Parameters Of Normal Distribution Research Articles

On Inference of Weitzman Overlapping Coefficient ∆(X,Y) in the Case of Two Normal Distributions

The Weitzman overlapping coefficient ∆(X,Y) is the most important and widely used overlapping coefficient, which represents the intersection area between two probability distributions. This research proposes a new general technique to estimate ∆(X,Y) assuming the existence of two independent random samples following normal distributions. In contrast to some studies in this scope that place some restrictions on the parameters of the two populations such as the equality of their means or the equality of their variances, this study did not assume any restrictions on the parameters of normal distributions. Two new estimators for ∆(X,Y) were derived based on the proposed new technique, and then the properties of the estimator resulting from taking their arithmetic mean was studied and compared with some corresponding estimators available in the literature based on the simulation method. An extensive simulation study was performed by assuming two normal distributions with different parameter values to cover most possible cases in practice. The parameter values were chosen taking into account the exact value of ∆(X,Y), which taken to be small (close to zero), medium (close to 0.5) and large (close to 1). The simulation results showed the effectiveness of the proposed technique in estimating ∆(X,Y). By comparing the proposed estimator of ∆(X,Y) with some existing corresponding estimators, its performance was better than the performances of the other estimators in almost all considered cases.

Spatiotemporal factor models for functional data with application to population map forecast

The proliferation of mobile devices has led to the collection of large amounts of population data. This situation has prompted the need to utilize this rich, multidimensional data in practical applications. In response to this trend, we have integrated functional data analysis (FDA) and factor analysis to address the challenge of predicting hourly population changes across various districts in Tokyo. Specifically, by assuming a Gaussian process, we avoided the large covariance matrix parameters of the multivariate normal distribution. In addition, the data were both time and spatially dependent between districts. To capture various characteristics, a Bayesian factor model was introduced, which modeled the time series of a small number of common factors and expressed the spatial structure through factor loading matrices. Furthermore, the factor loading matrices were made identifiable and sparse to ensure the interpretability of the model. We also proposed a Bayesian shrinkage method as a systematic approach for factor selection. Through numerical experiments and data analysis, we investigated the predictive accuracy and interpretability of our proposed method. We concluded that the flexibility of the method allows for the incorporation of additional time series features, thereby improving its accuracy.

Stacked collaborative transformer network with contrastive learning for video moment localization

Video grounding intends to perform temporal localization in multimedia information retrieval. The temporal bounds of the target video span are determined for the given input query. A novel interactive multi-head self-attention (IMSA) transformer is proposed to localize an unseen moment in the untrimmed video for the given image. A new semantic-trained self-supervised approach is considered in this paper to perform cross-domain learning to match the image query – video segment. It normalizes the convolution function enabling efficient correlation and collecting of semantically related video segments across time based on the image query. A double hostile Contrastive learning with Gaussian distribution parameters method is advanced to learn the representations of video. The proposed approach performs dynamically on various video components to achieve exact semantic synchronization and localization among queries and video. In the proposed approach, the IMSA model localizes frames greatly compared to other approaches. Experiments on benchmark datasets show that the proposed model can significantly increase temporal grounding accuracy. The moment occurrence is identified in the video with a start and end boundary ascertains an average recall of 86.45% and a mAP of 59.3%.

A novel single-loop estimation method for predictive failure probability-based global sensitivity analysis

The existing predictive failure probability (PFP)-based global sensitivity analysis methods may get stuck in practical application due to the large amount of calculation or insufficient precision. Therefore, a novel single-loop estimation method is proposed in this paper to effectively estimate PFP-based global sensitivity measures. Firstly, by introducing standard normal auxiliary variables and equivalent probability transformation, the overall uncertainty of each input variable is decomposed into its inherent uncertainty and distribution parameter uncertainty. Then, Bayes theorem-based formulations are derived for three PFP-based global sensitivity measures, where only the unconditional PFP and the conditional marginal and joint distributions of standard normal auxiliary variables and distribution parameters need to be known. These items can be evaluated simultaneously using only one set of functional calls. Finally, adaptive Kriging model is embedded into the proposed method in place of the time-demanding performance function to further enhance computational efficiency. The effectiveness of the proposed methods is validated through four benchmark reliability problems asnd one engineering problem.

