Building fires are preventable incidents that have proven to be both deadly and costly. Addressing their root causes will lead to safer neighbourhoods for families and businesses to live and operate in. Multiple studies have established the effect of residents’ socioeconomic compositions on an area’s building fire rates; however, the existing model based on the classical stepwise regression procedure has several limitations. This paper aims to construct a more accurate predictive model of building fire rates based on a set of explanatory socioeconomic variables. In building the socioeconomic model, a backward elimination by Robust Final Predictor Error (RFPE) criterion is proposed to enhance the forecasting capability of the model. The proposed method has been implemented on the census data and the fire incident data of the South East Queensland region in Australia. A cross-validation was then conducted to assess the model’s accuracy. In addition, comparative analyses of other elimination criteria, such as p-value, adjusted R-squared, Akaike’s Information Criterion (AIC), Bayesian Information Criterion (BIC) and predicted residual error sum of squared (PRESS), were conducted. The cross-validation analyses demonstrate that the proposed criterion is a more accurate predictive model based on a couple of goodness-of-fit measures. All in all, the RFPE equation was found to be a suitable criterion for the backward elimination procedure in the socioeconomic modelling of building fires.

In engineering practice, various types of information data are affected by many factors during the collection process. For example, information data measurement errors are caused by equipment performance and the working environment. During the transmission of detection information, the signal distortion caused by energy loss and signal interference causes unpredictable detection errors in the collected information data. Through the study of fractional calculus theory, it was found that it is suitable for studying nonlinear, non-causal, and non-stationary signals, and has the dual functions of improving detection information and enhancing signal strength. Therefore, under the influence of many factors, we applied the fractional difference algorithm to the field of information data processing. Multi-sensor detection data fusion algorithm based on the fractional partial differential equation was adopted to establish its online detection data. A multi-sensor detection data fusion algorithm based on a fractional partial differential equation is established, which effectively fuses the information data detection errors caused by various influencing factors and greatly improves the detection accuracy of information data. The effectiveness of this method is proved through its application in an experiment.

High-dimensional measurement error data are becoming more prevalent across various fields. Research on measurement error regression models has gained increasing attention due to the risk of drawing inaccurate conclusions if measurement errors are ignored. When the dimension p is larger than the sample size n, it is challenging to develop statistical inference methods for high-dimensional measurement error regression models due to the existence of bias, nonconvexity of objective function, high computational cost and many other difficulties. Over the past few years, some works have overcome the aforementioned difficulties and proposed several statistical inference methods. This paper mainly reviews the current development on estimation, hypothesis testing and variable screening methods for high-dimensional measurement error regression models and shows the theoretical results of these methods with some directions worthy of exploring for future research.

Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested by generalizing the uniform shrinkage of ridge regression to the non-uniform shrinkage, which was shown to perform well under sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package “g.ridge” (the first version published on 2023-12-07 at https://cran.r-project.org/package=g.ridge) that implements both the ridge estimator and generalized ridge estimators. The package equips with the generalized cross-validation for automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with the normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on “glmnet”, and hence, it can be the most recommended estimator under sparse and high-dimensional models. We demonstrate the package using the intracerebral hemorrhage data.

This study delves into the intricate interplay between cosmology and gravity in dilaton-based models, enhancing our understanding. Exploring boundary theories coupled to gravity, we derive a four-dimensional effective theory from the cosmological constant. Dilaton gravity is then scrutinized, revealing elegant solutions and insights into brane embedding. The analysis extends to probe scalar fields, employing the WKB approximation in both conformal and non-conformal cases. In summary, this work contributes to a nuanced understanding of the complex relationship between cosmology and gravity in dilaton-based frameworks.

In this work, in spite of Milne’s recommendation using the three-point Newton–Cotes open formula (Milne’s rule) as a predictor rule and three-point Newton–Cotes closed formula (Simpson’s rule) as a corrector rule for 4-th differentiable functions with bounded derivatives. There is still a great need to introduce such formulas in other Lp spaces. Often, we need to approximate real integrals under the assumptions of the function involved. Because of that, the aim of this work is to introduce several Lp error estimates for the proposed perturbed Milne’s quadrature rule. Numerical experiments showing that our proposed quadrature rule is better than the classical Milne rule for certain types of functions are provided as well.

The accuracy of estimating changes in terrestrial water storage (TWS) using Gravity Recovery and Climate Experiment (GRACE) level-2 products is limited by the leakage effect resulting from post-processing and the weaker signal magnitude in adjacent areas. TWS anomaly in Dnieper River basin, where characteristic with medium scale and adjacent weak TWS anomaly, is estimate in this work. Two categories of leakage error repaired method (including forward modeling, Data-driven, single and multiple scaling factor) are employed. Root mean square error (RMSE) and Nash-Sutcliffe Efficiency (NSE) are used to evaluate the efficiency of methods. Compare to independent methods, TWS anomaly inverted by multiple scaling factor depending on CPC Soil Moisture model is more accurate in terms with RMSE 2.32 and NSE 0.88, which scaling factors corresponding to trend term 1.02, annual term 1.04, and semi-annual term 1.14. Further, comprehensive climate insights behind of the TWS anomaly were confirmed. The temperate continental climate of this River basin is shown, according to the variation of TWS anomaly in spatial domain. Snowmelt is significant role in TWS anomaly of Dnieper River basin, which is accord with the precipitation record and the 14 years temperature spatial distribution of February. Overall, we compare TWS anomaly recovered by single and multiple scaling method, the leakage signal originates mainly from semi-annual term of the TWS anomaly.

Parasitic capacitance represents the main error source in measurement systems based on electrical impedance spectroscopy. The capacitive nature of electrodes’ impedance in tetrapolar configuration can give origin to phase errors when electrodes are coupled to parasitic capacitances. Nevertheless, reactive charges in tissue excitation systems are susceptible to instability. Based on such a scenario, mitigating capacitive effects associated with the electrode is a requirement in order to reduce errors in the measurement system. A literature review about the main compensation techniques for parasitic capacitance was carried out. The selected studies were categorized into three groups: (i) compensation in electronic instrumentation; (ii) compensation in measurement processing, and (iii) compensation by negative impedance converters. The three analyzed methods emerged as effective against fixed capacitance. No method seemed capable of mitigating the effects of electrodes’ capacitance, that changes in the frequency spectrum. The analysis has revealed the need for a method to compensate varying capacitances, since electrodes’ impedance is unknown.

One of the challenges in the healthcare sector is making accurate forecasts across insurance years for claims reserve. The state-of-the-art envisages various methods for estimating the claims reserve but without being applied to systems that do not present huge variability and heterogeneity, such as the healthcare sector. The methodology is based on generalized linear models using the Overdispersed Poisson distribution as shown in the state-of-the-art. In this context, we developed a method to estimate the parameters of the quasi-likelihood function using a Gauss-Newton algorithm optimized through a genetic algorithm. The genetic algorithm plays a crucial role in glimpsing the position of the global minimum to ensure a correct convergence of the Gauss-Newton method, where the choice of the initial guess is fundamental. The proposed methodology has been entirely developed using MATLAB and has been applied to estimate the claims reserve in the healthcare system of the Tuscany Region in Italy, as case study. The results obtained were validated by comparing them with the state-of-the-art by measuring the confidence intervals of the Overdispersed Poisson distribution parameters. Therefore local healthcare authorities could use the proposed and improved methodology to allocate the resources dedicated to healthcare and global management.

