Rank regression analysis of correlated water quality data from South East Queensland

With growing population and fast urbanization in Australia, it is a challenging task to maintain our water quality. It is essential to develop an appropriate statistical methodology in analyzing water quality data in order to draw valid conclusions and hence provide useful advices in water management. This paper is to develop robust rank-based procedures for analyzing nonnormally distributed data collected over time at different sites. To take account of temporal correlations of the observations within sites, we consider the optimally combined estimating functions proposed by Wang and Zhu (Biometrika, 93:459-464, 2006) which leads to more efficient parameter estimation. Furthermore, we apply the induced smoothing method to reduce the computational burden. Smoothing leads to easy calculation of the parameter estimates and their variance-covariance matrix. Analysis of water quality data from Total Iron and Total Cyanophytes shows the differences between the traditional generalized linear mixed models and rank regression models. Our analysis also demonstrates the advantages of the rank regression models for analyzing nonnormal data.

Nonparametric rank regression for analyzing water quality concentration data with multiple detection limits

Environmental data usually include measurements, such as water quality data, which fall below detection limits, because of limitations of the instruments or of certain analytical methods used. The fact that some responses are not detected needs to be properly taken into account in statistical analysis of such data. However, it is well-known that it is challenging to analyze a data set with detection limits, and we often have to rely on the traditional parametric methods or simple imputation methods. Distributional assumptions can lead to biased inference and justification of distributions is often not possible when the data are correlated and there is a large proportion of data below detection limits. The extent of bias is usually unknown. To draw valid conclusions and hence provide useful advice for environmental management authorities, it is essential to develop and apply an appropriate statistical methodology. This paper proposes rank-based procedures for analyzing non-normally distributed data collected at different sites over a period of time in the presence of multiple detection limits. To take account of temporal correlations within each site, we propose an optimal linear combination of estimating functions and apply the induced smoothing method to reduce the computational burden. Finally, we apply the proposed method to the water quality data collected at Susquehanna River Basin in United States of America, which dearly demonstrates the advantages of the rank regression models.

Rank regression for analysis of clustered data: A natural induced smoothing approach

We consider rank regression for clustered data analysis and investigate the induced smoothing method for obtaining the asymptotic covariance matrices of the parameter estimators. We prove that the induced estimating functions are asymptotically unbiased and the resulting estimators are strongly consistent and asymptotically normal. The induced smoothing approach provides an effective way for obtaining asymptotic covariance matrices for between- and within-cluster estimators and for a combined estimator to take account of within-cluster correlations. We also carry out extensive simulation studies to assess the performance of different estimators. The proposed methodology is substantially Much faster in computation and more stable in numerical results than the existing methods. We apply the proposed methodology to a dataset from a randomized clinical trial.

Weighted rank regression for clustered data analysis

We consider ranked-based regression models for clustered data analysis. A weighted Wilcoxon rank method is proposed to take account of within-cluster correlations and varying cluster sizes. The asymptotic normality of the resulting estimators is established. A method to estimate covariance of the estimators is also given, which can bypass estimation of the density function. Simulation studies are carried out to compare different estimators for a number of scenarios on the correlation structure, presence/absence of outliers and different correlation values. The proposed methods appear to perform well, in particular, the one incorporating the correlation in the weighting achieves the highest efficiency and robustness against misspecification of correlation structure and outliers. A real example is provided for illustration.

Rank-based regression for analysis of repeated measures

We consider rank-based regression models for repeated measures. To account for possible withinsubject correlations, we decompose the total ranks into between- and within-subject ranks and obtain two different estimators based on between- and within-subject ranks. A simple perturbation method is then introduced to generate bootstrap replicates of the estimating functions and the parameter estimates. This provides a convenient way for combining the corresponding two types of estimating function for more efficient estimation.

Induced smoothing for rank regression with censored survival times

Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be monotone in parameter components, and even in this case are step functions, requiring the equivalent of linear programming for computation. The lack of smoothness makes standard error or covariance matrix estimation even more difficult. An induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations, including conventional rank regression. The present paper applies induced smoothing to the Gehan-Wilcoxon weighted rank regression for the accelerated failure time model, for the more difficult case of survival time data subject to censoring, where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions. Smooth monotone parameter estimation and rapid, reliable standard error or covariance matrix estimation is obtained.

Standard errors and covariance matrices for smoothed rank estimators

A 'pseudo-Bayesian' interpretation of standard errors yields a natural induced smoothing of statistical estimating functions. When applied to rank estimation, the lack of smoothness which prevents standard error estimation is remedied. Efficiency and robustness are preserved, while the smoothed estimation has excellent computational properties. In particular, convergence of the iterative equation for standard error is fast, and standard error calculation becomes asymptotically a one-step procedure. This property also extends to covariance matrix calculation for rank estimates in multi-parameter problems. Examples, and some simple explanations, are given.

