The stereological estimation of moments of particle volume

1985 ◽  
Vol 22 (1) ◽  
pp. 82-98 ◽  
Author(s):  
E. B. Jensen ◽  
H. J. G. Gundersen
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Geometric Probability ◽  
Particle Volume ◽  
Shape Information ◽  
Weighted Distribution ◽  
Particle Aggregate ◽  
First Moment

In stereology or applied geometric probability quantitative characterization of aggregates of particles from information on lower-dimensional sections plays a major role. Most stereological methods developed for particle aggregates are based on the assumption that the particles are of the same, known (simple) shape. Information on the volume-weighted distribution of particle size may, however, be obtained under fairly general assumptions about particle shape if particle volume is chosen as size parameter. In fact, there exists in this case an unbiased stereological estimator of the first moment under the sole assumption that the particles are convex. In the present paper, we consider a particle aggregate in ℝ and derive estimators of the q th moment of the volume-weighted distribution of particle volume, based on point-sampling of particles and measurements on q -flats through sampled particles. The estimators are valid for arbitrarily shaped particles but if the particles are non-convex it is necessary for the determination of the estimators to be able to identify the different separated parts on a q-flat through the particle aggregate which belong to the same particle. Explicit forms of the estimators are given for q = 1. For q = 2, an explicit form of one of the estimators is derived for an aggregate of triaxial ellipsoids in three-dimensional space.

The stereological estimation of moments of particle volume

1985 ◽  
Vol 22 (01) ◽  
pp. 82-98 ◽  
Author(s):  
E. B. Jensen ◽  
H. J. G. Gundersen
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Geometric Probability ◽  
Particle Volume ◽  
Shape Information ◽  
Weighted Distribution ◽  
Particle Aggregate ◽  
First Moment

In stereology or applied geometric probability quantitative characterization of aggregates of particles from information on lower-dimensional sections plays a major role. Most stereological methods developed for particle aggregates are based on the assumption that the particles are of the same, known (simple) shape. Information on the volume-weighted distribution of particle size may, however, be obtained under fairly general assumptions about particle shape if particle volume is chosen as size parameter. In fact, there exists in this case an unbiased stereological estimator of the first moment under the sole assumption that the particles are convex. In the present paper, we consider a particle aggregate in ℝ and derive estimators of the q th moment of the volume-weighted distribution of particle volume, based on point-sampling of particles and measurements on q -flats through sampled particles. The estimators are valid for arbitrarily shaped particles but if the particles are non-convex it is necessary for the determination of the estimators to be able to identify the different separated parts on a q-flat through the particle aggregate which belong to the same particle. Explicit forms of the estimators are given for q = 1. For q = 2, an explicit form of one of the estimators is derived for an aggregate of triaxial ellipsoids in three-dimensional space.

scholarly journals Isothermic surfaces in sphere geometries as Moutard nets

2007 ◽  
Vol 463 (2088) ◽  
pp. 3171-3193 ◽  
Author(s):  
Alexander I Bobenko ◽  
Yuri B Suris
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauss Map ◽  
Point Property ◽  
Property A ◽  
Lie Geometry ◽  
Möbius Geometry ◽  
Isothermic Surfaces ◽  
Three Dimensional Space

We give an elaborated treatment of discrete isothermic surfaces and their analogues in different geometries (projective, Möbius, Laguerre and Lie). We find the core of the theory to be a novel characterization of discrete isothermic nets as Moutard nets. The latter are characterized by the existence of representatives in the space of homogeneous coordinates satisfying the discrete Moutard equation. Moutard nets admit also a projective geometric characterization as nets with planar faces with a five-point property: a vertex and its four diagonal neighbours span a three-dimensional space. Restricting the projective theory to quadrics, we obtain Moutard nets in sphere geometries. In particular, Moutard nets in Möbius geometry are shown to coincide with discrete isothermic nets. The five-point property, in this particular case, states that a vertex and its four diagonal neighbours lie on a common sphere, which is a novel characterization of discrete isothermic surfaces. Discrete Laguerre isothermic surfaces are defined through the corresponding five-plane property, which requires that a plane and its four diagonal neighbours share a common touching sphere. Equivalently, Laguerre isothermic surfaces are characterized by having an isothermic Gauss map. S-isothermic surfaces as an instance of Moutard nets in Lie geometry are also discussed.

X-ray topographic determination of the granular structure in a graphite mosaic crystal: a three-dimensional reconstruction

2000 ◽  
Vol 33 (4) ◽  
pp. 1023-1030 ◽  
Author(s):  
M. Ohler ◽  
M. Sanchez del Rio ◽  
A. Tuffanelli ◽  
M. Gambaccini ◽  
A. Taibi ◽  
...  
Keyword(s):  
Structural Parameters ◽  
Pyrolytic Graphite ◽  
Three Dimensional ◽  
X Ray ◽  
Dimensional Reconstruction ◽  
Mosaic Crystals ◽  
Spatial Locations ◽  
Crystalline Domains

Section topographs recorded at different spatial locations and at different rocking angles of a highly oriented pyrolytic graphite (HOPG) crystal allow three-dimensional maps of the local angular-dependent scattering power to be obtained. This is performed with a direct reconstruction from the intensity distribution on such topographs. The maps allow the extraction of information on local structural parameters such as size, form and internal mosaic spread of crystalline domains. This data analysis leads to a new method for the characterization of mosaic crystals. Perspectives and limits of applicability of this method are discussed.

