scholarly journals An evaluation of different measures of dynamically recrystallized grain size for paleopiezometry or paleowattometry studies

Solid Earth ◽  
2015 ◽  
Vol 6 (2) ◽  
pp. 475-495 ◽  
Author(s):  
M. A. Lopez-Sanchez ◽  
S. Llana-Fúnez
Keyword(s):  
Grain Size ◽  
Kernel Density ◽  
Kernel Density Estimator ◽  
Gaussian Kernel ◽  
Robust Estimator ◽  
Density Estimator ◽  
Lithospheric Deformation ◽  
Single Measure ◽  
Frequency Peak ◽  
Recrystallized Grain Size

Abstract. Paleopiezometry and paleowattometry studies are essential to validate models of lithospheric deformation and therefore increasingly common in structural geology. These studies require a single measure of dynamically recrystallized grain size in natural mylonites to estimate the magnitude of differential paleostress (or the rate of mechanical work). This contribution tests the various measures of grain size used in the literature and proposes the frequency peak of a grain size distribution as the most robust estimator for paleopiezometry or paleowattometry studies. The novelty of the approach resides in the use of the Gaussian kernel density estimator as an alternative to the classical histograms, which improves reproducibility. A free, open-source, easy-to-handle script named GrainSizeTools ( http://www.TEOS-10.org) was developed with the aim of facilitating the adoption of this measure of grain size in paleopiezometry or paleowattometry studies. The major advantage of the script over other programs is that by using the Gaussian kernel density estimator and by avoiding manual steps in the estimation of the frequency peak, the reproducibility of results is improved.

scholarly journals GrainSizeTools: a Python script for estimating the dynamically recrystallized grain size from grain sectional areas

2014 ◽  
Vol 6 (2) ◽  
pp. 3141-3196
Author(s):  
M. A. Lopez-Sanchez ◽  
S. Llana-Fúnez
Keyword(s):  
Grain Size ◽  
Structural Geology ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Gaussian Kernel ◽  
Lithospheric Deformation ◽  
Python Script ◽  
Size Population ◽  
Recrystallized Grain Size

Abstract. Paleopiezometry and paleowattometry studies, required to validate models of lithospheric deformation, are increasingly common in structural geology. These studies require a numeric parameter to characterize and compare the dynamically recrystallized grain size of natural mylonites with those obtained in rocks deformed under controlled conditions in the laboratory. We introduce a new tool, a script named GrainSizeTools, to obtain a single numeric value representative of the dynamically recrystallized grain size from the measurement of grain sectional areas (2-D data). For this, it is used an estimate of the most likely grain size of the grain size population, using an alternative tool to the classical histograms and bar plots: the peak of the Gaussian kernel density estimation. The results are comparable to those that can be obtained by other stereological software available, such as the StripStar and CSDCorrections, but with the advantage that the script is specifically developed to produce a single and reproducible value avoiding manual steps in the estimation, which penalizes reproducibility.

scholarly journals Gaussian Kernel Density Estimator for Voxel Size Selection in Atom Probe Tomography

2013 ◽  
Vol 19 (S2) ◽  
pp. 992-993 ◽  
Author(s):  
K. Kaluskar ◽  
K. Rajan
Keyword(s):  
Atom Probe Tomography ◽  
Kernel Density ◽  
Atom Probe ◽  
Kernel Density Estimator ◽  
Gaussian Kernel ◽  
Density Estimator ◽  
Voxel Size ◽  
Size Selection

Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013.

Online clutter estimation using a Gaussian kernel density estimator for multitarget tracking

2015 ◽  
Vol 9 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Xin Chen ◽  
Ratnasingham Tharmarasa ◽  
Thia Kirubarajan ◽  
Mike McDonald
Keyword(s):  
Kernel Density ◽  
Kernel Density Estimator ◽  
Gaussian Kernel ◽  
Density Estimator ◽  
Multitarget Tracking

scholarly journals A Fast-Converging Kernel Density Estimator for Dispersion in Horizontally Homogeneous Meteorological Conditions

Atmosphere ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 1343
Author(s):  
Gunther Bijloos ◽  
Johan Meyers
Keyword(s):  
Convergence Rate ◽  
Path Integral ◽  
Concentration Field ◽  
Kernel Density ◽  
Particle Dispersion ◽  
Meteorological Conditions ◽  
Kernel Density Estimator ◽  
Gaussian Kernel ◽  
Density Estimator ◽  
Data Set

Kernel smoothers are often used in Lagrangian particle dispersion simulations to estimate the concentration distribution of tracer gasses, pollutants etc. Their main disadvantage is that they suffer from the curse of dimensionality, i.e., they converge at a rate of 4/(d+4) with d the number of dimensions. Under the assumption of horizontally homogeneous meteorological conditions, we present a kernel density estimator that estimates a 3D concentration field with the faster convergence rate of a 1D kernel smoother, i.e., 4/5. This density estimator has been derived from the Langevin equation using path integral theory and simply consists of the product between a Gaussian kernel and a 1D kernel smoother. Its numerical convergence rate and efficiency are compared with that of a 3D kernel smoother. The convergence study shows that the path integral-based estimator has a superior convergence rate with efficiency, in mean integrated squared error sense, comparable with the one of the optimal 3D Epanechnikov kernel. Horizontally homogeneous meteorological conditions are often assumed in near-field range dispersion studies. Therefore, we illustrate the performance of our method by simulating experiments from the Project Prairie Grass data set.

scholarly journals Estimating the Gait Speed of Older Adults in Smart Home Environments

2022 ◽  
Vol 3 (2) ◽  
Author(s):  
Björn Friedrich ◽  
Enno-Edzard Steen ◽  
Sandra Hellmers ◽  
Jürgen M. Bauer ◽  
Andreas Hein
Keyword(s):  
Older Adults ◽  
Gait Speed ◽  
Smart Home ◽  
Kernel Density ◽  
Kernel Density Estimator ◽  
Gaussian Kernel ◽  
Measurement Unit ◽  
Density Estimator ◽  
Home Environments ◽  
Smart Home Environments

AbstractMobility is one of the key performance indicators of the health condition of older adults. One important parameter is the gait speed. The mobility is usually assessed under the supervision of a professional by standardised geriatric assessments. Using sensors in smart home environments for continuous monitoring of the gait speed enables physicians to detect early stages of functional decline and to initiate appropriate interventions. This in combination with a floor plan smart home sensors were used to calculate the distance that a person walked in the apartment and the inertial measurement unit data for estimating the actual walking time. A Gaussian kernel density estimator was applied to the computed values and the maximum of the kernel density estimator was considered as the gait speed. The proposed method was evaluated on a real-world dataset and the estimations of the gait speed had a deviation smaller than $$0.10 \, \frac{\mathrm{m}}{\mathrm{s}}$$ 0.10 m s , which is smaller than the minimal clinically important difference, compared to a baseline from a standardised geriatrics assessment.

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