Gaussian Decomposition Algorithm Research Articles

How Gaussian mixture modelling can help to verify reference intervals from laboratory data with a high proportion of pathological values

Abstract Objectives Although there are several indirect methods that can be used to verify reference limits, they have a common weakness in that they assume a low proportion of pathological values. This paper investigates whether a Gaussian decomposition algorithm can identify the non-pathological fraction even if it is not the main subset of mixed data. Methods All investigations are carried out in the R programming environment. The mclust package is used for Gaussian mixture modelling via the expectation maximization (EM) algorithm. For right-skewed distributions, logarithms of the original values are taken to approximate the Gaussian model. We use the Bayesian information criterion (BIC) for evaluation of the results. The reflimR and refineR packages serve as comparison procedures. Results We generate synthetic data mixtures with known normal distributions to demonstrate the feasibility and reliability of our approach. Application of the algorithm to real data from a Nigerian and a German population produces results, which help to interpret reference intervals of reflimR and refineR that are obviously too wide. In the first example, the mclust analysis of hemoglobin in Nigerian women supports the medical hypothesis that an anemia rate of more than 50 % leads to falsely low reference limits. Our algorithm proposes various scenarios based on the BIC values, one of which suggests reference limits that are close to published data for Nigeria but significantly lower than those established for the Caucasian population. In the second example, the standard statistical analysis of creatine kinase in German patients with predominantly cardiac diseases yields a reference interval that is clearly too wide. With mclust we identify overlapping fractions that explain this false result. Conclusions Gaussian mixture modelling does not replace standard methods for reference interval estimation but is a valuable adjunct when these methods produce discrepant or implausible results.

Velocity-coherent substructure in TMC-1: inflow and fragmentation

ABSTRACT Filamentary structures have been found nearly ubiquitously in molecular clouds and yet their formation and evolution is still poorly understood. We examine a segment of Taurus Molecular Cloud 1 (TMC-1) that appears as a single, narrow filament in continuum emission from dust. We use the Regularized Optimization for Hyper-Spectral Analysis (ROHSA), a Gaussian decomposition algorithm that enforces spatial coherence when fitting multiple velocity components simultaneously over a data cube. We analyse HC5N (9–8) line emission as part of the Green Bank Ammonia Survey and identify three velocity-coherent components with ROHSA. The two brightest components extend the length of the filament, while the third component is fainter and clumpier. The brightest component has a prominent transverse velocity gradient of 2.7 ± 0.1 km s−1 pc−1 that we show to be indicative of gravitationally induced inflow. In the second component, we identify regularly spaced emission peaks along its length. We show that the local minima between pairs of adjacent HC5N peaks line up closely with submillimetre continuum emission peaks, which we argue is evidence for fragmentation along the spine of TMC-1. While coherent velocity components have been described as separate physical structures in other star-forming filaments, we argue that the two bright components identified in HC5N emission in TMC-1 are tracing two layers in one filament: a lower density outer layer whose material is flowing under gravity towards the higher density inner layer of the filament.

Amoeba: Automated Molecular Excitation Bayesian Line-fitting Algorithm

Abstract The hyperfine transitions of the ground-rotational state of the hydroxyl radical (OH) have emerged as a versatile tracer of the diffuse molecular interstellar medium. We present a novel automated Gaussian decomposition algorithm designed specifically for the analysis of the paired on-source and off-source optical depth and emission spectra of these OH transitions. In contrast to existing automated Gaussian decomposition algorithms, Amoeba (Automated Molecular Excitation Bayesian line-fitting Algorithm) employs a Bayesian approach to model selection, fitting all four optical-depth and four emission spectra simultaneously. Amoeba assumes that a given spectral feature can be described by a single centroid velocity and full width at half maximum, with peak values in the individual optical-depth and emission spectra then described uniquely by the column density in each of the four levels of the ground-rotational state, thus naturally including the real physical constraints on these parameters. Additionally, the Bayesian approach includes informed priors on individual parameters that the user can modify to suit different data sets. Here we describe Amoeba and establish its validity and reliability in identifying and fitting synthetic spectra with known (but hidden) parameters, finding that the code performs very well in a series of practical tests. Amoeba’s core algorithm could be adapted to the analysis of other species with multiple transitions interconnecting shared levels (e.g., the 700 MHz lines of the first excited rotational state of CH). Users are encouraged to adapt and modify Amoeba to suit their own use cases.

