We revisit one of the classical search problems in which a diffusing target encounters a stationary searcher. Under the condition that the searcher’s detection region is much smaller than the search region in which t...We revisit one of the classical search problems in which a diffusing target encounters a stationary searcher. Under the condition that the searcher’s detection region is much smaller than the search region in which the target roams diffusively, we carry out an asymptotic analysis to derive the decay rate of the non-detection probability. We consider two different geometries of the search region: a disk and a square, respectively. We construct a unified asymptotic expression valid for both of these two cases. The unified asymptotic expression shows that the decay rate of the non-detection probability, to the leading order, is proportional to the diffusion constant, is inversely proportional to the search region, and is inversely proportional to the logarithm of the ratio of the search region to the searcher’s detection region. Furthermore, the second term in the unified asymptotic expansion indicates that the decay rate of the non-detection probability for a square region is slightly smaller than that for a disk region of the same area. We also demonstrate that the asymptotic results are in good agreement with numerical solutions.展开更多
In dynamic scenarios,visual simultaneous localization and mapping(SLAM)algorithms often incorrectly incorporate dynamic points during camera pose computation,leading to reduced accuracy and robustness.This paper prese...In dynamic scenarios,visual simultaneous localization and mapping(SLAM)algorithms often incorrectly incorporate dynamic points during camera pose computation,leading to reduced accuracy and robustness.This paper presents a dynamic SLAM algorithm that leverages object detection and regional dynamic probability.Firstly,a parallel thread employs the YOLOX object detectionmodel to gather 2D semantic information and compensate for missed detections.Next,an improved K-means++clustering algorithm clusters bounding box regions,adaptively determining the threshold for extracting dynamic object contours as dynamic points change.This process divides the image into low dynamic,suspicious dynamic,and high dynamic regions.In the tracking thread,the dynamic point removal module assigns dynamic probability weights to the feature points in these regions.Combined with geometric methods,it detects and removes the dynamic points.The final evaluation on the public TUM RGB-D dataset shows that the proposed dynamic SLAM algorithm surpasses most existing SLAM algorithms,providing better pose estimation accuracy and robustness in dynamic environments.展开更多
To ensure the structural integrity of life-limiting component of aeroengines,Probabilistic Damage Tolerance(PDT)assessment is applied to evaluate the failure risk as required by airworthiness regulations and military ...To ensure the structural integrity of life-limiting component of aeroengines,Probabilistic Damage Tolerance(PDT)assessment is applied to evaluate the failure risk as required by airworthiness regulations and military standards.The PDT method holds the view that there exist defects such as machining scratches and service cracks in the tenon-groove structures of aeroengine disks.However,it is challenging to conduct PDT assessment due to the scarcity of effective Probability of Detection(POD)model and anomaly distribution model.Through a series of Nondestructive Testing(NDT)experiments,the POD model of real cracks in tenon-groove structures is constructed for the first time by employing the Transfer Function Method(TFM).A novel anomaly distribution model is derived through the utilization of the POD model,instead of using the infeasible field data accumulation method.Subsequently,a framework for calculating the Probability of Failure(POF)of the tenon-groove structures is established,and the aforementioned two models exert a significant influence on the results of POF.展开更多
We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induc...We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induced by a probability bi-sequence.We also establish the Katok’s entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.展开更多
The Argo program measures temperature and salinity in the upper ocean(0–2000 m).These observations are critical for weather/climate studies,ocean circulation analysis,and sea-level monitoring.To address the limitatio...The Argo program measures temperature and salinity in the upper ocean(0–2000 m).These observations are critical for weather/climate studies,ocean circulation analysis,and sea-level monitoring.To address the limitations of traditional thresholds in Argo data quality control(QC),this study proposes a novel probability distribution-based inference method(PDIM)for temperature-salinity threshold inference.By integrating historical observations with climatological data,the method utilizes historical data corresponding to latitude and longitude grids,calculates temperature/salinity frequency distributions for each depth,and determines“zero probability”boundaries through combined frequency distribution and climatology data.Then a probability distribution model is established to detect outliers automatically based on the features in the probability density function,which eliminates the traditional dependence on the normal distribution hypothesis.When applied to global Argo datasets from China Argo Real-time Data Center(CARDC),PDIM successfully identifies suspicious profiles and sensor drifts with high reliability,achieving a low false positive rate(0.55%for temperature,0.18%for salinity)while maintaining competitive true positive rate(28.29%for temperature,55.15%for salinity).This method is expected to improve the reliability of Argo data QC and has important significance for Argo QC.展开更多
Estimating probability density functions(PDFs)is critical in data analysis,particularly for complex multimodal distributions.traditional kernel density estimator(KDE)methods often face challenges in accurately capturi...Estimating probability density functions(PDFs)is critical in data analysis,particularly for complex multimodal distributions.traditional kernel density estimator(KDE)methods often face challenges in accurately capturing multimodal structures due to their uniform weighting scheme,leading to mode loss and degraded estimation accuracy.This paper presents the flexible kernel density estimator(F-KDE),a novel nonparametric approach designed to address these limitations.F-KDE introduces the concept of kernel unit inequivalence,assigning adaptive weights to each kernel unit,which better models local density variations in multimodal data.The method optimises an objective function that integrates estimation error and log-likelihood,using a particle swarm optimisation(PSO)algorithm that automatically determines optimal weights and bandwidths.Through extensive experiments on synthetic and real-world datasets,we demonstrated that(1)the weights and bandwidths in F-KDE stabilise as the optimisation algorithm iterates,(2)F-KDE effectively captures the multimodal characteristics and(3)F-KDE outperforms state-of-the-art density estimation methods regarding accuracy and robustness.The results confirm that F-KDE provides a valuable solution for accurately estimating multimodal PDFs.展开更多
