High-precision chaotic radial basis function neural network model:Data forecasting for the Earth electromagnetic signal before a strong earthquake

The Earth’s natural pulse electromagnetic field data consists typically of an underlying variation tendency of intensity and irregularities.The change tendency may be related to the occurrence of earthquake disasters.Forecasting of the underlying intensity trend plays an important role in the analysis of data and disaster monitoring.Combining chaos theory and the radial basis function neural network,this paper proposes a forecasting model of the chaotic radial basis function neural network to conduct underlying intensity trend forecasting by the Earth’s natural pulse electromagnetic field signal.The main strategy of this forecasting model is to obtain parameters as the basis for optimizing the radial basis function neural network and to forecast the reconstructed Earth’s natural pulse electromagnetic field data.In verification experiments,we employ the 3 and 6 days’data of two channels as training samples to forecast the 14 and 21-day Earth’s natural pulse electromagnetic field data respectively.According to the forecasting results and absolute error results,the chaotic radial basis function forecasting model can fit the fluctuation trend of the actual signal strength,effectively reduce the forecasting error compared with the traditional radial basis function model.Hence,this network may be useful for studying the characteristics of the Earth’s natural pulse electromagnetic field signal before a strong earthquake and we hope it can contribute to the electromagnetic anomaly monitoring before the earthquake.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

Short-term forecast in the early stage of the COVID-19 outbreak in Italy. Application of a weighted and cumulative average daily growth rate to an exponential decay model

To estimate the size of the novel coronavirus(COVID-19)outbreak in the early stage in Italy,this paper introduces the cumulated and weighted average daily growth rate(WR)to evaluate an epidemic curve.On the basis of an exponential decay model(EDM),we provide estimations of the WR in four-time intervals from February 27 to April 07,2020.By calibrating the parameters of the EDM to the reported data in Hubei Province of China,we also attempt to forecast the evolution of the outbreak.We compare the EDM applied to WR and the Gompertz model,which is based on exponential decay and is often used to estimate cumulative events.Specifically,we assess the performance of each model to short-term forecast of the epidemic,and to predict the final epidemic size.Based on the official counts for confirmed cases,the model applied to data from February 27 until the 17th of March estimate that the cumulative number of infected in Italy could reach 131,280(with a credibility interval 71,415-263,501)by April 25(credibility interval April 12 to May 3).With the data available until the 24st of March the peak date should be reached on May 3(April 23 to May 23)with 197,179 cumulative infections expected(130,033e315,269);with data available until the 31st of March the peak should be reached on May 4(April 25 to May 18)with 202,210 cumulative infections expected(155.235 e270,737);with data available until the 07st of April the peak should be reached on May 3(April 26 toMay 11)with 191,586(160,861-232,023)cumulative infections expected.Based on the average mean absolute percentage error(MAPE),cumulated infections forecasts provided by the EDM applied to WR performed better across all scenarios than the Gompertz model.An exponential decay model applied to the cumulated and weighted average daily growth rate appears to be useful in estimating the number of cases and peak of the COVID-19 outbreak in Italy and the model was more reliable in the exponential growth phase.

Finite Element Implementation of the Exponential Drucker-Prager Plasticity Model for Adhesive Joints

This paper deals with the numerical implementation of the exponential Drucker-Parger plasticitymodel in the commercial finite element software,ABAQUS,via user subroutine UMAT for adhesive joint simulations.The influence of hydrostatic pressure on adhesive strength was investigated by a modified Arcan fixture designed particularly to induce a different state of hydrostatic pressure within an adhesive layer.The developed user subroutine UMAT,which utilizes an associated plastic flow during a plastic deformation,can provide a good agreement between the simulations and the experimental data.Better numerical stability at highly positive hydrostatic pressure loads for a very high order of exponential function can also be achieved compared to when a non-associated flow is used.

