scholarly journals Practical Volume Estimation of Zonotopes by a New Annealing Schedule for Cooling Convex Bodies

2020 ◽  
pp. 212-221
Author(s):  
Apostolos Chalkis ◽  
Ioannis Z. Emiris ◽  
Vissarion Fisikopoulos
Keyword(s):  
Convex Bodies ◽  
Volume Estimation ◽  
Annealing Schedule

scholarly journals Improving the Cavalieri estimator under non-equidistant sampling and dropouts

2020 ◽  
Vol 39 (3) ◽  
pp. 197-212
Author(s):  
Mads Stehr ◽  
Markus Kiderlen
Keyword(s):  
Stationary Point ◽  
Random Sampling ◽  
Convex Bodies ◽  
Three Dimensional ◽  
Estimation Procedure ◽  
Volume Estimation ◽  
Bounded Interval ◽  
Variance Estimators ◽  
Stationary Point Process ◽  
General Estimation

Motivated by the stereological problem of volume estimation from parallel section profiles, the so-called Newton-Cotes integral estimators based on random sampling nodes are analyzed. These estimators generalize the classical Cavalieri estimator and its variant for non-equidistant sampling nodes, the generalized Cavalieri estimator, and have typically a substantially smaller variance than the latter. The present paper focuses on the following points in relation to Newton-Cotes estimators: the treatment of dropouts, the construction of variance estimators, and, finally, their application in volume estimation of convex bodies.Dropouts are eliminated points in the initial stationary point process of sampling nodes, modeled by independent thinning. Among other things, exact representations of the variance are given in terms of the thinning probability and increments of the initial points under two practically relevant sampling models. The paper presents a general estimation procedure for the variance of Newton-Cotes estimators based on the sampling nodes in a bounded interval. Finally, the findings are illustrated in an application of volume estimation for three-dimensional convex bodies with sufficiently smooth boundaries.

Excess entropy of the systems of molecules differing in size and shape

1983 ◽  
Vol 48 (1) ◽  
pp. 192-198 ◽  
Author(s):  
Tomáš Boublík
Keyword(s):  
Equation Of State ◽  
Hard Spheres ◽  
Excess Entropy ◽  
Convex Bodies ◽  
Pure Substance ◽  
Liquid Equilibrium ◽  
Simple Rules ◽  
Different Shapes ◽  
The Mean

The excess entropy of mixing of mixtures of hard spheres and spherocylinders is determined from an equation of state of hard convex bodies. The obtained dependence of excess entropy on composition was used to find the accuracy of determining ΔSE from relations employed for the correlation and prediction of vapour-liquid equilibrium. Simple rules were proposed for establishing the mean parameter of nonsphericity for mixtures of hard bodies of different shapes allowing to describe the P-V-T behaviour of solutions in terms of the equation of state fo pure substance. The determination of ΔSE by means of these rules is discussed.

scholarly journals Occluded Grape Cluster Detection and Vine Canopy Visualisation Using an Ultrasonic Phased Array

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 2182
Author(s):  
Baden Parr ◽  
Mathew Legg ◽  
Stuart Bradley ◽  
Fakhrul Alam
Keyword(s):  
Near Field ◽  
Low Frequency ◽  
Volume Estimation ◽  
Yield Estimation ◽  
3D Scan ◽  
Management Processes ◽  
Canopy Volume ◽  
Ultrasonic Phased Array ◽  
Added Benefit ◽  
Grape Yield

Grape yield estimation has traditionally been performed using manual techniques. However, these tend to be labour intensive and can be inaccurate. Computer vision techniques have therefore been developed for automated grape yield estimation. However, errors occur when grapes are occluded by leaves, other bunches, etc. Synthetic aperture radar has been investigated to allow imaging through leaves to detect occluded grapes. However, such equipment can be expensive. This paper investigates the potential for using ultrasound to image through leaves and identify occluded grapes. A highly directional low frequency ultrasonic array composed of ultrasonic air-coupled transducers and microphones is used to image grapes through leaves. A fan is used to help differentiate between ultrasonic reflections from grapes and leaves. Improved resolution and detail are achieved with chirp excitation waveforms and near-field focusing of the array. The overestimation in grape volume estimation using ultrasound reduced from 222% to 112% compared to the 3D scan obtained using photogrammetry or from 56% to 2.5% compared to a convex hull of this 3D scan. This also has the added benefit of producing more accurate canopy volume estimations which are important for common precision viticulture management processes such as variable rate applications.

scholarly journals Quantitative evaluation and comparison of coronary artery characteristics by 3D coronary volume reconstruction

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yongcheol Kim ◽  
Jonathan James Hyett Bray ◽  
Benjamin Waterhouse ◽  
Alexander Gall ◽  
Georgia May Connolly ◽  
...  
Keyword(s):  
Coronary Artery ◽  
Coronary Angiography ◽  
Coronary Arteries ◽  
Intraclass Correlation ◽  
Quantitative Coronary Angiography ◽  
Volume Estimation ◽  
Diabetic Patients ◽  
Volume Reconstruction ◽  
3 Dimensional ◽  
Inter Observer Variability

