Number Of Independent Samples Research Articles

Laser-Doppler Anemometry Measurements of Turbulent Swirling Wakes

This study considers the development and evolution of the swirling turbulent wake and their link to the turbulence present in the wake. A wake generator produces swirling wakes with a minimum of artifacts that would complicate the flow. Four swirling wakes have been studied with swirl numbers ranging from 0.19 to 0.37, and the results are compared to those of a nonswirling wake. Two-component laser-Doppler anemometry has been used to measure mean and turbulence quantities in the wake, and the uncertainty of these quantities has been determined. Careful alignment of the laser-Doppler anemometry system and large numbers of independent samples were used to obtain second-order turbulence statistics with low uncertainty. The results indicate that swirl strength impacts wake behavior, and changes in the behavior are linked to modifications in the turbulence. Faster wake width growth and centerline velocity deficit decay have been observed for wakes with higher swirl strength. The results indicate that a minimum swirl level is required to significantly impact wake behavior, and, at some level of swirl, the enhanced wake evolution observed saturates. For the conditions tested, the swirl number that enhances wake diffusion before saturation has been determined to lie between 0.21 and 0.37.

Exploiting the potential of large eddy simulations (LES) for ducted fuel injection investigation in non-reacting conditions

The diesel combustion research is increasingly focused on ducted fuel injection (DFI), a promising concept to abate engine-out soot emissions in compression-ignition engines. A large set of experiments carried out in constant volume vessel and numerical simulations, at medium-low computational cost, showed that the duct adoption in front of the injector nozzle activates several soot mitigation mechanisms, leading to quasi-zero soot formation in several engine-like operating conditions. However, although the simplified CFD modelling so far played a crucial role for the preliminary understanding of DFI technology, a more accurate turbulence description approach, combined with a large set of numerical experiments for statistical purposes, is of paramount importance for a robust knowledge of the DFI physical behaviour.In this context, the present work exploits the potential of large eddy simulations (LES) to analyse the non-reacting spray of DFI configuration compared with the unconstrained spray. For this purpose, a previously developed spray model, calibrated and validated in the RANS framework against an extensive amount of experimental data related to both free spray and DFI, has been employed. The tests have been carried out considering a single-hole injector in an optical accessible constant volume vessel, properly replicated in the simulation environment. This high-fidelity simulation model has been adapted for LES, firstly selecting the best grid settings, and then carrying out several numerical experiments for both spray configurations until achieving a satisfying statistical convergence. With this aim, the number of independent samples for the averaging procedure has been increased exploiting the axial symmetry characteristics of the present case study.Thanks to this approach, a detailed description of the main DFI-enabled soot mitigation mechanisms has been achieved, shrinking the knowledge gap in the physical understanding of the impact of spray-duct interaction.

Quantification of limitations in statistical analysis of ultrasound echo envelope amplitudes

Ultrasound echo envelope statistics have been widely studied for quantitative tissue characterization. In ultrasound measurements, the size of the region-of-interest (ROI) is limited by several factors, such as the locality of the tissue characteristics and the depth dependence of the acoustic field of the ultrasound beam. In this case, the evaluated echo envelope statistics vary even when the envelope amplitudes follow the same population without any noise. In this study, the statistical variance of the moments caused by this finite number of samples was quantified based on the central limit theorem and the law of error propagation. The proposed principles were validated by random number simulation and used to quantify the statistical variance of Nakagami parameter estimation. Finally, the effective number of independent samples in an ultrasonic measurement was quantified based on the relationship between the ROI size and the ultrasound spatial resolution.

Calculating the limit of detection for a dilution series

AimsMicrobial samples are often serially diluted to estimate the number of microbes in a sample, whether as colony-forming units of bacteria or algae, plaque forming units of viruses, or cells under a microscope. There are at least three possible definitions for the limit of detection (LOD) for dilution series counts in microbiology. The statistical definition that we explore is that the LOD is the number of microbes in a sample that can be detected with high probability (commonly 0.95). Methods and resultsOur approach extends results from the field of chemistry using the negative binomial distribution that overcomes the simplistic assumption that counts are Poisson. The LOD is a function of statistical power (one minus the rate of false negatives), the amount of overdispersion compared to Poisson counts, the lowest countable dilution, the volume plated, and the number of independent samples. We illustrate our methods using a data set from Pseudomonas aeruginosa biofilms. ConclusionsThe techniques presented here can be applied to determine the LOD for any counting process in any field of science whenever only zero counts are observed. Significance and impact of studyWe define the LOD when counting microbes from dilution experiments. The practical and accessible calculation of the LOD will allow for a more confident accounting of how many microbes can be detected in a sample.

