Objective Endoscopic facet denervation (ED) and percutaneous cryoneurolysis (Cryo) have emerged as alternative interventional treatments for lumbar facet joint–mediated pain; however, comparative long-term outcome data remain limited. This study aimed to compare the long-term efficacy of ED and Cryo with respect to pain intensity, functional disability, and health-related quality of life. Methods In this multicenter randomized controlled trial, 80 patients with lumbar facet joint–mediated pain confirmed by dual diagnostic medial branch blocks were randomized in a 1:1 ratio to ED or Cryo (n = 40 per group). Pain intensity was assessed using the Numeric Rating Scale (NRS), functional disability using the Oswestry Disability Index (ODI), and quality of life using the EQ-5D-5L index and EQ visual analogue scale (EQ-VAS). Outcomes were evaluated at baseline and at 3, 6, 12, 24, 30, and 36 months following intervention. Within- and between-group comparisons were performed using adjusted statistical analyses. Results Both interventions resulted in significant reductions in back pain and functional disability at 3 months, with improvements sustained through 24 months and no significant differences between groups during this period. At 36 months, patients treated with Cryo maintained statistically significant pain reduction relative to baseline, whereas the effect in the ED group was attenuated. Functional and quality-of-life measures remained improved in both groups throughout follow-up. Although Cryo demonstrated more stable long-term trends, between-group differences did not reach statistical significance. Conclusion Both cryoneurolysis and endoscopic facet denervation provide durable improvements in pain, function, and quality of life over a 3-year follow-up in carefully selected patients with lumbar facet joint–mediated pain. Cryoneurolysis may be associated with greater long-term stability of clinical outcomes.

We propose a novel goodness-of-fit test for the multivariate logistic distribution, leveraging the properties of its characteristic function. The test statistic is constructed by measuring a weighted $ L<^>2 $ L2-distance between the empirical characteristic function of the standardized data and the theoretical characteristic function of the standard multivariate logistic distribution. The approach is grounded in a radial Fourier transform, expressed via the Hankel transform, and yields an explicit, closed-form expression involving three integrals. We derive the asymptotic distribution of the test statistic under both the null hypothesis and contiguous alternatives, and prove its affine invariance. Critical values are determined using Monte Carlo simulation. Through extensive simulations, we demonstrate that the proposed test has excellent control of Type I error and exhibits superior power relative to existing methods, including the multivariate Kolmogorov-Smirnov and energy tests, especially in higher dimensions or under heavy-tailed alternatives. Applications to real data further underscore the test's practical utility and robustness. MATLAB and R implementations are made publicly available.

In this paper, we propose a robust goodness-of-fit test based on the empirical characteristic function of the sample median. The test is specifically designed to address the challenges of statistical inference in small to moderate sample sizes, where traditional methods may be affected by a few extreme observations or by endpoint effects (e.g., bounded support, heavy tails). By leveraging the inherent robustness of the median and the descriptive power of the characteristic function, the proposed test exhibits stable and reliable performance across a wide range of settings. Our main contribution is the development of a goodness-of-fit procedure that combines a median-based subsampling scheme with the empirical characteristic function, resulting in a test that is both robust to outliers and effective in small-sample regimes. Although our theoretical results are derived under a two-dimensional asymptotic regime with both the number of subsamples n and the within-subsample size N increasing, the test is calibrated at fixed (n, N) using Monte Carlo simulation. The method is designed for scenarios with small within-subsample sizes N (single digits to low tens) and a small-to-moderate number of subsamples n (about 10–50). In simulations and applications from reliability and quality control, this regime yields accurate size and competitive power.

The article presents an alternative method for evaluating the calibration of a coordinate measuring machine (CMM) using a polynomial calibration curve, including its confidence interval, and its subsequent use in evaluating measurements. The methodology, based on the OEFPIL (Optimal Estimation of Functional Parameters by Iterated Linearization) algorithm and GUM principles, enables a more comprehensive and statistically sound evaluation of measurements using CMM. The procedure was applied to measurements along three coordinate axes and four diagonal directions, with confidence intervals set at a minimum coverage probability of 95 %. The proposed procedure allows for a more accurate and traceable determination of measurement uncertainty and provides a significant improvement over conventional MPE-based evaluation under conditions close to calibration. The paper presents quantitative results for a specific calibration and measurement case.

