Random Measurement Research Articles

Note on the density of ISE and a related diffusion

The integrated super-Brownian excursion (ISE) is the occupation measure of the spatial component of the head of the Brownian snake with lifetime process the normalized Brownian excursion. It is a random probability measure on \mathbb{R} , and it is known to describe the continuum limit of the distribution of labels in various models of random discrete labelled trees. We show that f_{\mathrm{ISE}} , its (random) density, has almost surely a derivative f'_{\mathrm{ISE}} which is continuous and (\frac{1}{2}-\varepsilon) -Hölder for any \varepsilon >0 but for no \varepsilon<0 (proving a conjecture of Bousquet-Mélou and Janson). We conjecture that f_{\mathrm{ISE}} can be represented as a second-order diffusion of the form df'_{\mathrm{ISE}}(t) ={2}\sqrt{f_{\mathrm{ISE}}(t)}\, dB_{t} + g\bigg(f'_{\mathrm{ISE}}(t), f_{\mathrm{ISE}}(t),\int_{-\infty}^{t} f_{\mathrm{ISE}}(s)\,ds\bigg)dt, for some continuous function g , for t>0 , and we give a number of remarks and questions in that direction. The proof of regularity is based on a moment estimate coming from a discrete model of trees, while the heuristic of the diffusion comes from an analogous statement in the discrete setting, which is a reformulation of explicit product formulas of Bousquet-Mélou and the first author (2012).

A detectable change in the air-sea CO2 flux estimate from sailboat measurements

The sailboat Seaexplorer collected underway sea surface partial pressure of CO2 (pCO2) data for 129 days (2018–2021), including an Antarctic circumnavigation. By comparing ensembles of data-driven air-sea CO2 fluxes computed with and without sailboat data and applying a detection algorithm, we show that these sailboat observations significantly increase the regional carbon uptake in the North Atlantic and decrease it in the Southern Ocean. While compensating changes in both basins limit the global effect, the Southern Ocean–particularly frontal regions (40°S–60°S) during summertime—exhibited the largest air-sea CO2 flux changes, averaging 20% of the regional mean. Assessing the sensitivity of the air-sea CO2 flux to measurement uncertainty, the results stay robust within the expected random measurement uncertainty (± 5 μatm) but remain undetectable with a measurement offset of 5 µatm. We thus conclude that sailboats fill essential measurement gaps in remote ocean regions.

Active Compensation Technology for the Target Measurement Error of Two-Axis Electro-Optical Measurement Equipment.

For two-axis electro-optical measurement equipment, there are many error sources in parts manufacturing, assembly, sensors, calibration, and so on, which cause some random errors in the final measurement results of the target. In order to eliminate the random measurement error as much as possible and improve the measurement accuracy, an active compensation technique for target measurement error is proposed in this paper. Firstly, the error formation mechanism and error transfer model establishment of the two-axis electro-optical measurement equipment were studied, and based on that, three error compensation and correction methods were proposed: the least square (LS)-based error compensation method, adaptive Kalman filter(AKF)-based error correction method, and radial basis function neural network (RBFNN)-based error compensation method. According to the theoretical analysis and numerical simulation comparison, the proposed RBFNN-based error compensation method was identified as the optimal error compensation method, which can approximate the random error space surface more precisely, so that a more accurate error compensation value can be obtained, and in order to improve the measurement accuracy with higher precision. Finally, the experimental results proved that the proposed active compensation technology was valid in engineering applicability and could efficiently enhance the measurement accuracy of the two-axis electro-optical measurement equipment.

A general class of improved population variance estimators under non-sampling errors using calibrated weights in stratified sampling.

This paper proposes a new calibration estimator for population variance within a stratified two-phase sampling design. It takes into account random non-response and measurement errors, specifically applying this method to estimate the variance in Gas turbine exhaust pressure data. The study integrates additional information from two highly positively correlated auxiliary variables to develop a general class of estimators tailored for the stratified two-phase sampling scheme. The properties of these estimators, in terms of their biases and mean square errors, have been thoroughly examined and extensively analyzed through numerical and simulation studies. Furthermore, the calibrated weights of the strata are derived. The proposed estimators outperform the natural estimator of population variance. Finally, suitable recommendations have been made for survey statisticians intending to apply these findings to real-life problems.

Random expert sampling for deep learning segmentation of acute ischemic stroke on non-contrast CT.