The Method of the Probability Analysis of Area with Dissolved Gases in Power Transformer Insulating Oil

Transformer insulating oil plays an extremely important role in power transformers and is used for insulation, arc suppression, cooling and other purposes. However, its other focus is on dissolved gases analysis in the oil to monitor internal operating conditions, which is the responsibility of preventive maintenance. This paper uses the normal distribution theory and the American National Standard Specification (hereinafter referred to as ANSI/IEEE C57.104) to reorganize as a diagnostic tool. The range of each gas from three stages of the specification - normal, caution, and abnormal are incorporated to a stage of abnormal, which divide into equal different values of 1000 as the maternal body of a qualitative normal distribution. Then the benchmark is been calculated from those parameters of a qualitative normal distribution. The data of detection has to pass through "Gas chromatography” to generate dissolved gases. At last, the benchmark value compares with dissolved gases to find the abnormal probability value as a diagnostic tool in maintenance evaluation of equipment. This method was developed using EXCEL application software, and repeatedly tested and verified with examples to confirm its feasibility and high accuracy. In addition, 10 cases accident data were extracted from the literature [11], and compared with the actual maintenance results. The accuracy was 80% for ANSI/IEEE C57.104 and 90% for this probability method. Therefore, this diagnostic method can replace the traditional multi-stage judgment and be represented by a single probability value to show. Based on technology sharing, the development process is specially written into a technical article as reference by scholars and electrical maintenance personnel in the field of power engineering.
 Design Methods: Making a qualitative normal distribution employs EXCEL software and the discriminative rule of ANSI/IEEE C57.104. Design Purpose: As a diagnostic tool with dissolved gases in insulating oil. Design Effectiveness: Probability Method is better than traditional; it has those efficacies - the accuracy and feasibly and compete with tried and tested actual case.

New Vessel Extraction Method by Using Skew Normal Distribution for MRA Images

Vascular-related diseases pose significant public health challenges and are a leading cause of mortality and disability. Understanding the complex structure of the vascular system and its processes is crucial for addressing these issues. Recent advancements in medical imaging technology have enabled the generation of high-resolution 3D images of vascular structures, leading to a diverse array of methods for vascular extraction. While previous research has often assumed a normal distribution of image data, this paper introduces a novel vessel extraction method that utilizes the skew normal distribution for more accurate probability distribution modeling. The proposed method begins with a preprocessing step to enhance vessel structures and reduce noise in Magnetic Resonance Angiography (MRA) images. The skew normal distribution, known for its ability to model skewed data, is then employed to characterize the intensity distribution of vessels. By estimating the parameters of the skew normal distribution using the Expectation-Maximization (EM) algorithm, the method effectively separates vessel pixels from the background and non-vessel regions. To extract vessels, a thresholding technique is applied based on the estimated skew normal distribution parameters. This segmentation process enables accurate vessel extraction, particularly in detecting thin vessels and enhancing the delineation of vascular edges with low contrast. Experimental evaluations on a diverse set of MRA images demonstrate the superior performance of the proposed method compared to previous approaches in terms of accuracy and computational efficiency. The presented vessel extraction method holds promise for improving the diagnosis and treatment of vascular-related diseases. By leveraging the skew normal distribution, it provides accurate and efficient vessel segmentation, contributing to the advancement of vascular imaging in the field of medical image analysis.

