Discovering context-aware conditional functional dependencies

Conditional functional dependencies（CFDs） are important techniques for data consistency. However, CFDs are limited to 1） provide the reasonable values for consistency repairing and 2） detect potential errors. This paper presents context-aware conditional functional dependencies（CCFDs） which contribute to provide reasonable values and detect po- tential errors. Especially, we focus on automatically discov- ering minimal CCFDs. In this paper, we present context rela- tivity to measure the relationship of CFDs. The overlap of the related CFDs can provide reasonable values which result in more accuracy consistency repairing, and some related CFDs are combined into CCFDs. Moreover, we prove that discover- ing minimal CCFDs is NP-complete and we design the pre- cise method and the heuristic method. We also present the dominating value to facilitate the process in both the precise method and the heuristic method. Additionally, the context relativity of the CFDs affects the cleaning results. We will give an approximate threshold of context relativity accord- ing to data distribution for suggestion. The repairing results are approved more accuracy, even evidenced by our empirical evaluation.

Nonparametric inferences for kurtosis and conditional kurtosis

Under the assumption of strictly stationary process, this paper proposes a nonparametric model to test the kurtosis and conditional kurtosis for risk time series. We apply this method to the daily returns of S＆P500 index and the Shanghai Composite Index, and simulate GARCH data for verifying the efficiency of the presented model. Our results indicate that the risk series distribution is heavily tailed, but the historical information can make its future distribution light-tailed. However the far future distribution＇s tails are little affected by the historical data.

Linking Management and Riparian Physical Functions to Water Quality and Aquatic Habitat

Stream and wetland riparian areas are able to sustain a state of resiliency based on the ecosystem’s ability to attain the functions of its ecological potential. This resiliency allows an area to provide and produce desired and valued water quality and aquatic habitat ecosystem services. Maintaining healthy aquatic and riparian habitats depends on “management” allowing for, or facilitating natural recovery of riparian functions. Altering grazing management practices in Maggie Creek lead to changes in riparian functionality, water quality, and aquatic habitat. Maggie Creek basin, historically renowned for its fishery, is one of only a few watersheds in Nevada capable of supporting Lahontan Cutthroat Trout (LCT) (Oncorhynchus clarkia ssp. Henshawi) meta-populations. Prior to 1993, the majority of Maggie Creek was grazed by cattle throughout the growing season. Decades of intensive grazing, water development, and road construction degraded aquatic and riparian habitats. By the early 1990’s, a majority of the Maggie Creek watershed was rated as nonfunctional or functional-at-risk condition with unstable banks, channel incision, loss of riparian vegetation, wide shallow channels, excessive erosion and deposition, reduced stream flows, and increased water temperatures. As mitigation for their 1993 South Operations Area Project mine dewatering, Newmont Mining Company, in cooperation with the Elko District Bureau of Land Management (BLM) and the Elko Land and Livestock Company, developed the Maggie Creek Watershed Restoration Project to enhance LCT habitat. The project was developed to enhance 82 miles of stream, 2000 acres of riparian habitat and 40,000 acres of upland watershed primarily through prescriptive livestock management. Beginning in 1994, grazing systems were implemented for portions of the perennial/intermittent streams. This greatly reduced the frequency and duration of hot season grazing on Maggie Creek and its tributaries. The objective of this paper is to compare 1994 and 2006 stream and wetland riparian assessments using proper functioning condition (PFC) protocol and water quality data.

A NEW FORMULATION OF BERNSTEIN-BEZIER BASED SMOOTHNESS CONDITIONS FOR pp FUNCTIONS

In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness rand total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5].

New smooth gap function for box constrained variational inequalities

A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.

APPROXIMATION RATES OF ERROR DISTRIBUTION OF DOUBLE KERNEL ESTIMATES OF CONDITIONAL DENSITY

In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .

Joint probability distribution of winds and waves from wave simulation of 20 years (1989-2008) in Bohai Bay

The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.

SOLUTION OF DIFFERENT HOLES SHAPE BORDERS OF FIBRE REINFORCED COMPOSITE PLATES BY INTEGRAL EQUATIONS

Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.

Estimated conditional score function for missing mechanism model with nonignorable nonresponse

Missing data mechanism often depends on the values of the responses,which leads to nonignorable nonresponses.In such a situation,inference based on approaches that ignore the missing data mechanism could not be valid.A crucial step is to model the nature of missingness.We specify a parametric model for missingness mechanism,and then propose a conditional score function approach for estimation.This approach imputes the score function by taking the conditional expectation of the score function for the missing data given the available information.Inference procedure is then followed by replacing unknown terms with the related nonparametric estimators based on the observed data.The proposed score function does not suffer from the non-identifiability problem,and the proposed estimator is shown to be consistent and asymptotically normal.We also construct a confidence region for the parameter of interest using empirical likelihood method.Simulation studies demonstrate that the proposed inference procedure performs well in many settings.We apply the proposed method to a data set from research in a growth hormone and exercise intervention study.

