Federated Learning Model for Auto Insurance Rate Setting Based on Tweedie Distribution

In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining the Tweedie regression model involves training on a centralized dataset,when the data is provided by multiple parties,training a privacy-preserving Tweedie regression model without exchanging raw data becomes a challenge.To address this issue,this study introduces a novel vertical federated learning-based Tweedie regression algorithm for multi-party auto insurance rate setting in data silos.The algorithm can keep sensitive data locally and uses privacy-preserving techniques to achieve intersection operations between the two parties holding the data.After determining which entities are shared,the participants train the model locally using the shared entity data to obtain the local generalized linear model intermediate parameters.The homomorphic encryption algorithms are introduced to interact with and update the model intermediate parameters to collaboratively complete the joint training of the car insurance rate-setting model.Performance tests on two publicly available datasets show that the proposed federated Tweedie regression algorithm can effectively generate Tweedie regression models that leverage the value of data fromboth partieswithout exchanging data.The assessment results of the scheme approach those of the Tweedie regressionmodel learned fromcentralized data,and outperformthe Tweedie regressionmodel learned independently by a single party.

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry.To study the mechanical behavior of a typical ductile cast iron(GJS-450)with nodular graphite,uni-axial quasi-static and dynamic tensile tests at strain rates of 10^(-4),1,10,100,and 250 s^(-1)were carried out.In order to investigate the influence of stress state on the deformation and fracture parameters,specimens with various geometries were used in the experiments.Stress strain curves and fracture strains of the GJS-450 alloy in the strain rate range of 10^(-4)to 250 s^(-1)were obtained.A strain rate-dependent plastic flow model was proposed to describe the mechanical behavior in the corresponding strain-rate range.The available damage model was extended to take the strain rate into account and calibrated based on the analysis of local fracture strains.Simulations with the proposed plastic flow model and the damage model were conducted to observe the deformation and fracture process.The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys.The predictions with the proposed plastic flow and damage models at various strain rates agree well with the experimental results,which illustrates that the rate-dependent plastic flow and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.The proposed plastic flow and damage models can be used to describe the deformation and fracture analysis of materials with similar properties.

Evaluation of the Impact of Refined Quality Control Management Model on the Qualified Rate of Disinfection and Sterilization of Surgical Instruments in the Sterilization Supply Center

Objective:To evaluate the application value of a refined quality control management model for a sterilization supply center.Methods:A retrospective analysis was conducted on the work situation of the sterilization supply center from January 2021 to January 2023.The work situation before January 31,2022,was classified as the control group;a routine quality control management model was implemented,and the work situation after January 31,2022,was classified as the observation group.The quality of medical device management and department satisfaction between the two groups were compared.Results:The timely recovery and supply rate,classification and cleaning pass rate,disinfection pass rate,packaging pass rate,sterilization pass rate,and department satisfaction score in the observation group were all higher than those of the control group(P<0.05).Conclusion:Implementing a refined quality control management model in the sterilization supply center can improve the quality management level of medical devices and department satisfaction and is worthy of promotion.

Country-based modelling of COVID-19 case fatality rate:A multiple regression analysis

BACKGROUND The spread of the severe acute respiratory syndrome coronavirus 2 outbreak worldwide has caused concern regarding the mortality rate caused by the infection.The determinants of mortality on a global scale cannot be fully understood due to lack of information.AIM To identify key factors that may explain the variability in case lethality across countries.METHODS We identified 21 Potential risk factors for coronavirus disease 2019(COVID-19)case fatality rate for all the countries with available data.We examined univariate relationships of each variable with case fatality rate(CFR),and all independent variables to identify candidate variables for our final multiple model.Multiple regression analysis technique was used to assess the strength of relationship.RESULTS The mean of COVID-19 mortality was 1.52±1.72%.There was a statistically significant inverse correlation between health expenditure,and number of computed tomography scanners per 1 million with CFR,and significant direct correlation was found between literacy,and air pollution with CFR.This final model can predict approximately 97%of the changes in CFR.CONCLUSION The current study recommends some new predictors explaining affect mortality rate.Thus,it could help decision-makers develop health policies to fight COVID-19.

Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

A new Ignition-Growth reaction rate model for shock initiation

Accurately predicting reactive flow is a challenge when characterizing an explosive under external shock stimuli as the shock initiation time is on the order of a microsecond.The present study constructs a new Ignition-Growth reaction rate model,which can describe the shock initiation processes of explosives with different initial densities,particle sizes and loading pressures by only one set of model parameters.Compared with the Lee-Tarver reaction rate model,the new Ignition-Growth reaction rate model describes better the shock initiation process of explosives and requires fewer model parameters.Moreover,the shock initiation of a 2,4-Dinitroanisole(DNAN)-based melt-cast explosive RDA-2(DNAN/HMX(octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazoncine)/aluminum)are investigated both experimentally and numerically.A series of shock initiation experiments is performed with manganin piezoresistive pressure gauges and corresponding numerical simulations are carried out with the new Ignition-Growth reaction rate model.The RDA-2 explosive is found to have higher critical initiation pressure and lower shock sensitivity than traditional explosives(such as the Comp.B explosive).The calibrated reaction rate model parameters of RDA-2 could provide numerical basis for its further application.

Modeling the Failure Rate of a Standby Multi-Component System and Improving Reliability

Evaluating the reliability of a system requires knowledge of the failure modes to which it is subjected. Complex topology systems generally require a high level of availability, which is a function of the arrangement of elements (components) in the system. To avoid serious failures for such complex systems, recourse can be had to the redundancy techniques available in the literature. These techniques help to improve system reliability, without affecting the reliability of system components. This paper is interested in the proposal of a model for evaluating the failure rate of a standby multi-components system and in improving the reliability of mechanical systems, arranged in a topology (series, parallel, or mixed).

Deterministic and Stochastic Analysis of a New Rumor Propagation Model with Nonlinear Propagation Rate in Social Network

This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.

A bounding surface visco-plasticity model considering generalized spacing ratio of soils

The non-unique critical state of soils with time-dependent behaviors is a significant issue in geotechnical engineering problems.However,previous bounding surface plasticity models cannot predict accurately the non-unique critical state of soils,because the distance between the compression line and critical state line charged by strain-rate effect is basically neglected.To fill this gap,a generalized spacing ratio of soils is defined in the elasto-viscoplastic framework,and a bounding surface visco-plasticity model is formulated and verified,which can consider the generalized spacing ratio.Specifically,the generalized spacing ratio of soils reflects the distance between the compression line and the critical state line of soils with time-dependent behaviors.Then,the generalized spacing ratio is introduced into an improved anisotropic bounding surface.A new expression of the visco-plastic multiplier is derived by solving the consistency equation of an anisotropic bounding surface.In the expression,a strain rate index is proposed to account for the strain-rate effect on visco-plastic strain increment,and a visco-plastic hardening modulus is derived to predict the visco-plastic response of soils in overconsolidation conditions.The model is then verified through constant strain rate tests and creep tests.Notably,it can capture the non-unique critical states of soils with time-dependent behaviors due to the generalized spacing ratio and the creep rupture of soils due to the visco-plastic multiplier that considers the stress ratio and visco-plastic strain rate.

Constitutive model of viscoelastic dynamic damage for the material of gas obturator in modular-charge howitzer

In order to investigate the mechanical response behavior of the gas obturator of the breech mechanism,made of polychloroprene rubber(PCR), uniaxial compression experiments were carried out by using a universal testing machine and a split Hopkinson pressure bar(SHPB), obtaining stress-strain responses at different temperatures and strain rates. The results revealed that, in comparison to other polymers, the gas obturator material exhibited inconspicuous strain softening and hardening effects;meanwhile, the mechanical response was more affected by the strain rate than by temperature. Subsequently, a succinct viscoelastic damage constitutive model was developed based on the ZWT model, including ten undetermined parameters, formulated with incorporating three parallel components to capture the viscoelastic response at high strain rate and further enhanced by integrating a three-parameter Weibull function to describe the damage. Compared to the ZWT model, the modified model could effectively describe the mechanical response behavior of the gas obturator material at high strain rates. This research laid a theoretical foundation for further investigation into the influence of chamber sealing issues on artillery firing.

