scholarly journals Adaptive Cartesian and torsional restraints for interactive model rebuilding

2021 ◽  
Vol 77 (4) ◽  
pp. 438-446
Author(s):  
Tristan Ian Croll ◽  
Randy J. Read
Keyword(s):  
Reference Model ◽  
Loss Functions ◽  
Distance Restraint ◽  
Von Mises Distribution ◽  
Similar Sequence ◽  
Current Implementation ◽  
Common Strategy ◽  
Resolution Model ◽  
The Face ◽  
Von Mises

When building atomic models into weak and/or low-resolution density, a common strategy is to restrain their conformation to that of a higher resolution model of the same or similar sequence. When doing so, it is important to avoid over-restraining to the reference model in the face of disagreement with the experimental data. The most common strategy for this is the use of `top-out' potentials. These act like simple harmonic restraints within a defined range, but gradually weaken when the deviation between the model and reference grows beyond that range. In each current implementation the rate at which the potential flattens at large deviations follows a fixed form, although the form chosen varies among implementations. A restraint potential with a tuneable rate of flattening would provide greater flexibility to encode the confidence in any given restraint. Here, two new such potentials are described: a Cartesian distance restraint derived from a recent generalization of common loss functions and a periodic torsion restraint based on a renormalization of the von Mises distribution. Further, their implementation as user-adjustable/switchable restraints in ISOLDE is described and their use in some real-world examples is demonstrated.

scholarly journals Adaptive conformational restraints for interactive model rebuilding in Cartesian and torsion space

2020 ◽  
Author(s):  
Tristan I Croll ◽  
Randy J Read
Keyword(s):  
Reference Model ◽  
Loss Functions ◽  
Distance Restraint ◽  
Reference Structure ◽  
Similar Sequence ◽  
Current Implementation ◽  
Common Strategy ◽  
Resolution Model ◽  
The Face ◽  
Von Mises

AbstractWhen building atomic models into weak and/or low-resolution density, a common strategy is to restrain its conformation to that of a higher-resolution model of the same or similar sequence. When doing so, it is important to avoid over-restraining to the reference model in the face of disagreement with the experimental data. The most common strategy for this is the use of “top-out” potentials. These act like simple harmonic restraints within a defined range, but gradually weaken when the deviation between the model and reference grows larger than a defined transition point. In each current implementation, the rate at which the potential flattens beyond the transition region follows a fixed form – although the form chosen varies between implementations. A restraint potential with a tuneable rate of flattening would provide greater flexibility to encode the confidence in any given restraint. Here we describe two new such potentials: a Cartesian distance restraint derived from a recent generalisation of common loss functions, and a periodic torsion restraint based on a renormalisation of the von Mises distribution. Further, we describe their implementation as user-adjustable/switchable restraints in ISOLDE, and demonstrate their use in some real-world examples.SynopsisNew forms of adaptive or top-out distance and torsion restraints are described, suitable for restraining a model to match a reference structure during interactive rebuilding. In addition, their implementation in ISOLDE is described along with some illustrative example applications.

An extension of the von mises distribution

1982 ◽  
Vol 11 (15) ◽  
pp. 1695-1706 ◽  
Author(s):  
E.A. Yfantis ◽  
L.E. Borgman
Keyword(s):  
Von Mises Distribution ◽  
Von Mises

Error-in-variables model of Malacca wind direction data with the von Mises distribution in southwest monsoon

2021 ◽  
Vol 15 (9) ◽  
pp. 471-479
Author(s):  
Nurkhairany Amyra Mokhtar ◽  
Basri Badyalina ◽  
Kerk Lee Chang ◽  
Fatin Farazh Ya'acob ◽  
Ahmad Faiz Ghazali ◽  
...  
Keyword(s):  
Wind Direction ◽  
Southwest Monsoon ◽  
Von Mises Distribution ◽  
Error In Variables ◽  
Von Mises

scholarly journals STATISTICAL MODEL FOR THE RELATIONSHIP BETWEEN MAIZE KERNEL ORIENTATION AND SEED LEAF AZIMUTH

2015 ◽  
Vol 52 (3) ◽  
pp. 359-370
Author(s):  
ADRIAN KOLLER ◽  
GUILHERME TORRES ◽  
MICHAEL BUSER ◽  
RANDY TAYLOR ◽  
BILL RAUN ◽  
...  
Keyword(s):  
Simulation Models ◽  
Circular Statistics ◽  
Von Mises Distribution ◽  
Canopy Closure ◽  
Canopy Architecture ◽  
Maize Kernel ◽  
Angular Data ◽  
Significant Yield ◽  
Von Mises ◽  
The Relationship

