Error Distribution Research Articles

Small sample adjustment for inference without assuming orthogonality in a mixed model for repeated measures analysis

ABSTRACT The mixed model for repeated measures (MMRM) analysis is sometimes used as a primary statistical analysis for a longitudinal randomized clinical trial. When the MMRM analysis is implemented in ordinary statistical software, the standard error of the treatment effect is estimated by assuming orthogonality between the fixed effects and covariance parameters, based on the characteristics of the normal distribution. However, orthogonality does not hold unless the normality assumption of the error distribution holds, and/or the missing data are derived from the missing completely at random structure. Therefore, assuming orthogonality in the MMRM analysis is not preferable. However, without the assumption of orthogonality, the small-sample bias in the standard error of the treatment effect is significant. Nonetheless, there is no method to improve small-sample performance. Furthermore, there is no software that can easily implement inferences on treatment effects without assuming orthogonality. Hence, we propose two small-sample adjustment methods inflating standard errors that are reasonable in ideal situations and achieve empirical conservatism even in general situations. We also provide an R package to implement these inference processes. The simulation results show that one of the proposed small-sample adjustment methods performs particularly well in terms of underestimation bias of standard errors; consequently, the proposed method is recommended. When using the MMRM analysis, our proposed method is recommended if the sample size is not large and between-group heteroscedasticity is expected.

Research on Multi-Parameter Error Model of Backcalculated Modulus Using Abaqus Finite Element Batch Modeling Based on Python Language

The error in modulus backcalculation is a crucial component in validating the rationality and reliability of results for engineering applications. The objective of this study is to identify the theoretical limitations associated with backcalculated modulus errors under typical parameter uncertainties and to determine the primary factors contributing to these errors. Firstly, using the actual measurements or data from the Long-Term Pavement Performance (LTPP) project, the statistical distributions of errors for typical parameters in the modulus backcalculation model were determined. Subsequently, a factor level table for orthogonal experimental design was developed, leading to the construction of 81 orthogonal design experimental schemes and their corresponding theoretical pavement structure models based on the actual error distributions. The deflection responses of 81 theoretical pavement structure models were then computed using an ABAQUS finite element batch analysis method devised in Python. Furthermore, a multi-parameter error model for modulus was established using multiple linear regression and variance analysis. Finally, the theoretical limitations of modulus errors under actual errors were analyzed. The results show that the errors of thickness, load amplitude and load frequency follow a normal distribution, while the distribution of backcalculated modulus errors follows an approximate mixed Gaussian distribution. When the errors of multiple parameters are combined randomly, the modulus errors range from −100% to 595%, and the probability of the modulus errors being less than 15% is highest in the asphalt surface layer, followed by the subgrade, and then the base and subbase layers. Within the same error range, the modulus error is random. However, with different error ranges, the overall level of modulus error increases in proportion to the size of those ranges. Compared to factors such as thickness, load amplitude, and load frequency, the errors in deflections have a highly contribution rate on the modulus errors exceeding 99%.

Tracer-Separator: A Deep Learning Model for Brain PET Dual-Tracer (18F-FDG and Amyloid) Separation.