Spatial Kinematic Analysis of the Upper Extremity Using a Biplanar Videotaping Method

1981 ◽  
Vol 103 (1) ◽  
pp. 11-17 ◽  
Author(s):  
N. A. Langrana
Keyword(s):  
Upper Extremity ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Assistive Device ◽  
Kinematic Data ◽  
Computer Aided ◽  
Extremity Motion ◽  
Accuracy And Repeatability ◽  
Three Dimensional Space

A biplanar videotaping system is used to generate spatial kinematic data of an upper extremity motion. The technique is based upon the characterization of each segment by four points in three-dimensional space using biplanar videotaping and subsequent analysis by computer-aided descriptive geometry. The tests were conducted to determine the system’s accuracy and repeatability. The results of the joint kinematics of the test subjects performing a diagonal reaching activity with and without an orthosis (or an assistive device) are presented.

Energy Harvesting Aspects of Irregular Vibrating Forces Acting on Piezoelectric Devices

2015 ◽  
pp. 143-158
Author(s):  
Alessandro Massaro
Keyword(s):  
Energy Harvesting ◽  
Piezoelectric Materials ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Output Current ◽  
Vibrating System ◽  
External Forces ◽  
Piezoelectric Devices ◽  
Three Dimensional Space

After a brief introduction of piezoelectric materials, this chapter focuses on the characterization of vibrating freestanding piezoelectric AlN devices forced by different external forces acting simultaneously. The analyzed vibrating forces are applied mainly to piezoelectric freestanding structures stimulated by irregular vibration phenomena. Particular kinds of theoretical noise signals are commented. The goal of the chapter is to analyze the effect of the noise in order to model the chaotic vibrating system and to predict the output current signals. Moreover, the author also shows a possible alternative way to detect different vibrating force directions in the three dimensional space by means of curved piezoelectric layouts.

Local bond order parameters for accurate determination of crystal structures in two and three dimensions

2018 ◽  
Vol 20 (42) ◽  
pp. 27059-27068 ◽  
Author(s):  
Hossein Eslami ◽  
Parvin Sedaghat ◽  
Florian Müller-Plathe
Keyword(s):  
Crystal Structures ◽  
Bond Order ◽  
Accurate Determination ◽  
Three Dimensional ◽  
Order Parameters ◽  
Three Dimensions ◽  
Local Order ◽  
Crystalline Structures

Local order parameters for the characterization of liquid and different two- and three-dimensional crystalline structures are presented.

Liquid chromatography mass spectrometry based characterization of epitope configurations

2020 ◽  
Vol 12 (45) ◽  
pp. 5476-5484
Author(s):  
Maren Christin Stillesby Levernæs ◽  
Arelí Urtubia Moe ◽  
Sigurd Leinæs Bøe ◽  
Elisabeth Paus ◽  
Léon Reubsaet ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Liquid Chromatography ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Liquid Chromatography Mass Spectrometry ◽  
Three Dimensional Structure ◽  
Chromatography Mass Spectrometry ◽  
Pre Treatment

Here we evaluate a quick and easy tool for determination of epitope configuration using immunocapture and liquid chromatography mass spectrometry (LC-MS) subsequent to pre-treatment of the target protein to disrupt its three-dimensional structure.

Three-Dimensional Anatomic Characterization of the Canine Laryngeal Abductor and Adductor Musculature

2000 ◽  
Vol 109 (5) ◽  
pp. 505-513 ◽  
Author(s):  
Corey W. Mineck ◽  
Roger Chan ◽  
Niro Tayama ◽  
Ingo R. Titze
Keyword(s):  
Vocal Fold ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Cross Sectional ◽  
3 Dimensional ◽  
Moment Arms ◽  
Intrinsic Laryngeal Muscle ◽  
Posterior Cricoarytenoid ◽  
Intrinsic Laryngeal Muscles

The biomechanics of vocal fold abduction and adduction during phonation, respiration, and airway protection are not completely understood. Specifically, the rotational and translational forces on the arytenoid cartilages that result from intrinsic laryngeal muscle contraction have not been fully described. Anatomic data on the lines of action and moment arms for the intrinsic laryngeal muscles are also lacking. This study was conducted to quantify the 3-dimensional orientations and the relative cross-sectional areas of the intrinsic abductor and adductor musculature of the canine larynx. Eight canine larynges were used to evaluate the 3 muscles primarily responsible for vocal fold abduction and adduction: the posterior cricoarytenoid, the lateral cricoarytenoid, and the interarytenoid muscles. Each muscle was exposed and divided into discrete fiber bundles whose coordinate positions were digitized in 3-dimensional space. The mass, length, relative cross-sectional area, and angle of orientation for each muscle bundle were obtained to allow for the calculations of average lines of action and moment arms for each muscle. This mapping of the canine laryngeal abductor and adductor musculature provides important anatomic data for use in laryngeal biomechanical modeling. These data may also be useful in surgical procedures such as arytenoid adduction.

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