Total Scatter Research Articles

A Consistent Set of Empirical Scaling Relations for Spiral Galaxies: The (vmax, MoM)–(σ0, MBH, ϕ) Relations

Abstract Using the latest sample of 48 spiral galaxies having a directly measured supermassive black hole mass, M BH, we determine how the maximum disk rotational velocity, v max (and the implied dark matter halo mass, M DM), correlates with the (i) black hole mass, (ii) central velocity dispersion, σ 0, and (iii) spiral-arm pitch angle, ϕ. We find that M BH ∝ v max 10.62 ± 1.37 ∝ M DM 4.35 ± 0.66 , significantly steeper than previously reported, and with a total root mean square scatter (0.58 dex) similar to that about the M BH–σ 0 relation for spiral galaxies—in stark disagreement with claims that M BH does not correlate with disks. Moreover, this M BH–v max relation is consistent with the unification of the Tully–Fisher relation (involving the total stellar mass, M *,tot) and the steep M BH ∝ M * , tot 3.05 ± 0.53 relation observed in spiral galaxies. We also find that σ 0 ∝ v max 1.55 ± 0.25 ∝ M DM 0.63 ± 0.11 , consistent with past studies connecting stellar bulges (with σ 0 ≳ 100 km s−1), dark matter halos, and a nonconstant v max/σ 0 ratio. Finally, we report that tan ∣ ϕ ∣ ∝ ( − 1.18 ± 0.19 ) log v max ∝ ( − 0.48 ± 0.09 ) log M DM , providing a novel formulation between the geometry (i.e., the logarithmic spiral-arm pitch angle) and kinematics of spiral galaxy disks. While the v max–ϕ relation may facilitate distance estimations to face-on spiral galaxies through the Tully–Fisher relation and using ϕ as a proxy for v max, the M DM–ϕ relation provides a path for determining dark matter halo masses from imaging data alone. Furthermore, based on a spiral galaxy sample size that is double the size used previously, the self-consistent relations presented here provide dramatically revised constraints for theory and simulations.

Joint Principal Component and Discriminant Analysis for Dimensionality Reduction.

Linear discriminant analysis (LDA) is the most widely used supervised dimensionality reduction approach. After removing the null space of the total scatter matrix St via principal component analysis (PCA), the LDA algorithm can avoid the small sample size problem. Most existing supervised dimensionality reduction methods extract the principal component of data first, and then conduct LDA on it. However, "most variance" is very often the most important, but not always in PCA. Thus, this two-step strategy may not be able to obtain the most discriminant information for classification tasks. Different from traditional approaches which conduct PCA and LDA in sequence, we propose a novel method referred to as joint principal component and discriminant analysis (JPCDA) for dimensionality reduction. Using this method, we are able to not only avoid the small sample size problem but also extract discriminant information for classification tasks. An iterative optimization algorithm is proposed to solve the method. To validate the efficacy of the proposed method, we perform extensive experiments on several benchmark data sets in comparison with some state-of-the-art dimensionality reduction methods. A large number of experimental results illustrate that the proposed method has quite promising classification performance.

Black Hole Mass Scaling Relations for Early-type Galaxies. I. MBH–M*, sph and MBH–M*,gal

Abstract Analyzing a sample of 84 early-type galaxies (ETGs) with directly measured supermassive black hole masses—nearly doubling the sample size of such galaxies with multicomponent decompositions—a symmetric linear regression on the reduced (merger-free) sample of 76 galaxies reveals with a total scatter of Δrms = 0.52 dex in the direction. Importantly, however, we discover that the ES/S0-type galaxies with disks are offset from the E-type galaxies by more than a factor of ten in their ratio, with ramifications for formation theories, simulations, and some virial factor measurements used to convert AGN virial masses into M BH. Separately, each population follows a steeper relation with slopes of 1.86 ± 0.20 and 1.90 ± 0.20, respectively. The offset mass ratio is mainly due to the exclusion of the disk mass, with the two populations offset by only a factor of two in their ratio in the M BH– diagram where and dex depending on the sample. For , we detect no significant bend nor offset in either the M BH– or M BH– relations due to barred versus non-barred, or core-Sérsic versus Sérsic, ETGs. For reference, the ensemble of late-type galaxies (which invariably are Sérsic galaxies) follow M BH– and M BH– relations with slopes equal to 2.16 ± 0.32 and 3.05 ± 0.70, respectively. Finally, we provide some useful conversion coefficients, υ, accounting for the different stellar mass-to-light ratios used in the literature, and we report the discovery of a local, compact massive spheroid in NGC 5252.