This paper presents a limited scope dynamic probabilistic risk assessment (D-PRA) on the survivability of commercial of the shelf (COTS) drones tasked with surveilling areas with varying radiation levels after a nuclear accident. The D-PRA is based on a discrete-dynamic event tree (D-DET) approach, which couples with the OpenEPL error propagation framework to model sequences leading to Loss of Mission (LOM) scenarios due to component failures in the drone’s navigation system. Radiation effects are simulated by calculating the total ionizing dose (TID) against the permissible limit per component, and errors are propagated within the electronic hardware and software blocks to quantify navigation system availability per radiation zone. The proposed methods are integrated into the traditional event tree/fault tree approach and the most vulnerable components are radiation-hardened (RAD-HARD) to the extent specified by a predefined mission success criterion. The results demonstrate the usefulness of the proposed approach in performing trade studies for incorporating COTS components into RAD-HARD drone designs.

Scientists are gradually becoming aware of the challenges in the understanding of the very root mechanisms of massively parallel computations that are observed in literally all scientific disciplines ranging from cosmology, physics, across chemistry, biochemistry, and ending in biology. This leads us to the main motivation and simultaneously to the central thesis of this review: “Can we design artificial, massively-parallel, self-organized, emergent, error-resilient, computational environments?” A large number of simulations along with examples and counter-examples, finalized by a list of the future directions, are giving hints and partial answers to the main thesis. This all together is opening the crucial question whether there is existing a deeper, beyond the Turing machine theoretical description of massively-parallel computing. Important information dealing with this topic is reviewed along with highly expressive animations generated by the open-source, Python software GoL-N24. The perspective, future directions including applications in robotics and biology of this research are discussed in the light of known information.

As renewable energy generation prediction system has been introduced into the energy trading market, making a model to accurately predict the quantity of solar photovoltaic (PV) energy generation has become a significant problem. Moreover, to encourage an accurate prediction of the quantity of energy generation, an incentive system has been implemented for those who predict the quantity of solar PV energy under the error rate of 8%. Therefore, it has become more important to investigate and analyze current prediction technology numerically and develop more advanced prediction system. In this study, we tried to develop a better model to improve the accuracy of solar PV energy generation quantity by comparing three models made with gradient boosting machine (GBM), Model 1, Model 2, Model 3 respectively. Model 1 was built with the whole training data set without any additional preprocessing. After conducting some additional preprocessing procedure to predict solar energy generation more accurately, we made Model 2 with the whole training data set and Model 3 with only upper 10% of energy generation capacity. To compare the accuracy of three models, normalized mean absolute error (nMAE) was used as an evaluation index. The nMAE of Model 1 was 9.64% while the Model 2 showed 8.41%. Also, Model 3, which was constructed with the training set of upper 10% energy generation capacity, outperformed with the nMAE of 8.08%. For further study, to check the effectiveness of models constructed with GBM, a time series model, autoregressive integrated moving average (ARIMA), was also built and the nMAE was compared.

As one of the fastest-growing new energy sources, wind power technology has attracted widespread attention from all over the world. In order to improve the quality of wind power generation, wind speed prediction is an indispensable task. In this paper, an error correction based Variational Mode Decomposition and Broad Learning System (VMD-BLS) hybrid model is proposed for wind speed prediction. First, the wind speed is decomposed into multiple components by the VMD algorithm, and then an ARMA model is established for each component to find the optimal number of sequence divisions. Second, the BLS model is used to predict each component, and the prediction results are summed to obtain the wind speed forecast value. However, in some traditional methods, there is always time lag, which will reduce the forecast accuracy. To deal with this, a novel error correction technique is developed by utilizing BLS. Through verification experiment with actual data, it proves that the proposed method can reduce the phenomenon of prediction lag, and can achieve higher prediction accuracy than traditional approaches, which shows our method’s effectiveness in practice.

This paper presents a calibration and thermal compensation method that aims to minimize cost and processing time while maintaining high accuracy. First, the number of positions to perform the calibration procedure is optimized, and then, based on this optimized calibration number, thermal compensation is performed, which is necessary for environments with large temperature variations, since calibration parameters change at different temperatures. The calibration procedures and algorithms were experimentally validated on marketed accelerometers. Based on the optimized calibration method, the calibrated results have been obtained nearly 100 times improvement. Thermal drift calibration experiments on the triaxial accelerometer show that the thermal compensation scheme in this paper can effectively reduce drift in the temperature range of -40°C to 60°C. The temperature drifts of x- and y-axes are reduced from -13.2 and 11.8 mg to -0.9 and -1.1 mg, respectively. The z-axis temperature drift is reduced from -17.9 to 1.8 mg. We have conducted various experiments on the proposed calibration method and demonstrated its capacity to calibrate the sensor frame error model (SFEM) parameters. Therefore, the MEMS sensors calibrated in this paper have certain engineering application values for tilt measurement.

People with Down syndrome have more visual problems than general population. They experience a premature aging, and it would be expected they will also have an acceleration in worsening visual function. A prospective observational study which includes visual acuity, refractive error, accommodation, binocular and colour vision was performed to young adults with (n=69) and without (n=65) Down syndrome and to a senior group (n=55) without Down syndrome. Results showed significant differences in visual acuity between groups (p<0.001) and it can be improved with a new prescription in 40% of the participants with Down syndrome. Regarding to accommodative state, no significant differences were found between groups of young people. Concerning binocular vision, 64.7% of strabismus was observed in the group with Down syndrome (p<0.001). Visual abnormalities are significant in young adults with Down syndrome and are different from those of older people without Down syndrome, some of which can be improved by providing the optimal prescription as well as regular eye examinations.

As a typical visual positioning system, monocular ranging is widely used in various fields. However, when the distance increases, there is a greater error. YOLOv8 network has the advantages of fast recognition speed and high accuracy. This paper proposes a method by combining YOLOv8 network recognition with a monocular ranging method to achieve target localization and grasping for the NAO robots. By establishing a visual distance error compensation model and applying it to correct the estimation results of the monocular distance measurement model, the accuracy of the NAO robot's long-distance monocular visual positioning is improved. Additionally, a grasping control strategy based on pose interpolation is proposed. Throughout, the proposed method's advantage in measurement accuracy was confirmed via experiments, and the grasping strategy has been implemented to accurately grasp the target object.

A method of accuracy error compensation for the time interval is examined, allowing to eliminate the dependence of accuracy error on the duration of measured intervals and minimising the influence of destabilising factors - ambient temperature changes and the initial deviation of the meter clock generator frequency from the nominal value. The compensation method is based on a calibration procedure that measures precise time intervals under conditions of changing ambient temperature. Then the dependence of the accuracy error on temperature for a particular meter is recorded. Based on these data, a correction table is compiled containing correction factors and temperature values at which these factors were determined. Under real measurement conditions, the correction factor corresponding to the current temperature is determined from the table for measured results correction. The table with correction factor values could be stored in the memory of the meter or processing computer. Experimental verification of the method showed that applying a correction for a meter with a standard XO class clock generator (certificated instability of ±50 ppm) can obtain an equivalent clock generator instability of ±0.15 ppm. The application of the method is efficient in cases where the use of high-end clocking to ensure the required measurement accuracy is not economically feasible.

