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.

Data driven prediction of fragment velocity distribution under explosive loading conditions

This study presents a machine learning-based method for predicting fragment velocity distribution in warhead fragmentation under explosive loading condition.The fragment resultant velocities are correlated with key design parameters including casing dimensions and detonation positions.The paper details the finite element analysis for fragmentation,the characterizations of the dynamic hardening and fracture models,the generation of comprehensive datasets,and the training of the ANN model.The results show the influence of casing dimensions on fragment velocity distributions,with the tendencies indicating increased resultant velocity with reduced thickness,increased length and diameter.The model's predictive capability is demonstrated through the accurate predictions for both training and testing datasets,showing its potential for the real-time prediction of fragmentation performance.

Does the Redshift Distribution of Swift Long GRBs Trace the Star-Formation Rate?

Gamma-ray bursts (GRBs) are extremely powerful explosions that have been traditionally classified into two categories: long bursts (LGRBs) with an observed duration T90 > 2 s, and short bursts (SGRBs) with an observed duration T90 T90 is the time interval during which 90% of the fluence is detected. LGRBs are believed to emanate from the core-collapse of massive stars, while SGRBs are believed to result from the merging of two compact objects, like two neutron stars. Because LGRBs are produced by the violent death of massive stars, we expect that their redshift distribution should trace the star-formation rate (SFR). The purpose of our study is to investigate the extent to which the redshift distribution of LGRBs follows and reflects the SFR. We use a sample of 370 LGRBs taken from the Swift catalog, and we investigate different models for the LGRB redshift distribution. We also carry out Monte Carlo simulations to check the consistency of our results. Our results indicate that the SFR can describe the LGRB redshift distribution well for high redshift bursts, but it needs an evolution term to fit the distribution well at low redshift.

The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

LOCALIZED RADON-WIGNER TRANSFORM AND GENERALIZED-MARGINAL TIME-FREQUENCY DISTRIBUTIONS

This paper introduces the localized Radon transform (LRT) into time-frequency distributions and presents the localized Radon-Wigner transform (LRWT). The definition of LRWT and a fast algorithm is derived, the properties of LRWT and its relationship with Radon-Wigner transform, Wigner distribution (WD), ambiguity function (AF), and generalized-marginal time-frequency distributions are analyzed.

A NEW QUADRATIC TIME-FREQUENCY DISTRIBUTIONAND A COMPARATIVE STUDY OF SEVERAL POPULARQUADRATIC TIME-FREQUENCY DISTRIBUTIONS

A new quadratic time-frequency distribution (TFD) with a compound kernel is proposed and a comparative study of several popular quadratic TFD is carried out. It is shown that the new TFD with compound kernel has stronger ability than the exponential distribution (ED) and the cone-shaped kernel distribution (CKD) in reducing cross terms, meanwhile almost not decreasing the time-frequency resolution of ED or CKD.

Adaptive Time-Frequency Distribution Based on Time-Varying Autoregressive and Its Application to Machine Fault Diagnosis

The time-varying autoregressive （TVAR） modeling of a non-stationary signal is studied. In the proposed method, time-varying parametric identification of a non-stationary signal can be translated into a linear time-invariant problem by introducing a set of basic functions. Then, the parameters are estimated by using a recursive least square algorithm with a forgetting factor and an adaptive time-frequency distribution is achieved. The simulation results show that the proposed approach is superior to the short-time Fourier transform and Wigner distribution. And finally, the proposed method is applied to the fault diagnosis of a bearing , and the experiment result shows that the proposed method is effective in feature extraction.