Multiplexed PET imaging revolutionized clinical decision-making by simultaneously capturing various radiotracer data in a single scan, enhancing diagnostic accuracy and patient comfort. Through a transformer-based deep learning, this study underscores the potential of advanced imaging techniques to streamline diagnosis and improve patient outcomes. The research cohort consisted of 120 patients spanning from cognitively unimpaired individuals to those with mild cognitive impairment, dementia, and other mental disorders. Patients underwent various imaging assessments, including 3D T1-weighted MRI, amyloid PET scans using either 18F-florbetapir (FBP) or 18F-flutemetamol (FMM), and 18F-FDG PET. Summed images of FMM/FBP and FDG were used as proxy for simultaneous scanning of 2 different tracers. A SwinUNETR model, a convolution-free transformer architecture, was trained for image translation. The model was trained using mean square error loss function and 5-fold cross-validation. Visual evaluation involved assessing image similarity and amyloid status, comparing synthesized images with actual ones. Statistical analysis was conducted to determine the significance of differences. Visual inspection of synthesized images revealed remarkable similarity to reference images across various clinical statuses. The mean centiloid bias for dementia, mild cognitive impairment, and healthy control subjects and for FBP tracers is 15.70 ± 29.78, 0.35 ± 33.68, and 6.52 ± 25.19, respectively, whereas for FMM, it is -6.85 ± 25.02, 4.23 ± 23.78, and 5.71 ± 21.72, respectively. Clinical evaluation by 2 readers further confirmed the model's efficiency, with 97 FBP/FMM and 63 FDG synthesized images (from 120 subjects) found similar to ground truth diagnoses (rank 3), whereas 3 FBP/FMM and 15 FDG synthesized images were considered nonsimilar (rank 1). Promising sensitivity, specificity, and accuracy were achieved in amyloid status assessment based on synthesized images, with an average sensitivity of 95 ± 2.5, specificity of 72.5 ± 12.5, and accuracy of 87.5 ± 2.5. Error distribution analyses provided valuable insights into error levels across brain regions, with most falling between -0.1 and +0.2 SUV ratio. Correlation analyses demonstrated strong associations between actual and synthesized images, particularly for FMM images (FBP: Y = 0.72X + 20.95, R2 = 0.54; FMM: Y = 0.65X + 22.77, R2 = 0.77). This study demonstrated the potential of a novel convolution-free transformer architecture, SwinUNETR, for synthesizing realistic FDG and FBP/FMM images from summation scans mimicking simultaneous dual-tracer imaging.

Effects of Digital Elevation Model Resolution on Unmanned Aerial Vehicle-Based Topographic Change Detection in Human-Altered Landscapes

UAV-based topographic change detection is widely used in geoscience communities. The change detection involves comparison of two digital elevation models (DEMs) produced by UAV surveys, which are affected by the DEM resolution. Coarse resolution DEMs introduce errors in change detection, but the DEM resolution effect remains poorly understood. Moreover, effective strategies for mitigating the resolution effect have yet to be investigated. This study generated UAV-based DEMs at resolutions ranging from 0.1 m to 10 m with various resampling methods. The impact of DEM resolution on topographic change detection was then evaluated by analyzing the difference of DEM (DoD) and volume budget errors with indices such as mean error (ME), standard deviation (STD), and Moran’s I. The results from two human-altered landscapes showed that the random errors of DoD increase rapidly with the DEM resolution coarsening, while DoD systematic errors (spatial distribution of errors) become stable after 4 m resolution. The volume budget errors also increase with DEM coarsening. Coarser resolution DEMs tend to underestimate the volume budget (gross erosion, gross deposition, and net changes). Moreover, selecting an appropriate method for generating DEM is beneficial in decreasing the errors caused by the resolution effect. Among the seven methods (MAX, MIN, MEAN, BIL, NEAR, NEB, and TIN), the BIL method is optimum for mitigating both DoD and volume errors. The NEAR, NEB, and TIN methods are equivalent, and they are superior to the aggregation methods (MAX, MIN, MEAN). The slope of DoD (SDoD) should be considered when selecting a resolution for change detection. Large errors tend to appear in areas with large SDoD and vice versa. Coarse resolution DEMs are tolerable in areas with low SDoD, while high resolution DEMs are necessary in areas with large SDoD.