The pathophysiology of Nonketotic Hyperglycinemia (NKH), a rare neuro-metabolic disorder associated with severe brain malformations and life-threatening neurological manifestations, remains incompletely understood. Therefore, a valid human neuronal model is essential. We aimed to investigate the impact of GLDC gene variants, which cause NKH, on cellular fitness during the differentiation process of human induced pluripotent stem cells (iPSCs) into iPSC-derived astrocytes and to identify sustainable mechanisms capable of overcoming GLDC deficiency. We developed the GLDC27-FiPS4F-1 line and performed metabolomic, mRNA abundance and protein analyses. The study showed that although GLDC27-FiPS4F-1 maintained the parental genetic profile, it underwent a metabolic switch to an altered serine-glycine-one-carbon metabolism with a coordinated cell growth and cell cycle proliferation response. We then differentiated the iPSCs into neural progenitor cells (NPCs) and astrocyte-lineage cells. Analysis showed that GLDC-deficient NPCs had shifted towards a more heterogeneous astrocyte lineage with increased expression of the radial glial markers GFAP and GLAST and the neuronal markers MAP2 and NeuN. In addition, we detected changes in other genes related to serine and glycine metabolism and transport, all consistent with the need to maintain glycine at physiological levels. These findings improve our understanding of the pathology and offer new perspectives for therapeutic options.

Tipping bucket rain gauges (TBRs) have been, and apparently will continue to be one of the most widely used pieces of equipment for rainfall monitoring, being frequently used for the calibration, validation and downscaling of radar and remote sensing data, due to their major advantages–low cost, simplicity, and low energy consumption. Thus, many works have focused and continue to focus on their main disadvantage–measurement biases (mainly in wind and mechanical underestimations). However, despite arduous scientific effort, calibration methodologies are not frequently implemented by monitoring networks operators or data users, propagating bias in databases and in the different applications of such data, causing uncertainty in the modeling, management, and forecasting in hydrological research, mainly due to a lack of knowledge. Within this context, this work presents a review of the scientific advances in TBR measurement uncertainties, calibration, and error reduction strategies from a hydrological point of view, by describing different rainfall monitoring techniques in Section 2, summarizing TBR measurement uncertainties in Section 3, focusing on calibration, and error reduction strategies in Section 4, a discussion and perspectives in Section 5, and conclusions in Section 6, providing an overview of the of the state of the art and future perspectives of the technology.

The bionic polarization imaging navigation sensor (BPINS) is a navigation sensor that provides absolute heading, and it is of practical engineering significance to model the measurement error of BPINS. The existing BPINSs are still modeled using photodiode-based measurements rather than imaging measurements and are not modeled systematically enough. This paper proposes a measurement model of BPINS that takes into account the geometric and polarization errors of the optical system. Firstly, the key error factors affecting the measurement accuracy of BPINS are systematically investigated and the Stokes vector-based measurement error model of BPINS is established. Secondly, based on its measurement error model, the effect of the error source on the measurement performance of BPINS is quantitatively analyzed by using Rayleigh scattering to generate scattered sunlight as a known incident light source. The experimental results show that the coordinate deviation of the principal point has a greater impact, followed by grayscale response inconsistency of CMOS and integration angle error of micro-polarization array, and finally lens attenuation. This finding can guide the subsequent calibration of BPINS, and the quantitative results provide an important reference for its optimal design.

This paper proposes a novel phase-resolved partial discharge (PRPD) sensor embedded in MV-class bushing for high-accuracy insulation analysis. The design, fabrication, and evaluation of a PRPD sensor embedded in MV-class bushing aimed to detect partial discharge (PD) pulses that are phase-synchronized with the applied primary HV signals. A prototype PRPD sensor was composed of a flexible printed circuit board (PCB) with dual-sensing electrodes, utilizing a capacitive voltage divider (CVD) principle for voltage measurement and D-dot principle for PD detection, and a signal transducer with passive elements. A PD simulator was prepared to emulate typical PD defects, i.e., a metal protrusion. The voltage measurement precision of the prototype PRPD sensor was satisfied with the accuracy class of 0.2 specified in IEC 61869-11, as the maximum corrected voltage error ratios and corrected phase errors in 80%, 100%, and 120% of the rated voltage (13.2 kV) were less than 0.2% and 10 minutes, respectively. In addition, the prototype PRPD sensor had good linearity and high sensitivity for PD detection compared with a conventional electrical detection method. According to performance evaluation tests, the prototype PRPD sensor embedded in the MV-class bushing can measure PRPD patterns phase-synchronized with the primary voltage without any additional synchronization equipment or system. Therefore, the prototype PRPD sensor holds potential as a substitute for conventional commercial PD sensors. Consequently, this advancement could lead to the enhancement of power system monitoring and maintenance, contributing to the digitalization and minimization of power apparatus.

In mobile applications such as geomagnetic surveying, two major effects hamper the use of optically pumped magnetometers: dead zones, sensor orientations where the sensors signal amplitude drops; and heading errors, a dependence of the measured magnetic field value on the sensor orientation. We present a concept for an omnidirectional magnetometer to overcome both these effects. The sensor uses two cesium vapor cells, interrogated by circularly-polarized amplitude-modulated laser light split into two beams running perpendicular to each other. This configuration is experimentally investigated using a setup wherein the laser beam and magnetic field direction can be freely adjusted relative to each other within a magnetically shielded environment. We demonstrate that a dead-zone free magnetometer can be realized with nearly isotropic magnetic-field sensitivity. While in the current configuration we observe heading errors emerging from light shifts and due to the nonlinear Zeeman effect, we introduce a straightforward approach to suppress these systematic effects in an advanced sensor realisation.

All sensing systems have some inherent error. Often, these errors are systematic, and observations taken within a similar region of space and time can have correlated error structure. However, the data from these systems are frequently assumed to have completely independent and uncorrelated error. This work introduces a correlated error model for GNSS-reflectometry (GNSS-R) using observations from NASA’s Cyclone Global Navigation Satellite System (CYGNSS). We validate our model against near-simultaneous observations between two CYGNSS satellites, and double difference our results with modeled observables to extract the correlated error structure due to the observing system itself. Our results are useful to catalogue for future GNSS-R missions and can be applied to construct an error covariance matrix for weather data assimilation.

In this paper, the problem of predicting future failure times based on a jointly type-II censored sample from k exponential populations is considered. The Bayesian prediction intervals and point predictors were then obtained. Generalized Bayes is a Bayesian study based on a learning-rate parameter. This study investigated the effects of the learning rate parameters on the prediction results. The loss functions of squared error, Linex, and general entropy were used as point predictors. Monte Carlo simulations were performed to show the effectiveness of the learning rate parameter in improving the results of prediction intervals and point predictors.