Vaccination is critical for controlling infectious diseases,but negative vaccination information can lead to vaccine hesitancy.To study how the interplay between information diffusion and disease transmission impacts ...Vaccination is critical for controlling infectious diseases,but negative vaccination information can lead to vaccine hesitancy.To study how the interplay between information diffusion and disease transmission impacts vaccination and epidemic spread,we propose a novel two-layer multiplex network model that integrates an unaware-acceptant-negative-unaware(UANU)information diffusion model with a susceptible-vaccinated-exposed-infected-susceptible(SVEIS)epidemiological framework.This model includes individual exposure and vaccination statuses,time-varying forgetting probabilities,and information conversion thresholds.Through the microscopic Markov chain approach(MMCA),we derive dynamic transition equations and the epidemic threshold expression,validated by Monte Carlo simulations.Using MMCA equations,we predict vaccination densities and analyze parameter effects on vaccination,disease transmission,and the epidemic threshold.Our findings suggest that promoting positive information,curbing the spread of negative information,enhancing vaccine effectiveness,and promptly identifying asymptomatic carriers can significantly increase vaccination rates,reduce epidemic spread,and raise the epidemic threshold.展开更多
The study aims to develop an empirical model to predict the rainfall intensity in Al-Diwaniyah City,Iraq,according to a statistical analysis based on probability and the specific rainfall return period.Rainfall data w...The study aims to develop an empirical model to predict the rainfall intensity in Al-Diwaniyah City,Iraq,according to a statistical analysis based on probability and the specific rainfall return period.Rainfall data were collected daily for 25 years starting in 2000.Daily rainfall data were converted to rainfall intensity for five duration periods ranging from one to five hours.The extreme values were checked,and data that deviated from the group trend were removed for each period,and then arranged in descending order using the Weibull formula to calculate the probability.Statistically,the model performance with a return period of two years is considered good when compared with observed results and other methods such as Talbot and Sherman with a coefficient of determination(R2)>0.97 and Nash-Sutcliffe efficiency(NSE)>0.80.The results showed that a mathematical equation was obtained that describes the relationship between rainfall intensity,probability,and rainfall duration,which can be used for a confined return period with a 50% probability.Therefore,decision-makers can rely on the model to improve the performance of the city’s current drainage system during flood periods in the future.展开更多
Decision-makers usually have an aspiration level,a target,or a benchmark they aim to achieve.This behavior can be rationalized within the expected utility framework,which incorporates the probability of success(achiev...Decision-makers usually have an aspiration level,a target,or a benchmark they aim to achieve.This behavior can be rationalized within the expected utility framework,which incorporates the probability of success(achieving the aspiration level)as an important aspect of decision-making.Motivated by these theories,this study defines the probability of success as the number of days a firm’s return outperformed its benchmark in the portfolio formation month.This study uses portfolio-level and firm-level analyses,revealing an economically substantial and statistically significant relationship between the probability of success and expected stock returns,even after controlling for common risk factors and various characteristics.Additional analyses support the behavioral theory of the firm,which posits that firms act to achieve short-term aspiration levels.展开更多
To address prediction errors and limited information extraction in machine learning(ML)-based interval prediction,a hybrid model was proposed for interval estimation and failure assessment of step-like landslides unde...To address prediction errors and limited information extraction in machine learning(ML)-based interval prediction,a hybrid model was proposed for interval estimation and failure assessment of step-like landslides under uncertainty.The model decomposed displacements into trend and periodic components via Variational Mode Decomposition(VMD)and K-shape clustering.The Residual and Moving Block Bootstrap methods were used to generate pseudo datasets.Polynomial regressionwas adopted for trend forecasting,whereas the Dense Convolutional Network(DenseNet)and Long Short-Term Memory(LSTM)networks were employed for periodic displacement prediction.An Extreme Learning Machine(ELM)was used to estimate the noise variance,enabling the construction of Prediction Intervals(PIs)and quantificationof displacement uncertainty.Failure probabilities(Pf)were derived from PIs using an improved tangential angle criterion and reliability analysis.The model was validated on three step-like landslides in the Three Gorges Reservoir Area,achieving stability assessment accuracies of 99.88%(XD01),99.93%(ZG93),99.89%(ZG118),and 100%for ZG110 and ZG111 across the Baishuihe and Bazimen landslides.For the Shuping landslide,the predictions aligned with fieldobservations before and after the 2014–2015 remediation,with P_(f)remaining near zero post-2015 except for occasional peaks.The model outperformed conventional ML approaches by yielding narrower PIs.At XD01 with 90%PI nominal confidencelevel(PINC),the coverage width-based criterion(CWC)and PI average width(PIAW)were 3.38 mm.The mean values of the PIs exhibited high accuracy,with a Mean Absolute Error(MAE)of 0.28 mm and Root Mean Square Error(RMSE)of 0.39 mm.These results demonstrate the robustness of the proposed model in improving landslide risk assessment and decision-making under uncertainty.展开更多
In order to solve the problems of high experimental cost of ammunition,lack of field test data,and the difficulty in applying the ammunition hit probability estimation method in classical statistics,this paper assumes...In order to solve the problems of high experimental cost of ammunition,lack of field test data,and the difficulty in applying the ammunition hit probability estimation method in classical statistics,this paper assumes that the projectile dispersion of ammunition is a two-dimensional joint normal distribution,and proposes a new Bayesian inference method of ammunition hit probability based on normal-inverse Wishart distribution.Firstly,the conjugate joint prior distribution of the projectile dispersion characteristic parameters is determined to be a normal inverse Wishart distribution,and the hyperparameters in the prior distribution are estimated by simulation experimental data and historical measured data.Secondly,the field test data is integrated with the Bayesian formula to obtain the joint posterior distribution of the projectile dispersion characteristic parameters,and then the hit probability of the ammunition is estimated.Finally,compared with the binomial distribution method,the method in this paper can consider the dispersion information of ammunition projectiles,and the hit probability information is more fully utilized.The hit probability results are closer to the field shooting test samples.This method has strong applicability and is conducive to obtaining more accurate hit probability estimation results.展开更多