Randomness and time-varying characteristics of chloride ion transport in existing harbor concrete structures

This paper presents a study on the durability testing of a concrete facility located within the North Bay Port region, which has been in service for 200 months. Based on the results of 20 sets of concrete samples, an improved Kolmogorov-Smirnov (K-S) test method and gross error discrimination method are proposed to analyze the random distribution functions of the apparent chloride diffusion coefficient (Dapp) and the apparent surface chloride concentration (Cs), and further explore the time-varying characteristics of chloride ion transmission in concrete. The research shows that the improved K-S method presented in this paper can effectively reduce the probability of type II errors by selecting a rational sample size, which can also improve detection efficiency. When the sample size does not exceed 10, the 2σ criterion proposed in this paper can effectively identify and eliminate gross errors. In general, Dapp and Cs follow the log-normal distribution, while the time factor (m) follows a normal distribution parameter. The value of Cs basically stabilized after exposure to 80 months, whereas Dapp tended to stabilize after exposure to 100 months. The value of m obtained through fitting short-term experimental data is typically overestimated, and its value decreases as the exposure time prolongs. Therefore, m should also be considered a time-varying parameter that decreases with time. The tested RC structure will begin to experience rebar corrosion after 48.5-60 years of exposure to the marine environment based on the probabilistic assessment.

Actuarial Measures for Inverse Gaussian Distributed Claim Severity

An insurance company must be able to manage risks in the form of claims submitted by policyholders. There are several risk measures or actuarial measures that can be used to predict future risks and help companies prepare reserves. These actuarial measures are Value at Risk (VaR), Tail Value at Risk (TVaR), Tail Variance (TV), and Tail Variance Premium (TVP). In this article, we will discuss these actuarial measures for inverse Gaussian distributed claim severity. The Kolmogorov-Smirnov test is used to test the fit of the inverse Gaussian distribution. The maximum likelihood estimator is used as a method to estimate the parameters of the inverse Gaussian distribution. The data used in this article is data on partial loss claims for motor vehicle insurance insurance company PT. ABC in 2019 Category 1 in all regions. However, after testing the goodness of fit of the distribution using the Kolmogorov-Smirnov test for region 3, it did not come from a population with an inverse Gaussian distribution. So the data used to proceed to the actuarial measures estimation stage is only region 1 and region 2. Based on the results of calculating the actuarial measures for inverse Gaussian distributed claim severity, it can be concluded that the value of losses expected by a company can be calculated by taking into account the actuarial measures for claim severity on motor vehicle insurance in Indonesia.

A New Workflow for Assessment of Fluid Components and Pore Volumes From 2D NMR Measurements in Formations With Complex Mineralogy and Pore Structure

It is challenging to reliably identify fluid components and estimate their saturations in formations with complex lithology, complex pore structure, or varying wettability conditions. Common practices for assessing fluid saturations rely on the interpretation of resistivity measurements. These techniques require model calibration, which is time consuming/expensive and can only differentiate conductive and nonconductive fluids. Interpretation of 2D NMR maps provides a viable alternative for identifying fluid components and fluid volumes. However, conventional techniques for the interpretation of 2D NMR rely on cutoffs in the T1-T2 or D-T2 maps. The application of cutoffs is prone to inaccuracies when fluid-component relaxation responses overlap. To address these shortcomings, we introduce a new workflow for identifying/tracking fluid components and estimating their volumes from the interpretation of 2D NMR measurements. We developed a workflow that approximates 2D NMR maps with a superposition of 2D Gaussian distributions. The algorithm automatically determines the optimum number of Gaussian distributions and their corresponding properties (i.e., amplitudes, variances, and means). Next, a clustering technique is implemented to the dataspace containing the Gaussian distribution parameters obtained for the entire logged interval. Each Gaussian is assigned to a cluster corresponding to different pore/fluid components. We then calculate the volumes under the Gaussian distributions corresponding to each cluster at each depth. The volumes associated with each cluster translate directly into the pore volumes corresponding to the different fluid components (e.g., heavy/light hydrocarbon, bound/free water) at each depth. A highlighted contribution of this work is that, in contrast to the alternative petrophysical interpretation techniques for fluid characterization, the introduced workflow does not require calibration efforts, user-defined cutoffs, or proprietary data sets. Furthermore, approximating 2D NMR data with a superposition of Gaussian distributions improves the accuracy of estimated pore volumes of fluid components with overlapping NMR responses. The clustering using the Gaussian distribution parameters as inputs enables depth tracking of different fluid components without making use of user-defined 2D cutoffs. Finally, the multidimensional nature of the introduced clustering provides the unique capability of identifying different fluid components with 2D NMR response located in the same range of coordinates in a T1-T2 map. We successfully verified the reliability and robustness of the new workflow for enhancing petrophysical interpretation in two organic-rich mudrock formations with complex mineralogy and pore structure.