Cryoneurolysis and endoscopic facet denervation are established minimally invasive treatment options for lumbar facet joint–mediated pain; however, comparative evidence regarding their long-term effectiveness remains limited. This study compared the 36-month clinical outcomes of both procedures in a prospective multicenter randomized clinical trial. Eighty patients with lumbar facet joint–mediated pain confirmed by dual controlled medial branch blocks (≥ 70

This paper explores weighted estimation strategies for nonlinear errors-in-variables (EIV) regression, with applications in metrology where accurate uncertainty propagation is critical. The OEFPIL (Optimal Estimating Equations for Parameters by Iterated Linearization) method enables full use of the structured uncertainty matrix, incorporating both Type A and Type B components, including correlations. Although theoretically optimal under the Gauss-Markov framework, using the full matrix may yield fitted models that appear biased or inconsistent with experimental intuition. As an alternative, we propose a locally weighted least squares (LWLS) method that improves interpretability at the cost of some statistical efficiency. We present the mathematical formulation and illustrate the trade-offs between statistical rigor and empirical consistency, relevant to practitioners in measurement science and uncertainty analysis.

Data fitting is an indispensable tool in modern metrology. However, as the models become more and more complex the most popular method, ordinary least squares regression, reaches its limit. As the relative uncertainty in the independent variable increases, we can no longer speak about an exactly known independent variable and an uncertain dependent variable. The increasing complexity of the measurement process may give rise to correlationsFurthermore correlations between data may become non negligible: typical sources are e.g. the use of reference samples or crosstalk between sensors. These problems can be treated with generalized least squares. A new algorithm-Optimum Estimate of Function Parameters by Iterated Linearization (OEFPIL) - has been recently suggested which can handle both a wide class of functions as well as general covariance matrices. We illustrate its application in the analysis of force distance curves in AFM which are used to evaluate the mechanical properties of samples such as the Young's modulus and adhesion. In this work we apply the new algorithm and compare the results to other methods. The uncertainties obtained by OEFPIL are in good agreement with uncertainties obtained by the Monte Carlo method but can be obtained in a more straightforward way.

Accurate measurement uncertainty assessment is a fundamental objective in modern metrology, where fitting data within complex measurement models plays a pivotal role as an initial step in expressing uncertainty. Often, sets of n-tuples of measurements, with the best-estimated values characterizing the measured objects along with their associated uncertainty budget, become available. These data represent direct measurements, construed as realizations of random variables characterized by a joint distribution, which may be fully known or partially known. Here, we present a new modelling approach suitable for a class of measurement problems based on using the errors-in-variables model together with algorithmic implementation in MATLAB.

When people experience pain in everyday situations, the experience is often long-lasting and fluctuating. However, pain research predominantly focuses on artificial brief and repeated singular painful events.Here, we aimed to approximate clinically relevant pain in 152 sessions from 38 participants who underwent four sessions each. We applied variable levels of contact heat pain to the forearm using a thermode. Participants were asked to continuously rate their pain experience through a potentiometer device. In a whole-brain approach, we related the dynamic fluctuations of cortical activity and connectivity to the time courses of pain. We also explored the variability of cortical processing across participants. In an individual approach, we compared the cortical processing pattern of each individual with the overall group findings.The results revealed a large discrepancy between the group results that are usually reported in publications and the 4-session individual processing patterns: the group findings corroborated previous work localising tonic pain encoding to the secondary somatosensory cortex. By contrast, this region was shadowed by a variety of activity patterns across individuals, represented by a low spatial correlation between group statistics and individual results.The current findings challenge the usefulness and applicability of group results. They do not inform us how pain is processed in the brain as none of the participants exhibited the processing pattern of the group statistics. Therapies to relieve pain that rely on the modulation of brain regions will fail unless they are adapted to an individual's unique pain processing characteristics.