Modeling,Simulation,and Risk Analysis of Battery Energy Storage Systems in New Energy Grid Integration Scenarios

Energy storage batteries can smooth the volatility of renewable energy sources.The operating conditions during power grid integration of renewable energy can affect the performance and failure risk of battery energy storage system(BESS).However,the current modeling of grid-connected BESS is overly simplistic,typically only considering state of charge(SOC)and power constraints.Detailed lithium(Li)-ion battery cell models are computationally intensive and impractical for real-time applications and may not be suitable for power grid operating conditions.Additionally,there is a lack of real-time batteries risk assessment frameworks.To address these issues,in this study,we establish a thermal-electric-performance(TEP)coupling model based on a multitime scale BESS model,incorporating the electrical and thermal characteristics of Li-ion batteries along with their performance degradation to achieve detailed simulation of grid-connected BESS.Additionally,considering the operating characteristics of energy storage batteries and electrical and thermal abuse factors,we developed a battery pack operational riskmodel,which takes into account SOCand charge-discharge rate(Cr),using amodified failure rate to represent the BESS risk.By integrating detailed simulation of energy storage with predictive failure risk analysis,we obtained a detailed model for BESS risk analysis.This model offers a multi-time scale integrated simulation that spans month-level energy storage simulation times,day-level performance degradation,minutescale failure rate,and second-level BESS characteristics.It offers a critical tool for the study of BESS.Finally,the performance and risk of energy storage batteries under three scenarios—microgrid energy storage,wind power smoothing,and power grid failure response—are simulated,achieving a real-time state-dependent operational risk analysis of the BESS.

The variation in basal channels and basal melt rates of Pine Island Ice Shelf

In recent years,there has been a significant acceleration in the thinning,calving and retreat of the Pine Island Ice Shelf(PIIS).The basal channels,results of enhanced basal melting,have the potential to significantly impact the stability of the PIIS.In this study,we used a variety of remote sensing data,including Landsat,REMA DEM,ICESat-1 and ICESat-2 satellite altimetry observations,and Ice Bridge airborne measurements,to study the spatiotemporal changes in the basal channels from 2003 to 2020 and basal melt rate from 2010 to 2017 of the PIIS under the Eulerian framework.We found that the basal channels are highly developed in the PIIS,with a total length exceeding 450 km.Most of the basal channels are ocean-sourced or groundingline-sourced basal channels,caused by the rapid melting under the ice shelf or near the groundingline.A raised seabed prevented warm water intrusion into the eastern branch of the PIIS,resulting in a lower basal melt rate in that area.In contrast,a deepsea trough facilitates warm seawater into the mainstream and the western branch of the PIIS,resulting in a higher basal melt rate in the main-stream,and the surface elevation changes above the basal channels of the mainstream and western branch are more significant.The El Ni?o event in 2015–2016 possibly slowed down the basal melting of the PIIS by modulating wind field,surface sea temperature and depth seawater temperature.Ocean and atmospheric changes were driven by El Ni?o,which can further explain and confirm the changes in the basal melting of the PIIS.

Quantum Realities and Observer-Dependent Universes: An Advanced Observer Model

This paper presents a novel observer model that integrates quantum mechanics, relativity, idealism, and the simulation hypothesis to explain the quantum nature of the universe. The model posits a central server transmitting multi-media frames to create observer-dependent realities. Key aspects include deriving frame rates, defining quantum reality, and establishing hierarchical observer structures. The model’s impact on quantum information theory and philosophical interpretations of reality are examined, with detailed discussions on information loss and recursive frame transmission in the appendices.

Application of Exponential Distribution in Modeling of State Holding Time in HIV/AIDS Transition Dynamics