With the implementation of General Senior High School Mathematics Curriculum Standards(2017 Edition,Revised in 2020),probability and statistics,as important carriers of the core mathematical competencies“mathematical...With the implementation of General Senior High School Mathematics Curriculum Standards(2017 Edition,Revised in 2020),probability and statistics,as important carriers of the core mathematical competencies“mathematical modeling”and“data analysis,”have increasingly highlighted their educational value.By summarizing the historical evolution of probability and statistics thinking and combining with teaching practice cases,this study explores its unique role in cultivating students’core mathematical competencies.The research proposes a project-based teaching strategy relying on real scenarios and empowered by technology.Through cases,it demonstrates how to use modern educational technology to realize the whole-process exploration of data collection,model construction,and conclusion verification,so as to promote the transformation of middle school probability and statistics teaching from knowledge imparting to competency development,and provide a practical reference for curriculum reform.展开更多
On May 22,2021,an M_(S)7.4 earthquake occurred in Maduo County,Qinghai Province,on the western plateau of China.The level of seismic monitoring in this area was inadequate,and incomplete seismic waveforms were obtaine...On May 22,2021,an M_(S)7.4 earthquake occurred in Maduo County,Qinghai Province,on the western plateau of China.The level of seismic monitoring in this area was inadequate,and incomplete seismic waveforms were obtained from a few broadband seismometers located within 300 km of the epicentre.All waveforms showed“truncation”phenomena.The waveforms of earthquakes can guide ground motion inputs in near-fault areas.This paper uses the empirical Green's function method to consider the uncertainties in source parameters and source rupture processes by synthesizing high-probability,accurate waveforms in Maduo County(MAD station)near the epicentre.The acceleration waveform at the DAW strong-motion station,located 176 km from the epicentre,is first synthesized with the observed waveform of the mainshock.This critical step not only provides a more accurate source and rupture model of the Maduo earthquake but also establishes an essential reference standard.Secondly,the inferred models are rigorously applied to synthesize the acceleration waveform of the MAD station,ensuring that the results maintain a high accuracy and probability.The findings suggest that(1)the simulated acceleration waveform for the MAD station can better characterize the actual ground motion characteristics of the M_(S)7.4 earthquake in Maduo County,with high accuracy and probability in peak ground acceleration(Abbreviated as PGA)ranges of 140–240 and 350–390 cm/s^(2),respectively,and(2)the M_(S)7.4 earthquake did not undergo a complete supershear rupture process.The first asperity located on the east side of the epicentre is most likely to undergo supershear rupture.However,the Maduo earthquake may have been a complete subshear rupture.(3)The fault dislocation model of the three-asperity model better matches the actual source rupture process of the Maduo earthquake.This method can provide relatively accurate acceleration waveforms for regions with limited earthquake monitoring capabilities and assist in analysis of building seismic damage response,earthquake-induced geological disasters and sand liquefaction,and estimation of regional disaster losses.展开更多
Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator ...Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator and Bayesian model averaging(BMA)to optimize the predictions of RCfrom sophisticated theoretical models.The CBP estimator treats the residual between the theoretical and experimental values of RCas a continuous variable and derives its posterior probability density function(PDF)from Bayesian theory.The BMA method assigns weights to models based on their predictive performance for benchmark nuclei,thereby accounting for the unique strengths of each model.In global optimization,the CBP estimator improved the predictive accuracy of the three theoretical models by approximately 60%.The extrapolation analyses consistently achieved an improvement rate of approximately 45%,demonstrating the robustness of the CBP estimator.Furthermore,the combination of the CBP and BMA methods reduces the standard deviation to below 0.02 fm,effectively reproducing the pronounced shell effects on RCof the Ca and Sr isotope chains.The studies in this paper propose an efficient method to accurately describe RCof unknown nuclei,with potential applications in research on other nuclear properties.展开更多
Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the random...Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the randomness of structural parameters,working condition and vibration environment are considered for fatigue life predication and reliability assessment.First,the lowcycle fatigue problem is modelled as stochastic static system with random parameters,while the high-cycle fatigue problem is considered as stochastic dynamic system under random excitations.Then,to deal with the two failure modes,the novel Direct Probability Integral Method(DPIM)is proposed,which is efficient and accurate for solving stochastic static and dynamic systems.The probability density functions of accumulated damage and fatigue life of turbine blade for low-cycle and high-cycle fatigue problems are achieved,respectively.Furthermore,the time–frequency hybrid method is advanced to enhance the computational efficiency for governing equation of system.Finally,the results of typical examples demonstrate high accuracy and efficiency of the proposed method by comparison with Monte Carlo simulation and other methods.It is indicated that the DPIM is a unified method for predication of random fatigue life for low-cycle and highcycle fatigue problems.The rotational speed,density,fatigue strength coefficient,and fatigue plasticity index have a high sensitivity to fatigue reliability of engine turbine blade.展开更多
This paper focuses on the ideological and political construction of the course“Probability Theory and Mathematical Statistics.”Aiming at the current situation in teaching where emphasis is placed on knowledge impart...This paper focuses on the ideological and political construction of the course“Probability Theory and Mathematical Statistics.”Aiming at the current situation in teaching where emphasis is placed on knowledge imparting while value guidance is neglected,and combined with the requirements of ideological and political education policies in the new era,this paper explores the integration path between professional courses and ideological and political education.Through literature analysis,case comparison,and empirical research,the study proposes a systematic implementation plan covering the design of teaching objectives,the reconstruction of teaching content,and the optimization of the evaluation system.The purpose is to cultivate students’sense of social responsibility and innovative awareness by excavating the ideological and political elements in mathematics.The research results provide practical reference for colleges and universities to deepen the reform of ideological and political education in courses,and promote the implementation of the fundamental task of fostering virtue through education in STEM education.展开更多