Dimensionality Reduction of Hyperspectral Image Using Spatial-Spectral Regularized Sparse Hypergraph Embedding

Many graph embedding methods are developed for dimensionality reduction (DR) of hyperspectral image (HSI), which only use spectral features to reflect a point-to-point intrinsic relation and ignore complex spatial-spectral structure in HSI. A new DR method termed spatial-spectral regularized sparse hypergraph embedding (SSRHE) is proposed for the HSI classification. SSRHE explores sparse coefficients to adaptively select neighbors for constructing the dual sparse hypergraph. Based on the spatial coherence property of HSI, a local spatial neighborhood scatter is computed to preserve local structure, and a total scatter is computed to represent the global structure of HSI. Then, an optimal discriminant projection is obtained by possessing better intraclass compactness and interclass separability, which is beneficial for classification. Experiments on Indian Pines and PaviaU hyperspectral datasets illustrated that SSRHE effectively develops a better classification performance compared with the traditional spectral DR algorithms.

Monte Carlo Study of Unflattened Photon Beams Shaped by Multileaf Collimator

This study investigates basic dosimetric properties of unflattened 6 MV photon beam shaped by multileaf collimator and compares them with those of flattened beams. Monte Carlo simulation model using BEAM code was developed for a 6MV photon beam based on Varian Clinic 600 unique performance linac operated with and without a flattening filter in beam line. Dosimetric features including lateral profiles, central axis depth dose, photon and electron spectra were calculated for flattened and unflattened cases, separately. An increase in absolute depth dose with a factor of more than 2.4 was observed for unflattened beam which was dependent on depth. PDDs values were found to be lower for unflattened beam for all field sizes. Significant decrease in calculated mlc leakage was observed when the flattening filter was removed from the beam line. The total scatter factor, SCP was found to show less variation with field sizes for unflattened beam indicating a decrease in head scatter. The beam profiles for unflattened case are found to have lower relative dose value in comparison with flattened beam near the field edge, and it falls off faster with distance. Our study showed that increase in the dose rate and lower peripheral dose could be considered as realistic advantages for unflattened 6MV photon beams.

Ab Initio Calculation of Total X-ray Scattering from Molecules.

We present a method to calculate total X-ray scattering cross sections directly from ab initio electronic wave functions in atoms and molecules. The approach can be used in conjunction with multiconfigurational wave functions and exploits analytical integrals of Gaussian-type functions over the scattering operator, which leads to accurate and efficient calculations. The results are validated by comparison to experimental results and previous theory for the molecules H2 and CO2. Importantly, we find that the inelastic component of the total scattering varies strongly with molecular geometry. The method is appropriate for use in conjunction with quantum molecular dynamics simulations for the analysis of new ultrafast X-ray scattering experiments and to interpret accurate gas-phase scattering experiments.

Sparse modified marginal fisher analysis for facial expression recognition

Marginal Fisher analysis (MFA) is an efficient method for dimension reduction, which can extract useful discriminant features for image recognition. Since sparse learning can achieve better generalization ability and lessen the amount of computations in recognition tasks, this paper introduces sparsity into MFA and proposes a novel sparse modified MFA (SMMFA) method for facial expression recognition. The goal of SMMFA is to extract discriminative features by using the resulted sparse projection matrix. First, a modified MFA is proposed to find the original projection matrix. Similar to MFA, the modified MFA also defines the intra-class graph and the inter-class graph to describe geometry structure in the same class and local discriminant structure between different classes, respectively. In addition, the modified MFA removes the null space of the total scatter matrix. The sparse solution of SMMFA can be gained by solving the l1 –minimization problem on the original projection matrix using the linearized Bregman iteration. Experimental results show that the proposed SMMFA can effectively extract intrinsic features and has better discriminant power than the state-of-the-art methods.

