Mong-Na Lo Huang

Nutrient removal in gravel- and soil-based wetland microcosms with and without vegetation

Abstract In this study, four lab-scale microcosms, including gravel-beds with and without plants, and soil-beds with and without plants, were used to conduct the nutrient removal tests. The influent used in the tests is primary treated sewage, while the plant selected was Napier grass (Pennisetum purpureum). The purpose of this study is to compare the removal efficiencies of nitrogenous and phosphorus nutrients among these four microcosm wetland systems based on statistical analyses. Three factors, namely, with/without vegetation (F1), medium types of gravel/soil (F2), and time period for the test run of first/second stage (F3), and four combined effects of factors, F1 by F2 (F1,2), F1 by F3 (F1,3), F2 by F3 (F2,3), and F1 by F2 by F3 (F1,2,3), were run by an ANOVA model to analyze the relationships between the amounts of nutrient removed from the wetland systems and these seven factors. We found that the removals of ammonia (NH3-N), nitrate (NO3−-N), and soluble reactive phosphorus (SRP) were related to these factors and combined effects of the factors. It was found that the main removal mechanism for NH3-N was nitrification, which could be enhanced by the root zone effect in the vegetated gravel-bed wetland systems, while NO3−-N was removed mainly by denitrification and plant uptake in vegetated systems. However, the main removal mechanism for SRP was chemical adsorption in the unsaturated soil-bed systems. The effect of plant litter was also a significant mechanism affecting nutrient removal in the surface flow pattern soil-bed wetland systems without harvest.

Natural disinfection of wastewater in marine outfall fields

In this study the natural disinfection effects of marine environment on wastewater without the process of chlorination before being discharged into the ocean through submarine outfall pipes were investigated. The effects of four natural factors, including light intensity, salinity, volumetric mixing ratio of seawater to wastewater and the existence of predators, to the disinfection of wastewater in marine environment were examined. Under the condition that with or without the existence of predatory microorganisms in wastewater, experiments are performed based on rotatable central composite designs with different factor level combinations of the three factors mentioned above. Under each factor level combinations, the numbers of E.coli are measured at the beginning of each experiment and every half hour later on for two hours. Then through statistical analysis, it was found that both light intensity and salinity have significant effects to the die-off rate constant with or without the existence of predators. The effects of the three environment factors can explain a larger portion (about 90%) of the variations exhibiting in the estimated die-off rate constants in the case of without the existence of predators than that (about 50%) for the case with the existence of predators, which indicates that there may be random effects of predatory microorganisms in wastewater causing more variations in the die-off rate constants. Furthermore, through paired t-test, it also indicates that the die-off rate constants for with the existence of predators is significantly larger than that for without the existence of predators. Finally, for the primarily treated sewage from Kaohsiung, Taiwan, by natural disinfection it is estimated that it takes about 100 min during the daytime and 196 min during the nighttime to reach the national guideline concentration of E. coli (1000 cfu/100 ml) of Taiwan in marine environment.

Characterizations of the Poisson process as a renewal process via two conditional moments

Given two independent positive random variables, under some minor conditions, it is known that fromE(Xr∥X+Y)=a(X+Y)r andE(Xs∥X+Y)=b(X+Y)s, for certain pairs ofr ands, wherea andb are two constants, we can characterizeX andY to have gamma distributions. Inspired by this, in this article we will characterize the Poisson process among the class of renewal processes via two conditional moments. More precisely, let {A(t), t≥0} be a renewal process, with {Sk, k≥1} the sequence of arrival times, andF the common distribution function of the inter-arrival times. We prove that for some fixedn andk, k≤n, ifE(Skr∥A(t)=n)=atr andE(Sks∥A(t)=n)=bts, for certain pairs ofr ands, wherea andb are independent oft, then {A(t), t≥0} has to be a Poisson process. We also give some corresponding results about characterizingFto be geometric whenF is discrete.