Fires are one of the most destructive natural disasters and have serious long-term effects on the environment,economy,and human health.In Inner Mongolia Autonomous Region,China,frequent fire disturbance occurs due to ...Fires are one of the most destructive natural disasters and have serious long-term effects on the environment,economy,and human health.In Inner Mongolia Autonomous Region,China,frequent fire disturbance occurs due to the intensification of climate change and human activities.It is crucial to understand the fire regime and estimate the probability of regional fire occurrence and reducing fire losses.However,most studies have primarily focused on the dynamic changes,probability of occurrence,and driving mechanisms of wildfires in the grassland and forest land ecosystems in Inner Mongolia,while insufficient research has been conducted on the spatiotemporal variations in active fires and their impact on the wildfire risk in forest land and grassland.Therefore,in this study,we analyzed the active fire regime based on Moderate Resolution Imaging Spectroradiometer(MODIS)thermal anomalies and burned area products from 2000 to 2022.Combined with climate,topographic,landscape,anthropogenic,and vegetation datasets,logistic regression(LR),support vector machine(SVM),random forest(RF),and convolutional neural network(CNN)models were chosen to estimate the probability of active fire occurrence at the seasonal timescale.The results revealed that:(1)a total of 100,343 active fires occurred in Inner Mongolia and the burned area reached 6.59×104 km².The number of ignition point exhibited a significant increasing trend,while the burned area exhibited a nonsignificant decreasing trend;(2)four active fire belts were detected,namely,the Hetao-Tumochuan Plain fire belt,Xiliao River Plain fire belt,Songnen Plain fire belt,and Hailar River Eroded Plain fire belt.The centroid of the active fires has shifted 456.4 km toward the southwest;(3)RF model achieved the highest accuracy in estimating the probability of active fire occurrence,followed by CNN,and LR and SVM models had lower accuracies;and(4)the distribution of the high and extremely high fire risk areas largely aligned with the four fire belts.The probability of active fire occurrence was the highest in spring,followed by that in autumn,and it gradually decreased in summer and winter.Our results revealed active fires migrated to the southwest and ignition sources increased,despite reduction of the burned area was not significant.The RF model outperformed the other models in predicting the probability of active fire occurrence.These findings contribute to future fire prevention and prediction in Inner Mongolia.展开更多
The estimation of the probability of informed trading(PIN)model and its extensions poses significant challenges owing to various computational problems.To address these issues,we propose a novel estimation method call...The estimation of the probability of informed trading(PIN)model and its extensions poses significant challenges owing to various computational problems.To address these issues,we propose a novel estimation method called the expectation-conditional-maximization(ECM)algorithm,which can serve as an alternative to the existing methods for estimating PIN models.Our method provides optimal estimates for the original PIN model as well as two of its extensions:the multilayer PIN model and the adjusted PIN model,along with its restricted versions.Our results indicate that estimations using the ECM algorithm are generally faster,more accurate,and more memory-efficient than the standard methods used in the literature,making it a robust alternative.More importantly,the ECM algorithm is not limited to the models discussed and can be easily adapted to estimate future extensions of the PIN model.展开更多
This study presents an innovative approach to calculating the failure probability of slopes by incorporating fuzzylimit-state functions,a method that significantly enhances the accuracy and efficiency of slope stabili...This study presents an innovative approach to calculating the failure probability of slopes by incorporating fuzzylimit-state functions,a method that significantly enhances the accuracy and efficiency of slope stability analysis.Unlike traditional probabilistic techniques,this approach utilizes a least squares support vector machine(LSSVM)optimized with a grey wolf optimizer(GWO)and K-fold cross-validation(CV)to approximate the limit-statefunction,thus reducing computational complexity.The novelty of this work lies in its application to one-dimensional(1D),two-dimensional(2D),and three-dimensional(3D)slope models,demonstrating its versatility andhigh precision.The proposed method consistently achieves error margins within 3%of Monte Carlo simulation(MCS)results,while substantially reducing computation time,particularly for 2D and 3D models.This makes theapproach highly practical for real-world engineering applications.Furthermore,by applying fuzzy mathematics tohandle uncertainties in geotechnical properties,the method offers a more realistic and comprehensive understandingof slope stability.As water is the main factor influencing the stability of slopes,this aspect is investigatedby calculating the phreatic line after the change in water level.Relevant examples are used to show that the failureprobability of a slope under water wading condition can increase by more than 20%(increase rates in 1D,2D and3D conditions being 25%,27%and 31%,respectively)compared with the natural condition.The influence ofdiverse fuzzy membership functions—linear,normal,and Cauchy—on failure probability is also considered.Thisresearch not only provides a strategy for better calculation of the slope failure probability but also pioneers theintegration of computational intelligence,fuzzy logic and fluid-dynamics in geotechnical engineering,presentingan innovative and efficient tool for slope stability analysis.展开更多
文摘We revisit one of the classical search problems in which a diffusing target encounters a stationary searcher. Under the condition that the searcher’s detection region is much smaller than the search region in which the target roams diffusively, we carry out an asymptotic analysis to derive the decay rate of the non-detection probability. We consider two different geometries of the search region: a disk and a square, respectively. We construct a unified asymptotic expression valid for both of these two cases. The unified asymptotic expression shows that the decay rate of the non-detection probability, to the leading order, is proportional to the diffusion constant, is inversely proportional to the search region, and is inversely proportional to the logarithm of the ratio of the search region to the searcher’s detection region. Furthermore, the second term in the unified asymptotic expansion indicates that the decay rate of the non-detection probability for a square region is slightly smaller than that for a disk region of the same area. We also demonstrate that the asymptotic results are in good agreement with numerical solutions.