Ensemble average method for runtime saving in Large Eddy Simulation of free and Ducted Fuel Injection (DFI) sprays

Computational Fluid Dynamics (CFD) with Large Eddy Simulation (LES) turbulence model is a valuable tool to investigate complex problems. However, for high Reynolds number problems, the associated huge computational cost often leads researchers to the use of more simplified and less accurate approaches, especially if statistics is needed for the generalization of the results and comparison against experimental data. Therefore, the introduction of innovative methodologies to reduce the computational cost maintaining results reliability would be of paramount importance for LES-based investigation.In this context, the aim of this work is to assess a runtime saving methodology to ensemble average several axial symmetric spray simulations obtained with LES. In particular, the number of independent samples for the average procedure has been increased by exploiting the axial symmetry characteristics of a diesel spray case study, extracting more realizations from a single simulation. This ensemble average approach was compared with the standard one, based on one realization per simulation, at equal statistical sample size. Main spray physical quantities and turbulence characteristics were examined, both globally and locally. The same procedure was also applied to a different diesel-relevant spray configuration, known as ducted fuel injection.The reliability of this ensemble average methodology has been herein proven for both spray configurations, highlighting a dramatic runtime saving without any worsening of the accuracy level. In particular, this approach, as applied in this work, guaranteed a computational cost reduction of 50–75%. Thereby, the present methodological assessment could motivate researchers involved in the investigation of spray processes to undertake the path of statistically significant LES analysis.

Improving working volume and total scattering cross section using polarization convertor stirrer in a reverberation chamber

AbstractIn our paper, a stirrer made of a polarization converter for a reverberation chamber (RC) is proposed. A cylindrical polarization converter (PC) stirrer with two unit structures arranged alternatively is placed in RC to take the place of a traditional metallic stirrer. Because of the scattering property of the PC stirrer, it is possible to enlarge the working volume and improve the scattering performance of the stirrer in the RC while maintaining the field uniformity and field anisotropy coefficient to meet the testing standard of the International Electrotechnical Commission 61000‐4‐21. Metallic stirrer and PC stirrer are both placed in the RC simultaneously to make a measurement for guaranteeing the same testing environment. Some parameters of the RC stirred by the PC stirrer or metallic stirrer have been measured and analyzed, such as field uniformity, field anisotropy, coefficient independent sample number and total scattering cross‐section (TSCS), and so on. Testing results verify that the RC stirred by a PC stirrer outperforms the classic RC stirred by a conventional metallic stirrer in terms of some performance, indicating that the proposal has a significant impact on RC testing technology that requires a larger working volume and better TSCS.

Improved Analytical Formula for the SAR Doppler Centroid Estimation Standard Deviation for a Dynamic Sea Surface

The existing formulas for the synthetic aperture radar (SAR) Doppler centroid estimation standard deviation (STD) suffer from various limitations, especially for a dynamic sea surface. In this study, we derive an improved version of these formulas through three steps. First, by considering the ocean wavenumber spectrum information, a new strategy for determining the number of independent samples of the sea wave velocity field is adopted in the new formula. This is contrary to the method used in the existing formulas, where the number of SAR geometric resolution cells is taken as the number of samples assuming that adjacent SAR resolution cells are statistically uncorrelated. Second, the pulse repetition frequency and Doppler bandwidth are decoupled in the new formula, unlike in the existing formulas where they are unchangeably related to each other. Third, the effects of thermal noise and Doppler aliasing are jointly quantified in a mathematically exact manner instead of being treated separately, as in the existing formulas. Comprehensive SAR raw data simulations for the ocean surface show that the new formula has a better performance in predicting the Doppler centroid estimation STD than the existing formulas.

Analytical Approximations for the Maximum-to-mean Ratio of the E-field in a Reverberation Chamber: A Review

The expected value of the maximum value of the rectangular E-field is important in radiated susceptibility testing in a reverberation chamber. In this paper, different forms of equations for the maximum-to-mean ratio of the rectangular E-field are reviewed. Important derivations are summarized and detailed. It is interesting to note that some series which could be difficult to deal with from mathematics could be solved efficiently from physical point of view. The relationship between the independent sample number N and the parameters in generalized extreme value distribution is also given.

