K.E. Gorlen ◽  
C.R. Swyt
Keyword(s):  
Energy Loss ◽  
Signal To Noise Ratio ◽  
Statistical Error ◽  
Scanning Transmission Electron Microscope ◽  
Reference Image ◽  
Inverse Power Law ◽  
Transmission Electron ◽  
Least Squares Fit ◽  
Scanning Transmission ◽  
Single Number

The determination of elemental distributions by electron energy loss spectroscopy necessitates removal of the non-characteristic spectral background from a core-edge at each point in the image. In the scanning transmission electron microscope this is made possible by computer controlled data acquisition. Data may be processed by fitting the pre-edge counts, at two or more channels, to an inverse power law, AE-r, where A and r are parameters and E is energy loss. Processing may be performed in real-time so a single number is saved at each pixel. Detailed analysis, shows that the largest contribution to noise comes from statistical error in the least squares fit to the background. If the background shape remains constant over the entire image, the signal-to-noise ratio can be improved by fitting only one parameter. Such an assumption is generally implicit in subtraction of the “reference image” in energy selected micrographs recorded in the CTEM with a Castaing-Henry spectrometer.

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