基金the National Natural Science Foundation of China(No.62063006)to the Guangxi Natural Science Foundation under Grant(Nos.2023GXNSFAA026025,AA24010001)+3 种基金to the Innovation Fund of Chinese Universities Industry-University-Research(ID:2023RY018)to the Special Guangxi Industry and Information Technology Department,Textile and Pharmaceutical Division(ID:2021 No.231)to the Special Research Project of Hechi University(ID:2021GCC028)to the Key Laboratory of AI and Information Processing,Education Department of Guangxi Zhuang Autonomous Region(Hechi University),No.2024GXZDSY009。
文摘In dynamic scenarios,visual simultaneous localization and mapping(SLAM)algorithms often incorrectly incorporate dynamic points during camera pose computation,leading to reduced accuracy and robustness.This paper presents a dynamic SLAM algorithm that leverages object detection and regional dynamic probability.Firstly,a parallel thread employs the YOLOX object detectionmodel to gather 2D semantic information and compensate for missed detections.Next,an improved K-means++clustering algorithm clusters bounding box regions,adaptively determining the threshold for extracting dynamic object contours as dynamic points change.This process divides the image into low dynamic,suspicious dynamic,and high dynamic regions.In the tracking thread,the dynamic point removal module assigns dynamic probability weights to the feature points in these regions.Combined with geometric methods,it detects and removes the dynamic points.The final evaluation on the public TUM RGB-D dataset shows that the proposed dynamic SLAM algorithm surpasses most existing SLAM algorithms,providing better pose estimation accuracy and robustness in dynamic environments.
基金supported by the National Major Science and Technology Project,China(No.J2019-Ⅳ-0007-0075)the Fundamental Research Funds for the Central Universities,China(No.JKF-20240036)。
文摘To ensure the structural integrity of life-limiting component of aeroengines,Probabilistic Damage Tolerance(PDT)assessment is applied to evaluate the failure risk as required by airworthiness regulations and military standards.The PDT method holds the view that there exist defects such as machining scratches and service cracks in the tenon-groove structures of aeroengine disks.However,it is challenging to conduct PDT assessment due to the scarcity of effective Probability of Detection(POD)model and anomaly distribution model.Through a series of Nondestructive Testing(NDT)experiments,the POD model of real cracks in tenon-groove structures is constructed for the first time by employing the Transfer Function Method(TFM).A novel anomaly distribution model is derived through the utilization of the POD model,instead of using the infeasible field data accumulation method.Subsequently,a framework for calculating the Probability of Failure(POF)of the tenon-groove structures is established,and the aforementioned two models exert a significant influence on the results of POF.
文摘We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induced by a probability bi-sequence.We also establish the Katok’s entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.
基金The National Key Research and Development Program of China under contract No.2021YFC3101503the Hunan Provincial Natural Science Foundation of China under contract No.2023JJ10053+1 种基金the National Natural Science Foundation of China under contract Nos 42276205 and 42406195the Youth Independent Innovation Science Foundation under contract No.ZK24-54.
文摘The Argo program measures temperature and salinity in the upper ocean(0–2000 m).These observations are critical for weather/climate studies,ocean circulation analysis,and sea-level monitoring.To address the limitations of traditional thresholds in Argo data quality control(QC),this study proposes a novel probability distribution-based inference method(PDIM)for temperature-salinity threshold inference.By integrating historical observations with climatological data,the method utilizes historical data corresponding to latitude and longitude grids,calculates temperature/salinity frequency distributions for each depth,and determines“zero probability”boundaries through combined frequency distribution and climatology data.Then a probability distribution model is established to detect outliers automatically based on the features in the probability density function,which eliminates the traditional dependence on the normal distribution hypothesis.When applied to global Argo datasets from China Argo Real-time Data Center(CARDC),PDIM successfully identifies suspicious profiles and sensor drifts with high reliability,achieving a low false positive rate(0.55%for temperature,0.18%for salinity)while maintaining competitive true positive rate(28.29%for temperature,55.15%for salinity).This method is expected to improve the reliability of Argo data QC and has important significance for Argo QC.
基金supported by the Natural Science Foundation of Guangdong Province(Grant 2023A1515011667)Science and Technology Major Project of Shenzhen(Grant KJZD20230923114809020)Key Basic Research Foundation of Shenzhen(Grant JCYJ20220818100205012).
文摘Estimating probability density functions(PDFs)is critical in data analysis,particularly for complex multimodal distributions.traditional kernel density estimator(KDE)methods often face challenges in accurately capturing multimodal structures due to their uniform weighting scheme,leading to mode loss and degraded estimation accuracy.This paper presents the flexible kernel density estimator(F-KDE),a novel nonparametric approach designed to address these limitations.F-KDE introduces the concept of kernel unit inequivalence,assigning adaptive weights to each kernel unit,which better models local density variations in multimodal data.The method optimises an objective function that integrates estimation error and log-likelihood,using a particle swarm optimisation(PSO)algorithm that automatically determines optimal weights and bandwidths.Through extensive experiments on synthetic and real-world datasets,we demonstrated that(1)the weights and bandwidths in F-KDE stabilise as the optimisation algorithm iterates,(2)F-KDE effectively captures the multimodal characteristics and(3)F-KDE outperforms state-of-the-art density estimation methods regarding accuracy and robustness.The results confirm that F-KDE provides a valuable solution for accurately estimating multimodal PDFs.