SUMMARYHand-planted plots of across-row-oriented corn seeds (Zeamays L.) produce highly structured leaf canopies and have shown significant yield advantage over randomly planted plots in prior studies. For further investigation of the phenomenon by simulation, the objective of this study was to develop a probabilistic model for the correlation between seed orientation and initial plant orientation. In greenhouse trials, the azimuthal orientation of kernels of four different hybrids was recorded at planting. At collar setting of the seed leaf, the orientation of the seed leaf was determined and the angular data subjected to the analytical methods of circular statistics. The results indicate that the correlation between seed azimuth and seed leaf azimuth can be described by a von Mises distribution. The probabilistic seed to seed leaf azimuth model described herein may be implemented in simulation models to investigate the effect of canopy architecture, canopy closure and light interception efficiency of corn under conditions of seed oriented planting.

Detecting Nonlinear Associations, Plus Comments on Testing Hypotheses About the Correlation Coefficient

2001 ◽  
Vol 26 (1) ◽  
pp. 73-83 ◽  
Author(s):  
Rand R. Wilcox
Keyword(s):  
T Test ◽  
Test Statistic ◽  
The Social ◽  
Zero Correlation ◽  
Common Strategy ◽  
Kolmogorov Smirnov ◽  
Nonlinear Associations ◽  
Student’S T ◽  
Von Mises ◽  
Student’S T Test

Let (Yi,Xi ), i = 1, . . . , n, be a random sample from some p + 1 variate distribution where Xi is a vector of length p. In the social sciences, the most common strategy for detecting an association between Y and the marginal distributions is to test the hypothesis that the corresponding correlations are zero using a standard Student’s t test. There are two practical problems with this strategy. First, for reasons described in the article, there are situations where the correlation between two random variables is zero, but Student’s t test is not even asymptotically correct. In fact, the probability of rejecting can approach one as the sample size gets large, even though the hypothesis of a zero correlation is true. Of course, one can also apply standard methods based on a linear regression model and the least squares estimator, but the same practical problems arise. Second, Student’s t test can miss nonlinear associations. This latter problem is the main motivation for this article. Results of a former study suggest an approach that avoids both of the difficulties just described. Based on simulations, it is found that the Cramér-von Mises form of the test statistic is generally better than the Kolmogorov-Smirnov form. Situations arise where this method has less power than Student’s t test, but this is due in part to t test’s use of an incorrect estimate of the standard error.

High-Resolution Three-Dimensional-pQCT Images Can Be an Adequate Basis for In-Vivo μFE Analysis of Bone

2000 ◽  
Vol 123 (2) ◽  
pp. 176-183 ◽  
Author(s):  
W. Pistoia ◽  
B. van Rietbergen ◽  
A. Laib ◽  
P. Ru¨egsegger
Keyword(s):  
High Resolution ◽  
Trabecular Bone ◽  
Elastic Properties ◽  
Bone Structure ◽  
Reference Model ◽  
Von Mises Stress ◽  
Micro Ct ◽  
Von Mises

Micro-finite element (μFE) models based on high-resolution images have enabled the calculation of elastic properties of trabecular bone in vitro. Recently, techniques have been developed to image trabecular bone structure in vivo, albeit at a lesser resolution. The present work studies the usefulness of such in-vivo images for μFE analyses, by comparing their μFE results to those of models based on high-resolution micro-CT (μCT) images. Fifteen specimens obtained from human femoral heads were imaged first with a 3D-pQCT scanner at 165 μm resolution and a second time with a μCT scanner at 56 μm resolution. A third set of images with a resolution of 165 μm was created by downscaling the μCT measurements. The μFE models were created directly from these images. Orthotropic elastic properties and the average tissue von Mises stress of the specimens were calculated from six FE-analyses per specimen. The results of the 165 μm models were compared to those of the 56 μm model, which was taken as the reference model. The results calculated from the pQCT-based models, correlated excellent with those calculated from the reference model for both moduli R2>0.95 and for the average tissue von Mises stress R2>0.83. Results calculated from the downscaled micro-CT models correlated even better with those of the reference models (R2>0.99 for the moduli and R2>0.96 for the average von Mises stress). In the case of the 3D-pQCT based models, however, the slopes of the regression lines were less than one and had to be corrected. The prediction of the Poisson’s ratios was less accurate (R2>0.45 and R2>0.67) for the models based on 3D-pQCT and downscaled μCT images respectively). The fact that the results from the downscaled and original μCT images were nearly identical indicates that the need for a correction in the case of the 3D-pQCT measurements was not due to the voxel size of the images but due to a higher noise level and a lower contrast in these images, in combination with the application of a filtering procedure at 165 micron images. In summary: the results of μFE models based on in-vivo images of the 3D-pQCT can closely resemble those obtained from μFE models based on higher resolution μCT system.

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