Search for: All records

Abstract We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to$$\textrm{GU}(2,n-2)$$ $\text{GU}(2,n-2)$. More concretely, we realize irreducible components of the supersingular locus as closed subschemes of flag schemes over Deligne–Lusztig varieties defined by explicit conditions after taking perfections. Moreover, we study the intersections of the irreducible components. Stratifications of Deligne–Lusztig varieties defined using powers of Frobenius action appear in the description of the intersections. 

Objective: Structural measurements after separation of cortical from trabecular bone are of interest to a wide variety of communities but are difficult to obtain because of the lack of accurate automated techniques. Methods: We d present a structure-based algorithm for separating cortical from trabecular bone in binarized images. Using the thickness of the cortex as a seed value, bone connected to the cortex within a spatially local threshold value is identified and separated from the remaining bone. The algorithm was tested on seven biological data sets from four species imaged using micro-computed tomography (μ-CT) and high-resolution peripheral quantitative computed tomography (HR-pQCT). Area and local thickness measurements were compared to images segmented manually. Results: The algorithm was approximately 11 times faster than manual measurements and the median error in cortical area was -4.47 ± 4.15%. The median error in cortical thickness was approximately 0.5 voxels for μ-CT data and less than 0.05 voxels for HR-pQCT images resulting in an overall difference of -28.1 ± 71.1 μm. Conclusion: A simple and readily implementable methodology has been developed that is repeatable, efficient, and requires few user inputs, providing an unbiased means of separating cortical from trabecular bone. Significance: Automating the segmentation of variably thick cortices will allow for the evaluation of large data sets in a time-efficient manner and allow for full-field analyses that have been previously limited to small regions of interest. The MATLAB code can be downloaded from https://github.com/TBL-UIUC/downloads.git.