基金supported by the National Social Science Foundation of China(Grant Nos.21BGL217 and 22CGL050)the Philosophy and Social Science Fund of Education Department of Jiangsu Province(Grant No.2020SJA2346).
文摘Vaccination is critical for controlling infectious diseases,but negative vaccination information can lead to vaccine hesitancy.To study how the interplay between information diffusion and disease transmission impacts vaccination and epidemic spread,we propose a novel two-layer multiplex network model that integrates an unaware-acceptant-negative-unaware(UANU)information diffusion model with a susceptible-vaccinated-exposed-infected-susceptible(SVEIS)epidemiological framework.This model includes individual exposure and vaccination statuses,time-varying forgetting probabilities,and information conversion thresholds.Through the microscopic Markov chain approach(MMCA),we derive dynamic transition equations and the epidemic threshold expression,validated by Monte Carlo simulations.Using MMCA equations,we predict vaccination densities and analyze parameter effects on vaccination,disease transmission,and the epidemic threshold.Our findings suggest that promoting positive information,curbing the spread of negative information,enhancing vaccine effectiveness,and promptly identifying asymptomatic carriers can significantly increase vaccination rates,reduce epidemic spread,and raise the epidemic threshold.
文摘The study aims to develop an empirical model to predict the rainfall intensity in Al-Diwaniyah City,Iraq,according to a statistical analysis based on probability and the specific rainfall return period.Rainfall data were collected daily for 25 years starting in 2000.Daily rainfall data were converted to rainfall intensity for five duration periods ranging from one to five hours.The extreme values were checked,and data that deviated from the group trend were removed for each period,and then arranged in descending order using the Weibull formula to calculate the probability.Statistically,the model performance with a return period of two years is considered good when compared with observed results and other methods such as Talbot and Sherman with a coefficient of determination(R2)>0.97 and Nash-Sutcliffe efficiency(NSE)>0.80.The results showed that a mathematical equation was obtained that describes the relationship between rainfall intensity,probability,and rainfall duration,which can be used for a confined return period with a 50% probability.Therefore,decision-makers can rely on the model to improve the performance of the city’s current drainage system during flood periods in the future.
文摘Decision-makers usually have an aspiration level,a target,or a benchmark they aim to achieve.This behavior can be rationalized within the expected utility framework,which incorporates the probability of success(achieving the aspiration level)as an important aspect of decision-making.Motivated by these theories,this study defines the probability of success as the number of days a firm’s return outperformed its benchmark in the portfolio formation month.This study uses portfolio-level and firm-level analyses,revealing an economically substantial and statistically significant relationship between the probability of success and expected stock returns,even after controlling for common risk factors and various characteristics.Additional analyses support the behavioral theory of the firm,which posits that firms act to achieve short-term aspiration levels.
基金funding support from the National Science Fund for Distinguished Young Scholars(Grant No.52125904)the National Key R&D Plan(Grant No.2022YFC3004403)the National Natural Science Foundation of China(Grant No.52039008).
文摘To address prediction errors and limited information extraction in machine learning(ML)-based interval prediction,a hybrid model was proposed for interval estimation and failure assessment of step-like landslides under uncertainty.The model decomposed displacements into trend and periodic components via Variational Mode Decomposition(VMD)and K-shape clustering.The Residual and Moving Block Bootstrap methods were used to generate pseudo datasets.Polynomial regressionwas adopted for trend forecasting,whereas the Dense Convolutional Network(DenseNet)and Long Short-Term Memory(LSTM)networks were employed for periodic displacement prediction.An Extreme Learning Machine(ELM)was used to estimate the noise variance,enabling the construction of Prediction Intervals(PIs)and quantificationof displacement uncertainty.Failure probabilities(Pf)were derived from PIs using an improved tangential angle criterion and reliability analysis.The model was validated on three step-like landslides in the Three Gorges Reservoir Area,achieving stability assessment accuracies of 99.88%(XD01),99.93%(ZG93),99.89%(ZG118),and 100%for ZG110 and ZG111 across the Baishuihe and Bazimen landslides.For the Shuping landslide,the predictions aligned with fieldobservations before and after the 2014–2015 remediation,with P_(f)remaining near zero post-2015 except for occasional peaks.The model outperformed conventional ML approaches by yielding narrower PIs.At XD01 with 90%PI nominal confidencelevel(PINC),the coverage width-based criterion(CWC)and PI average width(PIAW)were 3.38 mm.The mean values of the PIs exhibited high accuracy,with a Mean Absolute Error(MAE)of 0.28 mm and Root Mean Square Error(RMSE)of 0.39 mm.These results demonstrate the robustness of the proposed model in improving landslide risk assessment and decision-making under uncertainty.
基金supported by the National Natural Science Foundation of China(No.71501183).
文摘In order to solve the problems of high experimental cost of ammunition,lack of field test data,and the difficulty in applying the ammunition hit probability estimation method in classical statistics,this paper assumes that the projectile dispersion of ammunition is a two-dimensional joint normal distribution,and proposes a new Bayesian inference method of ammunition hit probability based on normal-inverse Wishart distribution.Firstly,the conjugate joint prior distribution of the projectile dispersion characteristic parameters is determined to be a normal inverse Wishart distribution,and the hyperparameters in the prior distribution are estimated by simulation experimental data and historical measured data.Secondly,the field test data is integrated with the Bayesian formula to obtain the joint posterior distribution of the projectile dispersion characteristic parameters,and then the hit probability of the ammunition is estimated.Finally,compared with the binomial distribution method,the method in this paper can consider the dispersion information of ammunition projectiles,and the hit probability information is more fully utilized.The hit probability results are closer to the field shooting test samples.This method has strong applicability and is conducive to obtaining more accurate hit probability estimation results.