Identification of Major Sources of PM2.5 in St. Louis Missouri USA

The objective of this study is to examine the use of the conditional probability function(CPF) and nonparametric regression(NPR) to identify the relationship between wind direction and concentration of PM2.5(particulate matter with aerodynamic diameter less than or equal to 2.5 μm). Twenty four-hour integrated PM2.5 mass and species concentrations were measured at the St. Louis-Midwest Supersite in East St. Louis,Illinois,USA in the periods of 22-28 June 2001,7-13 November 2001,and 19-25 March 2002. Wind directions were measured on site. The concentrations of 15 elements and ions,i.e. Al,As,Cd,Cr,Cu,Fe,Mn,Ni,Pb,Se,Zn,OC,EC,SO4,and NO3 were calculated using the CPF and NPR. The comparison between the results obtained from the CPF and NPR demonstrated that they both agreed well with the locations of the known local point sources. The CPF was simpler and easier to calculate than NPR. In contrast,NPR provided PM2.5 concentrations but with some uncertainties. This study indicates that both methods can be utilized to promote the source apportionment study of ambient PM2.5.

Conditional Log-Laplace Functional for a Class of Branching Processes in Random Environments

A conditional log-Laplace functional （CLLF） for a class of branching processes in random environments is derived. The basic idea is the decomposition of a dependent branching dynamic into a no-interacting branching and an interacting dynamic generated by the random environments. CLLF will play an important role in the investigation of branching processes and superprocesses with interaction.

Approximating Conditional Density Functions Using Dimension Reduction

We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ^τX, where the unit vector θ is selected such that the average Kullback-Leibler discrepancy distance between the two conditional density functions obtains the minimum. Our approach is nonparametric as far as the estimation of the conditional density functions is concerned. We have shown that this nonparametric estimator is asymptotically adaptive to the unknown index θ in the sense that the first order asymptotic mean squared error of the estimator is the same as that when θ was known. The proposed method is illustrated using both simulated and real-data examples.

Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model

This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index model,and this approach represents a good compromise between nonparametric and parametric models.Then we give under general conditions and when the variables are independent,the quadratic error and asymptotic normality of estimator by local linear method,based on the single-index structure.Finally,wecomplete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area.

Stokes flow before plane boundary with mixed stick-slip boundary conditions

A general theorem for the Stokes flow over a plane boundary with mixed stick-slip boundary conditions is established. This is done by using a representation for the velocity and pressure fields in the three-dimensional Stokes flow in terms of a biharmonic function and a harmonic function. The earlier theorem for the Stokes flow due to fundamental singularities before a no-slip plane boundary is shown to be a special case of the present theorem. Furthermore, in terms of the Stokes stream function, a corollary of the theorem is also derived, providing a solution to the problem of the axisymmetric Stokes flow along a rigid plane with stick-slip boundary conditions. The formulae for the drag and torque exerted by the fluid on the boundary are established. An illustrative example is given.

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-Ⅱ hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size,we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively,and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.

ASYMPTOTIC NORMALITY OF THE NONPARAMETRIC KERNEL ESTIMATION OF THE CONDITIONAL HAZARD FUNCTION FOR LEFT-TRUNCATED AND DEPENDENT DATA

Under some mild conditions, we derive the asymptotic normality of the Nadaraya-Watson and local linear estimators of the conditional hazard function for left-truncated and dependent data. The estimators were proposed by Liang and Ould-Sa?d [1]. The results confirm the guess in Liang and Ould-Sa?d [1].

LOCAL POLYNOMIAL DOUBLE-SMOOTHING ESTIMATION OF A CONDITIONAL DISTRIBUTION FUNCTION WITH DEPENDENT

Based on the idea of local polynomial double-smoother, we propose an estimator of a conditional cumulative distribution function with dependent and left-truncated data. It is assumed that the observations form a stationary a-mixing sequence. Asymptotic normality of the estimator is established. The finite sample behavior of the estimator is investigated via simulations.

Improvement and application of wall function boundary condition for high-speed compressible flows

In order to develop a wall function boundary condition for high-speed flows so as to reduce the grid-dependence of the simula- tion for the skin friction and heat flux, a research was performed to improve the compressible wall function boundary condition proposed by Nichols. Values of parameters in the velocity law-of-the-wall were revised according to numerical experiments and the expression of temperature law-of-the-wall was modified based on theoretical analysis and numerical simulation. Be- sides, the formula of the heat conduction term in near-wall region was derived so that the coupling between the wall function boundary condition and CFD code was realized more accurately. Whereafter, the application study of the modified wall func- tion was carried out. The numerical case of supersonic turbulent boundary layer on a flat plate illustrated that the modified wall function produces reasonable results of skin friction and heat flux, and profiles of velocity, temperature and turbulent eddy viscosity for coarse grids with the initial wall spacing of y＋〈400, and that the modifications to the original wall function can obviously improve the simulation precision. As for the application of separation flows, it was found from the numerical cases of supersonic cavity flow and hypersonic axisymmetric compression comer that the compressible velocity law-of-the-wall originally established based on the fully-developed attached turbulent boundary layer approximately holds in the near-wall re- gion inside the separation flows, which ensures that reliable skin friction and heat flux can be given by the wall function inside the separation flows, while for the region near separation and reattachment points, the wall function gives results with a rela- tively large error, because the velocity law-of-the-wall used in the wall function takes on obvious deviation from the real ve- locity profiles near the separation and reattachment points.

Existence and Uniqueness of Positive Solutions for Some Singular Boundary Value Problems with Linear Functional Boundary Conditions

By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f（t, u） is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0, 1] positive solutions as well as the C1 [0, 1] positive solutions.