A preliminary study on the standard value of left ventricular mechanic dyssynchrony by speckle tracking

Abstract Background Speckle tracking imaging automatic functional imaging (AFI) is a new method to measure left ventricular mechanical dyssynchrony. Parameter peak strain dispersion (PSD) is the standard deviation when the long axial strain of 17 segments of the left ventricle (LV) reach there’s peak. There is no unified standard value at present. Li C[1] included 59 healthy women aged 43.08 ± 8.22 years old, whose PSD was 31.44±3.83ms. Ji X[2] included 57 healthy volunteers aged 43.30 ±6.03 years old whose PSD value was 23.8±2.2ms. Some studies referred to the standard range of Yu index and used PSD>32.6ms as an indicator of left ventricular mechanic dyssynchrony. Purpose To investigate the standard value range of PSD and PSD/R-R interval. Methods Healthy volunteers who came to our hospital for physical examination from March 2020 to September 2021 were included, excluding hypertension, diabetes, hyperlipidemia, coronary heart disease and other diseases. According to the 20∼29 years old, 30∼39 years old, 40∼49 years old, 50∼59 years old, 60∼69 years old and 70∼79 years old, 10 males and 10 females were included, respectively. GE Vivid E95 was used to collect echocardiographic images, and the following parameters were measured: ①The general parameters of the heart, such as the diameter of the atrium(LA) and the left ventricle (LV) and the thickness of the left ventricular wall .; ②the values of PSD and PSD/ R-R interval. The normal distribution parameters were represented by mean plus or minus the standard deviation. Analysis of variance and post hoc test (LSDt-test) were used to analyse measured values statistically. Results Values of general echocardiographic data such as BSA, atrial and ventricular diameter, interventricular septal thickness, left ventricular posterior wall thickness, and LV ejection fraction were consistent with the guideline of Recommendations for Cardiac Chamber Quantification by Echocardiography in Adults: An Update from the American Society of Echocardiography and the European Association of Cardiovascular Imaging published in 2015. The range of PSD values for subjects in this study was 43±9ms, and the maximum was 65ms. The range of PSD/R-R was 5±1%, and the maximum was 7%. The values of PSD and PSD/R-R were 36±5ms(27∼45ms) and 4.4±0.76%(3∼6.4%) for 20∼39 years old, 42±5ms(34.9-54ms), 5.0±0.8%(3.5-6.7%) in 40∼59 years; 51±8ms(34∼65ms), 5.8±0.9%(3.9∼7%) in age 60∼79. Conclusions The preliminary study has shown that left ventricular mechanical dyssynchrony is associated with age. The standard value range of PSD is inconsistent in different age groups, and PSD and PSD/R-R values increase with age.PSD values at different agesBar chart of PSD values at different age

Distributed collaboration: Cognitive difference and collaborative decision for multi-robot radioactive source search

Accidental loss of radioactive sources can pose a significant threat to human health and the ecological environment. This paper proposes a distributed collaborative decision algorithm for multi-robot radioactive source search to solve this problem. The algorithm utilizes a Gaussian parameter fusion method based on cognitive consistency to estimate the posterior probability distribution of source parameters within a Bayesian framework. Also, the algorithm enhances the cognitive consistency of robots through the fusion of shared Gaussian distribution parameters and cognitive difference variables. Each robot calculates a reward function for its next action based on the deviation angle and distance. In addition, the proposed algorithm uses a distributed collaborative search strategy to guide the robot's search through the robot's behavioral decisions and behavioral decisions from neighboring robots. Experimental results show that the algorithm achieves a mean search time of only 1.74s and a 100% search success rate. Therefore, the algorithm not only guarantees accuracy but also shortens the search time and reduces the risk of losing radioactive sources.