Decomposition of LiDAR waveforms with negative tails by Gaussian mixture model

Waveform decomposition techniques are commonly used to extract attributes of targets from light detection and ranging (LiDAR) waveforms. The conventional Gaussian decomposition (GD) cannot deal with system waveforms (SWs) with non-Gaussian shapes, whereas the recently proposed B-spline-based decomposition method holds an assumption of similarity transformation. We present a multi-Gaussian decomposition (MGD) algorithm that employs a Gaussian mixture model (GMM) to represent the SW. Compared with the GD algorithm, the MGD algorithm exploits the characteristic of the SW using the GMM and hence can fit the received waveforms better than the GD algorithm. In contrast to the B-spline-based method, the proposed algorithm holds a more reasonable assumption that a received waveform is a convolution result of the SW with the target response, which accords with the ranging principle better. The MGD algorithm was validated using the experimental waveforms with negative tails collected by our self-designed LiDAR system. The GD algorithm and the B-spline-based decomposition were also introduced and studied for comparison. The experimental results show that the GMM with six components fit the SW with an acceptable residual. The experimental results also show that the MGD algorithm produced better decomposition results than the other two algorithms in terms of range retrieval, whereas the B-spline-based decomposition showed the best performance with regards to the root-mean-square-error for waveform fitting.

Spatial distribution of the aromatic and aliphatic carbonaceous nanograin features in the protoplanetary disk around HD 100546

Context. Carbonaceous nanograins are present at the surface of protoplanetary disks around Herbig Ae/Be stars, where most of the ultraviolet energy from the central star is dissipated. Efficiently coupled to the gas, they are unavoidable to understand the physics and chemistry of these disks. Furthermore, nanograins are able to trace the outer flaring parts of the disk and possibly the gaps from which the larger grains are missing. However, their evolution through the disks, from internal to external regions, is only poorly understood so far. Aims. Our aim is to examine the spatial distribution and evolution of the nanodust emission in the emblematic (pre-)transitional protoplanetary disk HD 100546. This disk shows many structures (annular gaps, rings, and spirals) and reveals very rich carbon nanodust spectroscopic signatures (aromatic, aliphatic) in a wide spatial range of the disk (~20−200 au). Methods. We analysed adaptive optics spectroscopic observations in the 3–4 μm range (angular resolution of ~0.1′′) and imaging and spectroscopic observations in the 8–12 μm range (angular resolution of ~0.3′′). The hyperspectral cube was decomposed into a sum of spatially coherent dust components using a Gaussian decomposition algorithm. We compared the data to model predictions using the heterogeneous dust evolution model for interstellar solids (THEMIS), which is integrated in the radiative transfer code POLARIS by calculating the thermal and stochastic heating of micro- and nanometre-sized dust grains for a given disk structure. Results. We find that the aromatic features at 3.3, 8.6, and 11.3 μm, and the aliphatic features between 3.4 and 3.5 μm are spatially extended; each band shows a specific morphology dependent on the local physical conditions. The aliphatic-to-aromatic band ratio, 3.4/3.3, increases with the distance from the star from ~0.2 (at 0.2′′ or 20 au) to ~0.45 (at 1′′ or 100 au), suggesting UV processing. In the 8–12 μm observed spectra, several features characteristic of aromatic particles and crystalline silicates are detected. Their relative contribution changes with the distance to the star. The model predicts that the features and adjacent continuum are due to different combinations of grain sub-populations, in most cases with a high dependence on the intensity of the UV field. The model reproduces the spatial emission profiles of the bands well, except for the inner 20-40 au, where the observed emission of the 3.3 and 3.4 μm bands is, unlike the predictions, flat and no longer increases with the UV field. Conclusions. With our approach that combines observational data in the near- to mid-IR and disk modelling, we deliver constraints on the spatial distribution of nano-dust particles as a function of the disk structure and radiation field.

