scholarly journals Geometric analysis on generalized Hermite operators

2011 ◽  
Vol 47 (4) ◽  
pp. 710-771 ◽  
Author(s):  
Der-Chen Chang ◽  
Sheng-Ya Feng
Keyword(s):  
Geometric Analysis ◽  
Hermite Operators

Liquid crystalline ordering of paired helical filaments in neurofibrillary tangles of Alzheimer's disease

1986 ◽  
Vol 44 ◽  
pp. 348-349
Author(s):  
D.F. Clapin ◽  
V.J.A. Montpetit
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Neurofibrillary Tangles ◽  
Liquid Crystalline ◽  
Amyloid Fibrils ◽  
Geometric Analysis ◽  
Paired Helical Filaments ◽  
Microscopic Level ◽  
Light Microscopic Level ◽  
Regular Spacing

Alzheimer's disease is characterized by the accumulation of abnormal filamentous proteins. The most important of these are amyloid fibrils and paired helical filaments (PHF). PHF are located intraneuronally forming bundles called neurofibrillary tangles. The designation of these structures as "tangles" is appropriate at the light microscopic level. However, localized domains within individual tangles appear to demonstrate a regular spacing which may indicate a liquid crystalline phase. The purpose of this paper is to present a statistical geometric analysis of PHF packing.

Geometric analysis

1976 ◽  
Vol 55 (2) ◽  
pp. 67
Author(s):  
C.A. Gladman ◽  
R.A. Williams
Keyword(s):  
Geometric Analysis

Geometry and Physics: Volume II

2018 ◽  
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Geometric Analysis ◽  
Mathematical Physics ◽  
Poisson Geometry ◽  
Special Holonomy ◽  
Low Dimensional Topology ◽  
Generalized Complex Structures ◽  
Wide Range ◽  
Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

scholarly journals Hip geometry in hip fracture patients in Greenland occurring over a 7.7-year period

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Inuuteq Fleischer ◽  
Mogens Laursen ◽  
Stig Andersen
Keyword(s):  
Hip Fracture ◽  
Femoral Neck ◽  
Fracture Risk ◽  
Cortical Thickness ◽  
Geometric Analysis ◽  
Osteoporotic Fractures ◽  
Premature Death ◽  
Neck Length ◽  
Hip Geometry ◽  
Lesser Trochanter

Abstract Background Hip geometry influences hip fracture risk. Hip fractures are common, and they are associated with pain, disability, premature death and marked costs on society. Osteoporotic fractures are frequent in Arctic populations and increase with advancing age in this society with a steep rise in life expectancy. Greenland Inuit is a distinct ethnic group, and data on hip geometry is missing. We thus aimed to describe hip geometry in 7.7 years of consecutive hip fracture patients in Greenland. Methods We evaluated collodiaphysial angle, femoral neck length, the outer and inner diameter of the femur at 2 and 5 centimetres below the centre of the lesser trochanter and the cortical thickness from pelvic and hip radiographs in all patients operated in Greenland over 7.7 years. We included all 84 patients with one non-fractured hip visible for geometric analysis. Analyses were conducted in duplicate. Results We found a collodiaphysial angle of 134.8/132.6o in men/women (p = 0.06) and a femoral neck length of 38.0/33.9 mm in men/women (p = 0.001). Cortical thickness was affected by sex in the adjusted analysis (p < 0.001). Cortical thickness index at 5 cm below the centre of the lesser trochanter decreased with age (p = 0.026) and may be influenced by height (2 cm below the centre of the lesser trochanter, p = 0.053). Conclusion Our findings differed from European data and suggest a delicate balance in hip geometry in Arctic populations. Ethnic peculiarities influence the structure of the hip and may influence fracture risk. A focus on hip geometry and risk factors for osteoporotic fractures in Arctic populations is warranted.