Distribution of large-scale detachment faults on mid-ocean ridges in relation to spreading rates

Large-scale detachment faults on mid-ocean ridges （MORs） provide a window into the deeper earth. They have megamullion on their corrugated surfaces, with exposed lower crustal and upper mantle rocks, rela- tively high residual Bouguer gravity anomaly and P-wave velocity, and are commonly associated with ocean- ic core complex. According to 30 detachment faults identified on MORs, we found that their distances to the axis mostly range from 5 to 50 km, half-spreading rates range from 6.8 to 17 mm/a, and activity time ranges from recent to 3 Ma. Most of the detachment faults are developed on the slow spreading Mid-Atlantic Ridge （MAR） and ultra-slow spreading Southwest Indian Ridge （SWIRl, with the dominant half-spreading rates of 7-13 mm/a, especially 10-13 mm/a. Furthermore, they mostly occur at the inside corner of one segment end and result in an asymmetric seafloor spreading. The detachment faults on MORs are mainly controlled by the tectonism and influenced by the magmatism. Long-lived detachment faults tend to be formed where the ridge magma supply is at a moderate level, although the tectonism is a first-order controlling factor. At the slow spreading ridges, detachment faults tend to occur where local magma supply is relatively low, whilst at the ultra-slow spreading ridges, they normally occur where local magma supply is relatively high. These faults are accompanied by hydrothermal activities, with their relationships being useful in the study of hydrothermal polymetallic sulfides and their origin.

The W transform and its improved methods for time-frequency analysis of seismic data

The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improve the resolution of the linear time-frequency analysis method in the low-frequency region,we have proposed a W transform method,in which the instantaneous frequency is introduced as a parameter into the linear transformation,and the analysis time window is constructed which matches the instantaneous frequency of the seismic data.In this paper,the W transform method is compared with the Wigner-Ville distribution(WVD),a typical nonlinear time-frequency analysis method.The WVD method that shows the energy distribution in the time-frequency domain clearly indicates the gravitational center of time and the gravitational center of frequency of a wavelet,while the time-frequency spectrum of the W transform also has a clear gravitational center of energy focusing,because the instantaneous frequency corresponding to any time position is introduced as the transformation parameter.Therefore,the W transform can be benchmarked directly by the WVD method.We summarize the development of the W transform and three improved methods in recent years,and elaborate on the evolution of the standard W transform,the chirp-modulated W transform,the fractional-order W transform,and the linear canonical W transform.Through three application examples of W transform in fluvial sand body identification and reservoir prediction,it is verified that W transform can improve the resolution and energy focusing of time-frequency spectra.

Effect of growth rate on microstructure and solute distribution of Al-Zn-Mg alloy

An Al-5.3%Zn-5.3%Mg alloy was unidirectionally solidified to determine morphological transition and solute distribution by a modification of the Bridgman technique for crystal growth with growth rates ranging from 4-500 μm/s and a temperature gradient of 25 K/cm. It was determined that growth rates from 6.5-9.5 μm/s generated a cell morphology, where the lower limit corresponds to the plane front to cellular transition and the upper limit indicates the cellular to columnar dendrite transition. The microstructures of the alloys solidified from 30 μm/s to growth rates less than 500 μm/s were mainly composed of columnar dendrites, while the microstructures solidified at growth rates greater than 500 μm/s were equiaxed. Regarding experimental results on solute distribution, a prediction of the model developed by Rappaz and Boettinger for dendrite solidification of multicomponent alloys was applied with excellent agreement. Results of solute distribution were employed to derive the precipitation fraction of τ-phase needed to increase the electrochemical properties of the alloy to be used as an Al-sacrificial anode.

Higher-order expansions of powered extremes of logarithmic general error distribution

In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).

Effect of impeller type and scale-up on spatial distribution of shear rate in a stirred tank

The main spatial distribution features of shear rate in a stirred tank operated with five different radial and axial flow impellers were presented with particle image velocimetry(PIV)experiments.Not only the average shear rate in the whole tank but also the local value in the vicinity of impeller increases linearly with impeller speed.Furthermore,the shear coefficient(Ks,imp)at the impeller outlet is linearly related to the impeller flow number(Nq)and decreases with the increase of Nq in general at the constant power consumption per unit volume(Pv).During scale-up based on the constant Pv and geometric similarity,CFD results show that the volume-averaged shear rate(cavg)for RDT decreases faster than that of other impellers with the impeller tip velocity(Utip).The novel multi-blade combined(MBC)impeller with the increased height-to-diameter ratio of the stirred tank is able to more effectively improve the distribution uniformity of shear rate at the same Pv after scale-up.These studies provide a data basis for selecting the impeller types and improving the shear rate environment in the large-scale stirred tank.