It has been known for nearly over 150 years that fatigue life data exhibits a considerable amount of variability. Furthermore, statistically modeling fatigue life adequately is challenging. Different empirical approaches have been used, each of which has merit; however, none is appropriate universally. Even when a sufficiently robust database exists, the scatter in the fatigue lives may be extremely large and difficult to characterize. The complications in empirical modeling are exacerbated for long life estimation when experimental observations are rare. The purpose of this work is to review traditional and more modern empirically based methodologies for estimating the cumulative distribution functions for fatigue life, given an applied load. To assess the applicability of the methods confidence bounds will be estimated. The analyses will be performed on an historic set of data for annealed aluminum wire tested in reverse torsion fatigue. These data are available in publications. It is recommended that a time dependent distribution function that is an based on principles of reliability that can be generalized for a variety of modeling applications should be considered for fatigue life estimation.

ORB (Oriented FAST and Rotated Brief) features are the most commonly used features in visual SLAM and visual odometry that have high computational speed, and rotation scale invariance. However, due to the homogenization of ORB features, the corner properties of specific features are poor in some artificial environments, and it can lead to poor matching performance when the environmental texture is not rich. The underlying reason is that the pixel grayscale changes in the less-richly textured regions on the image are not obvious, leading to a certain degree of mis-matching in the matching process. At the same time, when the camera motion speed is low, there is much overlap between adjacent frames. This results in minimal or almost no changes in the projection of feature points, and the system is highly sensitive to errors, In this case, even small errors can cause significant fluctuations in the calculation results. In response to the above issues, an improved feature point method for stereo vision mileage calculation is proposed to solve the problem of system stability deterioration when cameras move at low speeds in artificial envi-ronments. Firstly, weight calculation based on different texture regions is used to solve the problem of low corner properties of feature points caused by environmental texture differences. Then, keyframes are used for motion model estimation to improve the system's stability under low-speed motion. The experimental results of the dataset showed that the key frame rate was optimal between 10% and 12%, and the positioning accuracy was higher than these open-source systems compared with three common open-source VO systems.

Diversified techniques have been applied in many research papers for the optimization of rehabilitation robotic movements in order to maintain smoothness and accuracy. Smooth and precise control is needed necessarily for upper limb rehabilitation robotic applications having five degree of freedom. The preferred parameters which are used for the controlling were validated by mathematical model and these tuning parameters were optimized. Designing optimization algorithms to control complex physical robots has been a challenging task. In this study, a number of optimization techniques will be analyzed to determine the optimal parameters of a PID controller with a dynamic model of the upper limb rehabilitation system. For determining optimal control parameters for PID, there exists a number of tuning methods such as Zeigler Nichols and fuzzy logic which are classical methods. Swarm intelligence-based optimization algorithms are inspired by the behaviors of living things in nature. Several researchers have reported the optimal design of PID controller parameters using optimization techniques. The proposed control technique has been implemented on a 5-DOF RAX hardware and before any clinical trials, six healthy subjects went for trials under strict protocol. It has been discovered that the proposed control technique rejects the external unwanted disturbances as well as keeps the system stable under extreme perturbed and harsh conditions. In this research paper mathematical models have been validated to determine the PID parameters for the optimization. The comparative study is carried out with four different cost functions since a well-designed objective function leads to better performance of the system and indicates control design expectations. These objective functions are an integral squared error (ISE) and integral absolute error (IAE). In this research work, the effects of different cost functions on optimization techniques for controller parameters were analyzed. The performance of the controller with different cost functions has examined for robustness analysis. The cost function of particle swarm optimization, Firefly, Ant Bee Colony and Ant Colony optimization were developed for the better optimization results.

Laser scanning 3D imaging technology, because it can get accurate three-dimensional surface data, has been widely used in the search for wrecks and rescue operations, underwater resource development, and other fields. At present, the conventional underwater rotating laser scanning imaging system maintains a relatively fixed light window. However, in low-light situations underwater, the rotation of the scanning device causes some degree of water fluctuation, which warps the light strip data that the system sensor receives about the object's surface. To solve the problem, this research studies an underwater 3D scanning and imaging system that makes use of a fixed-light window and a spinning laser (FWLS). A refraction error compensation algorithm is investigated that is based on the fundamentals of linear laser scanning imaging and the dynamic refraction mathematical model is established by the motion of the imaging device. During the imaging process, the incident angle between the laser and the light window varies due to the scanning mode of the system. The experimental results show that the reconstruction radius error is reduced by 60% (from 2.5 mm to about 1 mm) when the measurement data for a standard sphere with a radius of 20 mm are compensated. Moreover, the compensated point cloud data exhibits a higher degree of correspondence with the model of the standard spherical point cloud. This study has a specific reference value for the refractive error analysis of an underwater laser scanning imaging system, and it provides certain research ideas for the subsequent refractive error analysis of various scanning imaging modalities.

Magnetic Resonance Imaging (MRI) is widely used in clinics and research due to its accurate disease identification and non-invasive nature. MRI is based on Nuclear Magnetic Resonance (NMR), which is also extensively employed in various fields. NMR and its modern versions involve intricate pre-processing steps before data analysis. These steps are initially processed in the time domain and subsequently in the frequency domain. While our previous review focused on time domain pre-processing (https://www.preprints.org/manuscript/202310.2032/v1), this review delves into the mathematical and statistical aspects of frequency domain pre-processing. We discuss essential pre-processing steps like phase error correction, baseline correction, solvent filtering, calibration and alignment, reference deconvolution, binning/bucketing and peak picking, peak fitting/deconvolution and compound identification, integration and quantification, normalization and transformation. Furthermore, we offer practical recommendations for each step.

Spatial regression models have garnered significant attention across several disciplines, including functional magnetic resonance imaging analysis, econometrics, home price analysis, and many other domains. The phenomenon of sparsity is often found in nature, when a limited number of factors contribute significantly to the overall variation. Spatial regression models frequently use sparsity to indicate less complex computational and more superficial covariance structures. The spatial error model is a significant spatial regression model that focuses on the geographical dependence present in the error terms rather than the response variable. This study proposes an effective approach for estimating the vector of regression coefficients in the spatial error model, taking into consideration of the prior knowledge that some coefficients are insignificant and there is multicollinearity among the regressors. It also introduces pretest and shrinkage ridge estimators for spatial error regression models, evaluating their performance compared to traditional maximum likelihood estimators. It also assesses their efficacy using real-world data and bootstrapping techniques for comparison purposes.

Verifying the accuracy of a 3D-printed object involves using an image processing system. This system compares images of the CAD model of the object to be printed with its 3D-printed counterparts to identify any discrepancies. It is important to note that the integrity of the accuracy measurement is heavily dependent on the image processing settings chosen. This study focuses on this issue by developing a customized image processing system. The system generates binary images of a given CAD model and its 3D-printed counterparts and then compares them pixel-by-pixel to determine the accuracy. Users can experiment with various image processing settings, such as grayscale to binary image conversion threshold, noise reduction parameters, masking parameters, and pixel-fineness adjustment parameters, to see how they affect accuracy. The study concludes that the grayscale to binary image conversion threshold has the most significant impact on accuracy and that the optimal threshold varies depending on the color of the 3D-printed object. The system can also effectively eliminate noise (filament marks) during image processing, ensuring accurate measurements. Additionally, the system can measure the accuracy of highly complex porous structures where the pores size, depth, and distribution are random. The insights gained from this study can be used to develop intelligent systems for the metrology of additive manufacturing.

