Evaluation of Serum Anti-Müllerian Hormone (AMH) Values for 28,016 Bulgarian Women: Prognostic Statistical Model of Age Specific AMH Declining

The present study aims to establish a relationship between serum AMH levels and age in a large group of women living in Bulgaria, as well as to establish reference age-specific AMH levels in women that would serve as an initial estimate of ovarian age. A total of 28,016 women on the territory of the Republic of Bulgaria were tested for serum AMH levels with a median age of 37.0 years (interquartile range 32.0 to 41.0). For women aged 20 - 29 years, the Bulgarian population has relatively high median levels of AMH, similar to women of Asian origin. For women aged 30 - 34 years, our results are comparable to those of women living in Western Europe. For women aged 35 - 39 years, our results are comparable to those of women living in the territory of India and Kenya. For women aged 40 - 44 years, our results were lower than those for women from the Western European and Chinese populations, close to the Indian and higher than Korean and Kenya populations, respectively. Our results for women of Bulgarian origin are also comparable to US Latina women at age 30, 35 and 40 ages. On the base on constructed a statistical model to predicting the decline in AMH levels at different ages, we found non-linear structure of AMH decline for the low AMH 3.5) the dependence of the decline of AMH on age was confirmed as linear. In conclusion, we evaluated the serum level of AMH in Bulgarian women and established age-specific AMH percentile reference values based on a large representative sample. We have developed a prognostic statistical model that can facilitate the application of AMH in clinical practice and the prediction of reproductive capacity and population health.

Comparative Analysis of Statistical Thickness Models for the Determination of the External Specific Surface and the Surface of the Micropores of Materials: The Case of a Clay Concrete Stabilized Using Sugar Cane Molasses

In this work, four empirical models of statistical thickness, namely the models of Harkins and Jura, Hasley, Carbon Black and Jaroniec, were compared in order to determine the textural properties (external surface and surface of micropores) of a clay concrete without molasses and clay concretes stabilized with 8%, 12% and 16% molasses. The results obtained show that Hasley’s model can be used to obtain the external surfaces. However, it does not allow the surface of the micropores to be obtained, and is not suitable for the case of simple clay concrete (without molasses) and for clay concretes stabilized with molasses. The Carbon Black, Jaroniec and Harkins and Jura models can be used for clay concrete and stabilized clay concrete. However, the Carbon Black model is the most relevant for clay concrete and the Harkins and Jura model is for molasses-stabilized clay concrete. These last two models augur well for future research.

Adaptive Maneuvering Frequency Method of Current Statistical Model

Current statistical model(CSM) has a good performance in maneuvering target tracking. However, the fixed maneuvering frequency will deteriorate the tracking results, such as a serious dynamic delay, a slowly converging speedy and a limited precision when using Kalman filter(KF) algorithm. In this study, a new current statistical model and a new Kalman filter are proposed to improve the performance of maneuvering target tracking. The new model which employs innovation dominated subjection function to adaptively adjust maneuvering frequency has a better performance in step maneuvering target tracking, while a fluctuant phenomenon appears. As far as this problem is concerned, a new adaptive fading Kalman filter is proposed as well. In the new Kalman filter, the prediction values are amended in time by setting judgment and amendment rules,so that tracking precision and fluctuant phenomenon of the new current statistical model are improved. The results of simulation indicate the effectiveness of the new algorithm and the practical guiding significance.

A Fuzzy Adaptive Algorithm Based on“Current”Statistical Model for Maneuvering Target Tracking

The basic"current"statistical model and adaptive Kalman filter algorithm can not track a weakly maneuvering target precisely,though it has good estimate accuracy for strongly maneuvering target.In order to solve this problem,a novel nonlinear fuzzy membership function was presented to adjust the upper and lower limit of target acceleration adaptively,and then the validity of the new algorithm for feeblish maneuvering target was proved in theory.At last,the computer simulation experiments indicated that the new algorithm has a great advantage over the basic"current"statistical model and adaptive algorithm.

