Research on Partial Coefficients for Design of Quarter-circular Caisson Breakwater

The quarter-circular caisson breakwater （QCB） is a new type of breakwater, and it can be applied in deepwater. The stability of QCB under wave force action can be enhanced, and the rubble mound engineering can be less than that of semi-circular breakwaters in deepwater. In order to study the wave force distribution acting on the QCB, to find wave force formula for this type of breakwater, firstly in this paper, the distribution characteristics of the horizontal force, the downward vertical force and the uplift force on the breakwater were gotten based on physical model wave flume experiments and on the analysis of the wave pressure experimental data. Based on a series of physical model tests acted by irregular waves, a kind of calculation method, which was modified by Goda formula, was proposed to carry out the wave force on the QCB. Secondly, the reliability method with correlated variables was adopted to analyze the QCB, considering the high correlation between wave forces or moments. Utilizing the observed wave data in engineering field, the reliability index and failure probability of QCB were obtained. Finally, a factor Q=0.9 is given to modify the zero pressure height above SWL of QCB, and wave force partial coefficient 1.34 to the design expressions of QCB for anti-sliding, as well as 1.67 for anti-overturning, were presented.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Coefficient of Partial Correlation and Its Calculation

This thesis offers the general concept of coefficient of partial correlation.Starting with regres-sion analysis,the paper,by using samples,infers the general formula of expressing coefficient of partial correlation by way of simple correlation coefficient.

Efficient Shrinkage Estimation about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.

MODEL SELECTION METHOD BASED ON MAXIMAL INFORMATION COEFFICIENT OF RESIDUALS

The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this ar- ticle, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coe^cient （MIC）, a recently proposed dependence measure, captures a wide range of associ- ations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient （PMIC） is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given.

Stability analysis of concrete gravity dam on complicated foundation with multiple slide planes

A key problem in gravity dam design is providing enough stability to prevent slide, and the difficulty increases if there are several weak structural planes in the dam foundation. Overload and material weakening were taken into account, and a .finite difference strength reserve method with partial safety factors based on the reliability method was developed and used to study the anti-slide stability of a concrete gravity dam on a complicated foundation with multiple slide planes. Possible slide paths were obtained, and the stability of the foundation with possible failure planes was evaluated through analysis of the stress distribution characteristics. The results reveal the mechanism and process of sliding due to weak structural planes and their deformations, and provide a reference for anti-slide stability analysis of gravity dams in complicated geological conditions.

Probabilistic limit state design methodof the axial resistance of post grouting pile

The reliability of post grouting pile axial resistance was studied by proposing a design method for its probabilistic limit state,which is represented by the partial coefficients of load,end,and side resistance.The hyperbolic,modified hyperbolic,and polynomial models were employed to predict the ultimate bearing capacity of test piles that were not loaded to damage in field tests.The results were used for the calculation and calibration of the reliability index.The reliability of the probabilistic limit state design method was verified by an engineering case.The results show that the prediction results obtained from the modified hyperbolic model are closest to those obtained through the static load test.The proposed corresponding values of total,side,and end resistance partial coefficients are 1.84,1.66,and 2.73 when the dead and live load partial coefficients are taken as 1.1 and 1.4,respectively.Meanwhile,the corresponding partial coefficients of total,side,and end resistance are 1.70,1.56,and 2.34 when the dead and live load partial coefficients are taken as 1.2 and 1.4,respectively.

Zonal Differences in Correlation Patterns Between Soil Organic Carbon and Climate Factors at Multi-extent

Studying the relationship between climate factors and soil organic carbon （SOC） is vitally important. However, how SOC responses to climate （temperature and precipitation） at cohesive extents is poorly studied. Two transects of approximately the same length （transect P and transect T） were selected to examine the variation of SOC content in relation to mean annual temperature （MAT） and mean annual precipitation （MAP）. The coefficients of partial correlation between SOC density and MAT （Rt） and MAP （Rp） were determined to quantify the relationships between SOC density and the two climate factors. The results indicated that for transect T, Rt was statistically significant once the extent level was greater than or equal to two fundamental extent units, while for transect P, Rp showed statistical significance only at extent levels which were greater than two fundamental extent traits. At the same extent levels but in different transects, Rts exhibited no zonal difference, but Rps did once the extent level was greater than two fundamental extent units. Therefore, to study the relationship between SOC density and different climate factors, different minimum extent levels should be ex- amined. The results of this paper could deepen the understanding of the impacts that SOC pool has on terrestrial ecosystem and global carbon cycling.

Penalized profile least squares-based statistical inference for varying coefficient partially linear errors-in-variables models

The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.

Comparing Land Degradation and Regeneration Trends in China Drylands

The aim of this paper is to offer a statistically sound method to make a precise account of the speed of land degradation and regeneration processes.Most common analyses of land degradation focus instead on the extent of degraded areas,rather than on the intensity of degradation processes.The study was implemented for the Potential Extent of Desertification in China(PEDC),composed by arid,semi-arid,and dry sub-humid regions and refers to the period 2002 to 2012.The metrics were standard partial regression coefficients from stepwise regressions,fitted using Net Primary Productivity as the dependent variable,and year number and aridity as predictors.The results indicate that:①the extension of degrading lands(292896 km 2 or 9.12%of PEDC)overcomes the area that is recovering(194560 km 2 or 6.06%of PEDC);and②the intensity of degrading trends is lower than that of increasing trends in three land cover types(grassland,desert,and crops)and in two aridity levels(semi-arid and dry sub-humid).Such an outcome might pinpoint restoration policies by the Chinese government,and document a possible case of hysteresis.