Outlining acutely infarcted tissue on non-contrast CT is a challenging task for which human inter-reader agreement is limited. We explored two different methods for training a supervised deep learning algorithm: one that used a segmentation defined by majority vote among experts and another that trained randomly on separate individual expert segmentations. The data set consisted of 260 non-contrast CT studies in 233 patients with acute ischemic stroke recruited from the multicenter DEFUSE 3 (Endovascular Therapy Following Imaging Evaluation for Ischemic Stroke 3) trial. Additional external validation was performed using 33 patients with matched stroke onset times from the University Hospital Lausanne. A benchmark U-Net was trained on the reference annotations of three experienced neuroradiologists to segment ischemic brain tissue using majority vote and random expert sampling training schemes. The median of volume, overlap, and distance segmentation metrics were determined for agreement in lesion segmentations between (1) three experts, (2) the majority model and each expert, and (3) the random model and each expert. The two sided Wilcoxon signed rank test was used to compare performances (1) to 2) and (1) to (3). We further compared volumes with the 24 hour follow-up diffusion weighted imaging (DWI, final infarct core) and correlations with clinical outcome (modified Rankin Scale (mRS) at 90 days) with the Spearman method. The random model outperformed the inter-expert agreement ((1) to (2)) and the majority model ((1) to (3)) (dice 0.51±0.04 vs 0.36±0.05 (P<0.0001) vs 0.45±0.05 (P<0.0001)). The random model predicted volume correlated with clinical outcome (0.19, P<0.05), whereas the median expert volume and majority model volume did not. There was no significant difference when comparing the volume correlations between random model, median expert volume, and majority model to 24 hour follow-up DWI volume (P>0.05, n=51). The random model for ischemic injury delineation on non-contrast CT surpassed the inter-expert agreement ((1) to (2)) and the performance of the majority model ((1) to (3)). We showed that the random model volumetric measures of the model were consistent with 24 hour follow-up DWI.

Control of the Probe-Sample Interaction Force at the Piconewton Scale by a Magnetic Microprobe in Aqueous Solutions

This article describes the design and implementation of a control system that controls the probe-sample interaction force at the piconewton scale by manipulating a magnetic microprobe in aqueous solutions under a microscope. The control system has two functions, namely accurate force generation by magnetic flux control and precise control of the probe-sample interaction force. Magnetic flux control uses an improved six-input-six-output digital control law along with a disturbance estimator to achieve two control objectives. First, the magnetic flux at each pole tip of a previously developed hexapole electromagnetic actuator can be individually and precisely controlled at frequencies over 4 kHz, and the experimental results precisely followed the theoretical predictions based on the design. Second, together with the optimized flux allocation, the flux control system generates precise magnetic forces, making the six-input hexapole actuator behave like a decoupled three-axis force generator with a bandwidth of more than 4 kHz. Interaction force control compares the measured deformation of the sample with the expected deformation, updated in real time by a deformation predictor, to generate the magnetic force to control the interaction between the probe and the sample. Digital control laws, the estimator, and the predictor are all implemented using a high-speed Field Programmable Gate Array (FPGA) system. Experiments confirm that through mathematical modeling, digital control technology, high-speed electronics, and real-time computation, accurate three-dimensional force generation at the piconewton scale with high bandwidth and precise interaction force control with zero-mean random error, attributed to random thermal force and measurement noise, are achieved.

Comparing revised latent state-trait models including autoregressive effects.

Understanding the longitudinal dynamics of behavior, their stability and change over time, are of great interest in the social and behavioral sciences. Researchers investigate the degree to which an observed measure reflects stable components of the construct, situational fluctuations, method effects, or just random measurement error. An important question in such models is whether autoregressive effects occur between the residuals, as in the trait-state occasion model (TSO model), or between the state variables, as in the latent state-trait model with autoregression (LST-AR model). In this article, we compare the two approaches by applying revised latent state-trait theory (LST-R theory). Similarly to Eid et al. (2017) regarding the TSO model, we show how to formulate the LST-AR model using definitions from LST-R theory, and we discuss the practical implications. We demonstrate that the two models are equivalent when the trait loadings are allowed to vary over time. This is also true for bivariate model versions. The different but same approaches to modeling latent states and traits with autoregressive effects are illustrated with a longitudinal study of cancer-related fatigue in Hodgkin lymphoma patients. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A statistical framework for planning and analysing test-retest studies of repeatability.

There is an increasing number of potential quantitative biomarkers that could allow for early assessment of treatment response or disease progression. However, measurements of such biomarkers are subject to random variability. Hence, differences of a biomarker in longitudinal measurements do not necessarily represent real change but might be caused by this random measurement variability. Before utilizing a quantitative biomarker in longitudinal studies, it is therefore essential to assess the measurement repeatability. Measurement repeatability obtained from test-retest studies can be quantified by the repeatability coefficient, which is then used in the subsequent longitudinal study to determine if a measured difference represents real change or is within the range of expected random measurement variability. The quality of the point estimate of the repeatability coefficient, therefore, directly governs the assessment quality of the longitudinal study. Repeatability coefficient estimation accuracy depends on the case number in the test-retest study, but despite its pivotal role, no comprehensive framework for sample size calculation of test-retest studies exists. To address this issue, we have established such a framework, which allows for flexible sample size calculation of test-retest studies, based upon newly introduced criteria concerning assessment quality in the longitudinal study. This also permits retrospective assessment of prior test-retest studies.