Correct data processing and uncertainty assessment is crucial for metrology. One of the most common methods used is function fitting using non-linear least squares. This numerical method has been implemented in probably all data processing software and is quick and easy to use. Unfortunately, it has its limitations – notably it works only for very simple models of the uncertainties present in the system. Uncertainties in the dependent variable cannot be taken into account, and neither do correlations. Errors-in-variables models minimize a generalized distance of the points from the fitted function. The metric used to compute the distance is given by the inverse of the covariance matrix. Thus, the estimates of the uncertainties entering the computation may affect the resulting estimates of the fitted parameters. In this contribution we illustrate the use of an iterative EIV algorithm on an example from nanoindentation, especially the sensitivity of the results to input data including uncertainties.

Scanning thermal microscopy is a unique tool for the study of thermal properties at the nanoscale. However, calibration of the method is a crucial problem. When analyzing local thermal conductivity, direct calibration is not possible and reference samples are used instead. As the calibration dependence is non-linear and there are only a few calibration points, this represents a metrological challenge that needs complex data processing. In this contribution we present use of the OEFPIL algorithm for robust and single-step evaluation of local thermal conductivities and their uncertainties, simplifying this procedure. Furthermore, we test the suitability of SThM calibration for automated measurement.

The paper presents a comprehensive design of metrological equipment for torque sensor verification and calibration, detailing the process from conception to construction and highlighting the specifics of the structural design to meet metrological requirements. The measuring device’s functionality and the individual structural components are described, as is the methodology for creating a complete product. The paper addresses the crucial issue of measurement uncertainty and the required accuracy, achieved through the construction of a special measuring arm made of carbon material. FEM analyses of the carbon arm are presented and compared with the required metrological accuracies. In addition, we discuss the different properties of various carbon structures in Pre-preg materials used in the construction of the measuring arm and present the results of measurements on such carbon materials. This paper provides a comprehensive insight into the design and construction of metrological equipment for torque sensors, with a focus on its compliance with metrological requirements. The proposed device aims to establish the foundations for primary metrology of torque in Slovakia and has potential applications in a wide range of industries.

The experience of pain has been dissociated into two interwoven aspects: a sensory-discriminative aspect and an affective-motivational aspect. We aimed to explore which of the pain descriptors is more deeply rooted in the human brain. Participants were asked to evaluate applied cold pain. The majority of the trials showed distinct ratings: some were rated higher for unpleasantness and others for intensity. We compared the relationship between functional data recorded from 7 T MRI with unpleasantness and intensity ratings and revealed a stronger relationship between cortical data and unpleasantness ratings. The present study underlines the importance of the emotional-affective aspects of pain-related cortical processes in the brain. The findings corroborate previous studies showing a higher sensitivity to pain unpleasantness compared to ratings of pain intensity. For the processing of pain in healthy subjects, this effect may reflect the more direct and intuitive evaluation of emotional aspects of the pain system, which is to prevent harm and to preserve the physical integrity of the body.

We propose a numerical algorithm for the inversion of the bivariate characteristic function. This will allow the complex probability distribution specified by the characteristic function to be used in practise. Subsequently, it will be possible to create numerical algorithms for a copula function. We will also propose an algorithm for generating random numbers for the case where the bivariate distribution is specified by its characteristic function. This algo-rithm will be based on the conditional characteristic function. The concept and application of the algorithms will be illustrated using a version of the bivariate logistic distribution specified by its characteristic function.(c) 2022 Elsevier Inc. All rights reserved.

The Tsallis q-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the q-distribution family, which is characterized by a non-additive entropy. Due to their versatility and practicality, q-Gaussians are a natural choice for modeling input quantities in measurement models. This paper presents the characteristic function of a linear combination of independent q-Gaussian random variables and proposes a numerical method for its inversion. The proposed technique makes it possible to determine the exact probability distribution of the output quantity in linear measurement models, with the input quantities modeled as independent q-Gaussian random variables. It provides an alternative computational procedure to the Monte Carlo method for uncertainty analysis through the propagation of distributions.

Laplace transform has a wide spectrum of applications in various areas of mathematics and physics. It also finds use in statistics, where the evaluation of probability density function (PDF) or cumulative distribution function (CDF) of convolved probability distributions is required, as working with Laplace transform can be more efficient than working directly with PDF or CDF. The important factor is to have an effective algorithm for numerical inversion of the transform, so that the evaluation of PDF or CDF would be possible in reasonable time with sufficient accuracy. This article concerns the comparison of different methods for computation of the inverse transform and demonstration of their usage on particular probability distributions.