基金2021 Annual Research Project of Yili Normal University(2021YSBS012)。
文摘With the implementation of General Senior High School Mathematics Curriculum Standards(2017 Edition,Revised in 2020),probability and statistics,as important carriers of the core mathematical competencies“mathematical modeling”and“data analysis,”have increasingly highlighted their educational value.By summarizing the historical evolution of probability and statistics thinking and combining with teaching practice cases,this study explores its unique role in cultivating students’core mathematical competencies.The research proposes a project-based teaching strategy relying on real scenarios and empowered by technology.Through cases,it demonstrates how to use modern educational technology to realize the whole-process exploration of data collection,model construction,and conclusion verification,so as to promote the transformation of middle school probability and statistics teaching from knowledge imparting to competency development,and provide a practical reference for curriculum reform.
基金jointly supported by the Youth Fund of the National Natural Science Foundation(No.42104053)the Research Project Fund of the Institute of Geophysics,China Earthquake Administration(No.DQJB22R30)the independent project initiated by the institute of Geophysics,China Earthquake Administration(No.JY2022Z41)。
文摘On May 22,2021,an M_(S)7.4 earthquake occurred in Maduo County,Qinghai Province,on the western plateau of China.The level of seismic monitoring in this area was inadequate,and incomplete seismic waveforms were obtained from a few broadband seismometers located within 300 km of the epicentre.All waveforms showed“truncation”phenomena.The waveforms of earthquakes can guide ground motion inputs in near-fault areas.This paper uses the empirical Green's function method to consider the uncertainties in source parameters and source rupture processes by synthesizing high-probability,accurate waveforms in Maduo County(MAD station)near the epicentre.The acceleration waveform at the DAW strong-motion station,located 176 km from the epicentre,is first synthesized with the observed waveform of the mainshock.This critical step not only provides a more accurate source and rupture model of the Maduo earthquake but also establishes an essential reference standard.Secondly,the inferred models are rigorously applied to synthesize the acceleration waveform of the MAD station,ensuring that the results maintain a high accuracy and probability.The findings suggest that(1)the simulated acceleration waveform for the MAD station can better characterize the actual ground motion characteristics of the M_(S)7.4 earthquake in Maduo County,with high accuracy and probability in peak ground acceleration(Abbreviated as PGA)ranges of 140–240 and 350–390 cm/s^(2),respectively,and(2)the M_(S)7.4 earthquake did not undergo a complete supershear rupture process.The first asperity located on the east side of the epicentre is most likely to undergo supershear rupture.However,the Maduo earthquake may have been a complete subshear rupture.(3)The fault dislocation model of the three-asperity model better matches the actual source rupture process of the Maduo earthquake.This method can provide relatively accurate acceleration waveforms for regions with limited earthquake monitoring capabilities and assist in analysis of building seismic damage response,earthquake-induced geological disasters and sand liquefaction,and estimation of regional disaster losses.
基金supported by the National Natural Science Foundation of China(Nos.12475135,12035011,and 12475119)the Shandong Provincial Natural Science Foundation,China(No.ZR2020MA096)the Fundamental Research Funds for the Central Universities(No.22CX03017A)。
文摘Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator and Bayesian model averaging(BMA)to optimize the predictions of RCfrom sophisticated theoretical models.The CBP estimator treats the residual between the theoretical and experimental values of RCas a continuous variable and derives its posterior probability density function(PDF)from Bayesian theory.The BMA method assigns weights to models based on their predictive performance for benchmark nuclei,thereby accounting for the unique strengths of each model.In global optimization,the CBP estimator improved the predictive accuracy of the three theoretical models by approximately 60%.The extrapolation analyses consistently achieved an improvement rate of approximately 45%,demonstrating the robustness of the CBP estimator.Furthermore,the combination of the CBP and BMA methods reduces the standard deviation to below 0.02 fm,effectively reproducing the pronounced shell effects on RCof the Ca and Sr isotope chains.The studies in this paper propose an efficient method to accurately describe RCof unknown nuclei,with potential applications in research on other nuclear properties.
基金supports of the National Natural Science Foundation of China(Nos.12032008,12102080)the Fundamental Research Funds for the Central Universities,China(No.DUT23RC(3)038)are much appreciated。
文摘Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the randomness of structural parameters,working condition and vibration environment are considered for fatigue life predication and reliability assessment.First,the lowcycle fatigue problem is modelled as stochastic static system with random parameters,while the high-cycle fatigue problem is considered as stochastic dynamic system under random excitations.Then,to deal with the two failure modes,the novel Direct Probability Integral Method(DPIM)is proposed,which is efficient and accurate for solving stochastic static and dynamic systems.The probability density functions of accumulated damage and fatigue life of turbine blade for low-cycle and high-cycle fatigue problems are achieved,respectively.Furthermore,the time–frequency hybrid method is advanced to enhance the computational efficiency for governing equation of system.Finally,the results of typical examples demonstrate high accuracy and efficiency of the proposed method by comparison with Monte Carlo simulation and other methods.It is indicated that the DPIM is a unified method for predication of random fatigue life for low-cycle and highcycle fatigue problems.The rotational speed,density,fatigue strength coefficient,and fatigue plasticity index have a high sensitivity to fatigue reliability of engine turbine blade.