MFAN: Mixing Feature Attention Network for trajectory prediction

Accurate trajectory prediction of surrounding agents is essential for autonomous vehicles, where the key challenge is to understand the complex interactions among agents. Previous works treat all interacted features between agents equally in modeling interaction, while neglecting their different importance to the interaction, thus inevitably limiting the interaction modeling ability. Besides, existing methods suffer from significant performance degradation when domain shifts, resulting in severely deviant prediction from reality. To address these issues, we propose a novel prediction framework, dubbed Mixing Feature Attention Network (MFAN). Specifically, the proposed mixing feature attention is a parallel design to adaptively determine the importance of different interacted features and simultaneously capture the global interaction feature to improve interaction modeling. Meanwhile, the spatial global interaction is modeled from a spatial edge-featured graph input to capture the enhanced spatial interaction. The temporal motion pattern is modeled from a temporal edge-featured graph input to enhance the domain adaption. Finally, we estimate the parameters of bivariant Gaussian distribution for trajectory prediction. Experimental results show that our method achieves superior performance in trajectory prediction while maintaining low computational complexity and performs accurate prediction even when domain shifts.

A study of the effects of Gaussian distribution of coherence length of source on the diffraction of partial temporal coherence beam from multi slits: Theory and simulation

First, we have generalized the notion of Franhoufer diffraction of temporal coherent light from a single slit to the case of arbitrary n-slits. The diffraction pattern is investigated for different values of recently (Koushki and Alavi, 2019) introduced parameter η “decoherence parameter”. It is shown that for multi-slits, the temporal decoherence effects appear for η≥1 i.e., the coherence length is shorter that the size of the slits. Results of our study reproduce the previous studies for perfect temporal case, when coherence length tends to infinity. Then to bring the problem closer to reality, we do not fix the coherence length and consider a Gaussian distribution function for it. Numerical study of the effects of coherence parameters of Gaussian distribution on far field diffraction pattern is performed.

Dynamic response analysis of a train braking system with time-varying coefficient of friction excitations

Coefficient of friction (COF) is a key parameter that reflects the interface tribological behavior and influences the system dynamic response. In this research, the tribological properties of the train braking system friction blocks with different perforation diameters are experimentally explored using a block-on-disc apparatus. And the distribution law of the interface COF is revealed by statistical analysis. It is found that the histogram of the COF approximately follows a normal distribution. Considering the time-varying of the COF, a time-varying COF model is then established based on the normal distribution parameters. Further, the time-varying COF model is integrated into a proposed train braking system numerical model to construct the association between the disc–block friction properties and the braking system dynamic response. Based on this, the dynamic behavior of the braking system subject to interface time-varying COF excitations and block perforation structure is analyzed. The results show the time-varying COF excitations should be considered to accurately reveal the dynamic response of the braking system. Moreover, the friction block processed a perforation diameter of 2 mm obviously reduces disc–block friction vibration and improves the stability of the train braking system.

The effect of the volume of tests and the number of participants on the assessment of qualification in interlaboratory comparison tests

