The UNIFORM C^(0)ESTIMATE AND WEIGHTED ESTIMATE OF GENERALIZED CHRISTOFFEL-MINKOWSKI PROBLEMS

In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the weighted gradient estimate and uniform C^(0)estimate for the positive convex even solutions,which is a generalization of Guan-Xia[1]and Guan[2].

Discussion of Fan et al.’s paper “Gaining effciency via weighted estimators for multivariate failure time data”

In the analysis of correlated data, it is ideal to capture the true dependence structure to increase effciency of the estimation. However, for multivariate survival data, this is extremely

Rejoinder for Gaining effciency via weighted estimators for multivariate failure time data

We thank all the discussants for their interesting and stimulating contributions. They have touched various aspects that have not been considered by the original articles.

Robust Estimators for Poisson Regression

The present paper proposes a new robust estimator for Poisson regression models. We used the weighted maximum likelihood estimators which are regarded as Mallows-type estimators. We perform a Monte Carlo simulation study to assess the performance of a suggested estimator compared to the maximum likelihood estimator and some robust methods. The result shows that, in general, all robust methods in this paper perform better than the classical maximum likelihood estimators when the model contains outliers. The proposed estimators showed the best performance compared to other robust estimators.

Weighted Probability Density Estimator with Updated Bandwidths

In this paper,the authors study a class of weighted version of probability density estimator.It is shown that the weighted estimator contains some existing estimators of probability density,no matter they are recursive or non-recursive.Some statistical results including weak consistency,strong consistency,rate of strong consistency,and asymptotic normality are established under some mild conditions.Moreover,the random weighted estimator is also investigated.Some numerical simulations and a real data analysis are presented to study the numerical performances of the estimators.

A robust triaxial localization method of AE source using refraction path

Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE source using refraction path is proposed.Firstly,the control equation of the refraction path is established according to the sensor coordinates and arrival times.Secondly,considering the influence of time-difference-of-arrival(TDOA)errors,the residual of the governing equation is calculated to estimate the equation weight.Thirdly,the refraction points in different directions are solved using Snell’s law and orthogonal constraints.Finally,the source coordinates are iteratively solved by weighted correction terms.The feasibility and accuracy of the proposed method are verified by pencil-lead breaking experiments.The simulation results show that the new method is almost unaffected by the refraction ratio,and always holds more stable and accurate positioning performance than the traditional method under different ratios and scales of TDOA outliers.

Data-Based Filters for Non-Gaussian Dynamic Systems With Unknown Output Noise Covariance

This paper proposes linear and nonlinear filters for a non-Gaussian dynamic system with an unknown nominal covariance of the output noise.The challenge of designing a suitable filter in the presence of an unknown covariance matrix is addressed by focusing on the output data set of the system.Considering that data generated from a Gaussian distribution exhibit ellipsoidal scattering,we first propose the weighted sum of norms(SON)clustering method that prioritizes nearby points,reduces distant point influence,and lowers computational cost.Then,by introducing the weighted maximum likelihood,we propose a semi-definite program(SDP)to detect outliers and reduce their impacts on each cluster.Detecting these weights paves the way to obtain an appropriate covariance of the output noise.Next,two filtering approaches are presented:a cluster-based robust linear filter using the maximum a posterior(MAP)estimation and a clusterbased robust nonlinear filter assuming that output noise distribution stems from some Gaussian noise resources according to the ellipsoidal clusters.At last,simulation results demonstrate the effectiveness of our proposed filtering approaches.

On the rate of complete convergence for weighted sums of NSD random variables and an application

In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.

WEIGHTED WEAK TYPE ESTIMATES INVOLVING SPACES GENERATED BY BLOCKS

The problem studied in this paper is how to establish weighted estimates of weak type near L^1 for those operators that are not of weak type(1,1).

Weighted Estimates for the Maximal Commutator of Singular Integral Operator on Spaces of Homogeneous Type

Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.

Weighted Likelihood Estimation Method Based on the Multidimensional Nominal Response Model

The Monte Carlo study evaluates the relative accuracy of Warm＇s （1989） weighted likelihood estimate （WLE） compared to the maximum likelihood estimate （MLE） using the nominal response model. And the results indicate that WLE was more accurate than MLE.

