Analytic expressions of radial integral on multiple transitions for Coulomb-Born approximation

2001 ◽  
Vol 34 (9) ◽  
pp. 1935-1942 ◽  
Author(s):  
A Ohsaki ◽  
T Kai ◽  
E Kimura ◽  
S Nakazaki
Keyword(s):  
Born Approximation ◽  
Radial Integral ◽  
Analytic Expressions

Dynamical Scattering in Crystalline Biological Specimens. I. Criteria of Validity for Scattering Approximations

1975 ◽  
Vol 33 ◽  
pp. 192-193
Author(s):  
Robert M. Glaeser ◽  
Bing K. Jap
Keyword(s):  
Biological Sciences ◽  
Electron Microscopy ◽  
Electron Microscope ◽  
Electron Diffraction ◽  
Born Approximation ◽  
Materials Science ◽  
Image Data ◽  
Dynamical Effect ◽  
Crystallographic Structure ◽  
Electron Microscope Image

The dynamical scattering effect, which can be described as the failure of the first Born approximation, is perhaps the most important factor that has prevented the widespread use of electron diffraction intensities for crystallographic structure determination. It would seem to be quite certain that dynamical effects will also interfere with structure analysis based upon electron microscope image data, whenever the dynamical effect seriously perturbs the diffracted wave. While it is normally taken for granted that the dynamical effect must be taken into consideration in materials science applications of electron microscopy, very little attention has been given to this problem in the biological sciences.

Structural studies of small amorphous volumes by electron diffraction

1990 ◽  
Vol 48 (4) ◽  
pp. 122-123
Author(s):  
Pierre Moine
Keyword(s):  
Electron Diffraction ◽  
Born Approximation ◽  
Structural Information ◽  
Fundamental Relation ◽  
X Rays ◽  
Structural Studies ◽  
Diffraction Experiment ◽  
Transmission Electron ◽  
Amorphous Structures ◽  
Diffraction Patterns

Qualitatively, amorphous structures can be easily revealed and differentiated from crystalline phases by their Transmission Electron Microscopy (TEM) images and their diffraction patterns (fig.1 and 2) but, for quantitative structural information, electron diffraction pattern intensity analyses are necessary. The parameters describing the structure of an amorphous specimen have been introduced in the context of scattering experiments which have been, so far, the most used techniques to obtain structural information in the form of statistical averages. When only small amorphous volumes (< 1/μm in size or thickness) are available, the much higher scattering of electrons (compared to neutrons or x rays) makes, despite its drawbacks, electron diffraction extremely valuable and often the only feasible technique.In a diffraction experiment, the intensity IN (Q) of a radiation, elastically scattered by N atoms of a sample, is measured and related to the atomic structure, using the fundamental relation (Born approximation) : IN(Q) = |FT[U(r)]|.

CNN performance dependence on linear image processing

2020 ◽  
Vol 2020 (10) ◽  
pp. 310-1-310-7
Author(s):  
Khalid Omer ◽  
Luca Caucci ◽  
Meredith Kupinski
Keyword(s):  
Image Processing ◽  
Texture Classification ◽  
Full Rank ◽  
Detection Performance ◽  
Ideal Observer ◽  
Training Data ◽  
Image Texture ◽  
Training Images ◽  
Analytic Expressions ◽  
Linear Compression

This work reports on convolutional neural network (CNN) performance on an image texture classification task as a function of linear image processing and number of training images. Detection performance of single and multi-layer CNNs (sCNN/mCNN) are compared to optimal observers. Performance is quantified by the area under the receiver operating characteristic (ROC) curve, also known as the AUC. For perfect detection AUC = 1.0 and AUC = 0.5 for guessing. The Ideal Observer (IO) maximizes AUC but is prohibitive in practice because it depends on high-dimensional image likelihoods. The IO performance is invariant to any fullrank, invertible linear image processing. This work demonstrates the existence of full-rank, invertible linear transforms that can degrade both sCNN and mCNN even in the limit of large quantities of training data. A subsequent invertible linear transform changes the images’ correlation structure again and can improve this AUC. Stationary textures sampled from zero mean and unequal covariance Gaussian distributions allow closed-form analytic expressions for the IO and optimal linear compression. Linear compression is a mitigation technique for high-dimension low sample size (HDLSS) applications. By definition, compression strictly decreases or maintains IO detection performance. For small quantities of training data, linear image compression prior to the sCNN architecture can increase AUC from 0.56 to 0.93. Results indicate an optimal compression ratio for CNN based on task difficulty, compression method, and number of training images.

Multi-channel distorted-wave Born approximation for rovibrational transition rates in molecular collisions

2021 ◽  
Vol 155 (3) ◽  
pp. 034105
Author(s):  
Taha Selim ◽  
Arthur Christianen ◽  
Ad van der Avoird ◽  
Gerrit C. Groenenboom
Keyword(s):  
Born Approximation ◽  
Transition Rates ◽  
Distorted Wave ◽  
Distorted Wave Born Approximation ◽  
Molecular Collisions

scholarly journals Phase Stability under Thermal Drifts in Photodiode-Conditioning Transimpedance Amplifiers for Distance Metrology

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3455
Author(s):  
Francisco Javier Meca Meca ◽  
Ernesto Martín-Gorostiza ◽  
Miguel Ángel García-Garrido ◽  
David Salido-Monzú
Keyword(s):  
Delay Time ◽  
Measurement Errors ◽  
Continuous Wave ◽  
Signal To Noise Ratio ◽  
Circuit Board ◽  
Transimpedance Amplifiers ◽  
Optical Distance ◽  
High Measurement ◽  
Analytic Expressions ◽  
Measured Distance

Transimpedance amplifiers (TIA) are widely used for front-end signal conditioning in many optical distance measuring applications in which high accuracy is often required. Small effects due to the real characteristics of the components and the parasitic elements in the circuit board may cause the error to rise to unacceptable levels. In this work we study these effects on the TIA delay time error and deduce analytic expressions, taking into account the trade-off between the uncertainties caused by the delay time instability and by the signal-to-noise ratio. A specific continuous-wave phase-shift case study is shown to illustrate the analysis, and further compared with real measurements. General strategies and conclusions, useful for designers of this kind of system, are extracted too. The study and results show that the delay time thermal stability is a key determinant factor in the measured distance accuracy and, without an adequate design, moderate temperature variations of the TIA can cause extremely high measurement errors.

scholarly journals Elasticity of connected semiflexible quadrilaterals

Soft Matter ◽  
2021 ◽  
Vol 17 (1) ◽  
pp. 102-112
Author(s):  
Mohammadhosein Razbin ◽  
Alireza Mashaghi
Keyword(s):  
Thermal Fluctuations ◽  
Analytic Expressions ◽  
Probability Densities

The analytic expressions for the probability densities associated with the thermal fluctuations and the elasticity of the structure are obtained.

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