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 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 Exploration of diffusion kernel density estimation in agricultural drought risk analysis: a case study in Shandong, China

2015 ◽  
Vol 3 (11) ◽  
pp. 6757-6789
Author(s):  
W. Chen ◽  
Z. Shao ◽  
L. K. Tiong
Keyword(s):  
Risk Analysis ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Standardized Precipitation Index ◽  
Kernel Density ◽  
Agricultural Drought ◽  
Gaussian Kernel ◽  
Spatial And Temporal Variation ◽  
Drought Risk ◽  
Diffusion Kernel

Abstract. Drought caused the most widespread damage in China, making up over 50 % of the total affected area nationwide in recent decades. In the paper, a Standardized Precipitation Index-based (SPI-based) drought risk study is conducted using historical rainfall data of 19 weather stations in Shandong province, China. Kernel density based method is adopted to carry out the risk analysis. Comparison between the bivariate Gaussian kernel density estimation (GKDE) and diffusion kernel density estimation (DKDE) are carried out to analyze the effect of drought intensity and drought duration. The results show that DKDE is relatively more accurate without boundary-leakage. Combined with the GIS technique, the drought risk is presented which reveals the spatial and temporal variation of agricultural droughts for corn in Shandong. The estimation provides a different way to study the occurrence frequency and severity of drought risk from multiple perspectives.

scholarly journals Ther varom mid j hia: Tracing linguistic diffusion in the history of Norwegian using kernel density estimation

2019 ◽  
Vol 27 (1) ◽  
pp. 5-34
Author(s):  
Tam Blaxter
Keyword(s):  
Density Estimation ◽  
Middle Ages ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Gaussian Kernel ◽  
Historical Sources ◽  
Nearest Neighbours ◽  
Different Types ◽  
Language Data ◽  
History Of

Abstract Tracing the diffusion of linguistic innovations in space from historical sources is challenging. The complexity of the datasets needed in combination with the noisy reality of historical language data mean that it has not been practical until recently. However, bigger historical corpora with richer spatial and temporal information allow us to attempt it. This paper presents an investigation into changes affecting first person non-singular pronouns in the history of Norwegian: first, individual changes affecting the dual (vit > mit) and plural (vér > mér), followed by loss of the dual-plural distinction by merger into either form or replacement of both by Danish-Swedish vi. To create dynamic spatial visualisations of these changes, the use of kernel density estimation is proposed. This term covers a range of statistical tools depending on the kernel function. The paper argues for a Gaussian kernel in time and an adaptive uniform (k-nearest neighbours) kernel in space, allowing uncertainty or multiple localisation to be incorporated into calculations. The results for this dataset allow us to make a link between Modern Norwegian dialectological patterns and language use in the Middle Ages; they also exemplify different types of diffusion process in the spread of linguistic innovations.

From Gaussian kernel density estimation to kernel methods

2012 ◽  
Vol 4 (2) ◽  
pp. 119-137 ◽  
Author(s):  
Shitong Wang ◽  
Zhaohong Deng ◽  
Fu-lai Chung ◽  
Wenjun Hu
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Methods ◽  
Kernel Density ◽  
Gaussian Kernel
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