Random Measurement Research Articles

Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors

A method for mitigating errors in near-term quantum computers utilizing randomized measurements explores the trade-off between the number of measurement settings and the number of repetitions of each measurement.

Spatial Tightness at the Edge of Gibbsian Line Ensembles

Consider a sequence of Gibbsian line ensembles, whose lowest labeled curves (i.e., the edge) have tight one-point marginals. Then, given certain technical assumptions on the nature of the Gibbs property and underlying random walk measure, we prove that the entire spatial process of the edge is tight. We then apply this black-box theory to the log-gamma polymer Gibbsian line ensemble, which we construct. The edge of this line ensemble is the transversal free energy process for the polymer, and our theorem implies tightness with the ubiquitous KPZ class 2/3 exponent, as well as Brownian absolute continuity of all the subsequential limits. A key technical innovation which fuels our general result is the construction of a continuous grand monotone coupling of Gibbsian line ensembles with respect to their boundary data (entrance and exit values, and bounding curves). Continuous means that the Gibbs measure varies continuously with respect to varying the boundary data, grand means that all uncountably many boundary data measures are coupled to the same probability space, and monotone means that raising the values of the boundary data likewise raises the associated measure. This result applies to a general class of Gibbsian line ensembles where the underlying random walk measure is discrete time, continuous valued and log-convex, and the interaction Hamiltonian is nearest neighbor and convex.

Truncated Poisson–Dirichlet approximation for Dirichlet process hierarchical models

The Dirichlet process was introduced by Ferguson in 1973 to use with Bayesian nonparametric inference problems. A lot of work has been done based on the Dirichlet process, making it the most fundamental prior in Bayesian nonparametric statistics. Since the construction of Dirichlet process involves an infinite number of random variables, simulation-based methods are hard to implement, and various finite approximations for the Dirichlet process have been proposed to solve this problem. In this paper, we construct a new random probability measure called the truncated Poisson–Dirichlet process. It sorts the components of a Dirichlet process in descending order according to their random weights, then makes a truncation to obtain a finite approximation for the distribution of the Dirichlet process. Since the approximation is based on a decreasing sequence of random weights, it has a lower truncation error comparing to the existing methods using stick-breaking process. Then we develop a blocked Gibbs sampler based on Hamiltonian Monte Carlo method to explore the posterior of the truncated Poisson–Dirichlet process. This method is illustrated by the normal mean mixture model and Caron–Fox network model. Numerical implementations are provided to demonstrate the effectiveness and performance of our algorithm.

Polynomially growing harmonic functions on connected groups

We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for sufficiently “nice” random walk measures) a connected, compactly generated, locally compact group has polynomial volume growth if and only if the space of linear growth harmonic functions has finite dimension. This characterization is interesting in light of the fact that Gromov’s theorem regarding finitely generated groups of polynomial growth does not have an analog in the connected case. That is, there are examples of connected groups of polynomial growth that are not nilpotent by compact. Also, the analogous result for the discrete case has only been established for solvable groups and is still open for general finitely generated groups.

Maximum likelihood FIR filter for systems with Bernoulli distributed random delays and measurement failures

A new solution for the state estimation problems for the state-space model with random time delay and measurement failures is proposed, and the batch and iterative versions of the finite impulse response (FIR) filter are constructed based on the theorem of maximum likelihood in this paper. First, the state model is addressed with the maximum likelihood in the situation of random delays and measurement failures. Then the state-space model is expressed as a linear probability function following a random Bernoulli distribution. Finally, the proposed algorithm is compared to an adaptive Kalman filter and the UFIR filter using a drifting stochastic resonator and rotary flexible joint simulation analysis. It shows that the proposed maximum likelihood FIR method has improved estimation performance and robustness in coping with random delays and measurement failures compared to some commonly used algorithms.

Reliability and applicability of a low-cost, camera-based gait evaluation method for clinical use

Background There is the need for the development of reliable and easy to use in clinical setting gait assessment tools. An open-access video analysis software that administers the calculation of kinematical and spatio-temporal characteristics of human movement is Kinovea® however, its repeatability as a gait analysis tool has not been well addressed. The purpose of the study was to examine the applicability and reliability of an objective, quantitative, low-cost and easy to use in the clinical setting, gait evaluation method, using Kinovea® software. Methods Data collected from 44 healthy subjects recording gait in sagittal and frontal plane using two smartphones. Time consumption of the procedure was captured. Kinovea® software was used to calculate kinematical and spatial parameters. Results Intra- and inter-rater reliability of the video processing as well as intra-rater reliability of the measurement procedure represented good to excellent and there were less random measurement error. There was no measurement error due to random variation for the most of the calculated parameters, except of the pelvis position. Conclusions The results suggest that excepting low accuracy in calculation of pelvis position, gait evaluation using Kinovea® software is objective, quantitative, low-cost, reliable and easy to use in the clinical setting.