VB-Based Gaussian Sum Cubature Kalman Filter for Adaptive Estimation of Unknown Delay and Loss Probability

The traditional Kalman filter assumes that all measurements can be obtained in real time, which is invalid in practical engineering. Therefore, a variational Bayesian- (VB-) based Gaussian sum cubature Kalman filter is proposed to solve the nonlinear tracking problem of multistep random measurement delay and loss (MRMDL) with unknown probability. First, the measurement model with MRMDL is modified by Bernoulli random variables. Then, the expression of the likelihood function is reformulated as a mixture of multiple Gaussian distributions, and the cubature rule is used to improve the estimation accuracy under the framework of Gaussian sum filter in the process of time update. Finally, by constructing a hierarchical Gaussian model, the unknown and time-varying measurement delay and loss probability are estimated in real time with the state jointly using the VB method in the measurement update stage. The algorithm does not need to calculate the equivalent noise covariance matrix so as to avoid the possible division by zero operation, which improves the stability of the algorithm. Simulation results for a target tracking problem show that the proposed algorithm has a better performance in the presence of MRMDL and can estimate the unknown measurement delay and loss probability accurately.

Assessing the spatial distribution of positional error associated to dense point cloud measurements using regional Gaussian random fields

Being able to assess the amount of uncertainty locally associated to dense point clouds generated by measurement can help investigate the relations between the metrological performance of a chosen measuring technology, and the local geometric and surface properties of the measurand geometry. In previous research it was demonstrated that spatial statistics based on Gaussian Random Fields and measurement repeats could be used to obtain spatial maps capturing both local dispersion and local bias associated to the position of points within measured clouds. However, the previous method had scalability limitations when handling very dense point clouds, due to it requiring the resolution of a global, increasingly larger, covariance matrix in order to solve the random field fitting problem. This work presents a variant to the previous method, where the covariance matrix is solved only locally, making the method better scalable to handle denser point clouds. Despite the new method not being able to return an equally rich information content in relation to spatial covariance, it still allows to obtain almost equally accurate information on local bias and variance, with significant gains in terms of processing speed and, importantly, making it now possible to handle very dense clouds which would be unviable to process with the original method.

The role of the working memory storage component in a random-like series generation.

People are not equipped with an internal random series generator. When asked to produce a random series they simply try to reproduce an output of known random process. However, this endeavor is very often limited by their working memory capacity. Here, we investigate the model of random-like series generation that accounts for the involvement of storage and processing components of working memory. In two studies, we used a modern, robust measure of randomness to assess human-generated series. In Study 1, in the experimental design with the visibility of the last generated elements as a between-subjects variable, we tested whether decreasing cognitive load on working memory would mitigate the decay in the level of randomness of the generated series. Moreover, we investigated the relationship between randomness judgment and algorithmic complexity of human-generated series. Results showed that when people did not have to solely rely on their working memory storage component to maintain active past choices they were able to prolongate their high-quality performance. Moreover, people who were able to better distinguish more complex patterns at the same time generated more random series. In Study 2, in the correlational design, we examined the relationship between working memory capacity and the ability to produce random-like series. Results revealed that individuals with longer working memory capacity also were to produce more complex series. These findings highlight the importance of working memory in generating random-like series and provide insights into the underlying mechanisms of this cognitive process.

Impulse Control of Conditional McKean–Vlasov Jump Diffusions

In this paper, we consider impulse control problems involving conditional McKean–Vlasov jump diffusions, with the common noise coming from the σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document}-algebra generated by the first components of a Brownian motion and an independent compensated Poisson random measure. We first study the well-posedness of the conditional McKean–Vlasov stochastic differential equations (SDEs) with jumps. Then, we prove the associated Fokker–Planck stochastic partial differential equation (SPDE) with jumps. Next, we establish a verification theorem for impulse control problems involving conditional McKean–Vlasov jump diffusions. We obtain a Markovian system by combining the state equation with the associated Fokker–Planck SPDE for the conditional law of the state. Then we derive sufficient variational inequalities for a function to be the value function of the impulse control problem, and for an impulse control to be the optimal control. We illustrate our results by applying them to the study of an optimal stream of dividends under transaction costs. We obtain the solution explicitly by finding a function and an associated impulse control, which satisfy the verification theorem.