Marginally restricted linear-optimal designs

Abstract In this work, we consider the problem of constructing linear-optimal designs for regression models, when some of the factors are not under the control of the experimenters. Such designs are referred to as marginally restricted (MR for brevity) linear-optimal designs. At first we make use of Frechet derivative to the general function o to characterize MR o-optimal designs. Then we apply this result to prove an equivalence theorem for MR linear-optimal designs. Particularly, we discuss applications to design problems in extrapolation at a point and A-optimality, which are special cases for linear criteria. An iterative algorithm for generating MR linear-optimal designs is also presented.

Model robust extrapolation designs

Abstract We seek designs which are optimal in some sense for extrapolation when the true regression function is in a certain class of regression functions. More precisely, the class is defined to be the collection of regression functions such that its (h + 1)-th derivative is bounded. The class can be viewed as representing possible departures from an ‘ideal’ model and thus describes a model robust setting. The estimates are restricted to be linear and the designs are restricted to be with minimal number of points. The design and estimate sought is minimax for mean square error. The optimal designs for cases X = [0, ∞] and X = [-1, 1], where X is the place where observations can be taken, are discussed.

Optimal designs for dual response polynomial regression models

Abstract In this paper, the D- and Ds-optimal design problems in linear regression models with a one-dimensional control variable and a k-dimensional response variable are considered. The response variables are correlated with a known covariance matrix. Some of the D- and Ds-optimal designs with polynomial models for k=2 are found explicitly. It is noted that the number of support points for the D- and Ds-optimal designs highly depend on the correlation between the two response variables except on some special cases.

Limiting spectral distribution of large-dimensional sample covariance matrices generated by VARMA

The existence of a limiting spectral distribution (LSD) for a large-dimensional sample covariance matrix generated by the vector autoregressive moving average (VARMA) model is established. In particular, we obtain explicit forms of the LSDs for random matrices generated by a first-order vector autoregressive (VAR(1)) model and a first-order vector moving average (VMA(1)) model, as well as random coefficients for VAR(1) and VMA(1). The parameters for these explicit forms are also estimated. Finally, simulations demonstrate that the results are effective.

Ds-Optimal Designs for Quadratic Log Contrast Model for Experiments with Mixtures

The approximate D s -optimal design for discriminating between linear and quadratic log contrast models for experiments with mixtures suggested by Aitchison and Bacon-Shone (1984) is investigated, where the experimental domain is restricted further as in Chan (1992). It is found that for a symmetric subspace of the finite dimensional simplex, there is a D s -optimal design with the nice structure that puts a weight 1/2 k−1 on the centroid of this subspace and the remaining weight is uniformly distributed on the vertices of the experimental domain. Finally, the D s -efficiency of the D-optimal design for quadratic model and the design given by Aitchison and Bacon-Shone (1984) are also discussed.

Optimal extrapolation designs for a partly linear model

Abstract Consider the partly linear regression model Y i = β x i + g ( t i ) + ϵ i , i = 1,…, n , where β is an unknown parameter, g is an unknown function satisfying certain smoothing condition, β and g ( t ) are to be estimated, and ϵ i s are independent errors with mean 0 and variance σ 2 . Assume that for each x i ∈[−1, 1] and t i ∈[0, 1] an experiment can be performed with the observation Y i . The Y i s are used to estimate β and g ( t ) using the estimation scheme as in Chen (1988). In this paper, the optimal designs for extrapolating the expected response f ( x , 0 , t 0 ) = β x 0 + g ( t 0 ), where x 0 t 0 ∈[0, 1], of the above partly linear model are discussed. The optimal extrapolation designs for a related model Y i = β 1 x i + β 2 x 2 i + ( g ( t i + ϵ i are also discussed.

Testing for variance changes in autoregressive models with unknown order

The problem of change point in autoregressive process is studied in this article. We propose a Bayesian information criterion-iterated cumulative sums of squares algorithm to detect the variance changes in an autoregressive series with unknown order. Simulation results and two examples are presented, where it is shown to have good performances when the sample size is relatively small.