Predicting Asphaltene Aggregate Structure from Molecular Dynamics Simulation: Comparison to Neutron Total Scattering Data

Molecular dynamics (MD) simulation is quickly growing in popularity as a technique for understanding asphaltene aggregate structure and dynamics. However, verification of the results of simulations against experimental data has, to date, been sparse. Here, we present total scattering data from Athabasca asphaltenes, as both a solid and dispersed at high concentrations in deuterated 1-methylnaphthalene. The advantage of total scattering is that the expected scattering can be calculated from knowledge of the atomic positions in the system of question, meaning that simulation and experiment can be directly compared. We find that the MD simulations for model monodisperse systems reproduce the general form of the scattering curves well, particularly for the slope and shape for the small-angle scattering curve of dispersed asphaltenes. However, we find a number of limitations in the MD techniques as commonly used in the literature; specifically, the size of the aggregates formed is considerably smaller than obs...

基于总散射测量的表面质量检测新方法

基于总散射测量的表面质量检测新方法

Quality Assurance Procedure for Linear Accelerators Measuring Direct Tissue Maximum Ratio with a Calibration Water Phantom

In this paper, we proposed an efficient quality assurance method which can measure direct tissue maximum ratio (TMRDir), total scatter factor (Scp, Dir), wedge factor (WFDir), tissue phantom ratio 20/10 (TPR20/10Dir) by using a calibration water phantom and a Farmer chamber. The TMRDir was compared with the calculated TMR (TMRCal) that was calculated from the percentage depth dose at the time of the linear accelerator installation. Scp, Dir, WFDir and TPR20/10Dir calculated from TMRDir were compared with Scp, BD, WFBD, and TPR20/10BD measured at the time of the linear accelerator installation. The difference between TMRDir and TMRCal was approximately within 1% except for using 60° wedge filter. The difference between Scp, Dir and Scp, BD was within 1%, between WFDir and WFBD was within 2%, between TPR20/10Dir and TPR20/10BD was within 1%, these differences were acceptable levels of AAPM TG-142 report. Also, coefficient of variation (CV) of TMRDir, ScpDir, WFDir and TPR20/10Dir when changing days and measuring multiple times were approximately within 1%, these CVs were reference levels of AAPM TG-106 report. We validated that was an efficient quality assurance method by measuring direct tissue maximum ratio, but the propose method has limited in measurable field size.

Investigation of Estimation Accuracy of Phantom Scatter Factor by Clarkson Method Considering Depth in MLC Irregular Field

In monitor unit (MU) independent verification by calculation for irregular field (MLC field) using multileaf collimator in X-ray therapy, it has become common to use collimator scatter factor (Sc) and phantom scatter factor (Sp) instead of total scatter factor (Sc, p). It is usually expressed as Sc, p (A)=Sc (A)×Sp (A), and the field size A is considered but the depth d is not. Sc is data of in-air output, and measure with a mini-phantom at constant depth to remove electron contamination. On the other hand, Sp is obtained from measurement data of Sc, p and Sc, and can be expressed as Sc, p (d, A)=Sc (constant depth, A)×Sp (d, A) at an arbitrary depth d, thus Sp depends on the depth of Sc, p. Therefore, Sp needs to consider depth. In addition, a linear accelerator equipped with the tertiary MLC has two field sizes, that are collimator field by upper and lower collimators and MLC field by tertiary MLC below them. In MU independent verification by calculation, it is often used that the estimated value of Sp obtained by converting MLC field to equivalent square field and referring to data of Sp in square field. To convert the MLC field to equivalent square field, a conversion formula from sector radius r to equivalent square field L by Clarkson's sector integration (Clarkson method) is used. In this study, using 24 types of MLC fields to evaluate estimation accuracy due to the difference of conversion formula in Clarkson method, we estimated value of Sp using r=0.5611L of B-Clarkson method and using r=0.5580L of A-Clarkson method. And the difference with the measured value of Sp obtained by measuring Sc, p and Sc in the same MLC fields was compared. While, to evaluate estimation accuracy due to the different depths using these Clarkson methods, the difference between estimated value and measured value of Sp similarly obtained at depth of 5, 10 and 15 cm was compared. As results, estimated value of Sp using A-Clarkson method than using B-Clarkson method was close to measured value, and it was the same trend at depth of 5, 10 and 15 cm. Therefore, it was suggested that estimation accuracy of Sp by A-Clarkson method is higher than B-Clarkson method when verifying beams with different depths in MU independent verification by calculation for MLC field.