Effect of droplet characteristics on liquid-phase distribution in spray zone of internal mixing air-mist nozzle

In continuous casting production,droplet characteristics are important parameters for evaluating the nozzle atomization quality,and have a significant impact on the secondary cooling effect and the slab quality.In order to study the behavior of atomized droplets after reaching the slab surface and to optimize the spray cooling effect,the influence of droplet diameter and droplet velocity on the migration behavior of droplets in the secondary cooling zone was analyzed by FLUENT software.Results show that the droplets in the spray zone and on the slab surface are mainly concentrated in the center,thus,the liquid volume fraction in the center is higher than that of either side.As the droplet diameter increases,the region of high liquid volume fraction on the slab surface becomes wider,and the liquid phase distribution in the slab width direction becomes uneven.Although increasing the droplet velocity at the nozzle exit has little effect on droplet diffusion in the spray zone,the distribution becomes more uneven due to more liquid reaches the slab surface per unit time.A prediction formula of the maximum water flow rate on the slab surface for specific droplet characteristics was proposed based on dimensionless analysis and validated by simulated data.A nozzle spacing of 210 mm was recommended under the working conditions in this study,which ensures effective coverage of the spray water over the slab surface and enhances the distribution uniformity of water flow rate in the transverse direction.

Individual Differences in Blood Alcohol Concentrations after Moderate Drinking Are Mainly Regulated by Gastric Emptying Rate Together with Ethanol Distribution Volume

Blood alcohol concentration (BAC) differs greatly among individuals, even when people of the same sex and age drink alcohol under the same drinking conditions. In this study, we investigated the main factors involved in the internal reg-ulation of individual differences in BAC, focusing on the alcohol dehydrogenase 1B (ADH1B) genotype, blood acetal-dehyde concentration (BAcH), amount of habitual alcohol consumption, pharmacokinetic parameters of BAC, distribution volume of ethanol (Vd), and gastric emptying rate (GER) under the same drinking conditions. Twenty healthy Japanese males aged between 40 and 59 years old and having the aldehyde dehydrogenase 2 (ALDH2) genotype of ALDH 2*1/*2 were recruited for this study. The subjects were given 0.32 g ethanol/kg body weight in the form of commercially available beer (5%, v/v). The results showed that BAC-max differed greatly among individuals with a more than two-fold variation. When the BAC-time curve was compared among ADH1B genotypes (ADH1B*1/*1, *1/*2, and *2/*2), there were no differences in BAC among the genotypes. Although BAcH, monthly alcohol consumption, elimination rate of blood ethanol (β value) and ethanol disappearance rate from the body (EDR) can affect BAC, all of them had no correlations with BAC-max. However, Vd (liter/kg), ΔPlasma glucose concentration (ΔPGC = PGC30 min ? PGC0 min) and the serum concentration of gastric inhibitory polypeptide (GIP) did correlate with BAC-max. Model 2 in multiple linear regression analysis showed the optimal model for Vd and GIP with positive correlations with BAC-max. As GIP and ΔPGC are both reflected by gastric emptying rate (GER), we concluded that the individual differences in BAC after moderate drinking are mainly regulated by GER together with Vd. These findings demonstrate that together with body water content, the gastrointestinal tract plays an important role in the regulation of individual differences in BAC, involving first pass metabolism of ethanol.

Modeling and forecasting exchange rate volatility in Bangladesh using GARCH models:a comparison based on normal and Student's t-error distribution

Background:Modeling exchange rate volatility has remained crucially important because of its diverse implications.This study aimed to address the issue of error distribution assumption in modeling and forecasting exchange rate volatility between the Bangladeshi taka(BDT)and the US dollar($).Methods:Using daily exchange rates for 7 years(January 1,2008,to April 30,2015),this study attempted to model dynamics following generalized autoregressive conditional heteroscedastic(GARCH),asymmetric power ARCH(APARCH),exponential generalized autoregressive conditional heteroscedstic(EGARCH),threshold generalized autoregressive conditional heteroscedstic(TGARCH),and integrated generalized autoregressive conditional heteroscedstic(IGARCH)processes under both normal and Student’s t-distribution assumptions for errors.Results and Conclusions:It was found that,in contrast with the normal distribution,the application of Student’s t-distribution for errors helped the models satisfy the diagnostic tests and show improved forecasting accuracy.With such error distribution for out-of-sample volatility forecasting,AR(2)–GARCH(1,1)is considered the best.