Concurrent validity and test-retest reliability for the assessment of body segment lengths using two-dimensional video-recordings in weightlifting

ABSTRACT The aims of this study were 1) to propose a simple two-dimensional (2D) video-based method to measure segment lengths in the clean and jerk during weightlifting competitions, and 2) to check concurrent validity and test-retest reliability compared to 3D video-based measurements. In the first part of the study, key body positions for the assessment of segment lengths via 2D measurement method were determined. In the second part, concurrent validity was verified, comparing the 2D segment length measurements to 3D measurements. In the third part, the test-retest reliability of the 2D approach was investigated. In the clean and in the jerk, the lift-off/start position and the position of maximum barbell velocity displayed a minimised offset between ‘real’ 3D segment lengths and 2D projections of the segment lengths. For the concurrent validity assessment, the overall random measurement error was 4.3% with concordance correlation coefficients ranging from 0.64 to 0.88. The standard error of measurement in the test-retest procedure was 2.4% on average with intraclass correlation coefficients ranging from 0.85 to 0.96. The proposed 2D video-based approach to measure body segment lengths during weightlifting exercises is proven to be a valid and reliable procedure.

Oculomotor randomness is higher in autistic children and increases with the severity of symptoms.

A variety of studies have suggested that at least some children with autism spectrum disorder (ASD) view the world differently. Differences in gaze patterns as measured by eye tracking have been demonstrated during visual exploration of images and natural viewing of movies with social content. Here we analyzed the temporal randomness of saccades and blinks during natural viewing of movies, inspired by a recent measure of "randomness" applied to micro-movements of the hand and head in ASD (Torres et al., 2013; Torres & Denisova, 2016). We analyzed a large eye-tracking dataset of 189 ASD and 41 typically developing (TD) children (1-11 years old) who watched three movie clips with social content, each repeated twice. We found that oculomotor measures of randomness, obtained from gamma parameters of inter-saccade intervals (ISI) and blink duration distributions, were significantly higher in the ASD group compared with the TD group and were correlated with the ADOS comparison score, reflecting increased "randomness" in more severe cases. Moreover, these measures of randomness decreased with age, as well as with higher cognitive scores in both groups and were consistent across repeated viewing of each movie clip. Highly "random" eye movements in ASD children could be associated with high "neural variability" or noise, poor sensory-motor control, or weak engagement with the movies. These findings could contribute to the future development of oculomotor biomarkers as part of an integrative diagnostic tool for ASD.

An image compression-then-encryption algorithm using piecewise asymptotic deterministic random measurement matrix

An image compression-then-encryption algorithm using piecewise asymptotic deterministic random measurement matrix

The Nesterov accelerated gradient algorithm for Auto-Regressive Exogenous models with random lost measurements: Interpolation method and auxiliary model method

For ARX models with random lost measurements, this article proposes an interpolation and auxiliary model based Nesterov accelerated gradient algorithm. This algorithm utilizes the interpolation and auxiliary model methods to fill in lost measurements. The parameters are estimated with better accuracy based on the interpolated input and predicted output data. Two simulation examples are presented to verify the effective of the proposed algorithm.

The quest for psychological symmetry through figural goodness, randomness, and complexity: A selective review.

Of the four interrelated concepts in the title, only symmetry has an exact mathematical definition. In mathematical development, symmetry is a graded variable-in marked contrast with the popular binary conception of symmetry in and out of the laboratory (i.e. an object is either symmetrical or nonsymmetrical). Because the notion does not have a direct graded perceptual counterpart (experimental participants are not asked about the amount of symmetry of an object), students of symmetry have taken various detours to characterize the perceptual effects of symmetry. Current approaches have been informed by information theory, mathematical group theory, randomness research, and complexity. Apart from reviewing the development of the main approaches, for the first time we calculated associations between figural goodness as measured in the Garner tradition and measures of algorithmic complexity and randomness developed in recent research. We offer novel ideas and analyses by way of integrating the various approaches.

Estimation of the density for censored and contaminated data

AbstractConsider a situation where one is interested in estimating the density of a survival time that is subject to random right censoring and measurement errors. This happens often in practice, like in public health (pregnancy length), medicine (duration of infection), ecology (duration of forest fire), among others. We assume a classical additive measurement error model with Gaussian noise and unknown error variance and a random right censoring scheme. Under this setup, we develop minimal conditions under which the assumed model is identifiable when no auxiliary variables or validation data are available, and we offer a flexible estimation strategy using Laguerre polynomials for the estimation of the error variance and the density of the survival time. The asymptotic normality of the proposed estimators is established, and the numerical performance of the methodology is investigated on both simulated and real data on gestational age.

Regularity of pullback random attractors and invariant sample measures for nonautonomous stochastic &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;$ p $&lt;/tex-math&gt;&lt;/inline-formula&gt;-Laplacian lattice systems

Regularity of pullback random attractors and invariant sample measures for nonautonomous stochastic &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;$ p $&lt;/tex-math&gt;&lt;/inline-formula&gt;-Laplacian lattice systems

Scaling limit of the cluster size distribution for the random current measure on the complete graph

Scaling limit of the cluster size distribution for the random current measure on the complete graph