No evidence for interstellar fireballs in the CNEOS database

Context. The detection of interstellar meteors, especially meteorite-dropping meteoroids, would be transformative, as this would enable direct sampling of material from other stellar systems on Earth. One candidate is the fireball observed by U.S. government sensors on January 8, 2014. It has been claimed that fragments of this meteoroid have been recovered from the ocean floor near Papua New Guinea and that they support an extrasolar origin. Based on its parameters reported in the Center for Near Earth Object Studies (CNEOS) catalog, the fireball exhibits a hyperbolic excess velocity that indicates an interstellar origin; however, the catalog does not report parameter uncertainties. Aims. To achieve a clear confirmation of the fireball’s interstellar origin, we assessed the underlying error distributions of the catalog data. Our aim was also to confirm whether the fragments of this meteoroid survived passage through the atmosphere and assess all conditions needed to unambiguously determine the fragments’ origin. Methods. We approached the investigation of the entire catalog using statistical analyses and modeling, and we provide a comprehensive analysis of the individual hyperbolic CNEOS cases. Results. We have developed several independent arguments indicating substantial uncertainties in the velocity and radiant position of the CNEOS events. We determined that all the hyperbolic fireballs exhibit significant deviations from the majority of the events in one of their velocity components, and we show that such mismeasurements can produce spurious parameters. According to our estimation of the speed measurement uncertainty for the catalog, we found that it is highly probable that such a catalog containing only Sun-bound meteors would show at least one event that appears highly unlikely to be Sun-bound. We also establish that it is unlikely that any fragments from a fireball traveling at the high inferred velocities could survive passage through the atmosphere. When assuming a much lower velocity, some fragments of this meteoroid could survive; however, they would be of a common Solar System origin and thus highly probable to be indistinguishable from the quantity of other local micrometeorites that have gradually accumulated on the sea floor. Conclusions. We conclude that there is no evidence in the CNEOS data to confirm or reject the interstellar origin of any of the nominally hyperbolic fireballs in the CNEOS catalog. Therefore, the claim of an interstellar origin for the fireball recorded over Papua New Guinea in 2014 remains unsubstantiated. We have also gathered arguments that refute the claim that the collected spherules from the sea floor originated in the body of this fireball.

Bayesian Empirical Likelihood Regression for Semiparametric Estimation of Optimal Dynamic Treatment Regimes.

We propose a semiparametric approach to Bayesian modeling of dynamic treatment regimes that is built on a Bayesian likelihood-based regression estimation framework. Methods based on this framework exhibit a probabilistic coherence property that leads to accurate estimation of the optimal dynamic treatment regime. Unlike most Bayesian estimation methods, our proposed method avoids strong distributional assumptions for the intermediate and final outcomes by utilizing empirical likelihoods. Our proposed method allows for either linear, or more flexible forms of mean functions for the stagewise outcomes. A variational Bayes approximation is used for computation to avoid common pitfalls associated with Markov Chain Monte Carlo approaches coupled with empirical likelihood. Through simulations and analysis of the STAR*D sequential randomized trial data, our proposed method demonstrates superior accuracy over Q-learning and parametric Bayesian likelihood-based regression estimation, particularly when the parametric assumptions of regression error distributions may be potentially violated.

The Linguistic Ecologic Analysis of the Error-prone Emergency Prevention and Control Slogans during the COVID-19 Epidemic in China

As a typical form of emergency language service, the emergency prevention and control slogans (EPCS) play an important role in the prevention and control of social emergencies in China. However, due to the characteristics of "emergency", the prevention and control slogans are errorprone, which can cause a negative impact on the language ecology. Based on the theory of linguistic ecology, this paper conducts a thorough analysis of the error-prone slogans during the COVID-19 epidemic in China. First, error-prone slogans can be divided into four categories from the internal language ecological environment: language standardization errors, application appropriateness errors, content adaptability errors, and ethical compliance errors. Second, this paper assesses three aspects of error-prone slogans from external social ecological environment: the degree of errors, the distribution of errors, and the citizens' normative willingness. Finally, the paper puts forward suggestions to prevent language conflict, stop language exclusion, eliminate language dissent and govern the language environment in order to reduce error-prone emergency prevention and control slogans, improve the quality of emergency language services, and build a harmonious ecological environment inside and outside the language.

Estimating Carbon Stock in Unmanaged Forests Using Field Data and Remote Sensing

Unmanaged forest ecosystems play a critical role in addressing the ongoing climate and biodiversity crises. As there is no commercial interest in monitoring the health and development of such inaccessible habitats, low-cost assessment approaches are needed. We used a method combining RGB imagery acquired using an Unmanned Aerial Vehicle (UAV), Sentinel-2 data, and field surveys to determine the carbon stock of an unmanaged forest in the UNESCO World Heritage Site wilderness area Dürrenstein-Lassingtal in Austria. The entry-level consumer drone (DJI Mavic Mini) and freely available Sentinel-2 multispectral datasets were used for the evaluation. We merged the Sentinel-2 derived vegetation index NDVI with aerial photogrammetry data and used an orthomosaic and a Digital Surface Model (DSM) to map the extent of woodland in the study area. The Random Forest (RF) machine learning (ML) algorithm was used to classify land cover. Based on the acquired field data, the average carbon stock per hectare of forest was determined to be 371.423 ± 51.106 t of CO2 and applied to the ML-generated class Forest. An overall accuracy of 80.8% with a Cohen’s kappa value of 0.74 was achieved for the land cover classification, while the carbon stock of the living above-ground biomass (AGB) was estimated with an accuracy within 5.9% of field measurements. The proposed approach demonstrated that the combination of low-cost remote sensing data and field work can predict above-ground biomass with high accuracy. The results and the estimation error distribution highlight the importance of accurate field data.