Passive Target Tracking Based on Current Statistical Model

Bearing-only passive tracking is regarded as a nonlinear hard tracking problem. There are still no completely good solutions to this problem until now. Based on current statistical model, the novel solution to this problem utilizing particle filter (PF) and the unscented Kalman filter (UKF) is proposed. The new solution adopts data fusion from two observers to increase the observability of passive tracking. It applies the residual resampling step to reduce the degeneracy of PF and it introduces the Markov Chain Monte Carlo methods (MCMC) to reduce the effect of the “sample impoverish”. Based on current statistical model, the EKF, the UKF and particle filter with various proposal distributions are compared in the passive tracking experiments with two observers. The simulation results demonstrate the good performance of the proposed new filtering methods with the novel techniques.

Damage statistical mechanics model of top coal in steep top caving coal

Damage statistical mechanics model of horizontal section height in the top caving was constructed in the paper. The influence factors including supporting pressure, dip angle and characteristic of coal on horizontal section height were analyzed as well. By terms of the practice project analysis, the horizontal section height increases with the increase of dip angle β and thickness of coal seam M. Dip angle of coal seam β has tremendous impact on horizontal section height, while thickness of coal seam M has slight impact. When thickness of coal seam is below 10m, horizontal section height increases sharply. While thickness exceeds 15m, it is not major factor influencing on horizontal section height any long.

Joint multivariate statistical model and its applications to synthetic earthquake predic-tion

针对目前地震综合预报中的一些问题，利用近30年来迅速发展的多元统计分析中主成分分析、判别分析组成多元统计组合模型，在众多的地震预报指标(预报因子)中采用信息最大化方法，选择对中期预测信息累积贡献率大于90％地震预报指标，分别进行相关分析、预测、检验，最终应用马氏距离判别作外推综合预报；并以华北地区(30°～42°N，108°125°E)为例进行模型的应用检验，初步研究已取得了较好的效果．

Calculation of Vapour Pressure of Metals by Statistical-Mechanical Method With the Debye Model

Statistical expression of vapour pressure equations of metals is derived from the Debye model.The statistical distribution of T_(-p) ensemble is presented in an in-elab- orate mode and the partition function is defined.The vapour pressure of eleven metals have been calculated with the Debye equation and compared with those given by the E- instein equation and empirical equation.Comparison of results of calculation from dif- ferent methods show their evident accordance within the same orders of magnitude.

A Novel 3D Non-Stationary UAV-MIMO Channel Model and Its Statistical Properties

The wireless communication systems based on Unmanned Aerial Vehicles(UAVs) have found a wide range of applications recently. In this paper, we propose a new three-dimensional(3 D) non-stationary multiple-input multiple-output(MIMO) channel model for the communication links between the UAV and mobile terminal(MT). The new model originates the traditional geometry-based stochastic models(GBSMs) but considers the non-stationary propagation environment due to the rapid movements of the UAV, MT, and clusters. Meanwhile, the upgrade time evolving algorithms of time-variant channel parameters, i.e., the path number based on birth-death processes of clusters, path delays, path powers, and angles of arrival and departure, are developed and optimized. In addition, the statistical properties of proposed GBSM including autocorrelation function(ACF), cross-correlation function(CCF), and Doppler power spectrum density(DPSD) are investigated and analyzed. Simulation results demonstrate that our proposed model provides a good agreement on the statistical properties with the corresponding derived theoretical ones, which indicates its usefulness for the performance evaluation and validation of the UAV based communication systems.

