Impacts of the Minimum Purchase Price Policy for Grain on the Planting Area of Rice in Hubei Province Based on a Mixed Linear Model

Impacts of the minimum purchase price policy for grain on the planting area of rice in Hubei Province were analyzed based on a mixed linear model.After the indicator system containing the minimum purchase price policy and other factors influencing the planting area of rice was constructed,principal component analysis of the system was conducted,and then a mixed linear model where the planting area of rice was as the dependent variable was established.The results show that after the exclusion of the interference from other factors,the minimum purchase price policy for grain had a positive impact on the planting area of rice in Hubei Province.That is,the minimum purchase price policy significantly stimulated the growth of rice planting area in Hubei Province.

Comparison of isotope-based linear and Bayesian mixing models in determining moisture recycling ratio

Stable water isotopes are natural tracers quantifying the contribution of moisture recycling to local precipitation,i.e.,the moisture recycling ratio,but various isotope-based models usually lead to different results,which affects the accuracy of local moisture recycling.In this study,a total of 18 stations from four typical areas in China were selected to compare the performance of isotope-based linear and Bayesian mixing models and to determine local moisture recycling ratio.Among the three vapor sources including advection,transpiration,and surface evaporation,the advection vapor usually played a dominant role,and the contribution of surface evaporation was less than that of transpiration.When the abnormal values were ignored,the arithmetic averages of differences between isotope-based linear and the Bayesian mixing models were 0.9%for transpiration,0.2%for surface evaporation,and–1.1%for advection,respectively,and the medians were 0.5%,0.2%,and–0.8%,respectively.The importance of transpiration was slightly less for most cases when the Bayesian mixing model was applied,and the contribution of advection was relatively larger.The Bayesian mixing model was found to perform better in determining an efficient solution since linear model sometimes resulted in negative contribution ratios.Sensitivity test with two isotope scenarios indicated that the Bayesian model had a relatively low sensitivity to the changes in isotope input,and it was important to accurately estimate the isotopes in precipitation vapor.Generally,the Bayesian mixing model should be recommended instead of a linear model.The findings are useful for understanding the performance of isotope-based linear and Bayesian mixing models under various climate backgrounds.

The Marginal Rao-Blackwellized Particle Filter for Mixed Linear/Nonlinear State Space Models

In this paper, the marginal Rao-Blackwellized particle filter （MRBPF）, which fuses the Rao-Blackwellized particle filter （RBPF） algorithm and the marginal particle filter （MPF） algorithm, is presented. The state space is divided into linear and non-linear parts, which can be estimated separately by the MPF and the optional Kalman filter. Through simulation in the terrain aided navigation （TAN） domain, it is demonstrated that, compared with the RBPF, the root mean square errors （RMSE） and the error variance of the nonlinear state estimations by the proposed MRBPF are respectively reduced by 29% and 96%, while the unique particle count is increased by 80%. It is also found that the MRBPF has better convergence properties, and analysis has shown that the existing RBPF is nothing more than a special case of the MRBPF.

IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.

Responses of River Runoff to Climate Change Based on Nonlinear Mixed Regression Model in Chaohe River Basin of Hebei Province, China

Taking the nonlinear nature of runoff system into account,and combining auto-regression method and multi-regression method,a Nonlinear Mixed Regression Model (NMR) was established to analyze the impact of temperature and precipitation changes on annual river runoff process. The model was calibrated and verified by using BP neural network with observed meteorological and runoff data from Daiying Hydrological Station in the Chaohe River of Hebei Province in 1956–2000. Compared with auto-regression model,linear multi-regression model and linear mixed regression model,NMR can improve forecasting precision remarkably. Therefore,the simulation of climate change scenarios was carried out by NMR. The results show that the nonlinear mixed regression model can simulate annual river runoff well.

