scholarly journals Likelihood-based estimation of substructure content from single-wavelength anomalous diffraction (SAD) intensity data

2021 ◽  
Vol 77 (7) ◽  
Author(s):  
Kaushik S. Hatti ◽  
Airlie J. McCoy ◽  
Randy J. Read
Keyword(s):  
Signal To Noise Ratio ◽  
Target Function ◽  
Protein Composition ◽  
Likelihood Estimation ◽  
Accurate Estimate ◽  
Anomalous Scattering ◽  
Correlated Errors ◽  
Complex Correlation ◽  
Anomalous Signal ◽  
Correlation Parameters

SAD phasing can be challenging when the signal-to-noise ratio is low. In such cases, having an accurate estimate of the substructure content can determine whether or not the substructure of anomalous scatterer positions can successfully be determined. Here, a likelihood-based target function is proposed to accurately estimate the strength of the anomalous scattering contribution directly from the measured intensities, determining a complex correlation parameter relating the Bijvoet mates as a function of resolution. This gives a novel measure of the intrinsic anomalous signal. The SAD likelihood target function also accounts for correlated errors in the measurement of intensities from Bijvoet mates, which can arise from the effects of radiation damage. When the anomalous signal is assumed to come primarily from a substructure comprising one anomalous scatterer with a known value of f′′ and when the protein composition of the crystal is estimated correctly, the refined complex correlation parameters can be interpreted in terms of the atomic content of the primary anomalous scatterer before the substructure is known. The maximum-likelihood estimation of substructure content was tested on a curated database of 357 SAD cases with useful anomalous signal. The prior estimates of substructure content are highly correlated to the content determined by phasing calculations, with a correlation coefficient (on a log–log basis) of 0.72.

scholarly journals Likelihood-based estimation of substructure content from single-wavelength anomalous diffraction (SAD) intensity data

2021 ◽  
Author(s):  
Kaushik S Hatti ◽  
Airlie J McCoy ◽  
Randy J Read
Keyword(s):  
Measurement Errors ◽  
Target Function ◽  
Protein Composition ◽  
Likelihood Estimation ◽  
Accurate Estimate ◽  
Likelihood Method ◽  
Anomalous Scattering ◽  
Correlated Errors ◽  
Complex Correlation ◽  
Anomalous Signal

AbstractSAD phasing can be challenging when the signal-to-noise ratio is low. In such cases, having an accurate estimate of substructure content can determine whether or not the substructure of anomalous scatterer positions can successfully be determined. We propose a likelihood-based target function to accurately estimate the strength of the anomalous scattering contribution directly from measured intensities, determining a complex correlation parameter relating the Bijvoet mates as a function of resolution. This gives a novel measure of intrinsic anomalous signal. The SAD likelihood target function also accounts for correlated errors in the measurement of intensities from Bijvoet mates, which can arise from the effects of radiation damage. When the anomalous signal is assumed to come primarily from a substructure comprised of one anomalous scatterer with a known value of f” and when the protein composition of the crystal is estimated correctly, the refined complex correlation parameters can be interpreted in terms of the atomic content of the primary anomalous scatterer, before the substructure is known. The maximum likelihood estimation of substructure content was tested on a curated database of 357 SAD cases with useful anomalous signal. The prior estimates of substructure content are highly correlated to the content determined by phasing calculations, with a correlation coefficient (on a log-log basis) of 0.72.SynopsisAn intensity-based likelihood method is provided to estimate scattering from an anomalous substructure considering the effect of measurement errors in Bijvoet pairs and correlations between those errors.

scholarly journals Continuum Power CCA: A Unified Approach for Isolating Coupled Modes

2015 ◽  
Vol 28 (3) ◽  
pp. 1016-1030 ◽  
Author(s):  
Erik Swenson
Keyword(s):  
Signal To Noise Ratio ◽  
Full Range ◽  
Synthetic Data ◽  
Principal Component Regression ◽  
Principal Component ◽  
Accurate Estimate ◽  
Unified Approach ◽  
Coupled Modes ◽  
Multivariate Statistical ◽  
Sample Covariance