Spatial prediction of landslide susceptibility using GIS-based statistical and machine learning models in Wanzhou County,Three Gorges Reservoir, China

Landslide susceptibility mapping is vital for landslide risk management and urban planning.In this study,we used three statistical models[frequency ratio,certainty factor and index of entropy(IOE)]and a machine learning model[random forest(RF)]for landslide susceptibility mapping in Wanzhou County,China.First,a landslide inventory map was prepared using earlier geotechnical investigation reports,aerial images,and field surveys.Then,the redundant factors were excluded from the initial fourteen landslide causal factors via factor correlation analysis.To determine the most effective causal factors,landslide susceptibility evaluations were performed based on four cases with different combinations of factors("cases").In the analysis,465(70%)landslide locations were randomly selected for model training,and 200(30%)landslide locations were selected for verification.The results showed that case 3 produced the best performance for the statistical models and that case 2 produced the best performance for the RF model.Finally,the receiver operating characteristic(ROC)curve was used to verify the accuracy of each model's results for its respective optimal case.The ROC curve analysis showed that the machine learning model performed better than the other three models,and among the three statistical models,the IOE model with weight coefficients was superior.

New perspective in statistical modeling of wall-bounded turbulence

Despite dedicated effort for many decades,statistical description of highly technologically important wall turbulence remains a great challenge.Current models are unfortunately incomplete,or empirical,or qualitative.After a review of the existing theories of wall turbulence,we present a new framework,called the structure ensemble dynamics （SED）,which aims at integrating the turbulence dynamics into a quantitative description of the mean flow.The SED theory naturally evolves from a statistical physics understanding of non-equilibrium open systems,such as fluid turbulence, for which mean quantities are intimately coupled with the fluctuation dynamics.Starting from the ensemble-averaged Navier-Stokes（EANS） equations,the theory postulates the existence of a finite number of statistical states yielding a multi-layer picture for wall turbulence.Then,it uses order functions（ratios of terms in the mean momentum as well as energy equations） to characterize the states and transitions between states.Application of the SED analysis to an incompressible channel flow and a compressible turbulent boundary layer shows that the order functions successfully reveal the multi-layer structure for wall-bounded turbulence, which arises as a quantitative extension of the traditional view in terms of sub-layer,buffer layer,log layer and wake. Furthermore,an idea of using a set of hyperbolic functions for modeling transitions between layers is proposed for a quantitative model of order functions across the entire flow domain.We conclude that the SED provides a theoretical framework for expressing the yet-unknown effects of fluctuation structures on the mean quantities,and offers new methods to analyze experimental and simulation data.Combined with asymptotic analysis,it also offers a way to evaluate convergence of simulations.The SED approach successfully describes the dynamics at both momentum and energy levels, in contrast with all prevalent approaches describing the mean velocity profile only.Moreover,the SED theoretical framework is general,independent of the flow system to study, while the actual functional form of the order functions may vary from flow to flow.We assert that as the knowledge of order functions is accumulated and as more flows are analyzed, new principles（such as hierarchy,symmetry,group invariance,etc.） governing the role of turbulent structures in the mean flow properties will be clarified and a viable theory of turbulence might emerge.

Human induced dryland degradation in Ordos Plateau,China,revealed by multilevel statistical modeling of normalized difference vegetation index and rainfall time-series

Land degradation causes serious environmental problems in many regions of the world, and although it can be effectively assessed and monitored using a time series of rainfall and a normalized difference vegetation index （NDVI） from remotely-sensed imagery, dividing human-induced land degradation from vegetation dynamics due to climate change is not a trivial task. This paper presented a multilevel statistical modeling of the NDVI-rainfall relationship to detect human-induced land degradation at local and landscape scales in the Ordos Plateau of Inner Mongolia, China, and recognized that anthropogenic activities result in either positive （land restoration and re-vegetation） or negative （degradation） trends. Linear regressions were used to assess the accuracy of the multi- level statistical model. The results show that： （1） land restoration was the dominant process in the Ordos Plateau between 1998 and 2012; （2） the effect of the statistical removal of precipitation revealed areas of human-induced land degradation and improvement, the latter reflecting successful restoration projects and changes in land man- agement in many parts of the Ordos; （3） compared to a simple linear regression, multilevel statistical modeling could be used to analyze the relationship between the NDVI and rainfall and improve the accuracy of detecting the effect of human activities. Additional factors should be included when analyzing the NDVI-rainfall relationship and detecting human-induced loss of vegetation cover in drylands to improve the accuracy of the approach and elimi- nate some observed non-significant residual trends.