The results of a comparative analysis of statistical indicators for assessing the proficiency determined during interlaboratory comparison tests (ICT) are presented. The main statistical indicators were selected: the assigned value, standard deviation for assessment the proficiency and standard uncertainty of the assigned value. Statistical indicators were determined in accordance with Algorithm A, GOST R 50779.60. Comparison of the indicators was carried out on the basis of numerical experiment data (random number generation) for the ultimate tensile strength of a D16AT aluminum alloy depending on the number of samples and the number of participants in the ICT qualification program. The calculation and subsequent statistical analysis of the proficiency test scores was based on the values generated by the software. Random number generation is performed for a characteristic that has a normal distribution law with the parameters of the mean equal to 450 MPa and standard deviation equal to 5 MPa. The values of the normal distribution parameters chosen as an example corresponded to the average level of tensile strength values of standard specimens made of D16AT aluminum alloy sheets. The numerical experiment (generation of random values) was carried out for given cases of the number of participants and the number of proficiency testing samples (PTS) independently of each other using separate samples of the appropriate size. A total of 36,000 ultimate tensile strength values were generated for the proficiency testing samples made of D16AT aluminum alloy sheets. As a result of calculations, 48 average values were determined (according to the number of considered implementations of ICT programs, depending on the number of participants and the proficiency testing samples) for each selected statistical indicator of the ICT qualification program. The average value of each statistical indicator was determined on samples with a bulk of 250 to 2000 generated (experimental) values, depending on the number of participants and the number of proficiency testing samples. The analysis thus performed made it possible to evaluate the influence of the volume of tests and the number of participants on the assessment of the proficiency in interlaboratory comparative tests. It is shown that for the selected range of the number of ICT participants (from 5 to 20) and the number of PTS (from 5 to 10), the value of the assigned xpt value does not depend either on the number of tested PTS or the number of ICT participants. The maximum discrepancy between the assigned value and the given level of tensile strength (450 MPa) is 0.13%, which falls within the error (rounding) for this level of values and cannot lead to significant errors in proficiency testing during ICT. The standard deviation for the qualification assessment, regardless of the number of participants, decreases with an increase in the number of proficiency testing samples, but such a decrease is insignificant and does not exceed the standard deviation (SD) value of the ultimate tensile strength (for the selected model for generating experimental values, the SD value is accepted to be 5 MPa). In contrast to the assigned value and the standard deviation for the qualification assessment, it is shown that the standard uncertainty of the assigned value for the ultimate tensile strength of standard samples made of D16AT aluminum alloy sheets depends on the number of participants and the number of proficiency testing samples tested by each participant and decreases with an increase in the number of participants in ICT programs and the number of proficiency testing samples.

To Judge the Power Circuit Breaker Interrupting Time and the Prediction of Maintenance Schedule with Normal Distribution Probability

In this article, begins with the motivation for compiling, literature review, and normal distribution theory and characteristics with a shallow example to explain.
 Design Method: Making an approximately qualitative normal distribution with EXCEL software. First, the sample group plays an important role in the article, it with the cooperation of EXCEL application software and normal distribution rules, can be establish what those the relevant parameters of normal distribution. Taking the relevant parameters to drawn into a bell-shaped curve graph, then the standard score and probability of the area of the bell-shaped curve is out of converted. 
 Design Purpose: As a detection tool of judgement.
 In this way, an approximately qualitative normal distribution is been formed and its mean, variation and standard deviation are been took as a detection based to evaluated what the probability of any random variable of the same type.
 Design Effectiveness: To judge of equipment inspection data and work schedule prediction. However, an approximately qualitative normal distribution is been constructed with actual data to calculate out of being relevant parameters, with those ones to judge the interruption time of the circuit breaker what it good or bad in standard value. Another case that was estimated what the probability of arrival time for equipment's spare part with known parameters of qualitative normal distribution. Then review the confusing symbols in the above-mentioned construction design and explain in detail, so as to thoroughly understand the relationship between the parameters of the normal distribution theory. This article demonstrates writing skills with both text and pictures and operational instructions to enhance learning interest and aim to apply what you have learned.

Normality Test of NEPSE Sensitive Index

A return from the stock market is assumed to follow the random walk hypothesis. An investor is concerned about the risk and returns of the fund in which he or, she has invested. A risk-averse investor develops a portfolio with a secured return followed with a perfect prediction. Hence, a normality test for the market return is an easier way to diversify and eliminate risk. Thus, this paper tests the normality of the returns from the ‘blue-chip’ stocks in the context of NEPSE. A NEPSE Sensitive Index is an index calculated based on the trade of stocks for large, capital-based Nepalese listed companies with better earning histories and higher book values. The NEPSE sensitive index and NEPSE sensitive float index are tested for normality. The paper followed the data visualization technique, descriptive statistics, and test statistics to test the normality and find out the parameters of normal distribution. The paper found that the daily return from both indices best fit a normal distribution. Hence, two basic statistical parameters from the returns, i.e., the mean and standard deviation, are sufficient to estimate future trend for ‘blue-chip’ stock return in Nepal. The governing body should develop a new index that would better represent the market movement in the coming days that would be beneficial to predict the return movement from NEPSE.