Advantages and disadvantages of removed flattening filter Linac: A Monte Carlo study on full quantitative dosimetric data of 18 MV-Varian Linac

Introduction: During intensity modulated radiation therapy (IMRT) technique, theoretically, presence of flattening filter (FF) across the beamline of clinical linear accelerator (linac) is not essential to obtain uniform lateral profiles due to intensity modulation of photon beams by multileaf collimators (MLCs). The aim of this study was to investigate the dosimetrical properties of 18 MV photon Beam-Varian linac with and without FF. Materials and Methods: All dose measurements were performed on 18 MV, FF Mode-Varian 2100C/D linac. The FF and flattening filter free (FFF) modes of linac were modeled by MCNPX 2.4. code. The photon and contaminant electrons spectra, dose rate, present depth doses (PDD), lateral dose profiles, total and collimator scatter factors and out of field doses were calculated and compared with and without FF. Results: Removing the FF increased the photon and contaminant electron fluences by factors of 5.48 and 3.94 for a 5 × 5 cm2 field size, respectively. The surface dose increased up to 155%. The flatness of dose profile was disturbed and deteriorated with increase of field size. Despite the dependence of the total scattering factor on field size, the variation of collimator scattering factors was neglected. The out-of-field dose decreased about 81.5 % for a 5 × 5 cm2 field size. Conclusion: Removing FF from the linac’s head increases the dose rate and decreases the out-of-field dose, but the increased skin dose and deteriorated flatness of lateral dose profile are the main

Beam characteristic of P.E collimators Add-on multileaf collimator

Introduction: Multileaf collimators (MLCs) are computer-controlled devices which are Useful and cost-effective tools for conformal therapy and intensity modulation radiotherapy (IMRT). Nowadays MLCs are important and standard configuration of the new medical linear accelerators which are substitute of conventional Blocks and has eliminated the difficulties of working with blocks. MLCs are available from many manufacturers and their designs differ in the way they couple with conventional jaws, number and width of leaves and in their physical and dosimetric characteristics, well understanding on the mechanics and dosimetric characteristics of MLC is the basic task of medical physicist. Materials and Methods: In this study some mechanical and dosimetric characteristics of a P.E. Collimators Add-On MLC which is installed on VARIAN CLINAC 2100 C/D are presented. Scatter factors (Sc, Sp, Scp), central axis depth dose and beam profiles were measured before and after installation of MLC. mechanical and Leaf Leakages for 6MV and 18MV beams were measured with Gafchromic EBT3 films. Results: radiation and light fields were match below the 2mm acceptable level based on AAPM reports. Average leaf leakage was noted 1.79% for 6MV and 1.98% for 18MV beams, respectively. No significant differences were found in beam profiles, collimator (Sc), phantom (Sp) and total (Sc, p) scatter factors after MLC installation. The percent depth dose data for all fields and both beam energies were within 1.6 % of the original data. Conclusion: Based on the Mechanical and dosimetric results which have been achieved from our different standard tests, we found no significant differences between before and after MLC installation Values on Clinac 2100 C/D Varian LINAC.

A multilinear collaborative representation preserving projections method for feature extraction

In this paper, a multilinear collaborative representation preserving projections (MCRPP) is developed for feature extraction and recognition on tensor objects. MCRPP is an unsupervised method built on collaborative representation and multilinear algebra. MCRPP calculates the projection matrix by simultaneously considering both the distribution information of all the samples and the spatial structure information of the sample. MCRPP aims to preserve the sparse reconstruction relations of data in the reduced subspace via collaborative representation reconstruction. Redefining the local multilinear scatter and the total multilinear scatter, MCRPP seeks the projection matrix by maximizing the ratio between the total multilinear scatter and local multilinear scatter using generalized eigenvalue decomposition. The final experimental results on FERET, AR and Yale face databases demonstrate that MCRPP is an efficient and effective method for feature extraction and dimensionality reduction.

Retrieval of Total Scattering Cross Sections of Molecules from Inhomogeneously Broadened Absorption Lines

A new method of retrieving quantitative information on the hard, soft, and diffraction collision’s frequencies from inhomogeneously pressure-broadened line profiles was proposed and tested. The essence of the method lies in the processing of recorded profiles using various profiles’ models containing these frequencies treated as adjustable parameters in different manners. Three self-broadened H2O absorption lines free of an instrumental function were processed with the use of four model line profiles. Retrieved set of pressure line broadening and narrowing constants allows finding out the sought frequencies. The estimation of the total scattering cross section, ∼630 Å2, in pure water vapor was made.

