scholarly journals Density modification of cryo-EM maps

2020 ◽  
Author(s):  
Thomas C. Terwilliger ◽  
Oleg V. Sobolev ◽  
Pavel V. Afonine ◽  
Paul D. Adams ◽  
Randy J. Read
Keyword(s):  
Model Uncertainty ◽  
Model Bias ◽  
Electron Cryomicroscopy ◽  
Ensemble Models ◽  
Model Based ◽  
Information Density ◽  
Solvent Model ◽  
Incorrect Model ◽  
Expected Density

AbstractDensity modification uses expectations about features of a map such as a flat solvent and expected distributions of density in the region of the macromolecule to improve individual Fourier terms representing the map. This process transfers information from one part of a map to another and can improve the accuracy of a map. Here the assumptions behind density modification for maps from electron cryomicroscopy are examined and a procedure is presented that allows incorporation of model-based information. Density modification works best in cases where unfiltered, unmasked maps with clear boundaries between macromolecule and solvent are visible and where there is substantial noise in the map, both in the region of the macromolecule and the solvent. It also is most effective if the characteristics of the map are relatively constant within regions of the macromolecule and the solvent. Model-based information can be used to improve density modification, but model bias can in principle occur. Here model bias is reduced by using ensemble models that allow estimation of model uncertainty. A test of model bias is presented suggesting that even if the expected density in a region of a map is specified incorrectly by using an incorrect model, the incorrect expectations do not strongly affect the final map.SynopsisThe prerequisites for density modification of maps from electron cryomicroscopy are examined and a procedure for incorporating model-based information is presented.

scholarly journals Density modification of cryo-EM maps

2020 ◽  
Vol 76 (10) ◽  
pp. 912-925
Author(s):  
Thomas C. Terwilliger ◽  
Oleg V. Sobolev ◽  
Pavel V. Afonine ◽  
Paul D. Adams ◽  
Randy J. Read
Keyword(s):  
Model Uncertainty ◽  
Model Bias ◽  
Electron Cryomicroscopy ◽  
Ensemble Models ◽  
Model Based ◽  
Information Density ◽  
Solvent Model ◽  
Incorrect Model ◽  
Expected Density

Density modification uses expectations about features of a map such as a flat solvent and expected distributions of density in the region of the macromolecule to improve individual Fourier terms representing the map. This process transfers information from one part of a map to another and can improve the accuracy of a map. Here, the assumptions behind density modification for maps from electron cryomicroscopy are examined and a procedure is presented that allows the incorporation of model-based information. Density modification works best in cases where unfiltered, unmasked maps with clear boundaries between the macromolecule and solvent are visible, and where there is substantial noise in the map, both in the region of the macromolecule and the solvent. It also is most effective if the characteristics of the map are relatively constant within regions of the macromolecule and the solvent. Model-based information can be used to improve density modification, but model bias can in principle occur. Here, model bias is reduced by using ensemble models that allow an estimation of model uncertainty. A test of model bias is presented that suggests that even if the expected density in a region of a map is specified incorrectly by using an incorrect model, the incorrect expectations do not strongly affect the final map.

Uncertainty in Product Modelling within the Development Process

2015 ◽  
Vol 807 ◽  
pp. 89-98 ◽  
Author(s):  
Jan Würtenberger ◽  
Sebastian Gramlich ◽  
Tillmann Freund ◽  
Julian Lotz ◽  
Maximilian Zocholl ◽  
...  
Keyword(s):  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Development Process ◽  
Product Model ◽  
Modelling Uncertainty ◽  
Model Based ◽  
Product Models ◽  
Product Modelling ◽  
Uncertainty Parameter

This paper gives an overview about how to locate uncertainty in product modelling within the development process. Therefore, the process of product modelling is systematized with the help of characteristics of product models and typical working steps to develop a product model. Based on that, it is possible to distinguish between product modelling uncertainty, mathematic modelling uncertainty, parameter uncertainty, simulation uncertainty and product model uncertainty.

Robust Signal Recovery From Distorted Nonlinear Sensor Data

2003 ◽  
Author(s):  
Sugathevan Suranthiran ◽  
Suhada Jayasuriya
Keyword(s):  
Model Uncertainty ◽  
Signal Reconstruction ◽  
Sensor Data ◽  
Signal Recovery ◽  
Chirp Signal ◽  
Accurate Model ◽  
Design And Implementation ◽  
Novel Technique ◽  
Model Based ◽  
Nonlinear Sensors

In an attempt to facilitate the design and implementation of memory-less nonlinear sensors, the signal reconstruction schemes are analyzed and necessary modifications are proposed to improve the accuracy and minimize errors in sensor measurements. The problem of recovering chirp signal from the distorted nonlinear output is considered and an efficient reconstruction approach is developed. Model uncertainty is a serious issue with any model-based algorithms and a novel technique, which uses a norminal model instead of an accurate model and produces the results that are robust to model uncertainty, is proposed.

scholarly journals Friction compensation and observer-based adaptive sliding mode control of electromechanical actuator