Horizon detection and tracking in sea-ice conditions using machine vision

An automated process is proposed for horizon detection and tracking using machine vision cameras and in polar, sea-ice conditions. These conditions present unique challenges for machine vision applications, such as a large amount of clutter (e.g. icebergs) and secondary edge lines from broken ice pieces. The process is divided in two parts: a more computationally expensive, yet robust detection algorithm in the first stage, based on Convolutional Neural Networks, and used to detect the horizon line in an arbitrary sea-ice image; followed by a tracking algorithm, responsible of efficiently detecting the horizon line in the subsequent images of a sequence. We propose two tracking algorithms, one based on the traditional Canny and Hough line detection methods; and a second novel approach using entropy as a measure of randomness, to segment between sea-ice and sky. Our automated process was compared to manually obtained ground-truth data and the results indicate good agreement, especially for the texture-based tracking algorithm.

Analysis of information measures using generalized type-Ⅰ hybrid censored data

<abstract><p>An entropy measure of uncertainty has a complementary dual function called extropy. In the last six years, this measure of randomness has gotten a lot of attention. It cannot, however, be applied to systems that have survived for some time. As a result, the idea of residual extropy was created. To estimate the extropy and residual extropy, Bayesian and non-Bayesian estimators of unknown parameters of the exponentiated gamma distribution are generated. Bayesian estimators are regarded using balanced loss functions like the balanced squared error, balanced linear exponential and balanced general entropy. We use the Lindley method to get the extropy and residual extropy estimates for the exponentiated gamma distribution based on generalized type-Ⅰ hybrid censored data. To test the effectiveness of the proposed methodologies, a simulation experiment was carried out, and the actual data set was studied for illustrative purposes. In summary, the mean squared error values decrease as the number of failures increases, according to the results obtained. The Bayesian estimates of residual extropy under the balanced linear exponential loss function perform well compared to the other estimates. Alternatively, the Bayesian estimates of the extropy perform well under a balanced general entropy loss function in the majority of situations.</p></abstract>

Kinematic Calibration of a 6-DoF Parallel Manipulator With Random and Less Measurements

Parallel manipulator (PM) embraces more kinematic errors than serial mechanism. The substantial errors in PM usually demand more measurements, which leads to low efficiency and affects the accuracy of identification due to the ill-conditioning problem. Having realized this common problem in the kinematic calibration of PMs, we carried out a finite and instantaneous screw (FIS)-based kinematic calibration on a 6- <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> UHU PM before application to fracture reduction. <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> , U, and H denote actuated revolute joint, universal joint, and helical joint, respectively. The error model is built by the error mapping of serial chains in the FIS framework. Instead of devoting to the measurement planning for more precise identification, the identifiability of kinematic errors is thoroughly analyzed. Redundant errors are categorized as the ones within limb and among limbs. A minimal identification model is thus defined and an error conversion method is proposed for compensation. Calibration experiments show that the FIS method has an improved accuracy of the 6- <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> UHU PM at least one magnitude higher than the precision demand, i.e., mean position and orientation errors 0.0574 mm and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5.1197\,\,{\times }\,\, 10^{-4}$ </tex-math></inline-formula> rad after calibration. Compared with the conventional closed-loop vector (CLV) equation method, the accuracy improvement of FIS method is higher. In addition, comparisons with the commonly used configuration selection methods indicate that our method allows random and a smaller number of measurements and can reach satisfactory accuracy.