Abstract Various multivariate statistical methods exist for analyzing covariance and isolating linear relationships between datasets. The most popular linear methods are based on singular value decomposition (SVD) and include canonical correlation analysis (CCA), maximum covariance analysis (MCA), and redundancy analysis (RDA). In this study, continuum power CCA (CPCCA) is introduced as one extension of continuum power regression for isolating pairs of coupled patterns whose temporal variation maximizes the squared covariance between partially whitened variables. Similar to the whitening transformation, the partial whitening transformation acts to decorrelate individual variables but only to a partial degree with the added benefit of preconditioning sample covariance matrices prior to inversion, providing a more accurate estimate of the population covariance. CPCCA is a unified approach in the sense that the full range of solutions bridges CCA, MCA, RDA, and principal component regression (PCR). Recommended CPCCA solutions include a regularization for CCA, a variance bias correction for MCA, and a regularization for RDA. Applied to synthetic data samples, such solutions yield relatively higher skill in isolating known coupled modes embedded in noise. Provided with some crude prior expectation of the signal-to-noise ratio, the use of asymmetric CPCCA solutions may be justifiable and beneficial. An objective parameter choice is offered for regularization with CPCCA based on the covariance estimate of O. Ledoit and M. Wolf, and the results are quite robust. CPCCA is encouraged for a range of applications.

scholarly journals Assessing Neuronal Coherence with Single-Unit, Multi-Unit, and Local Field Potentials

2006 ◽  
Vol 18 (9) ◽  
pp. 2256-2281 ◽  
Author(s):  
Magteld Zeitler ◽  
Pascal Fries ◽  
Stan Gielen
Keyword(s):  
Unit Activity ◽  
Single Unit ◽  
Signal To Noise Ratio ◽  
Coherence Function ◽  
Accurate Estimate ◽  
Unit Recording ◽  
Output Spike ◽  
Monkey Visual Cortex ◽  
Neuronal Coherence ◽  
Unit Spike

The purpose of this study was to obtain a better understanding of neuronal responses to correlated input, in particular focusing on the aspect of synchronization of neuronal activity. The first aim was to obtain an analytical expression for the coherence between the output spike train and correlated input and for the coherence between output spike trains of neurons with correlated input. For Poisson neurons, we could derive that the peak of the coherence between the correlated input and multi-unit activity increases proportionally with the square root of the number of neurons in the multi-unit recording. The coherence between two typical multi-unit recordings (2 to 10 single units) with partially correlated input increases proportionally with the number of units in the multi-unit recordings. The second aim of this study was to investigate to what extent the amplitude and signal-to-noise ratio of the coherence between input and output varied for single-unit versus multi-unit activity and how they are affected by the duration of the recording. The same problem was addressed for the coherence between two single-unit spike series and between two multi-unit spike series. The analytical results for the Poisson neuron and numerical simulations for the conductance-based leaky integrate-and-fire neuron and for the conductance-based Hodgkin-Huxley neuron show that the expectation value of the coherence function does not increase for a longer duration of the recording. The only effect of a longer duration of the spike recording is a reduction of the noise in the coherence function. The results of analytical derivations and computer simulations for model neurons show that the coherence for multi-unit activity is larger than that for single-unit activity. This is in agreement with the results of experimental data obtained from monkey visual cortex (V4). Finally, we show that multitaper techniques greatly contribute to a more accurate estimate of the coherence by reducing the bias and variance in the coherence estimate.

scholarly journals A Geometric Calibration Method of Hydrophone Array Based on Maximum Likelihood Estimation with Sources in Near Field

2020 ◽  
Vol 8 (9) ◽  
pp. 678
Author(s):  
Nan Zou ◽  
Zhenqi Jia ◽  
Jin Fu ◽  
Jia Feng ◽  
Mengqi Liu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Signal To Noise Ratio ◽  
Near Field ◽  
Likelihood Estimation ◽  
Calibration Method ◽  
Optimization Method ◽  
High Signal ◽  
Geometric Calibration ◽  
Environment Experiment

Considering the requirement of the near-field calibration under strong underwater multipath condition, a high-precision geometric calibration method based on maximum likelihood estimation is proposed. It can be used as both auxiliary-calibration and self-calibration. According to the near-field geometry error model, the objective function of nonlinear optimization problem is constructed by using the unconditional maximum likelihood estimator. The influence of multipath on geometric calibration is studied. The strong reflections are considered as the coherent sources, and the compensation strategy for auxiliary-calibration is realized. The optimization method (differential evolution, DE) is used to solve the geometry errors and sources’ position. The method in this paper is compared with the eigenvector method. The simulation results show that the method in this paper is more accurate than the eigenvector method especially under high signal-to-noise ratio (SNR) and multipath environment. Experiment results further verify the effectiveness.