Visual Status in Children with Dyslexia at the Integrated Special Education Program in Selangor, Malaysia

Objective: Dyslexia is a learning disorder, characterized by difficulties in recognizing, decoding, and spelling words. Studies on visual status of individuals with dyslexia have yielded mixed findings. This study aimed to assess visual acuity and refractive errors in dyslexic children in Selangor, Malaysia.Material and Methods: A cross-sectional study was conducted in the integrated special education program (PPKI) for secondary schools across three randomly selected districts in Selangor. Children with dyslexia from 15 schools were enrolled. Distance and near visual acuity were measured, and non-cycloplegic refraction was performed to identify refractive errors. Descriptive analysis was used to describe the distribution of visual acuity and refractive errors. The Wilcoxon Signed-Rank test was used to compare habitual and corrected visual acuity (VA).Results: 137 dyslexic children, aged 13 to 19 years, participated in the study. 60% of the participants had good habitual distance VA. Meanwhile, the percentage of good habitual near VA were higher than distance VA. The Wilcoxon Signed-Rank test showed that corrected VA was significantly better than habitual VA. The most common ametropias observed were myopia and astigmatism.Conclusion: Dyslexic children in the PPKI program generally have good visual acuity and are emmetropic. However, uncorrected refractive error and suboptimal optical refraction were the primary causes of unsatisfactory habitual vision in some children. Findings highlight the need to screen for refractive errors and provide appropriate optical correction to this population to prevent further hindrance to their reading ability.

Garbage prediction using regression analysis for municipal corporations of Indian cities

AbstractGarbage management is exceptionally critical and poses enormous environmental challenges. It has always been a vital issue in municipal corporations. However, municipal agencies have developed and used garbage management systems. Garbage forecasting still plays a crucial role in the management system and helps improve or create a garbage management system. This research examines the information from 212 cities to suggest a helpful regression model for garbage forecasting and control. To establish a connection between the variables, the descriptive study employs statistical techniques to learn about the composition of data collected from municipal corporations and conduct correlation analysis. Population and garbage depend highly on one another, as evidenced by their correlation coefficient of 0.922,144. The primary research is used to build an alternate hypothesis that shows the chosen variables are highly dependent on one another. The dataset is scaled and divided into a training and testing 80:20 ratio during the pre‐processing data phase. This research aims to do a regression analysis with daily garbage production, urban area, and population as independent variables. This research initiates a variety of regression models, including multiple linear regression (MLR), artificial neural network (ANN), decision tree regression (DTR), and random forest regression (RFR). The MLR model's R2 value of 0.85 indicates that it has the potential to accurately forecast daily garbage production based on just two independent variables and a single dependent variable. Random Forest Regression (RFR) with (MSE: 100,078.749 & MAE: 182.212) shows that it has the lowest MSE among all the models, which provides the most accurate predictions on average and the fit values of 8.85 and 316.23 obtained from the error distribution with a bin value 25. The estimated results from each model are compared to the test data values on line graphs and Taylor plots. The mean square error and the mean absolute error in the analysis and the Taylor plot show that the RFR model is best suited for predicting daily garbage production in a city. This research, therefore, provides a Random Forest model that is optimal for such challenges and is recommended for this class of problem.