2.5D induced polarization forward modeling using the adaptive finite-element method

The conventional finite-element（FE） method often uses a structured mesh, which is designed according to the user’s experience, and it is not sufficiently accurate and flexible to accommodate complex structures such as dipping interfaces and rough topography. We present an adaptive FE method for 2.5D forward modeling of induced polarization（IP）. In the presented method, an unstructured triangulation mesh that allows for local mesh refinement and flexible description of arbitrary model geometries is used. Furthermore, the mesh refinement process is guided by dual error estimate weighting to bias the refinement towards elements that affect the solution at the receiver locations. After the final mesh is generated, the Jacobian matrix is used to obtain the IP response on 2D structure models. We validate the adaptive FE algorithm using a vertical contact model. The validation shows that the elements near the receivers are highly refined and the average relative error of the potentials converges to 0.4 % and 1.2 % for the IP response. This suggests that the numerical solution of the adaptive FE algorithm converges to an accurate solution with the refined mesh. Finally, the accuracy and flexibility of the adaptive FE procedure are also validated using more complex models.

Dynamic Case Retrieval Method With Subjective Preferences and Objective Information for Emergency Decision Making

Case-based reasoning(CBR) is one of the best methods for generating an effective solution in an emergency. In recent years, some methods for generating emergency alternatives have been included in practical CBR applications, but there have been no in-depth studies of these processes. In this study,we propose a new method for dynamic case retrieval with subjective preferences and objective information, which considers the personal preferences of the decision makers and changes in the attributes of the emergency as the situation develops. First,we present a formula for calculating the case similarity and changing trends in the case considered, where similar cases are obtained. Next, we describe a method for measuring the overall assessment value with respect to similar historical cases, which is obtained by aggregating the case similarity, the utility case similarity, the first response time, and the implementation effect.The subjective preferences and objective information are also integrated in the decision-making process. Finally, we present a case study based on the emergency response to a fire in a highrise building, which illustrates the applicability and feasibility of the proposed method.

Estimating liver weight of adults by body weight and gender

AIM： To estimate the standard liver weight for assessing adequacies of graft size in live donor liver transplantation and remnant liver in major hepatectomy for cancer. METHODS： In this study, anthropometric data of body weight and body height were tested for a correlation with liver weight in 159 live liver donors who underwent donor right hepatectomy including the middle hepatic vein. Liver weights were calculated from the right lobe graft weight obtained at the back table, divided by the proportion of the right lobe on the computed tomography. RESULTS： The subjects, all Chinese, had a mean age of 35.8 ± 10.5 years, and a female to male ratio of 118：41. The mean volume of the right lobe was 710.14 ±131.46 mL and occupied 64.55%±4.47% of the whole liver on computed tomography. Right lobe weighed 598.90±117.39 g and the estimated liver weight was 927.54 ± 168.78 g. When body weight and body height were subjected to multiple stepwise linear regression analysis, body height was found to be insignificant. Females of the same body weight had a slightly lower liver weight. A formula based on body weight and gender was derived： Estimated standard liver weight （g）=218＋BW （kg）× 12.3＋gender×51 （R^2 = 0.48） （female=0, male= 1）. Based on the anthropometric data of these 159 subjects, liver weights were calculated using previously published formulae derived from studies on Caucasian, .lapanese, Korean, and Chinese. All formulae overestimated liver weights compared to this formula. The Japanese formula overestimated the estimated standard liver weight （ESLW） for adults less than 60 kg.CONCLUSION： A formula applicable to Chinese males and females is available. A formula for individual races appears necessary.

Non-invasive evaluation of lower urinary tract symptoms(LUTS)in men

Lower urinary tract symptoms(LUTS)are common in males over the age of 40 years old and are likely to increase with an aging population.Currently urodynamic studies are the gold standard to determine the aetiology of voiding dysfunction and LUTS.However,due to its invasive nature,a great number of non-invasive ultrasound based investigations have been developed to assess patients with symptomatic LUTS.The clinical application of noninvasive tests could potentially stratify patients who would require more invasive investigations and allow more precise patient directed treatment.A PubMed literature review was performed and we will discuss the non-invasive investigations that have been developed thus far,focusing on bladder wall and detrusor wall thickness(BWT&DWT),ultrasound estimated bladder weight(UEBW)and intravesical prostatic protrusion(IPP).