The splitting method developed in a previous study for linear, multi – component, convection-diffusion mass transfer equations is extended to non-linear, multi-component, convection-diffusion mass transfer equations. The diffusion term is non-linear (the diffusion coefficients depend on chemical species concentrations). Theoretical results about the splitting error are presented, as well as numerical simulations for mixtures with n ≤ 5. The numerical experiments show second-order accuracy and stability for the present splitting algorithm.

This study presents the numerical investigation of bioconvective nanofluid (NF) flow compris-ing gyrotactic microorganisms through convective boundary conditions (CBC) enclosing heat and mass transmission analysis above an inclined extending cylinder. Via appropriate transfor-mation, the set of Partial Differential Equations is transformed into a scheme of nonlinear ODEs. A new set of variables are presented in the directive to get the first-order convectional equations and, then solved numerically by using bvp4c. The influence of several factors on velocity, ener-gy, concentration, and the density of motile microorganisms (DMM) is investigated and exam-ined. The analysis describes and addresses all physical measures of concentration such as Skin Friction (SF), Sherwood number (SN), DMM, and Nusselt number (NN). The present conse-quences display a validation with published. For confirmation of bvp4c, the ND-solve approach is also applied. Error analysis is also examined for the confirmation of the mathematical model.

During the hand-eye calibration process of the manipulator, the Euclidean distance error of the calibration results cannot be calculated because the true values of the hand-eye conversion matrix cannot be obtained. In this paper, a new method of projection error analysis is presented. Error analysis is carried out by using a priori knowledge that the location of AR markers is fixed in the calibration process. The coordinates of the AR marker center point are reprojected to the pixel coordinate system, and then compared with the true pixel coordinates of the AR marker center point obtained by corner detection or manual labeling in order to obtain the Euclidean distance between the two coordinates as the basis for error analysis. Experimental results show that the proposed optimization method can greatly improve the accuracy of hand-eye calibration results.

In Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a longstanding open problem from Convex and Discrete Geometry, it is essential to estimate covering functionals of convex bodies effectively. Recently, He et al. [J. Optim. Theory Appl. 2023, 196, 1036–1055.] and Yu et al. [Mathematics, 2023, 11, 2000] provided two deterministic global optimization algorithms having high computational complexity for this purpose. Since satisfactory estimations of covering functionals will be sufficient in Zong’s program, we propose a stochastic global optimization algorithm based on CUDA and provide an error estimation for the algorithm. The accuracy of our algorithm is tested by comparing numerical and exact values of covering functionals of convex bodies including the Euclidean unit disc, the three-dimensional Euclidean unit ball, the regular tetrahedron, and the regular octahedron. We also present estimations of covering functionals for the regular dodecahedron and the regular icosahedron.

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geometric means finally help to systematically derive handy formulas that approximate the inverse error function. Our approach can be used for applications in e.g. high-speed Monte Carlo simulations where this function is used extensively.

With the use of linear regression modeling, this study sought to forecast and analyze rainfall patterns in Ethiopia. The dataset included historical rainfall data as well as pertinent independent variables. The R-squared score and mean squared error (MSE) were used to assess the effectiveness of the linear regression model. The results showed that the model's ability to forecast and analyze rainfall patterns was not very good. Only around 5.3% of the variance in rainfall could be explained by the chosen independent variables, according to the R-squared score of 0.053. This low number indicated that there was little correlation between the selected variables and rainfall, and that a sizable percentage of the variation in the dependent variable was not captured by the model. The model's accuracy in forecasting rainfall was shown to be quite low by the MSE error, with significant squared discrepancies between the expected and actual amounts. These results support the notion that the linear regression model as it is now designed is not appropriate for studying or forecasting Ethiopia's rainfall patterns. Alternative modeling approaches, the inclusion of other pertinent factors, and the assurance of the availability of high-quality data that faithfully captures the intricate dynamics of rainfall in the area all require more investigation.

Drafting formations have been long recognized as highly effective for reducing drag and enhancing athletic performance, particularly in race walking events. The precise spacing and positioning of the race walkers are critical to optimizing the effectiveness of drafting. In this study, the drag reduction of 15 drafting formations is investigated using wind-tunnel experiments and CFD numerical simulations. The results show excellent consistency in drag reduction rate between the two methods, with differences being within 10%. This can be attributed to spacing replacing body shape differences as the primary factor influencing drag reduction. Optimal double, triple, and quadruple drafting formations produce the same results in both wind-tunnel experiments and CFD simulation, resulting in drag reductions of 67%, 66%, and 81% (wind-tunnel) and 65%, 72%, and 85% (CFD). The sources of drag differences in the two methods are discussed from various aspects. The flow field obtained through CFD analysis is used to examine the mechanism of drag reduction, revealing that drafting formations have a significant shielding effect on incoming air, which reduces the number and speed of airflow impacting the core race walker. This shielding effect is identified as the primary cause of drag reduction. Using an empirical model for mechanical power output, optimal double, triple, and quadruple drafting formations enhance sport economy (4.4-5.7%), speed (3.61-4.67%), and performance (173.8-223.3s) compared to race walking alone. The findings can serve as a reference for race walkers' positioning strategy and provide insights for considering drafting formations in various running events.

This study explores the prediction of concrete compressive strength using machine learning models, aiming to overcome the time-consuming and complex nature of conventional methods. Four models—Artificial Neural Network, Multiple Linear Regression, Support Vector Machine, and Regression Tree—are employed and compared for performance. Evaluation metrics such as Mean Absolute Deviation, Root Mean Square Error, Coefficient of Correlation, and Mean Absolute Percentage Error are used. After preprocessing 1030 samples, the dataset is split into 70% for training and 30% for testing. The ANN model, further divided into training, validation (15%), and testing (15%), outperforms others in accuracy and efficiency. This outcome streamlines compressive strength determination in the construction industry, saving time and simplifying the process.

The pointing accuracy of large radio telescopes is affected by antenna structure errors, installation errors, servo errors, gravity, and varying environmental factors. It is hard to estimate the pointing error of radio telescopes under solar radiation via the traditional multi-parameter static pointing models, due to the time-varying characteristics of the dynamic pointing error. There is still no effective way to estimate the dynamic pointing error of large radio telescopes under solar radiation up to now. To estimate the dynamic pointing error of large radio telescopes under solar radiation, a new way based on digital twin(DT) is tried in this paper. The operational framework of the DT system of large radio telescopes is introduced first. Then, the Wuqing 70-m radio telescope(WRT70) is taken as the research object, the digital models of which are created. Finally, the reliability of the WRT70's DT system is verified and the dynamic pointing error of WRT70(staying at the position of the elevation angle of 90° and the azimuth angle of 180°) on two sunny days in different seasons is estimated by the created DT system. The research results show that the pointing error of large radio telescopes under solar radiation fluctuates greatly and the seasonal differences are very striking. The maximum elevation pointing error of WRT70 under solar radiation around the winter solstice is over 40 arcsec, which should never be ignored. The way is feasible to estimate the dynamic pointing error of large radio telescopes staying at a specific position under solar radiation via constructing a DT system in this paper, but it is not yet able to estimate effectively the dynamic pointing error of large radio telescopes being in action. It is expected to establish a dynamic pointing error model and calibrate the dynamic pointing errors of large radio telescopes being in action by DT technology in the future.