Correlation Between Hyperglycemia and Length of Stay in Severe Head Injury Patients at Prof. Dr. Igng Ngoerah Hospital

Background: Head injury is one of the emergency cases in surgery that is often found in the emergency. From year to year, cases of head injuries have significantly increased. High blood glucose levels in head-injured patients are thought to correlate with the level of consciousness, especially in patients with severe head injuries. The severe head injury affects the various complications that occur, which affects the length of stay (LOS) in the hospital. Objectives: To determine the correlation between hyperglycemia and length of stay in patients with severe head injuries. Methods: This study is an analytical observational study with a prospective design. The research sample included patients with severe head injuries who came to the surgical emergency unit at Prof. Dr. IGNG Ngoerah Hospital and met the inclusion criteria in medical record data throughout November 2019 – April 2020, with 56 samples. Results: The mean random blood sugar measurement results were found to be higher in the LOS ≥7 days group (210.14±83.93 mg/dL) compared to the LOS group7 days (165.88±92.44 mg/dL). Multivariate analysis using logistic regression found a significant relationship between mean hyperglycemia and LOS in patients with severe head injuries (OR 7.46; 95% CI [1.839-30.300]; P = 0.005) Conclusion: There is a significant correlation between mean hyperglycemia and the length of stay in patients with severe head injuries at Prof. Dr. IGNG Ngoerah Hospital.

Random attractors and invariant measures for 3D stochastic globally modified Navier-Stokes equations with time-dependent delay and coefficient

In this article, we investigate the dynamics of three-dimensional, non-autonomous, and globally modified Navier-Stokes equations with time-dependent delay and additive noise. Based on the well-posedness of solutions, we demonstrate that the solution operators of such equations generate a non-autonomous random dynamical system. We further prove the existence and uniqueness of random attractors as well as the periodicity and the upper semicontinuity for this random dynamical system. We also prove the existence of invariant measures supported on the random attractors. Moreover, we rigorously find that every limit of a sequence of invariant measures must be an invariant measure of the corresponding limiting equations as the noise intensity $ \varepsilon\rightarrow0 $ or the modification parameter $ N\rightarrow N_0\in (0, +\infty) $.

Spatial Distributional of Irrigation Water Quality in Peaty Paddy Field of Paser Regency, East Kalimantan Province, Indonesia

Paddy is one of the main food-crop commodities in Indonesia. The main problem in paddy cultivation in Paser Regency is good water quality for plants. Water is the main requirement for paddy plants to grow and develop. Water quality to meet the needs of paddy plants is a very important factor. pH H2O, TDS (Total Dissolve Solid) and EC (Electrical Conductivity) are some of the water parameters used as a reference in determining land suitability for paddy plants. The purpose of this research is to spatially analyse the water parameters (pH H2O, TDS and EC) for the water needs of paddy plants in Paser Regency. Determination of sample points using stratified random sampling method and parameter measurements are carried out directly in the field in the irrigation area. Interpolation analysis used the IDW (Inverse Distance Weighted) method with a power weight of 2. RMSE values from the interpolation results for pH H2O 0.0001, TDS 0.1695 and EC 0.0003. The results of the interpolation of several parameters are then analysed by overlay to determine the spatial relationship between parameters. The results of the analysis show that the average values in Paser Regency are pH H2O 6.13, TDS 478.64 ppm and EC 0.82 mS/cm. The area of pH H2O (6.5-8.4) suitable for paddy plants is 391447.87 ha, TDS (&lt;2000 ppm) 1067265.23 ha and EC (&lt;3 mS/cm) 1066907.37 ha. Most of the pH H2O suitable for paddy plants is in the northern region, while the TDS and EC are better in the northern region although most of them are still suitable for paddy plants. Each parameter has a spatial relationship, where the value of each parameter influences each other. Overall, the northern area in Paser Regency is more suitable for paddy cultivation according to water parameters, namely pH H2O, TDS and EC.

Single-valued Plithogenic entropy measurement

In the last decade many researchers paid attention towards uncertainty measurement in given attributes arises unconsciously. These types of uncertainty measurement become more complex in case of dynamic changes in multi-variable, multi-attributes or Plithogenic attributes. It creates major problem at time of knowledge discovery and processing tasks. To resolve this issue, a method is proposed in this paper for precise measurement of randomness arises unconsciously for single valued Plithogenic attribute. In addition the selection of some important Plithogenic attributes at user defined granulation is discussed with an illustrative example.

An asymptotic threshold of sufficient randomness for causal inference

For sensitivity analysis with stochastic counterfactuals, we introduce a methodology to characterize uncertainty in causal inference from natural experiments. Our sensitivity parameters are standardized measures of variation in propensity and prognosis probabilities, and one minus their geometric mean is an intuitive measure of randomness in the data generating process. Within our latent propensity‐prognosis model, we show how to compute, from contingency table data, a threshold, , of sufficient randomness for causal inference. If the actual randomness of the data generating process is greater than this threshold, then causal inference is warranted. We demonstrate our methodology with two example applications.