A Virtual Reality Tool for Accuracy Assessment of 3D Models in an Immersive Virtual Environment

Abstract. Accurate validation and assessment techniques are essential for ensuring the reliability of spatial reconstructions derived from photogrammetry, enabling well-informed decision-making across diverse domains. This study presents a Virtual Reality (VR) based accuracy assessment tool tailored for evaluating the accuracy and quality of 3D models generated by Unmanned Aerial Vehicles (UAVs). Leveraging the Unity game engine platform, our workflow entails three key steps: aligning real-world coordinates with an arbitrary Unity coordinate system, transforming the positions of Ground Control Points (GCPs) from field survey to the arbitrary system using a reference GCP, and marking observed points on the 3D models. Absolute and Relative Root Mean Square Errors (RMSE), Mean Errors (ME), and Standard Deviation of errors (SD) are computed within the virtual environment via the game object transform properties. The error distributions around each GCP are visually depicted using Unity game engine components for enhanced interaction and comprehension. The efficacy of the tool is validated through experimentation on four 3D models generated from varying camera angles during UAV data capture. The tool provides the opportunity to directly interact with the 3D models and visualize the errors, which is quite distinct from traditional methods. Using the developed tool, results were obtained to indicate that configurations employing camera angles of 60° + 75º exhibit notable performance in terms of relative and absolute accuracy.

Clustering Functional Data With Measurement Errors: A Simulation-Based Approach.

Clustering analysis of functional data, which comprises observations that evolve continuously over time or space, has gained increasing attention across various scientific disciplines. Practical applications often involve functional data that are contaminated with measurement errors arising from imprecise instruments, sampling errors, or other sources. These errors can significantly distort the inherent data structure, resulting in erroneous clustering outcomes. In this article, we propose a simulation-based approach designed to mitigate the impact of measurement errors. Our proposed method estimates the distribution of functional measurement errors through repeated measurements. Subsequently, the clustering algorithm is applied to simulated data generated from the conditional distribution of the unobserved true functional data given the observed contaminated functional data, accounting for the adjustments made to rectify measurement errors. We illustrate through simulations show that the proposed method has improved numerical performance than the naive methods that neglect such errors. Our proposed method was applied to a childhood obesity study, giving more reliable clustering results.

Dynamic correction of forest fire spread prediction using observation error covariance matrix estimation technique based on FLC-GRU

BackgroundData assimilation (DA) techniques have played a significant role in improving the prediction accuracy of forest fire spread. The dynamic correction technique weights the predicted and observed values to obtain an analytical value that better reflects the position of the fire perimeter. The weighted importance of each contribution is determined by the magnitude of its associated error. However, as a crucial parameter affecting prediction accuracy, the covariance matrix of observation errors is often inaccurate and neglects its own temporal correlation. This is unfriendly to spread prediction results. To address this issue, we proposed a targeted technique for estimating the observation error covariance matrix (R matrix) based on the Fire Line Convolutional Gated Recurrent Unit (FLC-GRU).ResultsWe integrated this method into the DA framework and validated its applicability and accuracy using Observing System Simulation Experiment (OSSE). Through comparisons with traditional methods, the results indicate that using the FLC-GRU estimated R matrix for correction calculations leads to wildfire prediction locations that are closer to the true values.ConclusionsThe proposed approach learns the covariance matrix directly from time-series observed fire line data, without requiring any prior knowledge or assumptions about the error distribution, in contrast to classical posterior tuning methods. The proposed method significantly improves the rationality and accuracy of R matrix estimation, enhances the utility of observational data, and thereby improves the correction accuracy of forest fire spread predictions. Moreover, the study also demonstrates the applicability of the proposed method within the DA framework.

Optimal wideband digital fractional-order differentiators using gradient based optimizer

In this paper, we propose a novel optimization approach to designing wideband infinite impulse response (IIR) digital fractional order differentiators (DFODs) with improved accuracy at low frequency bands. In the new method, the objective function is formulated as an optimization problem with two tuning parameters to control the error distribution over frequencies. The gradient based optimizer (GBO) is effectively employed on the proposed objective function. A wide range of design examples are presented to illustrate the effectiveness of the proposed approach. The proposed approximations are compared to those of recent literature in terms magnitude, phase, and group delay errors. The result reveal that our method can attain approximations have a favorable low frequency performance (with about 60% of relative magnitude error reduction) and maintain a comparable accuracy at most of the Nyquist band to those of the existing ones. Thus, our approximations can be attractive for low frequency applications.

Deep Neural Network-Based Accelerated Failure Time Models Using Rank Loss.