A solution-free crystal-mounting platform for native SAD

2020 ◽  
Vol 76 (10) ◽  
pp. 938-945
Author(s):  
Jian Yu ◽  
Akira Shinoda ◽  
Koji Kato ◽  
Isao Tanaka ◽  
Min Yao
Keyword(s):  
Data Collection ◽  
Nucleic Acids ◽  
Protein Structures ◽  
Anomalous Scattering ◽  
X Rays ◽  
Long Wavelength ◽  
Light Atoms ◽  
Sad Phasing ◽  
Anomalous Signal

The native SAD phasing method uses the anomalous scattering signals from the S atoms contained in most proteins, the P atoms in nucleic acids or other light atoms derived from the solution used for crystallization. These signals are very weak and careful data collection is required, which makes this method very difficult. One way to enhance the anomalous signal is to use long-wavelength X-rays; however, these wavelengths are more strongly absorbed by the materials in the pathway. Therefore, a crystal-mounting platform for native SAD data collection that removes solution around the crystals has been developed. This platform includes a novel solution-free mounting tool and an automatic robot, which extracts the surrounding solution, flash-cools the crystal and inserts the loop into a UniPuck cassette for use in the synchrotron. Eight protein structures (including two new structures) have been successfully solved by the native SAD method from crystals prepared using this platform.

Mechanical Fault Detection Based on the Wavelet De-Noising Technique

2004 ◽  
Vol 126 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Jing Lin ◽  
Ming J. Zuo ◽  
Ken R. Fyfe
Keyword(s):  
Prior Information ◽  
Early Stage ◽  
Signal To Noise Ratio ◽  
Mechanical Vibration ◽  
Likelihood Estimation ◽  
Morlet Wavelet ◽  
Signal To Noise ◽  
Vibration Signals ◽  
Orthogonal Wavelets ◽  
Basic Wavelet

For gears and roller bearings, periodic impulses indicate that there are faults in the components. However, it is difficult to detect the impulses at the early stage of fault because they are rather weak and often immersed in heavy noise. Existing wavelet threshold de-noising methods do not work well because they use orthogonal wavelets, which do not match the impulse very well and do not utilize prior information on the impulse. A new method for wavelet threshold de-noising is proposed in this paper; it not only employs the Morlet wavelet as the basic wavelet for matching the impulse, but also uses the maximum likelihood estimation for thresholding by utilizing prior information on the probability density of the impulse. This method has performed excellently when used to de-noise mechanical vibration signals with a low signal-to-noise ratio.

scholarly journals Efficient and Accurate Frequency Estimator under Low SNR by Phase Unwrapping

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Shen Zhou ◽  
Liu Rongfang
Keyword(s):  
Frequency Estimation ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Likelihood Estimation ◽  
Accurate Method ◽  
Phase Unwrapping ◽  
Single Frequency ◽  
Low Snr ◽  
Cramer Rao Bound ◽  
Frequency Estimator

In the case of low signal-to-noise ratio, for the frequency estimation of single-frequency sinusoidal signals with additive white Gaussian noise, the phase unwrapping estimator usually performs poorly. In this paper, an efficient and accurate method is proposed to address this problem. Different from other methods, based on fast Fourier transform, the sampled signals are estimated with the variances approaching the Cramer-Rao bound, followed with the maximum likelihood estimation of the frequency. Experimental results reveal that our estimator has a better performance than other phase unwrapping estimators. Compared with the state-of-the-art method, our estimator has the same accuracy and lower computational complexity. Besides, our estimator does not have the estimation bias.

scholarly journals Can I solve my structure by SAD phasing? Anomalous signal in SAD phasing