Particle Size Distribution,Powder Agglomerates and Their Effects on Sinterability of Ultrafine Alumina Powders

An intensive study of the particle size distribution of four commercial ultrafine alumina powders to obtain information about the powder agglomeration and relate them to the compactibility and the sinterability has been made.

Phosphate Distribution and Movement in Soil－Root In－terface Zone：I． The Influence of Transpiration Rate

The experiments were conducted in the artificial climate laboratory using ￣(32)P labelled soil and soil-rootplane system to investigate phosphate distribution and its movement in the soil-root interface zone andtheir relations with phosphate uptake by plant as well as transpiration rate (atmosphere humidity). It wasfound that although the phosphate in the soilroot interface zone was of depletive distribution as a functionC/Co = ax￣b(C/Co is the relative content of fertilizer phosphate in a distance from the root surface x, aand b are the regression constants), and a relative accumulation zone of phosphate within 0.5 mm near theroot surface was often observed especially in the heavier texture soils because of root phosphate secretion.The depletion intensity of phosphate in the soil-root interface zone was in agreement with the phosphateuptake by plants under two humidities very well. However, the effects of air humidity on characteristics ofthe phosphate distribution near wheat or maize root surface were different. Wheat grew better under loweratmosphere humidity while maize, under higher humidity, which caused a more intensive uptake and thusa stronger depletion of phosphate in the rhizosphere. Moreover, the depletion intensity was greater by thebottom or the middle part of wheat roots and by the top or the middle part of maize roots. The depletivedistribution of phosphate in the rhizosphere soil and the relative contribution of phosphate diffusion to plant,which was more than 98% in the cultural experiments, indicated that diffusion was a major process forphosphorus supply to plants.

Downlink SINR and Rate Distribution of Ultra-Dense Het Nets with Burst Traffic

SINR distribution and rate overage distribution are crucial for optimization of deployment of Ultra-dense Het Nets.Most existing literatures assume that BSs have full queues and full-buffer traffic.In fact,due to ultra-dense deployment of small cells,traffic in small cell varies dramatically in time and space domains.Hence,it is more practical to investigate scenario with burst traffic.In this paper,we consider a two-tier non-uniform ultra-dense Het Net with burst traffic,where macro BSs are located according to Poisson Point Process(PPP),and pico BSs are located according to Poisson Hole Process(PHP).The closed-form expressions of SINR distribution and rate distribution are derived,and then validated through simulation.Our study shows that different from the result of full buffer case,the SINR distribution and rate distribution of users depend on the average transmission probabilities of BSs in burst traffic case.

Spatial Distributions of Atmospheric Radiative Fluxes and Heating Rates over China during Summer

The latitude-altitude distributions of radiative fluxes and heating rates are investigated by utilizing CloudSat satellite data over China during summer. The Tibetan Plateau causes the downward shortwave fluxes of the lower atmosphere over central China to be smaller than the fluxes over southern and northern China by generating more clouds. The existence of a larger quantity of clouds over central China reflects a greater amount of solar radiation back into space. The vertical gradients of upward shortwave radiative fluxes in the atmosphere below 8 km are greater than those above 8 km. The latitudinal-altitude distributions of downward longwave radiative fluxes show a slantwise decreasing trend from low latitudes to high latitudes that gradually weaken in the downward direction. The upward longwave radiative fluxes also weaken in the upward direction but with larger gradients. The maximum heating rates by solar radiation and cooling rates by longwave infrared radiation are located over 28 40°N at 7 8 km mean sea level (MSL), and they are larger than the rates in the northern and southern regions. The heating and cooling rates match well both vertically and geographically.

Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor

The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.