This research highlights the importance of error-correcting codes in ensuring secure and efficient data transmission over noisy channels. It discusses the application of Convolutional codes and the Viterbi algorithm for error detecting and correcting in applications where the data rate is high and the error probability is relatively low. This research extends beyond previous studies by conducting a comparative analysis of Convolutional codes, the Viterbi algorithm, and alternative coding methods utilized in satellite communication systems, by evaluating their effectiveness and efficiency relative to other coding approaches like BCH, LDPC, and turbo codes. The evaluation encompasses key performance metrics including error correction capabilities, computational complexity, and robustness against various error types. Additionally, practical implementation factors such as power consumption, computational requirements, and compatibility with existing hardware are considered. The analysis sheds light on the advantages and disadvantages of each coding method, offering insights into why convolutional codes and the Viterbi algorithm are particularly suitable for GPS systems.

This enables the chip to regulate the voice recognition function of the gadget, leading to a more natural and human-like process. Integrating this technique into the English language voice recognition system can greatly improve its precision in identifying the speech of a particular person. This research seeks to investigate and create an automatic error detection technique for an embedded speech instruction recognition system for English using artificial intelligence. The study commences with a conventional introduction to artificial intelligence, thereafter delving into a comprehensive investigation of the speech recognition algorithm. The MATLAB programme is used to determine the accurate number of words recognised by the system and its accuracy rate. The embedded teaching recognition system for English is then tested in different contexts to assess its performance. Several tests are performed to compare and analyse the results, which indicate that the integrated English voice recognition system achieves an accuracy rate of over 90% and has a low error rate in a calm environment. In a bustling environment with numerous auditory stimuli, the accurate recognition rate typically exceeds 60%.

This study aims to focus on using the Volterra series and machine learning for forecasting random and chaotic wind speed regimes, since the calm weather is mostly noticed at the local site, making the dataset selection difficult. A novel method is proposed to predict Volterra kernels up to the third order, using a forward-back propagation neural network with 12-month measurements at Fujairah site (UAE). Both daily and monthly wind speed data sets are investigated for forecasting. The three dominant hourly and daily kernels are extracted for each day and each month. Predicted future Volterra kernels are estimated from past values using both statistical analysis and individual neuro networks for each of the Volterra kernel coefficients. Due to the random nature of wind speed at the local site, a two-layer with 4 neurons per layer neuro network is used to locate the most variable and intense speed during 8-hours in the day. Forecasted wind speed is determined with errors arising from different sources such as the utilization of only 3rd-order Volterra kernels and the difficulty of machine training of the employed shallow network. Nevertheless, this work depicts a useful algorithm to forecast chaotic and random wind speed regimes. Computational time is a trade of the complexity of Volterra mathematical analysis.

In this paper, we consider the fourth-order parabolic equations with integer and fractional order time derivatives with Neumann boundary conditions. The integer order time derivatives are approximated by backward Euler difference quotients, and the fractional order time derivatives are approximated by L1 interpolation. We propose the block-centered finite difference scheme for fourth-order parabolic equations of integer and fractional order time derivatives. We prove the stability of the block-centered finite difference scheme and the second-order convergence of the discrete L2 norms of the approximate solution and its derivatives of every order. Numerical examples are given to verify the effectiveness of the block-centered finite difference scheme.

Purpose: To compare refractive prediction error (PE)s between phacotrabeculectomy and phacoemulsification. Methods: Refractive PE was defined as the difference of spherical equivalent between the predicted value using the Barrett Universal II formula and the actual value obtained at postoperative one month. Forty-eight eyes that had undergone phacotrabeculectomy (19 eyes, open-angle glaucoma; 29 eyes, angle-closure glaucoma) were matched with 48 eyes that had undergone phacoemulsification by age, average keratometry value and axial length (AL), and their PEs were compared. The factors associated with PE were analyzed by multivariable regression analyses. Results: Phacotrabeculectomy group showed a larger absolute PE compared to the phacoemulsification group (0.51 ± 0.37 Diopters vs. 0.38 ± 0.22, P=0.033). Larger absolute PE was associated with longer AL (P=0.010) and higher intraocular pressure (IOP) difference (P=0.012). Hyperopic shift (PE>0) was associated with shallower preoperative anterior chamber depth (ACD) (P=0.024) and larger IOP difference (P=0.031). In the phacotrabeculectomy group, the PE was inversely correlated with AL: long eyes showed myopic shift and short eyes hyperopic shift (P=0.002). Conclusions: Surgeons should be aware of the possibility of worse refractive outcomes when planning phacotrabeculectomy especially in eyes with high preoperative IOP, shallow ACD, and/or extreme AL.

The special affine Fourier transform (SAFT) is a useful and powerful analyzing tool in signal processing, optics and communications. In this paper, we mainly discuss the randomized nonuniform sampling and reconstruction for random signals bandlimited in the SAFT domain. First, we show that the nonuniform sampling is identical to the uniform sampling after a pre-filter in the sense of second order statistic characters. Then, we propose an approximate reconstruction based on sinc interpolation for the nonuniform sampling of random signals bandlimited in the SAFT domain. Finally, we give the mean square error estimate for the proposed approximate recovery approach.

Highly-skilled migrants and refugees finding employment in low-skill vocations, despite professional qualifications and educational background, has become a global tendency, mainly due to the language barrier. Employment prospects for displaced communities are mostly decided by their knowledge of the sublanguage of the vocational domain they are interested in working. Common vocational domains include agriculture, cooking, crafting, construction, and hospitality. The increasing amount of user-generated content in wikis and social networks provides a valuable source of data for data mining, Natural Language Processing and machine learning applications. This paper extends the contribution of the authors’ previous research on automatic vocational domain identification by further analyzing the results of the machine learning experiments with the domain-specific textual data set, considering 2 research directions: a. predictions analysis and b. data balancing. Wrong predictions analysis and the features that contributed to misclassification, along with correct predictions analysis and the features that were the most dominant, contributed to the identification of a primary set of terms for the vocational domains. Data balancing techniques were applied on the data set to observe their impact on the performance of the classification model. A novel 4-step methodology is proposed in this paper for the first time, consisting of successive applications of SMOTE oversampling on imbalanced data. Data oversampling obtains better results than data undersampling in imbalanced data sets, while hybrid approaches perform reasonably well.

The Earth’s synthetic gravitational and density models can be used to validate numerical procedures applied for a global (or large-scale regional) gravimetric forward and inverse modelling. Since the Earth’s lithospheric structure is better constrained by tomographic surveys than a deep mantle, most of existing 3-D density models describe only a lithospheric density structure, while 1-D density models are typically used to describe a deep mantle density structure below the lithosphere-asthenosphere boundary. The accuracy of currently available lithospheric density models is examined in this study. The error analysis is established to assess the accuracy of modelling the sub-lithospheric mantle geoid, while focusing on the largest errors (according to our estimates) that are attributed to lithospheric thickness and lithospheric mantle density uncertainties. Since a forward modelling of the sub-lithospheric mantle geoid comprises also numerical procedures of adding and subtracting gravitational contributions of similar density structures, the error propagation is derived for actual rather than random errors (that are described by the Gauss’ error propagation law). Possible systematic errors then either lessen or sum up after applying particular corrections to a geoidal geometry that are attributed to individual lithospheric density structures (such as sediments) or density interfaces (such as a Moho density contrast). The analysis indicates that errors in modelling of the sub-lithospheric mantle geoid attributed to lithospheric thickness and lithospheric mantle density uncertainties could reach several hundreds of meters, particularly at locations with the largest lithospheric thickness under cratonic formations. This numerical finding is important for a calibration and further development of synthetic density models of which mass equals the Earth’s total mass (excluding the atmosphere). Consequently, the (long-to-medium wavelength) gravitational field generated by a synthetic density model should closely agree with the Earth’s gravitational field.

