scholarly journals A robust expectation-maximization method for the interpretation of small-angle scattering data from dense nanoparticle samples

2019 ◽  
Vol 52 (5) ◽  
pp. 926-936
Author(s):  
M. Bakry ◽  
H. Haddar ◽  
O. Bunău
Keyword(s):  
Small Angle ◽  
Expectation Maximization ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Small Angle Scattering ◽  
Fine Tuning ◽  
Scattering Data ◽  
Model Parameters ◽  
Dry Powders ◽  
Angle Scattering

The local monodisperse approximation (LMA) is a two-parameter model commonly employed for the retrieval of size distributions from the small-angle scattering (SAS) patterns obtained from dense nanoparticle samples (e.g. dry powders and concentrated solutions). This work features a novel implementation of the LMA model resolution for the inverse scattering problem. The method is based on the expectation-maximization iterative algorithm and is free of any fine-tuning of model parameters. The application of this method to SAS data acquired under laboratory conditions from dense nanoparticle samples is shown to provide good results.

scholarly journals Analysis of small-angle scattering data using model fitting and Bayesian regularization

2018 ◽  
Vol 51 (4) ◽  
pp. 1151-1161 ◽  
Author(s):  
Andreas Haahr Larsen ◽  
Lise Arleth ◽  
Steen Hansen
Keyword(s):  
Prior Knowledge ◽  
Small Angle ◽  
Regularization Method ◽  
Prior Information ◽  
Form Factors ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Model Parameters ◽  
Bayesian Regularization ◽  
Angle Scattering

The structure of macromolecules can be studied by small-angle scattering (SAS), but as this is an ill-posed problem, prior knowledge about the sample must be included in the analysis. Regularization methods are used for this purpose, as already implemented in indirect Fourier transformation and bead-modeling-based analysis of SAS data, but not yet in the analysis of SAS data with analytical form factors. To fill this gap, a Bayesian regularization method was implemented, where the prior information was quantified as probability distributions for the model parameters and included via a functional S. The quantity Q = χ2 + αS was then minimized and the value of the regularization parameter α determined by probability maximization. The method was tested on small-angle X-ray scattering data from a sample of nanodiscs and a sample of micelles. The parameters refined with the Bayesian regularization method were closer to the prior values as compared with conventional χ2 minimization. Moreover, the errors on the refined parameters were generally smaller, owing to the inclusion of prior information. The Bayesian method stabilized the refined values of the fitted model upon addition of noise and can thus be used to retrieve information from data with low signal-to-noise ratio without risk of overfitting. Finally, the method provides a measure for the information content in data, N g, which represents the effective number of retrievable parameters, taking into account the imposed prior knowledge as well as the noise level in data.

scholarly journals Small-Angle Scattering from Fractals: Differentiating between Various Types of Structures

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 65 ◽  
Author(s):  
Eugen Mircea Anitas
Keyword(s):  
Small Angle ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Theoretical Models ◽  
Small Angle Scattering ◽  
X Rays ◽  
Fractal Structures ◽  
Practical Applications ◽  
Additional Information ◽  
Angle Scattering

Small-angle scattering (SAS; X-rays, neutrons, light) is being increasingly used to better understand the structure of fractal-based materials and to describe their interaction at nano- and micro-scales. To this aim, several minimalist yet specific theoretical models which exploit the fractal symmetry have been developed to extract additional information from SAS data. Although this problem can be solved exactly for many particular fractal structures, due to the intrinsic limitations of the SAS method, the inverse scattering problem, i.e., determination of the fractal structure from the intensity curve, is ill-posed. However, fractals can be divided into various classes, not necessarily disjointed, with the most common being random, deterministic, mass, surface, pore, fat and multifractals. Each class has its own imprint on the scattering intensity, and although one cannot uniquely identify the structure of a fractal based solely on SAS data, one can differentiate between various classes to which they belong. This has important practical applications in correlating their structural properties with physical ones. The article reviews SAS from several fractal models with an emphasis on describing which information can be extracted from each class, and how this can be performed experimentally. To illustrate this procedure and to validate the theoretical models, numerical simulations based on Monte Carlo methods are performed.

scholarly journals SASfit: a tool for small-angle scattering data analysis using a library of analytical expressions

2015 ◽  
Vol 48 (5) ◽  
pp. 1587-1598 ◽  
Author(s):  
Ingo Breßler ◽  
Joachim Kohlbrecher ◽  
Andreas F. Thünemann
Keyword(s):  
Data Analysis ◽  
Reference Material ◽  
Small Angle ◽  
Fractal Model ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Model Parameters ◽  
Angle Scattering ◽  
Confidence Assessment ◽  
Analysis Workflow

SASfitis one of the mature programs for small-angle scattering data analysis and has been available for many years. This article describes the basic data processing and analysis workflow along with recent developments in theSASfitprogram package (version 0.94.6). They include (i) advanced algorithms for reduction of oversampled data sets, (ii) improved confidence assessment in the optimized model parameters and (iii) a flexible plug-in system for custom user-provided models. A scattering function of a mass fractal model of branched polymers in solution is provided as an example for implementing a plug-in. The newSASfitrelease is available for major platforms such as Windows, Linux and MacOS. To facilitate usage, it includes comprehensive indexed documentation as well as a web-based wiki for peer collaboration and online videos demonstrating basic usage. The use ofSASfitis illustrated by interpretation of the small-angle X-ray scattering curves of monomodal gold nanoparticles (NIST reference material 8011) and bimodal silica nanoparticles (EU reference material ERM-FD-102).