AbstractNon-atherosclerotic abnormalities of vessel calibre, aneurysm and ectasia, are challenging to quantify and are often overlooked in qualitative reporting. Utilising a novel 3-dimensional (3D) quantitative coronary angiography (QCA) application, we have evaluated the characteristics of normal, diabetic and aneurysmal or ectatic coronary arteries. We selected 131 individuals under 50 years-of-age, who had undergone coronary angiography for suspected myocardial ischaemia between 1st January 2011 and 31st December 2015, at the Bristol Heart Institute, Bristol, UK. This included 42 patients with angiographically normal coronary arteries, 36 diabetic patients with unobstructed coronaries, and 53 patients with abnormal coronary dilatation (aneurysm and ectasia). A total of 1105 coronary segments were analysed using QAngio XA 3D (Research Edition, Medis medical imaging systems, Leiden, The Netherlands). The combined volume of the major coronary arteries was significantly different between each group (1240 ± 476 mm3 diabetic group, 1646 ± 391 mm3 normal group, and 2072 ± 687 mm3 abnormal group). Moreover, the combined coronary artery volumes correlated with patient body surface area (r = 0.483, p < 0.01). Inter-observer variability was assessed and intraclass correlation coefficient of the total coronary artery volume demonstrated a low variability of 3D QCA (r = 0.996, p < 0.001). Dedicated 3D QCA facilitates reproducible coronary artery volume estimation and allows discrimination of normal and diseased vessels.

scholarly journals An approximate point-based alternative for the estimation of variance under big BAF sampling

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Thomas B. Lynch ◽  
Jeffrey H. Gove ◽  
Timothy G. Gregoire ◽  
Mark J. Ducey
Keyword(s):  
Forest Inventory ◽  
Variance Estimation ◽  
Basal Area ◽  
Volume Estimation ◽  
Delta Method ◽  
Sampling Point ◽  
Variance Estimator ◽  
Computer Simulation Studies ◽  
New Formula ◽  
Estimation Of Variance

Abstract Background A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. Methods The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula. Results Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas. Conclusions A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of $\frac {1}{n}$ 1 n where n is the number of sample points.

scholarly journals Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

2020 ◽  
Vol 26 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Euclidean Space ◽  
Convex Functions ◽  
Convex Bodies ◽  
Integral Inequalities ◽  
Divergence Theorem ◽  
Several Variables ◽  
Type Integral ◽  
Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

scholarly journals Right ventricular ejection fraction as predictor of outcome in acute heart failure using RV ellipsoid model: A retrospective analysis of a prospective cross-sectional study

2021 ◽  
Vol 10 ◽  
pp. 204800402110027
Author(s):  
Eshan Ashcroft ◽  
Otar Lazariashvili ◽  
Jonathan Belsey ◽  
Max Berrill ◽  
Pankaj Sharma ◽  
...  
Keyword(s):  
Heart Failure ◽  
Ejection Fraction ◽  
Right Ventricular ◽  
Retrospective Analysis ◽  
Cross Sectional Study ◽  
Volume Estimation ◽  
Sectional Study ◽  
Cross Sectional ◽  
Ventricular Ejection Fraction ◽  
Rv Function

Objectives The right ventricular (RV) function is an important prognostic factor in acute and chronic heart failure (HF). Echocardiography is an essential imaging modality with established parameters for RV function which are useful and easy to perform. However, these fail to reflect global RV volumes due to reliability on one acoustic window. It is therefore attractive to calculate RV volumes and ejection fraction (RVEF/E) using an ellipsoid geometric model which has been validated against MRI in healthy adults but not in the HF patients. Design This is a retrospective analysis of a prospective cross-sectional study enrolling 418 consecutive patients with symptoms of HF according to a predefined study protocol. All patients underwent echocardiographic assessment of RV function using Tricuspid Annular Plane Systolic Excursion (TAPSE) and RV fractional area change (RVFAC) and RVEF/E. Setting Single centre study with multiple locations for acute in-patients including high dependency units. Participants Patients with acute or exacerbation of chronic HF older than 18 y.o. Main outcome measures Ability of RVEF/E to predict patient outcomes compared with two established parameters of RV function over two-year follow-up period. Primary outcome measure was all-cause mortality. Results RVEF/E is equal to TAPSE & RVFAC in predicting outcome (p ≤ 0.01 vs p ≤ 0.01) and provides additional benefit of RV volume estimation based on standard 2D echo measurements. Conclusions In this study we have shown that RVEF/E derived from ellipsoid model is not inferior to well established measures of RV function as a prognostic indicator of outcome in the acute HF.

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