The straightness error of guideway is one of the key indicators of ultra-precision machine, which plays an important role in the machining accuracy of work-piece. In order to measure straightness error of long distance ultra-precision guideway accurately, a splicing measurement for straightness error of guideway using high-precision flat mirror and displacement sensor was proposed in this paper, and the data splicing processing algorithm based on coordinate transformation was studied. Then comparative experiments on splicing measurement and direct measurement of straightness error were carried out on a hydrostatic guideway grinder. The maximum difference between the two measurements was about 0.3μm, which was far less than the straightness error of 5.8μm. The experiment demonstrated the correctness of the proposed splicing measurement method and data processing algorithm. To suppress the influence of straightness error on machining accuracy, a straightness error compensation algorithm based on error rotation transformation and vertical axis position correction was proposed, and the grinding experiment of a plane optics with size of 1400mm×500mm was carried out, whose flatness error after grinding was about 2.98μm. The straightness error of the grinding machine had been well suppressed.

The paper presents an error model of a measurement chain containing link performing discrete wavelet transform algorithm which is most often the last stage of measurement signal processing. The goal is to determine the uncertainty budget of the input quantities of the wavelet transform algorithm. The error model takes into account parts of analog, analog-to-digital and digital processing, describing the properties of subsequent fragments of the chain using their transmittance and processing functions. The proposed model enables the description of both deterministic and non-deterministic properties of signal errors. The proposed model was validated using an example measurement chain created for this purpose.

In this paper, the Phase-Scheduled-Command FXLMS algorithm with the phase error between the disturbance and command signal is analyzed in detail. The influence of the phase error on the convergence time constant, convergence rate, and performance of convergence is explained for both stationary and nonstationary disturbance signals case. For stationary disturbance, the phase error slightly increases the convergence rate but heavily increases the distance of the optimum vector from the initial value, leading to poor convergence time constant performance. For nonstationary disturbance, the existence of phase error leads to poor convergence performance in every step, resulting in poor sound profiling performance. And the estimation of the phase error influence is developed in the closed form. Simulations are performed to demonstrate the validity of the analysis results.

Critical distance concerns precise digital levelling, which has inaccurate results at a certain sighting distance. The influence of critical distance on a measured height difference has been confirmed by calibrating certain digital levels and their appropriate code devices on a vertical comparator under laboratory conditions. The paper describes the research based on experimental measurements done to find the influence of critical distance on height differences obtained by precise digital levels of Leica NA3003 and DNA03. The processing of the measurement results consisted of de-fining a random error on a station by using parameter estimation of an error model to specify a partial error on a station dependent on sighting distance and then the processing phase continues with the finding the relation between sighting distance and dispersion of height differences ac-quired by digital levelling under terrain conditions. The theoretical part involves the development of levelling accuracy theories that vary over time by view on random and systematic error propagation. The numerical and graphical solution of the experimental measurements involves ordering the height differences into sighting groups according to the sighting distances and the computed standard deviations, which represent a measure of height differences dispersion. The suspicious sighting groups are highlighted in the table and compared with theoretical data pro-vided by authors of calibrating the same digital levels

Introduction: While preparing for dive exams, divers are trained to perform rescue exercises. Currently, divers think they will manage and control their body at any time.Methods: At the bottom of the water, the student takes the instructor who simulates a sickness, up to the surface, by controlling the going up. Then, if the exercise is wrong, both divers go down and exercise again. If the exercise is successful, both divers go down to perform another exercise until they are tired or until they have no more air. Results: I discovered that there was a mistake in the preparation of divers for rescue training due to Descartes’ error, “I think, thus I am”, which is part of our collective memory. Going up and going down after a sickness simulation is a repetitive action of the body and going down is therefore part of the automatisms of rescue, which is very dangerous. Conclusions: The body is not necessarily controlled by the present thinking, and if divers forget sickness while going up in a real rescue situation, they will go down automatically because their bodies were trained like this. In addition, it is very easy to forget sickness. Divers should not go down after rescue, they should be on the dive boat or on the land. Descartes’ error has to be reversed: “I am, thus I think” is right. The divers’ rescue exercises must be simplified and divers should never go down after the simulation of a sickness.

This paper studies the maximum reliability of multi-hop relay UAV, in which UAV provides wireless services for remote users without direct communication link on the ground as a coded cooperative relay. In this paper, the analytical expressions of total power loss and total bit error rate are derived as reliability measures. Firstly, based on the environmental statistical parameters, a LOS probability model is proposed. Then the problem of minimizing the bit error rate of static and mobile UAVs is studied. The goal is to minimize the total bit error rate by jointly optimizing the height, elevation, power and path loss, and subject to the maximum allowable path loss con-straints, transmission power allocation constraints and UAV height and elevation constraints. At the same time the total path loss is minimized to achieve maximum ground communication cov-erage. However, the formulated joint optimization problem is non-convex and generally difficult to solve. Therefore, we decomposed the problem into two subproblems and proposed an effective joint optimization iteration algorithm. Finally, the simulation results are given, and the analysis shows that the optimal height of different reliability measures is slightly different, and using the mobility of UAVs can improve the reliability of communication performance.

Although data acquisition is a very usual technique, there are several aspects not always considered, as synchronization of acquired measures and evaluation of the errors that derive from this fact. The paper hereby aims to point this thing out, by mathematical determination of the necessary correction and implementing the software meant to evaluate the performances of the acquisition system. As an example, a three-phased acquisition system has been developed in order to monitor the currents and voltages on the three phases. Also other measures have been calculated, such as power and phase. The components on each phase don’t have to be fully identified because a whole system calibration can be made in the first stage. Calibration consists in finding the weighting coefficients for each quantity. The implemented solution for three-phased measures data acquisition starts from the hypothesis of a sampling frequency that respects Shannon theorem. The distance between two samples is small enough to consider a linear evolution between two moments for the same measure. Errors that affect the above mentioned, due to the different moments of time when samples are acquired, are analyzed and brought to the minimum value.

Due to the particular structure of the beveloid gear, it can’t be hobbed directly by an ordinary gear hobbing machine. The existing processing method is complex and high-cost. Therefore, the mass production and industrialization of beveloid gears are limited. To improve the machining efficiency and accuracy of processing beveloid gears, we proposed a hobbing method via the modification of ordinary hobbing machines. At first, we completed the derivation and calculation of the relevant processing parameters of the beveloid gear based on the study of the structural characteristics of the beveloid gear and the principle of hobbing machining. Then, we proposed and designed a beveloid gear hobbing method, and the modification of the ordinary hobbing machine was completed by using a hanging wheel mechanism in synchronous belt type. Finally, we completed the actual hobbing of the beveloid gear, and the feasibility of the proposed method was verified. After that, we analyzed the machining error of the trial-produced beveloid gear, the results showed that the accuracy of the trial-produced beveloid gear met the 6-level standard, which also verified the accuracy of the proposed method.