A mixed integer linear programming approach for municipal solid waste management

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Nonparametric Estimation in Linear Mixed Models with Uncorrelated Homoscedastic Errors

Today, Linear Mixed Models (LMMs) are fitted, mostly, by assuming that random effects and errors have Gaussian distributions, therefore using Maximum Likelihood (ML) or REML estimation. However, for many data sets, that double assumption is unlikely to hold, particularly for the random effects, a crucial component in which assessment of magnitude is key in such modeling. Alternative fitting methods not relying on that assumption (as ANOVA ones and Rao’s MINQUE) apply, quite often, only to the very constrained class of variance components models. In this paper, a new computationally feasible estimation methodology is designed, first for the widely used class of 2-level (or longitudinal) LMMs with only assumption (beyond the usual basic ones) that residual errors are uncorrelated and homoscedastic, with no distributional assumption imposed on the random effects. A major asset of this new approach is that it yields nonnegative variance estimates and covariance matrices estimates which are symmetric and, at least, positive semi-definite. Furthermore, it is shown that when the LMM is, indeed, Gaussian, this new methodology differs from ML just through a slight variation in the denominator of the residual variance estimate. The new methodology actually generalizes to LMMs a well known nonparametric fitting procedure for standard Linear Models. Finally, the methodology is also extended to ANOVA LMMs, generalizing an old method by Henderson for ML estimation in such models under normality.

Linear Mixed Model Analysis of Worldwide Longitudinal Infant Mortality Rate Data and Association with Human Development Index

A linear mixed model is used to determine the explaining infant mortality rate data of United Nations countries. The HDI （human development index） has a significant negative linear relationship with infant mortality rate. United Nations data shows that the infant mortality rate has a descending trend over the period 1990-2010. This study aims to assess the value of the HDI as a predictor of infant mortality rate. Findings in the paper suggest that significant percentage reductions in infant mortality might be possible for countries for controlling the HDI.

Combining Geographic Information Systems for Transportation and Mixed Integer Linear Programming in Facility Location-Allocation Problems

In this study, we aimed to assess the solution quality for location-allocation problems from facilities generated by the software TransCAD®?, a Geographic Information System for Transportation (GIS-T). Such facilities were obtained after using two routines together: Facility Location and Transportation Problem, when compared with optimal solutions from exact mathematical models, based on Mixed Integer Linear Programming (MILP), developed externally for the GIS. The models were applied to three simulations: the first one proposes opening factories and customer allocation in the state of Sao Paulo, Brazil;the second involves a wholesaler and a study of location and allocation of distribution centres for retail customers;and the third one involves the location of day-care centers and allocation of demand (0 - 3 years old children). The results showed that when considering facility capacity, the MILP optimising model presents results up to 37% better than the GIS and proposes different locations to open new facilities.

Adaptive Random Effects/Coefficients Modeling

Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.

Mixedness of the N-qubit states with exchange symmetry

The mixedness of the N-qubit quantum states with exchange symmetry has been studied, and the results show that the linear entropy of the single qubit reduced density matrix （RDM）, which can describe the mixedness, is completely determined by the expectation values 〈Sz〉 and 〈S±〉 for both the pure and the mixed states. The mixedness of the pure states can be used to describe the bipartite entanglement, as an example we have calculated the mixedness of the Dicke state and the spin squeezed Kitagawa-Ueda state. For the mixed states, we determine the mixedness properties of both the ground states and the thermal states in mean-field clusters of spin-1/2 particles interacting via the anisotropy Heisenberg XXZ interaction, and found for the ferromagnetic case （J 〈 0）, the mixedness will approximate to the pairwise entanglement when the anisotropic parameter △ 〉 △c.

Detection of gross errors using mixed integer optimization approach in process industry

A novel mixed integer linear programming (NMILP) model for detection of gross errors is presented in this paper. Yamamura et al.(1988) designed a model for detection of gross errors and data reconciliation based on Akaike information cri- terion (AIC). But much computational cost is needed due to its combinational nature. A mixed integer linear programming (MILP) approach was performed to reduce the computational cost and enhance the robustness. But it loses the super performance of maximum likelihood estimation. To reduce the computational cost and have the merit of maximum likelihood estimation, the simultaneous data reconciliation method in an MILP framework is decomposed and replaced by an NMILP subproblem and a quadratic programming (QP) or a least squares estimation (LSE) subproblem. Simulation result of an industrial case shows the high efficiency of the method.