An accelerated failure time (AFT) model assumes a log-linear relationship between failure times and a set of covariates. In contrast to other popular survival models that work on hazard functions, the effects of covariates are directly on failure times, the interpretation of which is intuitive. The semiparametric AFT model that does not specify the error distribution is sufficiently flexible and robust to depart from the distributional assumption. Owing to its desirable features, this class of model has been considered a promising alternative to the popular Cox model in the analysis of censored failure time data. However, in these AFT models, a linear predictor for the mean is typically assumed. Little research has addressed the non-linearity of predictors when modeling the mean. Deep neural networks (DNNs) have received much attention over the past few decades and have achieved remarkable success in a variety of fields. DNNs have a number of notable advantages and have been shown to be particularly useful in addressing non-linearity. Here, we propose applying a DNN to fit AFT models using Gehan-type loss combined with a sub-sampling technique. Finite sample properties of the proposed DNN and rank-based AFT model (DeepR-AFT) were investigated via an extensive simulation study. The DeepR-AFT model showed superior performance over its parametric and semiparametric counterparts when the predictor was nonlinear. For linear predictors, DeepR-AFT performed better when the dimensions of the covariates were large. The superior performance of the proposed DeepR-AFT was demonstrated using three real datasets.

Numerical evaluation of orientation averages and its application to molecular physics.

In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modeling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely related to integration over two- or three-dimensional unit spheres, a common problem discussed in numerical analysis. The computational cost of the integration depends significantly on the quadrature method, making the selection of an appropriate method crucial for the feasibility of simulations. After reviewing several classes of spherical quadrature methods in terms of their efficiency and error distribution, we derive guidelines for choosing the best quadrature method for orientation averages and illustrate these with three examples from chiral molecule physics. While Gauss quadratures allow for achieving numerically exact integration for a wide range of applications, other methods offer advantages in specific circumstances. Our guidelines can also be applied to higher-dimensional spherical domains and other geometries. We also present a Python package providing a flexible interface to a variety of quadrature methods.

Unsupervised machine learning model for detecting anomalous volumetric modulated arc therapy plans for lung cancer patients.

Volumetric modulated arc therapy (VMAT) is a new treatment modality in modern radiotherapy. To ensure the quality of the radiotherapy plan, a physics plan review is routinely conducted by senior clinicians; however, this process is less efficient and less accurate. In this study, a multi-task AutoEncoder (AE) is proposed to automate anomaly detection of VMAT plans for lung cancer patients. The feature maps are first extracted from a VMAT plan. Then, a multi-task AE is trained based on the input of a feature map, and its output is the two targets (beam aperture and prescribed dose). Based on the distribution of reconstruction errors on the training set, a detection threshold value is obtained. For a testing sample, its reconstruction error is calculated using the AE model and compared with the threshold value to determine its classes (anomaly or regular). The proposed multi-task AE model is compared to the other existing AE models, including Vanilla AE, Contractive AE, and Variational AE. The area under the receiver operating characteristic curve (AUC) and the other statistics are used to evaluate the performance of these models. Among the four tested AE models, the proposed multi-task AE model achieves the highest values in AUC (0.964), accuracy (0.821), precision (0.471), and F1 score (0.632), and the lowest value in FPR (0.206). The proposed multi-task AE model using two-dimensional (2D) feature maps can effectively detect anomalies in radiotherapy plans for lung cancer patients. Compared to the other existing AE models, the multi-task AE is more accurate and efficient. The proposed model provides a feasible way to carry out automated anomaly detection of VMAT plans in radiotherapy.

Uncertainty study of two-phase flow distribution characteristics measurement based on bubble trajectory tracking method