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881379 ◽  
Author(s):  
Mingyue Zhang ◽  
Man Zhou ◽  
Hui Liu ◽  
Baiqiang Zhang ◽  
Yulian Zhang ◽  
...  
Keyword(s):  
Model Uncertainty ◽  
Sliding Mode ◽  
Friction Torque ◽  
Friction Compensation ◽  
Sliding Mode Controller ◽  
Electromechanical Actuator ◽  
Adaptive Sliding Mode ◽  
Model Based ◽  
Adaptive Sliding Mode Controller ◽  
Actuator System

The performance of the electromechanical actuator system is usually affected by the nonlinear friction torque disturbance, model uncertainty, and unknown disturbances. In order to solve this problem, a model-based friction compensation method combined with an observer-based adaptive sliding mode controller for the speed loop of electromechanical actuator system is presented in this article. All the disturbances and model uncertainty of electromechanical actuator system are divided into two parts. One is model-based friction torque disturbance which can be identified by experiments, and the other is the residual disturbance which cannot be identified by experiments. A modified LuGre model is adopted to describe the friction torque disturbance of electromechanical actuator system. An extended state observer is designed to estimate the residual disturbance. An adaptive sliding mode controller is designed to control the system and compensate the friction torque disturbance and the residual disturbance. The stability of the electromechanical actuator system is discussed with Lyapunov stability theory and Barbalat’s lemma. Experiments are designed to validate the proposed method. The results demonstrate that the proposed control strategy not only provides better disturbance rejecting ability but also provides better steady state and dynamic performance.

Model-Based Probabilistic Robust Design With Data-Based Uncertainty Compensation for Partially Unknown System

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
XinJiang Lu ◽  
Han-Xiong Li ◽  
C. L. Philip Chen
Keyword(s):  
Robust Design ◽  
Model Uncertainty ◽  
Linear Structure ◽  
Parameter Variation ◽  
Design Approach ◽  
Design Stage ◽  
Process Data ◽  
Sensitivity Matrix ◽  
Model Based ◽  
Uncertainty Compensation

Model uncertainty often results from incomplete system knowledge or simplification made at the design stage. In this paper, a hybrid model/data-based probabilistic design approach is proposed to design a nonlinear system to be robust under the circumstances of parameter variation and model uncertainty. First, the system is formulated under a linear structure which will serve as a nominal model of the system. All model uncertainties and nonlinearities will be placed under a sensitivity matrix with its bound estimated from process data. On this basis, a model-based robust design method is developed to minimize the influence of parameter variation in relation to performance covariance. Since this proposed design approach possesses both merits from the model-based robust design as well as from the data-based uncertainty compensation, it can effectively achieve robustness for partially unknown nonlinear systems. Finally, two practical examples demonstrate and confirm the effectiveness of the proposed method.

Robust Control of Uncertain Systems With Nonlinearities Using Model-Based Online Robustness Measure

2007 ◽  
Author(s):  
Dirk So¨ffker ◽  
Yan Liu ◽  
Zhiping Qiu ◽  
Fan Zhang ◽  
Peter C. Mu¨ller
Keyword(s):  
Robust Control ◽  
Nonlinear Systems ◽  
Interval Analysis ◽  
Model Uncertainty ◽  
Control Method ◽  
System Stability ◽  
Theoretic Approach ◽  
Model Based ◽  
Robustness Measure ◽  
Observer Model

In this contribution, the dynamics of linear dynamical systems with nonlinearities or of nonlinear systems with structured uncertainties is controlled based on the stability analysis using the interval-analysis set-theoretic approach and combining the approach with online-optimization of the control parameters. For the online-analysis approach, a high-gain Proportional-Integral-Observer (PI-Observer) is used to estimate the model uncertainty. The estimation can be used as an online-measure of the actual model uncertainty bound which is assumed as known for the online interval analysis. Explicit expressions are given for computing the uncertain linear system stability margin in parameter space, which provides a measure of maximal parameter uncertainties preserving stability of uncertain system around known stable nominal system equilibrium. The robust PI-Observer model-based estimations are used as bounds to evaluate the system stability. The optimization of varied control gains can be used for the optimization of the introduced robustness measure, controlling uncertain nonlinear systems. The results show that the introduced new approach gives better results with respect to robustness and control performance than the classical nonlinear control method and the usual robust control method.

scholarly journals SUPER-HEDGING AMERICAN OPTIONS WITH SEMI-STATIC TRADING STRATEGIES UNDER MODEL UNCERTAINTY

2017 ◽  
Vol 20 (06) ◽  
pp. 1750036 ◽  
Author(s):  
ERHAN BAYRAKTAR ◽  
ZHOU ZHOU
Keyword(s):  
Discrete Time ◽  
Model Uncertainty ◽  
American Options ◽  
American Option ◽  
Trading Strategies ◽  
Martingale Measure ◽  
European Options ◽  
Model Based ◽  
Price Formula ◽  
Dynamic Trading

We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price [Formula: see text] is given by the supremum over the prices of the American option under randomized models. That is, [Formula: see text], where [Formula: see text] and the martingale measure [Formula: see text] are chosen such that [Formula: see text] and [Formula: see text] prices the European options correctly, and [Formula: see text] is the price of the American option under the model [Formula: see text]. Our result generalizes the example given in Hobson & Neuberger (2016) that the highest model-based price can be considered as a randomization over models.

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