Marginal Conceptual Predictive Statistic for Mixed Model Selection

We focus on the development of model selection criteria in linear mixed models. In particular, we propose the model selection criteria following the Mallows’ Conceptual Predictive Statistic (Cp) [1] [2] in linear mixed models. When correlation exists between the observations in data, the normal Gauss discrepancy in univariate case is not appropriate to measure the distance between the true model and a candidate model. Instead, we define a marginal Gauss discrepancy which takes the correlation into account in the mixed models. The model selection criterion, marginal Cp, called MCp, serves as an asymptotically unbiased estimator of the expected marginal Gauss discrepancy. An improvement of MCp, called IMCp, is then derived and proved to be a more accurate estimator of the expected marginal Gauss discrepancy than MCp. The performance of the proposed criteria is investigated in a simulation study. The simulation results show that in small samples, the proposed criteria outperform the Akaike Information Criteria (AIC) [3] [4] and Bayesian Information Criterion (BIC) [5] in selecting the correct model;in large samples, their performance is competitive. Further, the proposed criteria perform significantly better for highly correlated response data than for weakly correlated data.

Detection of Alzheimer’s disease onset using MRI and PET neuroimaging:longitudinal data analysis and machine learning

The scientists are dedicated to studying the detection of Alzheimer’s disease onset to find a cure, or at the very least, medication that can slow the progression of the disease. This article explores the effectiveness of longitudinal data analysis, artificial intelligence, and machine learning approaches based on magnetic resonance imaging and positron emission tomography neuroimaging modalities for progression estimation and the detection of Alzheimer’s disease onset. The significance of feature extraction in highly complex neuroimaging data, identification of vulnerable brain regions, and the determination of the threshold values for plaques, tangles, and neurodegeneration of these regions will extensively be evaluated. Developing automated methods to improve the aforementioned research areas would enable specialists to determine the progression of the disease and find the link between the biomarkers and more accurate detection of Alzheimer’s disease onset.

Classification of territory risk by generalized linear and generalized linear mixed models

Territory risk analysis has played an important role in the decision-making of auto insurance rate regulation.Due to the optimality of insurance loss data groupings,clustering methods become the natural choice for such territory risk classification.In this work,spatially constrained clustering is first applied to insurance loss data to form rating territories.The generalized linear model(GLM)and generalized linear mixed model(GLMM)are then proposed to derive the risk relativities of obtained clusters.Each basic rating unit within the same cluster,namely Forward Sortation Area(FSA),takes the same risk relativity value as its cluster.The obtained risk relativities from GLM or GLMM are used to calculate the performance metrics,including RMSE,MAD,and Gini coefficients.The spatially constrained clustering and the risk relativity estimate help obtain a set of territory risk benchmarks used in rate filings to guide the rate regulation process.

Randomized MILP framework for Securing Virtual Machines from Malware Attacks

Cloud computing involves remote server deployments with public net-work infrastructures that allow clients to access computational resources.Virtual Machines(VMs)are supplied on requests and launched without interactions from service providers.Intruders can target these servers and establish malicious con-nections on VMs for carrying out attacks on other clustered VMs.The existing system has issues with execution time and false-positive rates.Hence,the overall system performance is degraded considerably.The proposed approach is designed to eliminate Cross-VM side attacks and VM escape and hide the server’s position so that the opponent cannot track the target server beyond a certain point.Every request is passed from source to destination via one broadcast domain to confuse the opponent and avoid them from tracking the server’s position.Allocation of SECURITY Resources accepts a safety game in a simple format as input andfinds the best coverage vector for the opponent using a Stackelberg Equilibrium(SSE)technique.A Mixed Integer Linear Programming(MILP)framework is used in the algorithm.The VM challenge is reduced by afirewall-based controlling mechanism combining behavior-based detection and signature-based virus detection.The pro-posed method is focused on detecting malware attacks effectively and providing better security for the VMs.Finally,the experimental results indicate that the pro-posed security method is efficient.It consumes minimum execution time,better false positive rate,accuracy,and memory usage than the conventional approach.