Machine learning approach for label-free rapid detection and identification of virus using Raman spectra

ObjectiveThe objective of this study was to develop a robust method for rapid detection and identification of the virus based on Raman spectroscopy combined with machine learning approach. MethodsWe have used saliva spiked with different bacterial viruses such as P1 Phage, M13 Phage, and Lambda Phage, for demonstrating the utility of this method for virus detection. The Raman spectra collected from a large number of independent samples, each of different phages with and without saliva were used to train a supervised convolutional neural network (CNN) with its hyperparameters optimized by Bayesian optimization. The CNN method was not only able to detect the presence of a phage but was also able to identify the phage type using unprocessed Raman spectra having high noise. In addition, a semi-supervised auto-encoder was utilized for differentiating healthy saliva from saliva spiked with phages thereby making it possible to detect the presence of phages in saliva samples. ResultsThe CNN could identify the virus with an accuracy of 98.86% based on ten-fold cross-validation, precision of 98.8%, recall of 98.7%, and F1 score of 98.7%. The area under the curve of receiver operating characteristic curve was 0.99. Autoencoder was capable of differentiating healthy saliva from the virus spiked saliva with an accuracy of 99.7% in a semi-supervised manner. Thus, Raman spectroscopy coupled with machine learning approach was able to directly detect and identify the virus without consuming time for lengthy sample processing. ConclusionA robust method based on Raman spectroscopy coupled with machine learning may be capable of detection and identification of the virus even from the signal with low intensity and high noise. This label-free method is fast, sensitive, specific, and cost effective.

Improving the Reverberation Chamber Performance Using a Reconfigurable Source Stirring Antenna Array

An antenna array composed of 16 asymmetric distributed monopoles on a circular dielectric substrate is proposed to use as a reconfigurable source stirrer in a reverberation chamber (RC). The distance between antennas is above λ2 to ensure the isolation between antennas below −15 dB. In order to ensure the mutual independence of the stirring modes of the antenna array, the 16 monopoles are asymmetrically distributed on both sides with X and Y as axes. The stirring efficiency of a stirrer is related to its size, and usually a higher stirring efficiency means a larger stirrer. The source stirring technique can achieve high efficiency, but the rotation of a source stirring antenna is limited to the radius of the turntable in an RC. To solve this problem, we propose to use an antenna array as a reconfigurable source stirrer, which can achieve a high efficiency of source stirring. As the antenna array can achieve source stirring and mechanical stirring at the same time, the source stirring section is not limited to the radius of the turntable; the switch between the selected antennas of the antenna array can increase the actual stirring samples of the stirring. Thus, the efficiency can be improved significantly and has been verified by the measurement results. The volume occupied by the conventional mechanical stirrer is reduced, which improves the working volume. The figures of merit, such as the field uniformity (FU), the independent sample numbers, the average K-factor, and the total scattering cross-section (TSCS), are measured and compared to the conventional mechanical stirring, mechanical stirring, and source stirring of the antenna array. Measurement results of the reconfigurable stir are illustrated below. FU has the best convergence and the lowest value, below 0.5 dB. The independent sample number is the largest. K-factor is the lowest, and most ranges are below −15 dB. Additionally, the proposed method has the largest TSCS, above 2 m2. These confirm that the proposed reconfigurable source stirring technique outperforms other three stirring techniques significantly. The antenna array can be easy to disassemble and install in different RC. With a wide range of working band, the proposed method can be applied to 5G OTA testing.

Average Rician K-Factor-Based Uncertainty Model of Measured Antenna Efficiency Using the Reference Antenna Method in Reverberation Chambers

Along several decades of development, many methods based on reverberation chambers (RCs) have been proposed for accurate and efficient measurement of antenna efficiency. The standard reference antenna method (RAM) is applicable for almost all frequency bands of interest and all types of antennas, and thus, it may well be the most widely applied method in the industry. In this article, an average Rician <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -factor-based uncertainty model for the standard RAM is proposed. It takes both the number of independent samples and the nonideality of the RC into consideration. Extensive measurements are performed for different RC configurations. It is shown that the newly proposed uncertainty model provides good and stable estimations of the measurement uncertainties for both unloaded and loaded RCs. Moreover, it is experimentally verified that the differences in the radiation characteristics between the reference antenna and the antenna under test (AUT) have little effect on measurement uncertainty regardless of the loading conditions of the RC. The findings of this work allow more flexible and efficient antenna efficiency measurements, including estimation of the associated uncertainty.

A metric for evaluating biological information in gene sets and its application to identify co-expressed gene clusters in PBMC.