基金Shaanxi Provincial 14th Five-Year Plan for Educational Science Research(SGH24Q481)。
文摘This paper focuses on the ideological and political construction of the course“Probability Theory and Mathematical Statistics.”Aiming at the current situation in teaching where emphasis is placed on knowledge imparting while value guidance is neglected,and combined with the requirements of ideological and political education policies in the new era,this paper explores the integration path between professional courses and ideological and political education.Through literature analysis,case comparison,and empirical research,the study proposes a systematic implementation plan covering the design of teaching objectives,the reconstruction of teaching content,and the optimization of the evaluation system.The purpose is to cultivate students’sense of social responsibility and innovative awareness by excavating the ideological and political elements in mathematics.The research results provide practical reference for colleges and universities to deepen the reform of ideological and political education in courses,and promote the implementation of the fundamental task of fostering virtue through education in STEM education.
基金funded by the First-Class Discipline Research Special Project of Inner Mongolia(YLXKZX-NSD-040)the Natural Science Foundation of Inner Mongolia(2022LHQN04003,2023QN04009)+1 种基金the Fundamental Research Funds for the Inner Mongolia University of Finance and Economics(NCXKY25019,NCYWZ22003)the National Social Science Fund of China(22BZS134).
文摘Fires are one of the most destructive natural disasters and have serious long-term effects on the environment,economy,and human health.In Inner Mongolia Autonomous Region,China,frequent fire disturbance occurs due to the intensification of climate change and human activities.It is crucial to understand the fire regime and estimate the probability of regional fire occurrence and reducing fire losses.However,most studies have primarily focused on the dynamic changes,probability of occurrence,and driving mechanisms of wildfires in the grassland and forest land ecosystems in Inner Mongolia,while insufficient research has been conducted on the spatiotemporal variations in active fires and their impact on the wildfire risk in forest land and grassland.Therefore,in this study,we analyzed the active fire regime based on Moderate Resolution Imaging Spectroradiometer(MODIS)thermal anomalies and burned area products from 2000 to 2022.Combined with climate,topographic,landscape,anthropogenic,and vegetation datasets,logistic regression(LR),support vector machine(SVM),random forest(RF),and convolutional neural network(CNN)models were chosen to estimate the probability of active fire occurrence at the seasonal timescale.The results revealed that:(1)a total of 100,343 active fires occurred in Inner Mongolia and the burned area reached 6.59×104 km².The number of ignition point exhibited a significant increasing trend,while the burned area exhibited a nonsignificant decreasing trend;(2)four active fire belts were detected,namely,the Hetao-Tumochuan Plain fire belt,Xiliao River Plain fire belt,Songnen Plain fire belt,and Hailar River Eroded Plain fire belt.The centroid of the active fires has shifted 456.4 km toward the southwest;(3)RF model achieved the highest accuracy in estimating the probability of active fire occurrence,followed by CNN,and LR and SVM models had lower accuracies;and(4)the distribution of the high and extremely high fire risk areas largely aligned with the four fire belts.The probability of active fire occurrence was the highest in spring,followed by that in autumn,and it gradually decreased in summer and winter.Our results revealed active fires migrated to the southwest and ignition sources increased,despite reduction of the burned area was not significant.The RF model outperformed the other models in predicting the probability of active fire occurrence.These findings contribute to future fire prevention and prediction in Inner Mongolia.
基金supported by the Scientific and Technological Research Council of Turkey(TUBITAK)[grant no 122K637].
文摘The estimation of the probability of informed trading(PIN)model and its extensions poses significant challenges owing to various computational problems.To address these issues,we propose a novel estimation method called the expectation-conditional-maximization(ECM)algorithm,which can serve as an alternative to the existing methods for estimating PIN models.Our method provides optimal estimates for the original PIN model as well as two of its extensions:the multilayer PIN model and the adjusted PIN model,along with its restricted versions.Our results indicate that estimations using the ECM algorithm are generally faster,more accurate,and more memory-efficient than the standard methods used in the literature,making it a robust alternative.More importantly,the ECM algorithm is not limited to the models discussed and can be easily adapted to estimate future extensions of the PIN model.
基金Ministry of Education,Center for Scientific Research and Development of Higher Education Institutions“Innovative Application of Virtual Simulation Technology in Vocational Education Teaching”Special Project,Project No.ZJXF2022110.
文摘This study presents an innovative approach to calculating the failure probability of slopes by incorporating fuzzylimit-state functions,a method that significantly enhances the accuracy and efficiency of slope stability analysis.Unlike traditional probabilistic techniques,this approach utilizes a least squares support vector machine(LSSVM)optimized with a grey wolf optimizer(GWO)and K-fold cross-validation(CV)to approximate the limit-statefunction,thus reducing computational complexity.The novelty of this work lies in its application to one-dimensional(1D),two-dimensional(2D),and three-dimensional(3D)slope models,demonstrating its versatility andhigh precision.The proposed method consistently achieves error margins within 3%of Monte Carlo simulation(MCS)results,while substantially reducing computation time,particularly for 2D and 3D models.This makes theapproach highly practical for real-world engineering applications.Furthermore,by applying fuzzy mathematics tohandle uncertainties in geotechnical properties,the method offers a more realistic and comprehensive understandingof slope stability.As water is the main factor influencing the stability of slopes,this aspect is investigatedby calculating the phreatic line after the change in water level.Relevant examples are used to show that the failureprobability of a slope under water wading condition can increase by more than 20%(increase rates in 1D,2D and3D conditions being 25%,27%and 31%,respectively)compared with the natural condition.The influence ofdiverse fuzzy membership functions—linear,normal,and Cauchy—on failure probability is also considered.Thisresearch not only provides a strategy for better calculation of the slope failure probability but also pioneers theintegration of computational intelligence,fuzzy logic and fluid-dynamics in geotechnical engineering,presentingan innovative and efficient tool for slope stability analysis.