The wave speed of an FKPP equation with jumps via coordinated branching

We consider a Fisher–KPP equation with nonlinear selection driven by a Poisson random measure. We prove that the equation admits a unique wave speed s>0 given by s2 2= ∫[0,1] log(1+y) yR(dy), where R is the intensity of the impacts of the driving noise. Our arguments are based on upper and lower bounds via a quenched duality with a coordinated system of branching Brownian motions.

Offline Uncertainty Sampling in Data-driven Stochastic MPC

In this work, we exploit an offline-sampling based strategy for the constrained data-driven predictive control of an unknown linear system subject to random measurement noise. The strategy uses only past measured, potentially noisy data in a non-parametric system representation and does not require any prior model identification. The approximation of chance constraints using uncertainty sampling leads to efficient constraint tightening. Under mild assumptions, robust recursive feasibility and closed-loop constraint satisfaction is shown. In a simulation example, we provide evidence for the improved control performance of the proposed control scheme in comparison to a purely robust data-driven predictive control approach.

A SOC Estimation Method for Li-Ion Batteries under High-Rate Pulse Conditions based on AO-BPNN Model

The estimation of state of charge (SOC) in lithium-ion batteries is important for ensuring the safe and stable operation of battery systems. Under high-rate pulse conditions, the characteristics of short discharge time, high frequency, large current, strong interference, and complex transient characteristics that make lithium-ion batteries exhibit marked nonlinear characteristics. The existing battery management system has difficulties in capturing the rising and falling edge data of the pulses due to limitations in the sampling frequency. The short idle time makes it challenging to obtain accurate open-circuit voltage, and there are difficulties in identifying the model parameters. Therefore, using a combination of coulomb counting method, open-circuit voltage correction method, and Kalman filtering method to estimate SOC poses certain challenges. This study applies backpropagation neural network (BPNN) combined with Aquila optimizer (AO) algorithm to estimate SOC under high-rate pulse conditions, and experimental verification is performed using special 3-Ah lithium iron phosphate battery. We compared the estimation accuracy of the AO-BPNN model for SOC with the BPNN, support vector machine, extreme learning machine, and Fuzzy neural network models and verified the superiority of AO-BPNN. Furthermore, by utilizing data with larger acquisition intervals, we obtained accurate evaluation results and reduced the data requirements. The effectiveness of the assessment of AO-BPNN was individually verified under different high-rate pulse conditions and different static times through pulse experiments conducted under 9 operating conditions, with the estimation error controlled within 5%. Finally, the robustness of the proposed model was validated using test data with different sampling intervals and random measurement errors.

Test-Retest Reliability and Random Measurement Error of the Multifactorial Memory Questionnaire in Older Adults With Subjective Memory Complaints.

To examine the psychometric properties of the Multifactorial Memory Questionnaire (MMQ) in older adults with subjective memory complaints. The three MMQ subscale (Satisfaction, Ability, and Strategy) was administered twice, with a 3-month interval. The test-retest reliability was examined using intraclass correlation coefficients (ICCs). The random measurement error was examined by calculating the standard error of measurement (SEM) and minimal detectable change (MDC95). The test-retest reliabilities of the three MMQ subscales were generally acceptable. The SEM of the three MMQ subscales was higher than the acceptable criterion of 10%. Despite the influence of random measurement error, the change scores of the three MMQ subscales may represent true changes if they are larger than the MDC95 of 13.2 (Satisfaction), 18.4 (Ability), and 16.9 (Strategy). The MMQ appears to be a reliable measure for use in research settings, but may not yet be suitable for clinical use.

On the differentiation of random measures with respect to homothecy invariant convex bases

On the differentiation of random measures with respect to homothecy invariant convex bases

ОБ ОДНОМ МЕТОДЕ ОЦЕНКИ РЕПРЕЗЕНТАТИВНОСТИ ТЕСТИРОВАНИЯ АЛГОРИТМОВ ИСКУССТВЕННОГО ИНТЕЛЛЕКТА В СРЕДСТВАХ ИЗМЕРЕНИЙ

This paper proposes a machine learning approach to standardization in the field of intelligent change tools. Shows how machine learning methods can be used to compensate for random measurement errors. The essential operating factors and their variability are examined in detail, and it is also clearly shown how the creation of a regulatory and technical basis for testing intelligent measuring instruments and the corresponding conformity assessment system will ensure the development of AI algorithms that allow predicting measurement errors.