Recent technological advances have made the gathering of comprehensive gene expression datasets a commodity. This has shifted the limiting step of transcriptomic studies from the accumulation of data to their analyses and interpretation. The main problem in analyzing transcriptomics data is that the number of independent samples is typically much lower (<100) than the number of genes whose expression is quantified (typically >14,000). To address this, it would be desirable to reduce the gathered data's dimensionality without losing information. Clustering genes into discrete modules is one of the most commonly used tools to accomplish this task. While there are multiple clustering approaches, there is a lack of informative metrics available to evaluate the resultant clusters' biological quality. Here we present a metric that incorporates known ground truth gene sets to quantify gene clusters' biological quality derived from standard clustering techniques. The GECO (Ground truth Evaluation of Clustering Outcomes) metric demonstrates that quantitative and repeatable scoring of gene clusters is not only possible but computationally lightweight and robust. Unlike current methods, it allows direct comparison between gene clusters generated by different clustering techniques. It also reveals that current cluster analysis techniques often underestimate the number of clusters that should be formed from a dataset, which leads to fewer clusters of lower quality. As a test case, we applied GECO combined with k-means clustering to derive an optimal set of co-expressed gene modules derived from PBMC, which we show to be superior to previously generated modules generated on whole-blood. Overall, GECO provides a rational metric to test and compare different clustering approaches to analyze high-dimensional transcriptomic data.

Maximizing Statistical Power to Detect Differentially Abundant Cell States With scPOST

SummarySingle-cell human disease studies are able to identify differentially abundant cell states between conditions such as disease versus healthy, but require precious clinical samples and costly technologies. Therefore, it is critical to employ study design principles that maximize power to detect differential abundance. Here, we present single-cell POwer Simulation Tool (scPOST), a method that enables users to estimate power under different study designs. To approximate the specific experimental and clinical scenarios being investigated, scPOST takes prototype (public or pilot) single-cell data as input and generates large numbers of single-cell datasets in silico. We use scPOST to perform power analyses with three independent single-cell datasets that span diverse experimental conditions and tissues. Over thousands of simulations, we consistently observe that power to detect differential abundance is maximized by larger numbers of independent samples, reduced batch effects, and lower cell state frequency variation across samples.

Optimal rates of entropy estimation over Lipschitz balls

We consider the problem of minimax estimation of the entropy of a density over Lipschitz balls. Dropping the usual assumption that the density is bounded away from zero, we obtain the minimax rates $(n\ln n)^{-s/(s+d)}+n^{-1/2}$ for $0<s\leq 2$ for densities supported on $[0,1]^{d}$, where $s$ is the smoothness parameter and $n$ is the number of independent samples. We generalize the results to densities with unbounded support: given an Orlicz functions $\Psi $ of rapid growth (such as the subexponential and sub-Gaussian classes), the minimax rates for densities with bounded $\Psi $-Orlicz norm increase to $(n\ln n)^{-s/(s+d)}(\Psi ^{-1}(n))^{d(1-d/p(s+d))}+n^{-1/2}$, where $p$ is the norm parameter in the Lipschitz ball. We also show that the integral-form plug-in estimators with kernel density estimates fail to achieve the minimax rates, and characterize their worst case performances over the Lipschitz ball. One of the key steps in analyzing the bias relies on a novel application of the Hardy–Littlewood maximal inequality, which also leads to a new inequality on the Fisher information that may be of independent interest.

A General Method to Calculate the Source-Stirred Correlations in a Well-Stirred Reverberation Chamber

To identify the independent sample number in a platform-stirred reverberation chamber, the correlated angle of a rotating platform has to be identified. A general numerical method is proposed to calculate the farfield correlation in a source-stirred reverberation chamber. The proposed method is verified using a dipole antenna which has an analytical solution. General source antenna configurations are also investigated (e.g., a Vivaldi antenna) which show that the correlated angle is not sensitive to the radiation pattern of the source-stirred antenna for a large rotating radius.

Closed-Form Expressions for InSAR Sample Statistics and Its Application to Non-Gaussian Data

Aim of this article is to analytically derive the statistics of the magnitude and phase of the complex sample correlation coefficient between two Gaussian synthetic aperture radar (SAR) acquisitions, the foundation of interferometric SAR (InSAR), and polarimetric SAR. In particular, several novel closed-form expressions containing only elementary functions for the probability density functions (pdf) and the central moments are derived when the complex sample coherence is averaged over an integer number of independent samples (multilooking). Based on these rather simple expressions, a promising way to overcome the assumption of an underlying normal distribution for the InSAR data is proposed. Jointly, these two approaches permit a physically sound, robust, and highly accurate description of the InSAR statistics of severely heterogeneous scenes, a crucial prerequisite to many applications.