Rank correlation among different statistical models in ranking of winter wheat genotypes'

Several statistical methods have been developed for analyzing genotype×environment(GE)interactions in crop breeding programs to identify genotypes with high yield and stability performances.Four statistical methods,including joint regression analysis(JRA),additive mean effects and multiplicative interaction(AMMI)analysis,genotype plus GE interaction(GGE)biplot analysis,and yield–stability(YSi)statistic were used to evaluate GE interaction in20 winter wheat genotypes grown in 24 environments in Iran.The main objective was to evaluate the rank correlations among the four statistical methods in genotype rankings for yield,stability and yield–stability.Three kinds of genotypic ranks(yield ranks,stability ranks,and yield–stability ranks)were determined with each method.The results indicated the presence of GE interaction,suggesting the need for stability analysis.With respect to yield,the genotype rankings by the GGE biplot and AMMI analysis were significantly correlated(P<0.01).For stability ranking,the rank correlations ranged from 0.53(GGE–YSi;P<0.05)to0.97(JRA–YSi;P<0.01).AMMI distance(AMMID)was highly correlated(P<0.01)with variance of regression deviation(S2di)in JRA(r=0.83)and Shukla stability variance(σ2)in YSi(r=0.86),indicating that these stability indices can be used interchangeably.No correlation was found between yield ranks and stability ranks(AMMID,S2di,σ2,and GGE stability index),indicating that they measure static stability and accordingly could be used if selection is based primarily on stability.For yield–stability,rank correlation coefficients among the statistical methods varied from 0.64(JRA–YSi;P<0.01)to 0.89(AMMI–YSi;P<0.01),indicating that AMMI and YSi were closely associated in the genotype ranking for integrating yield with stability performance.Based on the results,it can be concluded that YSi was closely correlated with(i)JRA in ranking genotypes for stability and(ii)AMMI for integrating yield and stability.

Comparison of six statistical approaches in the selection of appropriate fish growth models

The performance of six statistical approaches,which can be used for selection of the best model to describe the growth of individual fish,was analyzed using simulated and real length-at-age data.The six approaches include coefficient of determination(R2),adjusted coefficient of determination(adj.-R2),root mean squared error(RMSE),Akaike's information criterion(AIC),bias correction of AIC(AICc) and Bayesian information criterion(BIC).The simulation data were generated by five growth models with different numbers of parameters.Four sets of real data were taken from the literature.The parameters in each of the five growth models were estimated using the maximum likelihood method under the assumption of the additive error structure for the data.The best supported model by the data was identified using each of the six approaches.The results show that R2 and RMSE have the same properties and perform worst.The sample size has an effect on the performance of adj.-R2,AIC,AICc and BIC.Adj.-R2 does better in small samples than in large samples.AIC is not suitable to use in small samples and tends to select more complex model when the sample size becomes large.AICc and BIC have best performance in small and large sample cases,respectively.Use of AICc or BIC is recommended for selection of fish growth model according to the size of the length-at-age data.

Ultrasonic backscatter characterization of cancellous bone using a general Nakagami statistical model

The goal of this study is to analyze the statistics of the backscatter signal from bovine cancellous bone using a Nakagami model and to evaluate the feasibility of Nakagami-model parameters for cancellous bone characterization. Ultrasonic backscatter measurements were performed on 24 bovine cancellous bone specimens in vitro and the backscatter signals were compensated for the frequency-dependent attenuation prior to the envelope detection. The statistics of the backscatter envelope were modeled using the Nakagami distribution. Our results reveal that the backscatter envelope mainly followed pre-Rayleigh distributions, and the deviations of the backscatter envelope from Rayleigh distribution decreased with increasing bone density. The Nakagami shape parameter(i.e., m) was significantly correlated with bone densities(R = 0.78–0.81, p < 0.001) and trabecular microstructures(|R| = 0.46–0.78, p < 0.05). The scale parameter(i.e.,?) and signal-to-noise ratio(SNR) also yielded significant correlations with bone density and structural features. Multiple linear regressions showed that bone volume fraction(BV/TV) was the main predictor of the Nakagami parameters,and microstructure produced significantly independent contribution to the prediction of Nakagami distribution parameters,explaining an additional 10.2% of the variance at most. The in vitro study showed that statistical parameters derived with Nakagami model might be useful for cancellous bone characterization, and statistical analysis has potential for ultrasonic backscatter bone evaluation.