AR Model Based on Time Series Modeling for Predicting Egg Market Price in 2021

Eggs,as a meat consumer product in China,are closely related to the vegetable basket project.Exploring and predicting the future trend of egg market price is of great significance for stabilizing egg price and market supply.In this study,the time series AR model was used for fitting the egg market prices in the 66 d from January 1 to March 7,2021,and the delay operator nlag18 was used for white noise test,giving pr>probability of chisq<0.005.The time series was not a white noise series,and then the stationary series was used for modeling.The optimal model was selected as the AR series(BIC(3,0)),and finally,the egg market price model AM was obtained as X_(t)=9.0556+(1+0.8926)ε_(t),which was the optimal model.The model showed that the egg price fluctuations in 2021 will be clustered,and the later price will be significantly affected by external factors in the previous period.The dynamic prediction results of the model showed that the egg price would stop falling in March 2020,and the egg price would continue to slow down in March.

Parameter Sensitivity and Qualitative Analysis of Dynamics of Ovarian Tumor Growth Model with Treatment Strategy

In this paper, we are interested to find the most sensitive parameter, local and global stability of ovarian tumor growth model. For sensitivity analysis, we use Latin Hypercube Sampling (LHS) method to generate sample points and Partial Rank Correlation Coefficient (PRCC) method, uses those sample points to find out which parameters are important for the model. Based on our findings, we suggest some treatment strategies. We investigate the sensitivity of the parameters for tumor volume, y, cell nutrient density, Q and maximum tumor size, ymax. We also use Scatter Plot method using LHS samples to show the consistency of the results obtained by using PRCC. Moreover, we discuss the qualitative analysis of ovarian tumor growth model investigating the local and global stability.

Energy consumption hierarchical analysis based on interpretative structural model for ethylene production

Interpretative structural model(ISM) can transform a multivariate problem into several sub-variable problems to analyze a complex industrial structure in a more efficient way by building a multi-level hierarchical structure model. To build an ISM of a production system, the partial correlation coefficient method is proposed to obtain the adjacency matrix, which can be transformed to ISM. According to estimation of correlation coefficient, the result can give actual variable correlations and eliminate effects of intermediate variables. Furthermore, this paper proposes an effective approach using ISM to analyze the main factors and basic mechanisms that affect the energy consumption in an ethylene production system. The case study shows that the proposed energy consumption analysis method is valid and efficient in improvement of energy efficiency in ethylene production.

Recent Progress in the Lp Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients

In this paper,we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients.We begin with an approach given by N.V.Krylov to parabolic equations in the whole space with VMOx coefficients.We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions,weighted Lp estimates with Muckenhoupt(Ap)weights,non-local elliptic and parabolic equations,as well as fully nonlinear elliptic and parabolic equations.

A statistical procedure to assess the significance level of barriers to gene flow

Although several methods are available to study the extent of isolation by distance （IBD） among natural populations, comparatively few exist to detect the presence of sharp genetic breaks in genetic distance datasets. In recent years, Monmonier＇s maximum-difference algorithm has been increasingly used by population geneticists. However, this method does not provide means to measure the statistical significance of such barriers, nor to determine their relative contribution to population differentiation with respect to IBD. Here, we propose an approach to assess the significance of genetic boundaries. The method is based on the calculation of a multiple regression from distance matrices, where binary matrices represent putative genetic barriers to test, in addition to geographic and genetic distances. Simulation results suggest that this method reliably detects the presence of genetic barriers, even in situations where IBD is also significant. We also illustrate the methodology by analyzing previously published datasets. Conclusions about the importance of genetic barriers can be misleading if one does not take into consideration their relative contribution to the overall genetic structure of species.

Global sensitivity analysis of a single-cell HBV model for viral dynamics in the liver

The predictive accuracy of mathematical models representing anything ranging from the meteorological to the biological system profoundly depends on the quality of model parameters derived from experimental data.Hence,robust sensitivity analysis(SA)of these critical model parameters aids in sifting the influential from the negligible out of typically vast parameter regimes,thus illuminating key components of the system under study.We here move beyond traditional local sensitivity analysis to the adoption of global SA techniques.Partial rank correlation coefficient(PRCC)based on Latin hypercube sampling is compared with the variance-based Sobol method.We selected for this SA investigation an infection model for the hepatitis-B virus(HBV)that describes infection dynamics and clearance of HBV in the liver[Murray&Goyal,2015].The model tracks viral particles such as the tenacious and nearly ineradicable covalently closed circular DNA(cccDNA)embedded in infected nuclei and an HBV protein known as p36.Our application of these SA methods to the HBV model illuminates,especially over time,the quantitative relationships between cccDNA synthesis rate and p36 synthesis and export.Our results reinforce previous observations that the viral protein,p36,is by far the most influential factor for cccDNA replication.Moreover,both methods are capable of finding crucial parameters of the model.Though the Sobol method is independent of model structure(e.g.,linearity and monotonicity)and well suited for SA,our results ensure that LHS-PRCC suffices for SA of a non-linear model if it is monotonic.