scholarly journals 2017 publication guidelines for structural modelling of small-angle scattering data from biomolecules in solution: an update

2017 ◽  
Vol 73 (9) ◽  
pp. 710-728 ◽  
Author(s):  
Jill Trewhella ◽  
Anthony P. Duff ◽  
Dominique Durand ◽  
Frank Gabel ◽  
J. Mitchell Guss ◽  
...  
Keyword(s):  
Small Angle ◽  
Task Force ◽  
Data Bank ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Quality Data ◽  
Angle Scattering ◽  
Publication Guidelines ◽  
Guidelines And Recommendations

In 2012, preliminary guidelines were published addressing sample quality, data acquisition and reduction, presentation of scattering data and validation, and modelling for biomolecular small-angle scattering (SAS) experiments. Biomolecular SAS has since continued to grow and authors have increasingly adopted the preliminary guidelines. In parallel, integrative/hybrid determination of biomolecular structures is a rapidly growing field that is expanding the scope of structural biology. For SAS to contribute maximally to this field, it is essential to ensure open access to the information required for evaluation of the quality of SAS samples and data, as well as the validity of SAS-based structural models. To this end, the preliminary guidelines for data presentation in a publication are reviewed and updated, and the deposition of data and associated models in a public archive is recommended. These guidelines and recommendations have been prepared in consultation with the members of the International Union of Crystallography (IUCr) Small-Angle Scattering and Journals Commissions, the Worldwide Protein Data Bank (wwPDB) Small-Angle Scattering Validation Task Force and additional experts in the field.

A Study of Beryllium-Based Materials and Comparison of Their X-Ray Homogeneities According to Small-Angle Scattering Data

2018 ◽  
Vol 63 (6) ◽  
pp. 874-882 ◽  
Author(s):  
A. A. Semenov ◽  
V. V. Volkov ◽  
A. V. Zabrodin ◽  
V. V. Gorlevskii ◽  
M. S. Sheverdyaev ◽  
...  
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
X Ray ◽  
Angle Scattering

scholarly journals Small-angle scattering data representation in SASCIF and integrative/hybrid methods dictionary

2017 ◽  
Vol 73 (a2) ◽  
pp. C1441-C1441
Author(s):  
Brinda Vallat ◽  
Benjamin Webb ◽  
John Westbrook ◽  
Andrej Sali ◽  
Helen Berman
Keyword(s):  
Small Angle ◽  
Hybrid Methods ◽  
Data Representation ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Angle Scattering

scholarly journals The canSAS standard for storing reduced one-dimensional small-angle scattering data in XML files

2008 ◽  
Vol 64 (a1) ◽  
pp. C554-C554
Author(s):  
P.R. Jemian ◽  
A.J. Jackson ◽  
S.M. King ◽  
K.C. Littrell ◽  
A.R.J. Nelson ◽  
...  
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
One Dimensional ◽  
Angle Scattering

Small-angle scattering of interacting particles. II. Generalized indirect Fourier transformation under consideration of the effective structure factor for polydisperse systems

1999 ◽  
Vol 32 (2) ◽  
pp. 197-209 ◽  
Author(s):  
B. Weyerich ◽  
J. Brunner-Popela ◽  
O. Glatter
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Structure Factor ◽  
Fourier Transformation ◽  
Hard Spheres ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Model Free ◽  
Angle Scattering ◽  
The Gift

The indirect Fourier transformation (IFT) is the method of choice for the model-free evaluation of small-angle scattering data. Unfortunately, this technique is only useful for dilute solutions because, for higher concentrations, particle interactions can no longer be neglected. Thus an advanced technique was developed as a generalized version, the so-called generalized indirect Fourier transformation (GIFT). It is based on the simultaneous determination of the form factor, representing the intraparticle contributions, and the structure factor, describing the interparticle contributions. The former can be determined absolutely free from model assumptions, whereas the latter has to be calculated according to an adequate model. In this paper, various models for the structure factor are compared,e.g.the effective structure factor for polydisperse hard spheres, the averaged structure factor, the local monodisperse approximation and the decoupling approximation. Furthermore, the structure factor for polydisperse rod-like particles is presented. As the model-free evaluation of small-angle scattering data is an essential point of the GIFT technique, the use of a structure factor without any influence of the form amplitude is advisable, at least during the first evaluation procedure. Therefore, a series of simulations are performed to check the possibility of the representation of various structure factors (such as the effective structure factor for hard spheres or the structure factor for rod-like particles) by the less exact but much simpler averaged structure factor. In all the observed cases, it was possible to recover the exact form factor with a free determined parameter set for the structure factor. The resulting parameters of the averaged structure factor have to be understood as apparent model parameters and therefore have only limited physical relevance. Thus the GIFT represents a technique for the model independent evaluation of scattering data with a minimum ofa prioriinformation.

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