2016 ◽  
Vol 72 (3) ◽  
pp. 346-358 ◽  
Author(s):  
Thomas C. Terwilliger ◽  
Gábor Bunkóczi ◽  
Li-Wei Hung ◽  
Peter H. Zwart ◽  
Janet L. Smith ◽  
...  
Keyword(s):  
Signal To Noise Ratio ◽  
Atomic Displacement ◽  
Peak Height ◽  
High Ratio ◽  
Data Set ◽  
High Data ◽  
Sad Phasing ◽  
Anomalous Signal ◽  
Displacement Factor ◽  
Difference Fourier

A key challenge in the SAD phasing method is solving a structure when the anomalous signal-to-noise ratio is low. A simple theoretical framework for describing measurements of anomalous differences and the resulting useful anomalous correlation and anomalous signal in a SAD experiment is presented. Here, the useful anomalous correlation is defined as the correlation of anomalous differences with ideal anomalous differences from the anomalous substructure. The useful anomalous correlation reflects the accuracy of the data and the absence of minor sites. The useful anomalous correlation also reflects the information available for estimating crystallographic phases once the substructure has been determined. In contrast, the anomalous signal (the peak height in a model-phased anomalous difference Fourier at the coordinates of atoms in the anomalous substructure) reflects the information available about each site in the substructure and is related to the ability to find the substructure. A theoretical analysis shows that the expected value of the anomalous signal is the product of the useful anomalous correlation, the square root of the ratio of the number of unique reflections in the data set to the number of sites in the substructure, and a function that decreases with increasing values of the atomic displacement factor for the atoms in the substructure. This means that the ability to find the substructure in a SAD experiment is increased by high data quality and by a high ratio of reflections to sites in the substructure, and is decreased by high atomic displacement factors for the substructure.

An Improved Parameter Estimation Method for Three-Parameter Weibull Distribution in the Life Analysis of Rolling Bearing

2012 ◽  
Vol 569 ◽  
pp. 442-446 ◽  
Author(s):  
Feng Long Yin ◽  
Ya Shun Wang ◽  
Chun Hua Zhang ◽  
Xiang Po Zhang
Keyword(s):  
Parameter Estimation ◽  
Weibull Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Rolling Bearing ◽  
Accurate Estimate ◽  
Distribution Model ◽  
Bearing Life ◽  
Mechanical Products ◽  
Life Analysis

Three-parameter Weibull distribution is playing a more and more important role in the reliability analysis of mechanical products. It can provide higher accuracy and better reflection of reliability in operating situation concerning fitting and parameter estimation for the rolling bearing life data. This paper focuses on the theory derivation of the maximum likelihood estimation of the three-parameter Weibull distribution, puts forward an improved method for the model parameter estimation and draws the life distribution model. Following that, the method has been proved to be correct and accurate by practical examples.The proposed method can provide a more accurate estimate way for the life analysis of rolling bearing based on three-parameter Weibull distribution.

scholarly journals Research on DOA Estimation Based on Acoustic Energy Flux Detection Using a Single MEMS Vector Hydrophone

Micromachines ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 168
Author(s):  
Xiaoyong Zhang ◽  
Guojun Zhang ◽  
Zhenzhen Shang ◽  
Shan Zhu ◽  
Peng Chen ◽  
...  
Keyword(s):  
Energy Flux ◽  
Signal To Noise Ratio ◽  
Likelihood Estimation ◽  
Doa Estimation ◽  
Acoustic Energy ◽  
Vector Hydrophone ◽  
Energy Center ◽  
Simulation Results ◽  
Micro Electromechanical System ◽  
Improved Algorithm

The principle of acoustic energy flux detection method using a single micro electromechanical system (MEMS) vector hydrophone is analyzed in this paper. The probability distribution of acoustic energy flux and the weighted histogram algorithm are discussed. Then, an improved algorithm is proposed. Based on the algorithm, the distribution range of the energy is obtained by a sliding window, the energy center of gravity in the range is considered as the result of direction of arrival (DOA) estimation, and it is proved to be the maximum likelihood estimation of the target direction. The simulation results show that, with the signal to noise ratio (SNR) from −10 dB to 10 dB, the root mean square error (RMSE) of the improved algorithm is reduced by 47.8% on average, and is more accurate in the presence of interference. The experimental results of lake test are consistent with the theory analysis and simulation results.

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