Synthesis and structure of mixed ligand isonitroso-β-ketoiminenickel(II) complexes. Crystal structure of (1-ethoxycarbonyl-2-npropylimino-1-propanoneoximato) (1-methoxycarbonyl-2-imino-1-propanoneoximato)nickel(II)

Mixed ligand complexes of the type Ni(R-AB)(AC') and Ni(R-AC)(AB') where AB/AC denote N-bonded isonitroso- [3-ketoimino ligands, AB'/AC' denote the corresponding Obonded ligands and R = Me, Et, n-Pr are synthesised and characterised. The complexes are neutral with square planar geometry around nickel(II). The bonding isomerism of the isonitroso group is discussed on the basis of i.r. and 1H n.m.r. studies. The crystal structure of the title complex, Ni(n-Pr-IEAI)(IMAI') has been determined from diffractometer data by Patterson and Fourier methods and refined by least squares to R = 0.088 for 2209 observed reflections. Unit cell constants are: a = 11.945(2), b = 22.436(7), c = 13.248(5) ~, [3 = 95.13(2) ~ The space group is P2Jc with Z = 8. Niekel(II) has a square planar coordination of two imine nitrogens, an isonitroso-nitrogen (from n-Pr-IEAI) and another isonitrosooxygen (from IMAI').

Reactivity of Cationic Terminal Borylene Complexes: Novel Mechanisms for Insertion and Metathesis Chemistry Involving Strongly Lewis Acidic Ligand Systems

The reactions of terminal borylene complexes of the type [CpFe(CO)(2)(BNR2)](+) (R = `Pr, Cy) with heteroallenes have been investigated by quantum-chemical methods, in an attempt to explain the experimentally observed product distributions. Reaction with dicyclohexylcarbodiimide (CyNCNCy) gives a bis-insertion product, in which 1 equiv of carbodiimide is assimilated into each of the Fe=B and B=N double bonds to form a spirocyclic boronium system. In contrast, isocyanates (R'NCO, R' = Ph, 2,6-wXy1, CY; XYl = C6H3Me2) react to give isonitrile complexes of the type [CpFe(CO)(2)(CNR')]+, via a net oxygen abstraction (or formal metathesis) process. Both carbodiimide and socyanate substrates are shown to prefer initial attack at the Fe=B bond rather than the B=N bond of the borylene complex. Further mechanistic studies reveal that the carbodiimide reaction ultimately leads to the bis-insertion compounds [CpFe(CO)(2)C(NCy)(2)B(NCY)(2)CNR2](+), rather than to the isonitrile system [CpFe(CO)(2)(CNCy)](+), on the basis of both thermodynamic (product stability) and kinetic considerations (barrier heights). The mechanism of the initial carbodiimide insertion process is unusual in that it involves coordination of the substrate at the (borylene) ligand followed by migration of the metal fragment, rather than a more conventional process: i.e., coordination of the unsaturated substrate at the metal followed by ligand migration. In the case of isocyanate substrates, metathesis products are competitive with those from the insertion pathway. Direct, single-step metathesis reactivity to give products containing a coordinated isonitrile ligand (i.e. [CpFe(CO)(2)(CNR')](+)) is facile if initial coordination of the isocyanate at boron occurs via the oxygen donor (which is kinetically favored); insertion chemistry is feasible when the isocyanate attacks initially via the nitrogen atom. However, even in the latter case, further reaction of the monoinsertion product so formed with excess isocyanate offers a number of facile (low energetic barrier) routes which also generate ['CpFe(CO)(2)(CNR')](+), rather than the bis-insertion product [CpFe(CO)(2)C(NR')(O)B(NR')(O)CNR2](+) (i.e., the direct analogue of the observed products in the carbodiimide reaction).

Closed-form solutions for low-rank non-rigid reconstruction

Recovering the motion of a non-rigid body from a set of monocular images permits the analysis of dynamic scenes in uncontrolled environments. However, the extension of factorisation algorithms for rigid structure from motion to the low-rank non-rigid case has proved challenging. This stems from the comparatively hard problem of finding a linear “corrective transform” which recovers the projection and structure matrices from an ambiguous factorisation. We elucidate that this greater difficulty is due to the need to find multiple solutions to a non-trivial problem, casting a number of previous approaches as alleviating this issue by either a) introducing constraints on the basis, making the problems nonidentical, or b) incorporating heuristics to encourage a diverse set of solutions, making the problems inter-dependent. While it has previously been recognised that finding a single solution to this problem is sufficient to estimate cameras, we show that it is possible to bootstrap this partial solution to find the complete transform in closed-form. However, we acknowledge that our method minimises an algebraic error and is thus inherently sensitive to deviation from the low-rank model. We compare our closed-form solution for non-rigid structure with known cameras to the closed-form solution of Dai et al. [1], which we find to produce only coplanar reconstructions. We therefore make the recommendation that 3D reconstruction error always be measured relative to a trivial reconstruction such as a planar one.