Semi-automated cerebral aneurysm segmentation and geometric analysis for WEB sizing utilizing a cloud-based computational platform

2021 ◽  
pp. 159101992110091
Author(s):  
Ansaar T Rai ◽  
Ryan G Brotman ◽  
Gerald R Hobbs ◽  
SoHyun Boo
Keyword(s):  
Geometric Analysis ◽  
Good Reliability ◽  
Moderate Agreement ◽  
Manual Methods ◽  
Web Device ◽  
Computational Platform ◽  
Neck Diameter ◽  
Aneurysm Diameter ◽  
Intra Class Correlation Coefficient ◽  
The Web

Background Accurate aneurysm measurements are important for selecting the WEB device. The objective was to validate a cloud-based platform, SurgicalPreview (SP) against manual measurements for aneurysm analysis. Methods Two sets of measurements each for SP and manual methods were obtained for 40 aneurysms. Reliability and agreement were assessed with intra-class correlation coefficient (ICC) and Bland-Altman plots respectively. Kappa coefficient was used to assess agreement for predicting WEB size. Results There was good reliability for repeat SP measurements: aneurysm diameter (ICC-1, 95%CI 0.98–1), height (ICC-1, 95%CI 0.99–1) and neck diameter (ICC-0.96, 95%CI 0.93–0.98). There was good reliability for the two manual diameter (ICC-0.97, 95%CI 0.9–0.97) and height (ICC-0.93, 95%CI 0.87–0.96) measurements and moderate for neck diameter (ICC-0.76, 95%CI 0.54–0.87). There was greater agreement for SP versus manual repeat measurements on Bland-Altman plots. Reliability between the SP and manual methods was good for aneurysm diameter (ICC-0.98, 95%CI 0.95–1) and height (ICC-0.96, 95%CI-0.93–0.98) and moderate for neck. (ICC-0.6, 95%CI -0.22–0.87). The Bland-Altman plots confirmed better agreement between the two methods for the aneurysm diameter and height than the neck. There was strong agreement between the methods for predicting the WEB diameter (Kappa-0.84, 95%CI 0.71–0.97) and moderate for predicting WEB height (Kappa-0.66, 95%CI 0.43–0.89). There was moderate agreement for predicted versus deployed WEB diameter: SP (Kappa-0.56, 95%CI 0.38–0.74), Manual (Kappa-0.53, 95%CI 0.34–0.71). Conclusion The SurgicalPreview® had greater agreement for repeat measurements. There was good reliability between the two methods for predicting WEB diameter and height and moderate agreement between predicted versus deployed WEB diameter.

Geometric Analysis of the Bilobed Flap for Nasal Reconstruction Surgery

FACE ◽  
2021 ◽  
pp. 273250162199390
Author(s):  
Daniel Henick ◽  
Kelvin K. Ampem-Darko ◽  
Farah Sayegh ◽  
Paymon Sanati-Mezrahi ◽  
Mehul Bhatt ◽  
...  
Keyword(s):  
Geometric Analysis ◽  
Nasal Reconstruction ◽  
Anatomical Features ◽  
Reconstruction Surgery ◽  
Repair Technique ◽  
Bilobed Flap ◽  
Calculated Ratio ◽  
Flap Design ◽  
Objectively Measured ◽  
Angle Of Rotation

Background: Reconstruction of the nose can be difficult due to its complex anatomical features. In 1989, Zitelli described a modified version of the bilobed flap design technique using 45° and 90° angles to improve nasal reconstructions. While the bilobed flap is still frequently referenced in scholarly literature, there seems to be inconsistency in preoperative flap design; these deviations can lead to suboptimal outcomes. The authors aim to illustrate the variability in bilobed flap execution and provide guidelines in preoperative design to improve consistency. Methods: A geometrically-based approach was used to characterize the inconsistency of bilobed repair technique. The pre-operative design images from fifteen scholarly articles were analyzed via a series of measurements and computations to quantify the angle of rotation and dimensions for the primary and secondary lobes. The “Error Quotient” was a calculated ratio that objectively measured the extent to which a bilobed design deviated from Zitelli’s specifications. Results: There was a noticeable variability in the design of both the primary and secondary lobes. Bilobed designs with smaller angles of rotation, particularly of the first lobe, were associated with higher Error Quotients and greater amounts of deviation from Zitelli’s design. Designs with the smallest Error Quotients had a primary lobe rotation that approached 45°. Conclusion: Consistency of application of the bilobed flap should be established to allow for optimal results, particularly with emphasis on design of the primary lobe. This can be accomplished by including a disposable protractor and marker in their sterile kit to measure a 45° rotation.