Markov modeling of HIV/AIDS progression was done under the assumption that the state holding time (waiting time) had a constant hazard. This paper discusses the properties of the hazard function of the Exponential distributions and its modifications namely;Parameter proportion hazard (PH) and Accelerated failure time models (AFT) and their effectiveness in modeling the state holding time in Markov modeling of HIV/AIDS progression with and without risk factors. Patients were categorized by gender and age with female gender being the baseline. Data simulated using R software was fitted to each model, and the model parameters were estimated. The estimated P and Z values were then used to test the null hypothesis that the state waiting time data followed an Exponential distribution. Model identification criteria;Akaike information criteria (AIC), Bayesian information criteria (BIC), log-likelihood (LL), and R2 were used to evaluate the performance of the models. For the Survival Regression model, P and Z values supported the non-rejection of the null hypothesis for mixed gender without interaction and supported the rejection of the same for mixed gender with interaction term and males aged 50 - 60 years. Both Parameters supported the non-rejection of the null hypothesis in the rest of the age groups. For Gender male with interaction both P and Z values supported rejection in all the age groups except the age group 20 - 30 years. For Cox Proportional hazard and AFT models, both P and Z values supported the non-rejection of the null hypothesis across all age groups. The P-values for the three models supported different decisions for and against the Null hypothesis with AFT and Cox values supporting similar decisions in most of the age groups. Among the models considered, the regression assumption provided a superior fit based on (AIC), (BIC), (LL), and R2 Model identification criteria. This was particularly evident in age and gender subgroups where the data exhibited non-proportional hazards and violated the assumptions required for the Cox Proportional Hazard model. Moreover, the simplicity of the regression model, along with its ability to capture essential state transitions without over fitting, made it a more appropriate choice.

RETRACTED: Nuclear Structure Study of Odd-Odd Yttrium Nuclei within Interacting-Boson Fermi-Fermion Model (IBFFM)

Short Retraction NoticeThe paper does not meet the standards of "Journal of Applied Mathematics and Physics". This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.Editor guiding this retraction: Prof. Wen-Xiu Ma (EiC of JAMP)The full retraction notice in PDF is preceding the original paper, which is marked "RETRACTED".

Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility

In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates (da/dN) of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-ΔK relations, the confidence-based da/dN-ΔK relations, and the probabilistic- and confidence-based da/dN-ΔK relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.

Quantitative Model for Estimating Soil Erosion Rates Using 137 Cs *1

A quantitative model was developed to relate the amount of 137 Cs loss from the soil profile to the rate of soil erosion. According to mass balance model, the depth distribution pattern of 137 Cs in the soil profile, the radioactive decay of 137 Cs, sampling year and the difference of 137 Cs fallout amount among years were taken into consideration. By introducing typical depth distribution functions of 137 Cs into the model, detailed equations for the model were got for different soils. The model shows that the rate of soil erosion is mainly controlled by the depth distribution pattern of 137 Cs, the year of sampling, and the percentage reduction in total 137 Cs. The relationship between the rate of soil loss and 137 Cs depletion is neither linear nor logarithmic. The depth distribution pattern of 137 Cs is a major factor for estimating the rate of soil loss. Soil erosion rate is directly related with the fraction of 137 Cs content near the soil surface. The influences of the radioactive decay of 137 Cs, sampling year and 137 Cs input fraction are not large compared with others.

Research on the influences of confining pressure and strain rate on NEPE propellant:Experimental assessment and constitutive model

In order to study the influences of confining pressure and strain rate on the mechanical properties of the Nitrate Ester Plasticized Polyether(NEPE)propellant,uniaxial tensile tests were conducted using the selfmade confining pressure system and material testing machine.The stress-strain responses of the NEPE propellant under different confining pressure conditions and strain rates were obtained and analyzed.The results show that confining pressure and strain rate have a remarkably influence on the mechanical responses of the NEPE propellant.As confining pressure increases(from 0 to 5.4 MPa),the maximum tensile stress and ultimate strain increase gradually.With the coupled effects of confining pressure and strain rate,the value of the maximum tensile stress and ultimate strain at 5.4 MPa and 0.0667 s^(-1)is 2.03 times and 2.19 times of their values under 0 MPa and 0.00333 s^(-1),respectively.Afterwards,the influence mechanism of confining pressure on the NEPE propellant was analyzed.Finally,based on the viscoelastic theory and continuous damage theory,a nonlinear constitutive model considering confining pressure and strain rate was developed.The damage was considered to be rate-dependent and pressuredependent.The constitutive model was validated by comparing experimental data with predictions of the constitutive model.The whole maximum stress errors of the model predictions are lower than 4%and the corresponding strain errors are lower than 7%.The results show that confining pressure can suppress the damage initiation and evolution of the NEPE propellant and the nonlinear constitutive model can describe the mechanical responses of the NEPE propellant under various confining pressure conditions and strain rates.This research can lay a theoretical foundation for analyzing the structural integrity of propellant grain accurately under working pressure loading.