Preparation and catalytic studies of palladium nanoparticles stabilized by dendritic phosphine ligand-functionalized silica

Silica is a prominently utilized heterogeneous metal catalyst support. Functionalization of the silica with poly(ether imine) based dendritic phosphine ligand was conducted, in order to assess the efficacy of the dendritic phosphine in reactions facilitated by a silica supported metal catalyst. The phosphinated poly(ether imine) (PETIM) dendritic ligand was bound covalently to the functionalized silica. For this purpose, the phosphinated dendritic ligand containing an amine at the focal point was synthesized initially. Complexation of the dendritic phosphine functionalized silica with Pd(COD)Cl-2 yielded Pd(II) complex, which was reduced subsequently to Pd(0), by conditioning with EtOH. The Pd metal nanoparticle thus formed was characterized by physical methods, and the spherical nanoparticles were found to have >85% size distribution between 2 nm and 4 nm. The metal nanoparticle was tested as a hydrogenation catalyst of olefins. The catalyst could be recovered and recycled more than 10 times, without a loss in the catalytic efficiency.

X-Ray Structure Of A Ternary Metal-Complex - Copper(Ii) Inosine 5'-Monophosphate Imidazole - Metal-Binding To The N(7) Atom Of The Nucleotide In A Mixed-Ligand System Containing An Aromatic Amine

A ternary metal-nucleotide complex, Na2[Cu(5’-IMP)2(im)o,8(H20)l,2(H20)2h]as~ 1be2e.n4 pHr2ep0a,r ed and its structure analyzed by X-ray diffraction (5’-IMP = inosine 5’-monophos hate; im = imidazole). The complex crystallizes in space group C222, with a = 8.733 (4) A, b = 23.213 (5) A, c = 21.489 (6) 1, and Z = 4. The structure was solved by the heavy-atom method and refined by full-matrix least-squares technique on the basis of 2008 observed reflections to a final R value of 0.087. Symmetry-related 5’-IMP anions coordinate in cis geometry through the N(7) atoms of the bases. The other cis positions of the coordination plane are statistically occupied by nitrogen atoms of disordered im groups and water oxygens with occupancies 0.4 and 0.6, respectively. Water oxygens in axial positions complete the octahedral coordination of Cu(I1). The complex is isostructural with C~S-[P~(S’-IMP),(NH~)~a] m”,o del proposed for Pt(I1) binding to DNA. The base binding observed in the present case is different from the typical ”phosphate only” binding shown from earlier studies on metal-nucleotide complexes containing various other ?r-aromatic amines.

Biochemical and structural characterization of residue 96 mutants of Plasmodium falciparum triosephosphate isomerase: active-site loop conformation, hydration and identification of a dimer-interface ligand-binding site

Plasmodium falciparum TIM (PfTIM) is unique in possessing a Phe residue at position 96 in place of the conserved Ser that is found in TIMs from the majority of other organisms. In order to probe the role of residue 96, three PfTIM mutants, F96S, F96H and F96W, have been biochemically and structurally characterized. The three mutants exhibited reduced catalytic efficiency and a decrease in substrate-binding affinity, with the most pronounced effects being observed for F96S and F96H. The k(cat) values and K-m values are (2.54 +/- 0.19) x 10(5) min(-1) and 0.39 +/- 0.049 mM, respectively, for the wild type; (3.72 +/- 0.28) x 10(3) min(-1) and 2.18 +/- 0.028 mM, respectively, for the F96S mutant;(1.11 +/- 0.03) x 10(4) min(-1) and 2.62 +/- 0.042 mM, respectively, for the F96H mutant; and (1.48 +/- 0.05) x 10(5) min(-1) and 1.20 +/- 0.056 mM, respectively, for the F96W mutant. Unliganded and 3-phosphoglycerate (3PG) complexed structures are reported for the wild-type enzyme and the mutants. The ligand binds to the active sites of the wild-type enzyme (wtPfTIM) and the F96W mutant, with a loop-open state in the former and both open and closed states in the latter. In contrast, no density for the ligand could be detected at the active sites of the F96S and F96H mutants under identical conditions. The decrease in ligand affinity could be a consequence of differences in the water network connecting residue 96 to Ser73 in the vicinity of the active site. Soaking of crystals of wtPfTIM and the F96S and F96H mutants resulted in the binding of 3PG at a dimer-interface site. In addition, loop closure at the liganded active site was observed for wtPfTIM. The dimer-interface site in PfTIM shows strong electrostatic anchoring of the phosphate group involving the Arg98 and Lys112 residues of PfTIM.

Mixed ligand complexes in vinyl polymerization-II: [NN-ethylenebis(salicylideneiminato)] (benzoylacetonato)cobalt(III) as an initiator

The polymerization of methyl methacrylate initiated by a mixed ligand complex. [NN-ethylenebis(salicylideneiminato)](benzoylacetonato)cobalt(III) has been studied in bulk and in benzene at 70° and 80°. The rate of polymerization is proportional to (concentration of the chelate)Image and the monomer exponent is close to 1.5. The activation energy and the kinetic and transfer constants are evaluated. A free radical mechanism has been proposed.