Impact of sample correlation on SISRE overbound for ARAIM

This paper analyzes the effect of error correlation on the SISRE bounding for GPS and Galileo satellites. For a given period of data collection, it computes the effective number of independent samples contained in a dataset applying an estimation variance analyses. Results show that the time between effective independent samples is highly dependent on the constellation and onboard clock type. On one hand, GPS satellites equipped with Rubidium clocks exhibit significantly longer error correlation than those with onboard Cesium clocks. On the other hand, Galileo satellites show substantially shorter correlation time among samples with less variability on a monthly basis. This paper also introduces a methodology to compute SISRE bounding accounting for the limited number of independent samples. Using a Bayesian approach, it computes the so-called uncertainty factor by which the Gaussian distribution needs to be inflated in order to account for the observation data independence.

Quantifying parameter uncertainty in a large-scale glacier evolution model using Bayesian inference: application to High Mountain Asia

AbstractThe response of glaciers to climate change has major implications for sea-level change and water resources around the globe. Large-scale glacier evolution models are used to project glacier runoff and mass loss, but are constrained by limited observations, which result in models being over-parameterized. Recent systematic geodetic mass-balance observations provide an opportunity to improve the calibration of glacier evolution models. In this study, we develop a calibration scheme for a glacier evolution model using a Bayesian inverse model and geodetic mass-balance observations, which enable us to quantify model parameter uncertainty. The Bayesian model is applied to each glacier in High Mountain Asia using Markov chain Monte Carlo methods. After 10,000 steps, the chains generate a sufficient number of independent samples to estimate the properties of the model parameters from the joint posterior distribution. Their spatial distribution shows a clear orographic effect indicating the resolution of climate data is too coarse to resolve temperature and precipitation at high altitudes. Given the glacier evolution model is over-parameterized, particular attention is given to identifiability and the need for future work to integrate additional observations in order to better constrain the plausible sets of model parameters.

Threshold Level Crossings, Excursions, and Extrema in Immunity and Fading Testing Using Multistirred Reverberation Chambers

Theoretical statistics and probability distributions are presented for level-crossing characteristics and failure rates in mono- and multistirred reverberation chambers, with supporting experimental results. Measured frequency responses for the spectral moments of the stir data exhibit power-law dependencies regardless of the scalar or vector nature of the field. For $d$ -dimensional homogeneous isotropic stirring involving $d$ stir or scan actions, the length of excursions above a high threshold exhibits a Weibull distribution with shape parameter $2/d$ . For excursions below low thresholds, their size follows a transformed inverse first-kind confluent hypergeometric function distribution with the same shape parameter. Excursion lengths decrease inversely proportionally with the root mean square (rms) rate of fluctuation. A lower bound on the equivalent number of independent samples is obtained that depends on the rms rate of fluctuation and on the dimensionality of the stir domain. For uncertain test levels with Gaussian prior probability density function (PDF), the total PDF is obtained in closed form. Among several other results, an expression for the mean time between failures based on energy levels is obtained and validated experimentally.

Average Rician K-Factor Based Analytical Uncertainty Model for Total Radiated Power Measurement in a Reverberation Chamber

Total radiated power (TRP) is commonly accepted as an important figure of merit (FoM) for evaluating the over-the-air (OTA) performance of wireless devices enabled by the emerging fifth generation (5G) mobile communication technology. The statistically homogeneous and isotropic electromagnetic (EM) environment created by a reverberation chamber (RC) makes it an accurate, efficient, and economic testing facility for TRP measurement. In this paper, an improved analytical uncertainty model which is based on the average Rician K-factor (K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">avg</sub> ) and the number of independent samples is proposed for TRP measurement using an RC. It has the flexibility to allow different stirring configurations in the calibration stage and the measurement stage, and gives insight into the measurement uncertainty without the tedious and inefficient empirical estimation processes. Estimators of K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">avg</sub> are modelled and analyzed. Specifically, the maximum likelihood estimator (MLE) of K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">avg</sub> is validated by the Monte Carlo simulation, and its unbiased correction is derived accordingly for improved uncertainty model accuracy. Extensive 9-Point estimation measurements are also conducted in order to evaluate the performance of the proposed analytical model.