We are losing love. By studying porn movies to understand love, I discovered that love originally comes from the body, from positive emotions and vibrations of the wonderful body, from the heart and all other parts of the body, such as sexual organs. António Damásio made Descartes’ error by postulating that feelings increase their power from homeostasis (mechanisms of life regu-lation from bacteria to humans). He made this mistake unconsciously because many people un-consciously have a very bad opinion of sexual organs. We consider them ugly because they come from the prehistoric period. I have combined António and Hanna Damásio’s work (body emotions, thinking and language). I discovered that porn actors do not talk during sex, and this is striking. Porn actors mirror what happens in society. This means that people come from prehistory, do not talk during sex, and still unconsciously behave like primitive animals during sexual intercourse; we do not respect the body sufficiently during sex. Therefore, love, which comes from the body, is smothered and buried. We must very delicately talk to the wonderful, delicious and respectful body to wake up love feelings, body emotions and vibrations during sex. We must invent talking movies with porn films. Language of positive emotions associated with the language of wonderful and delicious body will warm love feelings and will give envy to love through sexual intercourse because António Damásio discovered that emotions are social.

We consider a coded compressed sensing protocol for unsourced massive random access (URA) that concatenates a shared Patterned Reed-Muller (PRM) inner codebook to an outer error-correction code. In this paper, an iterative list PRM projection algorithm is proposed to supplant the signal detector associated with the inner PRM sequences. In particular, we first propose an enhanced paths-saving algorithm called list PRM projection detection for the single-user scenario that keeps multiple candidates for the first few layers to remedy the risk of spreading errors. On this basis, we further propose an iterative list PRM projection algorithm for the multi-user scenario. The vectors for PRM codes and channel coefficients are jointly detected in an iterative manner, which offers significant improvements regarding the convergence rate for signal recovery. Furthermore, the performances of the proposed algorithms are analyzed mathematically, and we verified that the theoretical simulations are consistent with the numerical simulations. Finally, we concatenate the inner PRM codes that employ the iterative list detection to two practical error-correction outer codes. According to the simulation results, we conclude that the packetized URA with the proposed iterative list projection detection works better than benchmarks in terms of the number of active users it can support in each slot and the amount of energy needed per bit to meet an expected error probability.

The inverse finite element method (iFEM) is a novel method for reconstructing the full-field displacement of structures by discrete measurement strain. In practical engineering applications, the accuracy of iFEM is reduced due to the positional offset of strain sensors during installation, and errors in structural installation. Therefore, coarse and fine two-stage calibration (CFTSC) method is proposed to enhance the accuracy of the reconstruction of structures. Firstly, the coarse calibration is based on a single-objective particle swarm optimization algorithm to optimize the displacement-strain transformation matrix related to the sensor position. Secondly, as selecting different training data can affect the training effect of self-constructed fuzzy networks, this paper proposes to screen the appropriate training data based on residual analysis. Finally, the experiments of the wing integrated antenna structure verify the efficient of the method on the reconstruction accuracy of the structural body displacement field.

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

The development of a Digital Track Model (DTM) within Kazakhstan's railway system presents an innovative approach to enhancing efficiency and safety across the network. This paper investigates the economic viability of DTM implementation, offering a comprehensive mathematical model that highlights potential reductions in maintenance costs and improvements in system accuracy and durability. The findings advocate for DTM's potential to significantly elevate railway operations, suggesting a pivotal step towards modernizing Kazakhstan's transit infrastructure.

In view of the limitations of the existing eccentricity error separation method of the rotary table, an eccentricity error separation method based on the phase feature of the moiré signal of single reading head is proposed herein. A grating pair transmission model is established based on the analysis of the principle of the rotary table, thereby the influence of eccentricity error on the phase feature of the moiré signal in the rotation course of the rotary table is clarified, and the corresponding model between the phase feature spectral components and the eccentricity error is established. The verification experiments of the proposed method are carried out based on the laboratory-made circuit system. After verifying the accuracy of the data acquisition of the laboratory-made circuit board, the verification experiments of the eccentricity error separation effect of the proposed method are carried out. The experimental data are compared with those of the traditional method and the results show that the error between the two methods is 2.34μm and the relative error is 2.3%.

This paper presents two control design strategies for voltage regulation in a single inductor dual output (SIDO) DC-DC Buck converter system. Based on a nominal multiple input multiple output (MIMO) plant model and performance requirements, both an LQR and a decoupled PI control laws are designed to control the power converter system, under parametric uncertainties such as voltage source variation, CPL power variation, and load resistance variation. Therefore, the SIDO converter can cascade operating, which may cause the undesired effects of voltage oscillation and reduce the system's stability margin. The control performance was assessed under both uncertainties resistive loading and power variation of a constant power load (CPL). A SIDO DC-DC Buck converter board has been developed for experimental tests. The experimental results show that the LQR strategy, compared to the PI strategy, presented a robust performance in the presence of parametric uncertainties in the resistive loads being, however, sensitive to uncertainties due to the presence of CPL loads.

To obtain a better estimation frequency band for source bearing estimation, source bearing estimation experiments using an ice-mounted geophone were performed at three sites on the Arctic ice cap. By transforming to the frequency domain, errors of the bearing estimation in a number of frequency bands within 1000 Hz and the horizontal peak displacements received by the geophone in the corresponding frequency bands were obtained. After comparing the variation of errors to the peak displacements in the same frequency band, it is found that the errors are related to the peak displacements, and higher peak displacement values mean smaller errors. When the incident angle of the acoustic source and the ice thickness meet certain conditions, some modes of the Lamb waves of the ice plate are excited, the peak displacements at the same frequency band are increased, the errors of bearing estimation are reduced, and the effective frequency band for bearing estimation is broadened. These results provide some new ideas for the bearing estimation of acoustic sources beneath Arctic ice.

Aimed for the difficulty and complexity of detecting the piston error for segmented telescope, this paper proposed a new piston error measurement method based on a hybrid artificial neural net-work. Firstly, we use Resnet network to learn the mapping relationship between the focal plane degradation image and the signs of the piston error. Then, based on the established theoretical re-lationship between modulation transfer function and the piston error, BP neural network is used here to learn the mapping relationship between the MTF and the absolute value of the piston error. After the training of the hybrid network is completed, a wide-range and high-precision detection of the piston error of the sub-mirrors can be achieved using the combined output of the two net-works only a focal plane image of a point source with broadband illumination is used as input. The detection range can reach the whole coherent length of the input broadband light, and the detec-tion accuracy can reach 10nm. The method proposed in this paper has the advantages of high de-tection accuracy, wide detection range, low hardware cost, small network scale and low training difficult.

The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wright function. The article demonstrates finite representations of the Wright function in terms of sums of generalized hypergeometric functions, which in turn provide connections with the theory of the Gaussian, Airy, Bessel, and Error functions, etc. The main application of the presented results is envisioned in computer algebra for testing numerical algorithms for the evaluation of the Wright function.

In this paper, we shall introduce the interval-valued spatial error model. Based on the idea of least square method of single-valued case, we give the parameter estimator for interval-valued spatial error model. The theoretical properties of the proposed estimator are proved. Finally, we give the numerical analysis and a real example.