ROHSA: Regularized Optimization for Hyper-Spectral Analysis

Context. Extracting the multiphase structure of the neutral interstellar medium is key to understanding star formation in galaxies. The radiative condensation of the diffuse warm neutral medium producing a thermally unstable lukewarm medium and a dense cold medium is closely related to the initial step leading the atomic-to-molecular (HI-to-H2) transition and the formation of molecular clouds. Up to now, the mapping of these phases out of 21 cm emission hyper-spectral cubes has remained elusive mostly due to the velocity blending of individual cold structures present on a given line of sight. As a result, most of the current knowledge about the HI phases rests on a small number of absorption measurements on lines of sight crossing radio sources. Aims. The goal of this work is to develop a new algorithm to perform separation of diffuse sources in hyper-spectral data. Specifically the algorithm was designed in order to address the velocity blending problem by taking advantage of the spatial coherence of the individual sources. The main scientific driver of this effort was to extract the multiphase structure of the HI from 21 cm line emission only, providing a means to map each phase separately, but the algorithm developed here should be generic enough to extract diffuse structures in any hyper-spectral cube. Methods. We developed a new Gaussian decomposition algorithm named ROHSA based on a multi-resolution process from coarse to fine grid. ROHSA uses a regularized nonlinear least-square criterion to take into account the spatial coherence of the emission and the multiphase nature of the gas simultaneously. In order to obtain a solution with spatially smooth parameters, the optimization is performed on the whole data cube at once. The performances of ROHSA were tested on a synthetic observation computed from numerical simulations of thermally bi-stable turbulence. We apply ROHSA to a 21 cm observation of a region of high Galactic latitude from the GHIGLS survey and present our findings. Results. The evaluation of ROHSA on synthetic 21 cm observations shows that it is able to recover the multiphase nature of the HI. For each phase, the power spectra of the column density and centroid velocity are well recovered. More generally, this test reveals that a Gaussian decomposition of HI emission is able to recover physically meaningful information about the underlying three-dimensional fields (density, velocity, and temperature). The application on a real 21 cm observation of a field of high Galactic latitude produces a picture of the multiphase HI, with isolated, filamentary, and narrow (σ ~ 1−2 km s−1) structures, and broader (σ ~ 4−10 km s−1), diffuse, and space-filling components. The test-case field used here contains significant intermediate-velocity clouds that were well mapped out by the algorithm. As ROHSA is designed to extract spatially coherent components, it performs well at projecting out the noise. Conclusions. In this paper we introduce ROHSA, a new algorithm that performs a separation of diffuse sources in hyper-spectral data on the basis of a Gaussian decomposition. The algorithm makes no assumption about the nature of the sources, except that each one has a similar line width. The tests we made shows that ROHSA is well suited to decomposing complex 21 cm line emission of regions of high Galactic latitude, but its design is general enough that it could be applied to any hyper-spectral data type for which a Gaussian model is relevant.

The Stellar and Gaseous Kinematics in NGC 253

This paper presents observations made at intermediate spectral and spatial resolutions along the major and minor axes of the starburst galaxy NGC 253. The spectral ranges analyzed are in the region of the stellar Mg I b (~5175 Å) line, in the near-IR Ca II triplet (~8550 Å) absorption features, and in the region of the Hα emission line. We compare the shape of the stellar features with those of reference stars and determine the line-of-sight velocity distribution of the stellar component by using a two-dimensional Gaussian decomposition algorithm, and we show for the first time the rotation curve of the stellar component in NGC 253. Comparing the recession velocity curves of the gas and stars, we show that the stellar component has a decoupled kinematics with respect to the gas, displaying a shallower velocity gradient and larger velocity dispersion than the gas in the inner regions. The minor-axis kinematics, together with the kinematics across the central 40'' along the major axis, suggest the presence of a rotating body with a kinematically misaligned axis with respect to the main disk of the galaxy. The asymmetries in the LOS velocity distribution along the minor axis, together with the steep velocity gradient of the gaseous component, suggest a merger scenario as the source of these kinematic signatures. The enclosed mass in the central regions is computed to be (2.4 ± 0.5) × 107 M☉ for a radius of r = 07 (10 pc). A double gaseous component in the central 6'' is detected from the [S III] λ9069 Å data along the minor axis; this seems to be the signature of a superbubble, due to a supernova rate of 0.05 yr-1.