A Telepresence-Guaranteed Control Scheme for Teleoperation Applications of Transferring Weight-Unknown Objects

Currently,most teleoperation work is focusing on scenarios where slave robots interact with unknown environments.However,in some fields such as medical robots or rescue robots,the other typical teleoperation application is precise object transportation.Generally,the object’s weight is unknown yet essential for both accurate control of the slave robot and intuitive perception of the human operator.However,due to high cost and limited installation space,it is unreliable to employ a force sensor to directly measure the weight.Therefore,in this paper,a control scheme free of force sensor is proposed for teleoperation robots to transfer a weight-unknown object accurately.In this scheme,the workspace mapping between master and slave robot is firstly established,based on which,the operator can generate command trajectory on-line by operating the master robot.Then,a slave controller is designed to follow the master command closely and estimate the object’s weight rapidly,accurately and robust to unmodeled uncertainties.Finally,for the sake of telepresence,a master controller is designed to generate force feedback to reproduce the estimated weight of the object.In the end,comparative experiments show that the proposed scheme can achieve better control accuracy and telepresence,with accurate force feedback generated in only 500 ms.

Robust LS-SVM regression for ore grade estimation in a seafloor hydrothermal sulphide deposit

Due to the geological complexities of ore body formation and limited borehole sampling, this paper propos- es a robust weighted least square support vector machine （LS-SVM） regression model to solve the ore grade estimation for a seafloor hydrothermal sulphide deposit in Solwara 1, which consists of a large proportion of incomplete samples without ore types and grade values. The standard LS-SVM classification model is applied to identify the ore type for each incomplete sample. Then, a weighted K-nearest neighbor （WKNN） algorithm is proposed to interpolate the missing values. Prior to modeling, the particle swarm optimiza- tion （PSO） algorithm is used to obtain an appropriate splitting for the training and test data sets so as to eliminate the large discrepancies caused by random division. Coupled simulated annealing （CSA） and grid search using 10-fold cross validation techniques are adopted to determine the optimal tuning parameter- s in the LS-SVM models. The effectiveness of the proposed model by comparing with other well-known techniques such as inverse distance weight （IDW）, ordinary kriging （OK）, and back propagation （BP） neural network is demonstrated. The experimental results show that the robust weighted LS-SVM outperforms the other methods, and has strong predictive and generalization ability.

SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS

For the 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null conditions with small initial data and the coefficients depending simultaneously on u and δu. Through construction of an approximate solution, combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction.

The RAMA Ped Card： Does it work for actual weight estimation in child patients at the emergency department

BACKGROUND: In emergency conditions, the actual weight of infants and young children are essential for treatments. The RAMATHIBODI Pediatric Emergency Drug Card or RAMA Ped Card has also been developed to estimate actual weight of the subjects. This study aimed to validate the RAMA Ped Card in correctly identifying the actual weight of infants and young adults.METHODS: This study was a prospective study. We enrolled all consecutive patients under 15 years of age who visited the emergency department(ED). All eligible patients' actual weight and height were measured at the screening point of the ED. The weight of each patient was also measured using the unlabeled RAMA Ped Card. The Cohen's kappa values and agreement percentages were calculated.RESULTS: During the study period, there were 345 eligible patients. The RAMA Ped Card had a 61.16% agreement with the actual weight with a kappa of 0.54(P<0.01), while the agreement with the actual height had a kappa of 0.90 and 91.59% agreement. Sub-group analysis found kappa scores with good range in two categories: in cases of accidents and in the infant group(kappa of 0.68 and 0.65, respectively).CONCLUSION: The RAMA Ped Card had a fair correlation with the actual weight in child patients presenting at the ED. Weight estimation in infant patients and children who presented with accidents were more accurate.

Power Inverted Topp–Leone Distribution in Acceptance Sampling Plans

We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile measures,moments,moment generating function,probability weighted moments,Bonferroni and Lorenz curve,stochastic ordering,incomplete moments,residual life function,and entropy measure.Acceptance sampling plans are developed for the PITL distribution,when the life test is truncated at a pre-specified time.The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors.The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk.Numerical results for given consumer’s risk,parameters of the PITL distribution and the truncation time are obtained.The estimation of the model parameters is argued using maximum likelihood,least squares,weighted least squares,maximum product of spacing and Bayesian methods.A simulation study is confirmed to evaluate and compare the behavior of different estimates.Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions.The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.