scholarly journals A deep learning-based and fully automated pipeline for thoracic aorta geometric analysis and TEVAR planning from computed tomography

2021 ◽  
Vol 22 (Supplement_1) ◽  
Author(s):  
S Saitta ◽  
F Sturla ◽  
A Caimi ◽  
A Riva ◽  
MC Palumbo ◽  
...  
Keyword(s):  
Aortic Arch ◽  
Thoracic Aorta ◽  
Geometric Analysis ◽  
Ground Truth ◽  
Radius Of Curvature ◽  
Geometric Features ◽  
Anatomical Landmarks ◽  
Landing Zone ◽  
Increased Risk ◽  
Automated Pipeline

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – National budget only. Main funding source(s): Ministry of Publich Health - Ricerca Corrente Introduction Thoracic endovascular aortic repair (TEVAR) represents a well-established alternative to open repair in selected patients. Its preoperative feasibility assessment and planning requires a computational tomography (CT)-based analysis of the geometric aortic features to identify an adequate proximal and distal landing zone (LZ) for endograft deployment. Yet, controversies persist on the definition and methods of measurement of specific geometric features of the LZs, including angulation and tortuosity, which are associated with an increased risk of postoperative endograft failure. In this respect, the development of a preoperative image processing method that provides an automatic and highly reproducible 3D identification of critical geometric features and specific anatomical landmarks, thus reducing the time and uncertainties related to manual segmentation, remains a largely unmet clinical need. In this study, we developed and applied a fully automated pipeline embedding a convolutional neural network (CNN), which feeds on 3D CT images to automatically segment the thoracic aorta, recognize the relevant anatomical landmarks and LZs, and quantifies the geometry of the aortic arch in each proximal LZ s (i.e. 0 to 3). Methods Ninety  CT scans of healthy aortas were retrieved, being the study conceived as a proof of concept analysis. The thoracic aorta was manually segmented by five independent and expert operators. 72 scans with the corresponding ground truth segmentations were randomly selected and used to train the CNN, which was based on a 3D U-Net architecture. The other 18 scans were used to test the CNN-based segmentations. The fully automated pipeline was obtained by integrating the CNN, 3D geometry skeletonization, and processing of the aortic centerline and wall via computational geometry (Figure). The resulting metrics included aortic arch centerline radius of curvature, proximal landing zones (PLZs) maximum diameters, angulation and tortuosity calculated according to previously published work. These parameters were statistically analyzed to compare standard arches vs. arches with a common origin of the innominate and left carotid artery (CILCA), and the different landing zones in each arch type. Results The CNN segmentation yielded a mean Dice score of 0.94 with respect to manual ground truth segmentations. Standard arches were characterized by significantly larger radius of curvature (p = 0.002) and lower tortuosity in zone 3 (p = 0.004) vs. CILCA arches. For both standard and CILCA arches, comparisons among PLZs revealed statistically significant differences in maximum zone diameters (p &lt; 0.0001), angulation (p &lt; 0.0001) and tortuosity (p &lt; 0.0001). Conclusions We developed a CNN-based automated pipeline for the automated, and reliable geometric quantification of standard and CILCA aortic arches. This tool has the potential to support TEVAR pre-procedural planning in a real clinical setting. Abstract Figure. Automatic pipeline scheme

scholarly journals Geometric Analysis of Uncertainty Sampling for Dense Neural Network Layer

2021 ◽  
pp. 1-1
Author(s):  
Aziz Kocanaogullari ◽  
Niklas Smedemark-Margulies ◽  
Murat Akcakaya ◽  
Deniz Erdogmus
Keyword(s):  
Neural Network ◽  
Geometric Analysis ◽  
Network Layer ◽  
Uncertainty Sampling
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