A Statistical Model for Investigating Climatic Trend Turning Points

A two-phase trend model is presented to investigate the turning-point signals of evolution trend in long-term series of a climatic element. Based on nonlinear fitting, the revised model brings out more evident improvement of the linear model proposed by Solow et al. (1987). Both theoretical deduction and case calculation show that our version can search the turning point and period accurately and objectively. In particular it is fit for computer exploring the turning points in long-range records from stations covering a large area, thus avoiding subjective judgement by a usual drawing method.

Comparison of Statistical Models for Regional Crop Trial Analysis

Based on the review and comparison of main statistical analysis models for estimating variety-environment cell means in regional crop trials, a new statistical model, LR-PCA composite model was proposed, and the predictive precision of these models were compared by cross validation of an example data. Results showed that the order of model precision was LR-PCA model > AMMI model > PCA model > Treatment Means (TM) model > Linear Regression (LR) model > Additive Main Effects ANOVA model. The precision gain factor of LR-PCA model was 1.55, increasing by 8.4% compared with AMMI.

Statistic PID Tracking Control for Non-Gaussian Stochastic Systems Based on T-S Fuzzy Model

A new robust proportional-integral-derivative （PID） tracking control framework is considered for stochastic systems with non-Gaussian variable based on B-spline neural network approximation and T-S fuzzy model identification. The tracked object is the statistical information of a given target probability density function （PDF）, rather than a deterministic signal. Following B-spline approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. Different from the previous related works, the time delay T-S fuzzy models with the exogenous disturbances are applied to identify the nonlinear weighting dynamics. Meanwhile, the generalized PID controller structure and the improved convex linear matrix inequalities （LMI） algorithms are proposed to fulfil the tracking problem. Furthermore, in order to enhance the robust performance, the peak-to-peak measure index is applied to optimize the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.

Evaluation of mobility impact on urban work zones using statistical models

This work correlated the detailed work zone location and time data from the Wis LCS system with the five-min inductive loop detector data. One-sample percentile value test and two-sample Kolmogorov-Smirnov(K-S) test were applied to compare the speed and flow characteristics between work zone and non-work zone conditions. Furthermore, we analyzed the mobility characteristics of freeway work zones within the urban area of Milwaukee, WI, USA. More than 50% of investigated work zones have experienced speed reduction and 15%-30% is necessary reduced volumes. Speed reduction was more significant within and at the downstream of work zones than at the upstream.

A STATISTICAL PREDICTION MODEL FOR SPRING RAINFALL OVER NORTHERN CHINA BASED ON THE INTERANNUAL INCREMENT APPROACH

The spring (March-April-May) rainfall over northern China (SPRNC) is predicted by using the interannual increment approach. DY denotes the difference between the current year and previous years. The seasonal forecast model for the DY of SPRNC is constructed based on the data that are taken from the 1965-2002 period (38 years), in which six predictors are available no later than the current month of February. This is favorable so that the seasonal forecasts can be made one month ahead. Then, SPRNC and the percentage anomaly of SPRNC are obtained by the predicted DY of SPRNC. The model performs well in the prediction of the inter-annual variation of the DY of SPRNC during 1965-2002, with a correlation coefficient between the predicted and observed DY of SPRNC of 0.87. This accounts for 76% of the total variance, with a low value for the average root mean square error (RMSE) of 20%. Both the results of the hindcast for the period of 2003-2010 (eight years) and the cross-validation test for the period of 1965-2009 (45 years) illustrate the good prediction capability of the model, with a small mean relative error of 10%, an RMSE of 17% and a high rate of coherence of 87.5% for the hindcasts of the percentage anomaly of SPRNC.