Trapping Amorphous Intermediates of Carbonates - A Combined Total Scattering and NMR Study.

Crystallization via metastable phases plays an important role in chemical manufacturing, biomineralization, and protein crystallization, but the kinetic pathways leading from metastable phases to the stable crystalline modifications are not well understood. In particular, the fast crystallization of amorphous intermediates makes a detailed characterization challenging. To circumvent this problem, we devised a system that allows trapping and stabilizing the amorphous intermediates of representative carbonates (calcium, strontium, barium, manganese, and cadmium). The long-term stabilization of these transient species enabled a detailed investigation of their composition, structure, and morphology. Total scattering experiments with high-energy synchrotron radiation revealed a short-range order of several angstroms in all amorphous intermediates. From the synchrotron data, a structural model of amorphous calcium carbonate was derived that indicates a lower coordination number of calcium compared to the crystalline polymorphs. Our study shows that a multistep crystallization pathway via amorphous intermediates is open to many carbonates. We could isolate and characterize these transient species, thereby providing new insights into their crystallization mechanism.

The Noise Level of Total Scattering Cross Section Measurement in a Reverberation Chamber

A chamber can be used to measure the total scattering cross section (TSCS) of an object, in which the time-domain response needs to be analyzed to extract the scattering damping time. It has been observed in measurements that the noise level in extracting the scattering damping time is much higher than that in extracting the chamber decay time. The reasons behind this phenomenon are explored in this letter. Analytical distributions of the noise in TSCS measurements are derived and validated by measurements. Good agreements between analytical results and measurement results have been obtained, which gives guidelines on the prediction of noise level and the required independent sample number in the total scattering cross section measurement.

When Crystals Go Nano – The Role of Advanced X‐ray Total Scattering Methods in Nanotechnology

AbstractInvited for the cover of this issue is the group of Norberto Masciocchi of the University of Insubria, and collaborator Antonella Guagliardi of the Institute of Crystallography of the National Research Council (CNR), Como, Italy, co‐founders of To.Sca.Lab. The cover image shows the colloidal semiconductor nanocrystals studied by advanced X‐ray Total Scattering methods and reciprocal‐space data analysis.

When Crystals Go Nano – The Role of Advanced X‐ray Total Scattering Methods in Nanotechnology

Controlling the stoichiometry, structure, defects, size, and shape of engineered nanomaterials (in the forms of powders, colloids, and thin films) is a fundamental issue in designing new functionalities and providing reproducible and efficient synthetic methods, thus enabling the construction of high‐tech devices. Nanosized materials arecomplexsystems; therefore, to meet these goals, advanced physicochemical methods and dedicated and robust characterization tools, bearing a solid statistical value, are required. Here we present frontier techniques based on X‐ray total scattering (mainly, but not only, synchrotron‐based) and the Debye scattering equation modeling. The method has been developed in the field of crystalline nanomaterials and nanocomposites, from very small colloidal semiconductor quantum dots to halide perovskites, metals, oxides, nanodrugs, and bioceramics, and provides atomic‐ to nanometer‐scale characterization to an unbeatable level. Examples from the recent scientific literature are presented.

Lepidocrocite-Type Titanate Formation from Isostructural Prestructures under Hydrothermal Reactions: Observation by Synchrotron X-ray Total Scattering Analyses.

The formation of titanium dioxides, such as rutile and anatase, is known to proceed through the formation of a lepidocrocite-type layered structure under hydrothermal conditions, but the nucleation of this intermediate is still not understood well. Here, the nucleation of lepidocrocite-type layered titanates under hydrothermal conditions is observed by tracking the structural changes by in situ time-resolved pair distribution function analyses. We found that titanate clusters or corrugated layered prestructures having <1 nm domains with lepidocrocite-type connectivity were formed even before thermal treatment in alkaline aqueous solution. Upon thermal treatment, a two-dimensional layered structure grew directly from the prestructure, not from the amorphous polymeric hydroxide dissolved in the solution. Thus, we conclude that the formation of the lepidocrocite-like prestructure is the key for forming a layered titanate under hydrothermal conditions.