A Medium/Long-Range Forecast of Pacific Subtropical High Based on Dynamic Statistic Model Reconstruction

Based on the 500-hPa geopotential height field series of T106 numerical forecast products, by empirical orthogonal function （EOF） time-space separation, and on the hypotheses of EOF space-models being stable, the EOF time coefficient series were taken as dynamical statistic model variables. The dynamic system reconstruction idea and genetic algorithm were introduced to make the dynamical model parameters optimized, and a nonlinear dynamic statistic model of EOF separating time coefficient series was established. By the model time integral and EOF time-space reconstruction, a medium/long-range forecast of subtropical high was carried out. The results show that the dynamical model forecast and T106 numerical forecast were approximately similar in the short-range forecast （≤5 days）, but in the medium/long-range forecast （≥5 days）, the forecast results of dynamical model was superior to that of T106 numerical products. A new method and idea were presented for diagnosing and forecasting complicated weathers such as subtropical high, and showed a better application outlook.

Modelling HIV/AIDS Cases in Zambia: A Comparative Study of the Impact of Mandatory HIV Testing

In this study, a time series modeling approach is used to determine an ARIMA model and advance counterfactual forecasting at a point of policy intervention. We consider monthly data of HIV/AIDS cases from the Ministry of Health (Copperbelt province) of Zambia, for the period 2010 to 2019 and have a total of 120 observations. Results indicate that ARIMA (1, 0, 0) is an adequate model which best fits the HIV/AIDS time series data and is, therefore, suitable for forecasting cases. The model predicts a reduction from an average of 3500 to 3177 representing 14.29% in HIV/AIDS cases from 2017 (year of policy activation) to 2019, but the actual recorded cases dropped from 3500 to 1514 accounting for 57.4% in the same time frame.

AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.

Predator Population Dynamics Involving Exponential Integral Function When Prey Follows Gompertz Model

The current study investigates the predator-prey problem with assumptions that interaction of predation has a little or no effect on prey population growth and the prey’s grow rate is time dependent. The prey is assumed to follow the Gompertz growth model and the respective predator growth function is constructed by solving ordinary differential equations. The results show that the predator population model is found to be a function of the well known exponential integral function. The solution is also given in Taylor’s series. Simulation study shows that the predator population size eventually converges either to a finite positive limit or zero or diverges to positive infinity. Under certain conditions, the predator population converges to the asymptotic limit of the prey model. More results are included in the paper.

Improved grey prediction model based on exponential grey action quantity

With the passage of time, it has become important to investigate new methods for updating data to better fit the trends of the grey prediction model. The traditional GM（1,1） usually sets the grey action quantity as a constant. Therefore, it cannot effectively fit the dynamic characteristics of the sequence, which results in the grey model having a low precision. The linear grey action quantity model cannot represent the index change law. This paper presents a grey action quantity model, the exponential optimization grey model（EOGM（1,1））, based on the exponential type of grey action quantity; it is constructed based on the exponential characteristics of the grey prediction model. The model can fully reflect the exponential characteristics of the simulation series with time. The exponential sequence has a higher fitting accuracy. The optimized result is verified using a numerical example for the fluctuating sequence and a case study for the index of the tertiary industry＇s GDP. The results show that the model improves the precision of the grey forecasting model and reduces the prediction error.

Development of 3D top coal caving angle model for fully mechanized extra-thick coal seam mining

During high-intensity,fully mechanized mining of extra-thick coal seam,the top coal would cave to a certain 3D form.Based on the data collected during drilling,a 3D model of top coal caving surface space was established to determine the relationship between the location of the stope roof and the caving surface,enabling the mathematical computation of the top caving angle(φ).The drilling method was employed to measure the top caving angle on two extra-thick fully mechanized coal caving faces under the conditions of three geological structures,namely,no geological structure,igneous rock structure,and fault structure.The results show that the value of top caving angle could be accurately estimated on-site with the 9-parameter 3D top coal caving surface model built with the drilling method.This method is a novel on-site measurement that can be easily applied.Our findings reveal that the characteristics of the coal-rock in the two mining faces are different;yet their caving angles follow the ruleφ_(igneous rock structure)<φ_(no geological structure)<φ_(fault structure).Finally,through the data fitting with two indexes(the top coal uniaxial compressive strength and the top caving angle),it is found that the relationship between the two indexes satisfies an exponential decay function.