Multivariate Contaminated Normal Censored Regression Model: Properties and Maximum Likelihood Inference

The Multivariate Contaminated Normal (MCN) distribution which contains two extra parameters with respect to parameters of the multivariate normal distribution, one for controlling the proportion of mild outliers and the other for specifying the degree of contamination, has been widely applied in robust statistics in the case of elliptically heavy-tailed empirical distributions. This article extends the MCN model to data with possibly censored values due to limits of quantification, referred to as the MCN with censoring (MCN-C) model, and further establishes the censored multivariate linear regression model where the random errors have the MCN distribution, named as the MCN censored regression (MCN-CR) model. Two computationally feasible Expectation Conditional Maximization (ECM) algorithms are developed for maximum likelihood estimation of MCN-C and MCN-CR models. An information-based method is used to approximate the standard errors of location parameters and regression coefficients. The capability and effectiveness of the MCN-C and MCN-CR models are illustrated via two real-data examples. A simulation study is conducted to investigate the superiority of the proposed models in terms of fit, accuracy of parameter estimation and censored data recovery as compared with classical approaches. Supplementary materials for this article are available online.

RDGCN: Reasonably dense graph convolution network for pedestrian trajectory prediction

The pedestrian trajectory prediction remains challenging due to its uncertainty and interference from surrounding pedestrians. There are two deficiencies in previous pedestrian trajectory prediction methods: 1. The temporal correlation of social interaction and the movement factors of groups are ignored; 2. Unreasonable interaction weight allocation. In order to eliminate these two deficiencies, a reasonably dense graph convolution network (RDGCN) was developed in this study. Spatial and temporal graphs were first constructed to model social interactions and movement factors. Then, asymmetric three-dimensional (3D) convolution was employed for the fusion of spatial-temporal information to capture the temporal correlation of social interactions and the movement factors of groups. The RSigmoid function was designed to assign interaction weights and to make the setting of interaction weight more reasonable. Finally, a U-TCN module was designed to estimate two-dimensional Gaussian distribution parameters of the future trajectories. On the ETH and UCY datasets, the proposed method outperformed versus other models in terms of average displacement error and final displacement error, and it was capable of predicting complex social behaviors and movement factors.

Effect of the Gaussian distribution parameters of the electron beam generated at the target on the simulated x-ray dose

The purpose of this work was to investigate by Monte Carlo method the adjustment of photon beams delivered by the medical LINear ACcelerator (LINAC) Elekta Synergy MLCi2. This study presents an optimization of the Gaussian distribution parameters of the accelerated electrons before the target simulated by two Monte Carlo codes and for three beams. The photon (x-ray) beam is produced by the interaction of accelerated electrons with the LINAC target. The electrons are accelerated by a potential difference created between the anode and the cathode of the gun and directed towards the target. In the Monte Carlo simulation, it is necessary to setup the spectrum parameters of the generated electrons to simulate the x-ray dose distribution. In this study, we modeled the LINAC geometry for photon beams 18MV and 6MV in cases Flattened (FF) and Flattening-Filter-Free (FFF). The Monte Carlo simulations are based on G4Linac_MT and GATE codes. The results of the optimized configurations determined after more than 20 tests for each beam energy show a very good agreement with the experimental measurements for different irradiation fields for the depth (PDD) and lateral (Profile) dose distribution. In all Monte Carlo calculations performed in this study, the statistical uncertainty is less than 2%. The results were also in very good agreement in terms of γ-index analysis, for the 3%/3 mm and 2%/2 mm criteria.