Assessment on Evaluating Parameters of Rice Core Collections Constructed by Genotypic Values and Molecular Marker Information

Eleven evaluating parameters for rice core collection were assessed based on genotypic values and molecular marke＇ information. Monte Carlo simulation combined with mixed linear model was used to eliminate the interference from environment in order to draw more reliable results. The coincidence rate of range （CR） was the optimal parameter. Mean Simpson index （MD）, mean Shannon-Weaver index of genetic diversity （M1） and mean polymorphism information content （MPIC） were important evaluating parameters. The variable rate of coefficient of variation （VR） could act as an important reference parameter for evaluating the variation degree of core collection. Percentage of polymorphic loci （p） could be used as a determination parameter for the size of core collection. Mean difference percentage （MD） was a determination parameter for the reliability judgment of core collection. The effective evaluating parameters for core collection selected in the research could be used as criteria for sampling percentage in different plant germplasm populations.

Genetic mapping of quantitative trait loci in crops

Dissecting the genetic architecture of complex traits is an ongoing challenge for geneticists.Two complementary approaches for genetic mapping,linkage mapping and association mapping have led to successful dissection of complex traits in many crop species.Both of these methods detect quantitative trait loci(QTL) by identifying marker–trait associations,and the only fundamental difference between them is that between mapping populations,which directly determine mapping resolution and power.Based on this difference,we first summarize in this review the advances and limitations of family-based mapping and natural population-based mapping instead of linkage mapping and association mapping.We then describe statistical methods used for improving detection power and computational speed and outline emerging areas such as large-scale meta-analysis for genetic mapping in crops.In the era of next-generation sequencing,there has arisen an urgent need for proper population design,advanced statistical strategies,and precision phenotyping to fully exploit high-throughput genotyping.

Assessment of different genetic distances in constructing cotton core subset by genotypic values

One hundred and sixty-eight genotypes of cotton from the same growing region were used as a germplasm group to study the validity of different genetic distances in constructing cotton core subset. Mixed linear model approach was employed to unbiasedly predict genotypic values of 20 traits for eliminating the environmental effect. Six commonly used genetic distances(Euclidean,standardized Euclidean,Mahalanobis,city block,cosine and correlation distances) combining four commonly used hierarchical cluster methods(single distance,complete distance,unweighted pair-group average and Ward's methods) were used in the least distance stepwise sampling(LDSS) method for constructing different core subsets. The analyses of variance(ANOVA) of different evaluating parameters showed that the validities of cosine and correlation distances were inferior to those of Euclidean,standardized Euclidean,Mahalanobis and city block distances. Standardized Euclidean distance was slightly more effective than Euclidean,Mahalanobis and city block distances. The principal analysis validated standardized Euclidean distance in the course of constructing practical core subsets. The covariance matrix of accessions might be ill-conditioned when Mahalanobis distance was used to calculate genetic distance at low sampling percentages,which led to bias in small-sized core subset construction. The standardized Euclidean distance is recommended in core subset construction with LDSS method.

A robust statistical procedure to discover expression biomarkers using microarray genomic expression data

Microarray has become increasingly popular biotechnology in biological and medical researches, and has been widely applied in classification of treatment subtypes using expression patterns of biomarkers. We developed a statistical procedure to identify expression biomarkers for treatment subtype classification by constructing an F-statistic based on Henderson method Ⅲ. Monte Carlo simulations were conducted to examine the robustness and efficiency of the proposed method. Simulation results showed that our method could provide satisfying power of identifying differentially expressed genes （DEGs） with false discovery rate （FDR） lower than the given type I error rate. In addition, we analyzed a leukemia dataset collected from 38 leukemia patients with 27 samples diagnosed as acute lymphoblastic leukemia （ALL） and 11 samples as acute myeloid leukemia （AML）. We compared our results with those from the methods of significance analysis of microarray （SAM） and microarray analysis of variance （MAANOVA）. Among these three methods, only expression biomarkers identified by our method can precisely identify the three human acute leukemia subtypes.