Optimal Quota-Share and Excess-of-Loss Reinsurance and Investment with Heston’s Stochastic Volatility Model

An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.

MODELLING OF TENSILE STRESS-STRAIN CURVE OF WOVEN FABRICS

A general shape of tensile stress-strain curves of woven fabrics is first recognised by puttingtested and predicted results together.An exponential function with two parameters is then selectedfor the prediction of tensile stress-strain relationship.The predicted results by using the proposedfunction show excellent agreement with experimental data.

Order Exponential Evaluation Model for Road Traffic Safety in City Clusters

This study presents an order exponential model for estimating road traffic safety in city clusters.The proposed model introduces the traffic flow intrinsic properties and uses the characteristics and regular patterns of traffic development to identify road traffic safety levels in city clusters.Additionally,an evaluation index system of city cluster road traffic safety was constructed based on the spatial and temporal distribution.Then Order Exponential Evaluation Model(OEEM),a comprehensive model using order exponent function for road traffic safety evaluation,was put forward,which considers the main characteristics and the generation process of traffic accidents.The model effectively controlled the unsafe behavior of the traffic system.It could define the levels of city cluster road traffic safety and dynamically detect road safety risk.The proposed model was verified with statistical data from three Chinese city clusters by comparing the common model for road traffic safety with an ideal model.The results indicate that the order exponent approach undertaken in this study can be extended and applied to other research topics and fields.

Prediction of a maximum pull-out load of anchor bolts using an optimal combination model

The mixed model of improved exponential and power function and unequal interval gray GM(1,1)model have poor accuracy in predicting the maximum pull-out load of anchor bolts.An optimal combination model was derived using the optimally weighted combination theory and the minimum sum of logarithmic squared errors as the objective function.Two typical anchor bolt pull-out engineering cases were selected to compare the performance of the proposed model with those of existing ones.Results showed that the optimal combination model was suitable not only for the slow P-s curve but also for the steep P-s curve.Its accuracy and stable reliability,as well as its prediction capability classification,were better than those of the other prediction models.Therefore,the optimal combination model is an effective processing method for predicting the maximum pull-out load of anchor bolts according to measured data.

Asymptotic Estimates of Gerber-Shiu Functions in the Renewal Risk Model with Exponential Claims

This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large. Under the assumption that the claim-size distribution is exponential, we establish an explicit asymptotic formula. Some straightforward consequences of this formula match existing results in the field.

A Computer Software-Epitimulator~ for Simulating Temporal Dynamics of Plant Disease Epidemic Progress

The objective of the present study was to develop a computer software for simulating the temporal development of plant disease epidemics using Richards, logistic, Gompertz, monomolecular, and exponential functions, respectively, and for predicting disease with a fitted model. The software was programmed using Visual Basic （VB6.0） and packaged with the Wise Installation System. The Fibonacci （＇0.618＇） section strategy was used to find out the most appropriate value for the shape parameter （m） in Richards function simulation through looping procedures. The software program was repeatedly tested, debugged and edited until it was run through favorably and produced ideal outputs. It was named Epitimulator based on the phrase ＇epidemic time simulator＇ and has been registered by the National Copyright Department of China （Reg. no. 2007SR18489）. It can be installed and run on personal computers with all versions of Windows operational systems. Data of disease index and survey time are keyed in or imported from Access files. The output of fitted models and related data of parameters can be pasted into Microsoft Excel worksheet or into Word document for editing as required and the simulated disease progress curves can be stored in separate graphic files. After being finally tested and completed, Epitimulator was applied to simulate the epidemic progress of corn northern leaf blight （Exserohilum turcicum） with recorded data from field surveys of corn crops and the fitted models were output. Comparison of the simulation results showed that the disease progress was always best described by Richards function, which resulted in the most accurate simulation model. Result also showed that forecast of northern leaf blight development was highly accurate by using the computed progress model from Richards function.