Bubbles undergo complex motions such as nonlinear trajectories in two-phase flow, where the position, velocity magnitude, and direction of bubble centers continuously change as they evolve under the influence of forces. The complexity of bubble trajectory increases the difficulty in measuring the flow field distribution characteristics, which has been understudied in the previous. The bubble trajectory tracking model based on the Monte Carlo method is constructed to study the uncertainty of two-phase flow distribution characteristics measurement by the conductivity probe. The Monte Carlo method is adopted to randomly generate the bubble velocity at the initial moment and the bubble force characteristics are embedded to simulate the three-dimensional motion of the bubble. The influence of various factors on the distribution of effective bubble numbers and velocity relative error at the local point is quantitatively analyzed. It is found that the lateral spacing of the sensors has the greatest influence on the measurement results of small-sized bubbles, the accuracy is greatly reduced when the space is larger than the radius of the measured bubbles. Moreover, the measurement accuracy of the probe for medium-sized bubbles is high, and the effect of bubble lateral velocity and aspect ratio on the effective bubble ratio and velocity relative error is negligible. In addition, the maximum measurement range of the probe at local points is investigated which is found to be 4 mm in the lateral direction and 2 mm in the longitudinal direction. Finally, uniformly distributed bubbles are generated in a 20 mm × 10 mm transverse plane and the distribution of the effective bubble ratio of the probe is found to be consistent at different measurement points, which verifies the reliability of the probe measurement.

THE INFLUENCE OF OBSERVATIONAL ERRORS IN GAIA DR3 ON THE RECONSTRUCTION OF GLOBULAR CLUSTER ORBITS ON A COSMOLOGICAL TIMESCALE

In recent years, the emerging field of astronomy focused on the history of galaxy formation, known as Galactic Archaeology, has been gaining popularity. Globular clusters have been involved in many key processes occurring in the Milky Way, making their study, particularly the reconstruction of their orbits, significantly important. The Gaia DR3 catalog provides parameters for 165 globular clusters, such as proper motions, radial velocity, and heliocentric distance, with certain accuracy. Therefore, it is important to examine the influence of measurement errors in these parameters on the initial data when converting to the Galactocentric coordinate system and, consequently, on the shape of the orbits. We integrated the orbits of globular clusters 10 billion years lookback. For physical justification during the integration, we used the external dynamic potential with the individual number 411321 from the cosmological simulation database IllustrisTNG-100, which best reproduces the potential of the Milky Way. The integration was performed using the parallel N-body code φ-GPU, based on a fourth-order Hermite scheme with hierarchical individual block timesteps. A total of 1,000 randomizations of the initial data were created considering a normal distribution of errors, and the influence of errors on the scatter of initial velocities and on the shape of the orbits was examined. The parameters with the largest relative errors are proper motions and radial velocity, while the smallest errors are in heliocentric distance. It was found that 85% of the globular clusters have relative errors in all parameters of no more than 10%, and 5.4% have errors of no more than 1%. Investigating the influence of measurement errors for clusters with different magnitudes of relative errors, we concluded that for most globular clusters, the influence of measurement errors on the shape of the orbits is not significant. Consequently, it is possible to reconstruct the orbits with high accuracy for these clusters. Since the reconstruction of globular cluster orbits involves cosmological timescales, accounting for measurement errors is an important aspect of the preparatory procedure before the main integration.

FNNGM: A neural-driven fractional-derivative multivariate fusion model for interpretable real-time CPI forecasts

Integrating models from diverse sources has attracted substantial interest in developing advanced time series forecasting technologies. However, current research lacks a comprehensive and deep fusion model to integrate multiple forecasting methodologies. To this end, this paper proposes a neural-driven fractional-derivative multivariate fusion model (FNNGM (p, n)) to assimilate the fractional-derivative dynamical system, the driving factor in grey multivariate models, and the neural network into a cohesive framework. Consequently, this fusion architecture can benefit from the synergy of the target system's dynamics, extensive exogenous information, and non-linear transformation. Additionally, FNNGM (p, n) fosters extra functionalities through its inherent memory layer and sequence decomposition, bolstering model interpretability with the visible memory mechanism and understandable model workflows. To showcase the utility of FNNGM (p, n), this paper conducts real-time monthly consumer price index (CPI) forecasts that span ten years (from 2013:08 to 2023:07), analyzing the interpretable results from FNNGM (p, n) and contrasting it against many prevailing benchmark models. The comparison results reveal FNNGM (p, n)’s highly concentrated error distributions and the minimum mean absolute percentage forecasting error (APFE), squared forecasting error (SFE), and absolute forecasting error (AFE) values of 0.22 %, 0.59, and 0.56, respectively. Furthermore, the ablation experiments are performed to explore the specific effects and compatibilities of the fusion components, validating the effectiveness of the proposed fusion approach.