Performance of a data-driven technique applied to changes in wave height and its effect on beach response

In this study the medium-term response of beach profiles was investigated at two sites： a gently sloping sandy beach and a steeper mixed sand and gravel beach. The former is the Duck site in North Carolina, on the east coast of the USA, which is exposed to Atlantic Ocean swells and storm waves, and the latter is the Milford-on-Sea site at Christchurch Bay, on the south coast of England, which is partially sheltered from Atlantic swells but has a directionally bimodal wave exposure. The data sets comprise detailed bathymetric surveys of beach profiles covering a period of more than 25 years for the Duck site and over 18 years for the Milford-on-Sea site. The structure of the data sets and the data-driven methods are described. Canonical correlation analysis （CCA） was used to find linkages between the wave characteristics and beach profiles. The sensitivity of the linkages was investigated by deploying a wave height threshold to filter out the smaller waves incrementally. The results of the analysis indicate that, for the gently sloping sandy beach, waves of all heights are important to the morphological response. For the mixed sand and gravel beach, filtering the smaller waves improves the statistical fit and it suggests that low-height waves do not play a primary role in the medium-term morohological resoonse, which is primarily driven by the intermittent larger storm waves.

基于均生函数水稻扬花低温冷害程度的EOF预测模型

提出一种定量、连续、同时反映低温有害天数和强度的低温指数，并基于均生函数对其作主成分ＥＯＦ分析，得到预测模型。

基于Microsoft Excel统计函数的农业气象预报模型研究

为了给当地政府、农业部门、农户提供准确及时的农作物播种期、发育期等农用天气预报,通过日平均气温稳定通过5℃初日与0℃初日间隔日数预报模型和水稻播种-抽穗天数预报模型的建立,介绍Microsoft Excel SLOPE、INTERCEPT、LINEST统计函数在农业气象预报中的应用。实践证明,这3种函数能对已知数据进行最佳线性拟和,可以轻而易举地处理诸多变量之间的相关关系,根据返回的数值数组,可以直接观察到所有自变量与因变量之间的相关程度和F值。因此,利用Microsoft Excel统计函数制作农业气象预报模型,不仅可以大大地减轻劳动强度,而且还可以提高工作效率和预报效果。

Univariate Time-Series Analysis of Second-Hand Car Importation in Zambia

Zambia largely depends on the international second-hand car (SHC) market for their motor vehicle supply. The importation of Second hand Cars in Zambia presents a time series problem. The data used in this paper is monthly data on SHC importation from 1st January, 2014 to 31st December, 2016. Data was analyzed using Exponential Smoothing (ES) and Autoregressive Integrated Moving Average (ARIMA) models. The results showed that ARIMA (2, 1, 2) was the best fit for the SHC importation since its errors were smaller than those of the SES, DES and TES. The four error measures used were Root-mean-square error (RMSE), Mean absolute error (MAE), Mean percentage error (MPE) and Mean absolute percentage error (MAPE). The forecasts were also produced using the ARIMA (2, 1, 2) model for the next 18 months from January 2017. Although there is percentage increase of 90.6% from November 2015 to December 2016, the SHC importation generally is on the decrease in Zambia with percentage change of 59.5% from January 2014 to December 2016. The forecasts also show a gradual percentage decrease of 1.12% by June 2018. These results are more useful to policy and decision makers of Government departments such as Zambia Revenue Authority (ZRA) and Road Development Agency (RDA) in a bid to plan and execute their duties effectively.