Multivariate monitoring of a biological wastewater treatment process: a case study at Melbourne Water's Western Treatment Plant

Biological wastewater treatment is a complex, multivariate process, in which a number of physical and biological processes occur simultaneously. In this study, principal component analysis (PCA) and parallel factor analysis (PARAFAC) were used to profile and characterise Lagoon 115E, a multistage biological lagoon treatment system at Melbourne Water's Western Treatment Plant (WTP) in Melbourne, Australia. In this study, the objective was to increase our understanding of the multivariate processes taking place in the lagoon. The data used in the study span a 7-year period during which samples were collected as often as weekly from the ponds of Lagoon 115E and subjected to analysis. The resulting database, involving 19 chemical and physical variables, was studied using the multivariate data analysis methods PCA and PARAFAC. With these methods, alterations in the state of the wastewater due to intrinsic and extrinsic factors could be discerned. The methods were effective in illustrating and visually representing the complex purification stages and cyclic changes occurring along the lagoon system. The two methods proved complementary, with each having its own beneficial features. (C) 2003 Elsevier B.V. All rights reserved.

Multivariate genetic analysis of cognitive abilities in an adolescent twin sample

The sources of covariation among cognitive measures of Inspection Time, Choice Reaction Time, Delayed Response Speed and Accuracy, and IQ were examined in a classical twin design that included 245 monozygotic (MZ) and 298 dizygotic (DZ) twin pairs. Results indicated that a factor model comprising additive genetic and unique environmental effects was the most parsimonious. In this model, a general genetic cognitive factor emerged with factor loadings ranging from 0.28 to 0.64. Three other genetic factors explained the remaining genetic covariation between various speed and Delayed Response measures with IQ. However, a large proportion of the genetic variation in verbal (54%) and performance (25%) IQ was unrelated to these lower order cognitive measures. The independent genetic IQ variation may reflect information processes not captured by the elementary cognitive tasks, Inspection Time and Choice Reaction Time, nor our working memory task, Delayed Response. Unique environmental effects were mostly nonoverlapping, and partly represented test measurement error.

Experimental evidence for multivariate stabilizing sexual selection

Stabilizing selection is a fundamental concept in evolutionary biology. In the presence of a single intermediate optimum phenotype (fitness peak) on the fitness surface, stabilizing selection should cause the population to evolve toward such a peak. This prediction has seldom been tested, particularly for suites of correlated traits. The lack of tests for an evolutionary match between population means and adaptive peaks may be due, at least in part, to problems associated with empirically detecting multivariate stabilizing selection and with testing whether population means are at the peak of multivariate fitness surfaces. Here we show how canonical analysis of the fitness surface, combined with the estimation of confidence regions for stationary points on quadratic response surfaces, may be used to define multivariate stabilizing selection on a suite of traits and to establish whether natural populations reside on the multivariate peak. We manufactured artificial advertisement calls of the male cricket Teleogryllus commodus and played them back to females in laboratory phonotaxis trials to estimate the linear and nonlinear sexual selection that female phonotactic choice imposes on male call structure. Significant nonlinear selection on the major axes of the fitness surface was convex in nature and displayed an intermediate optimum, indicating multivariate stabilizing selection. The mean phenotypes of four independent samples of males, from the same population as the females used in phonotaxis trials, were within the 95% confidence region for the fitness peak. These experiments indicate that stabilizing sexual selection may play an important role in the evolution of male call properties in natural populations of T. commodus.

New approximation for free surface flow of groundwater: capillarity correction

An existing capillarity correction for free surface groundwater flow as modelled by the Boussinesq equation is re-investigated. Existing solutions, based on the shallow flow expansion, have considered only the zeroth-order approximation. Here, a second-order capillarity correction to tide-induced watertable fluctuations in a coastal aquifer adjacent to a sloping beach is derived. A new definition of the capillarity correction is proposed for small capillary fringes, and a simplified solution is derived. Comparisons of the two models show that the simplified model can be used in most cases. The significant effects of higher-order capillarity corrections on tidal fluctuations in a sloping beach are also demonstrated. (c) 2004 Elsevier Ltd. All rights reserved.

Two-dimensional approximation for tide-induced watertable fluctuations in a sloping sandy beach

The prediction of watertable fluctuations in a coastal aquifer is important for coastal management. However, most previous approaches have based on the one-dimensional Boussinesq equation, neglecting variations in the coastline and beach slope. In this paper, a closed-form analytical solution for a two-dimensional unconfined coastal aquifer bounded by a rhythmic coastline is derived. In the new model, the effect of beach slope is also included, a feature that has not been considered in previous two-dimensional approximations. Three small parameters, the shallow water parameter (epsilon), the amplitude parameter (a) and coastline parameter (beta) are used in the perturbation approximation. The numerical results demonstrate the significant influence of both the coastline shape and beach slopes on tide-driven coastal groundwater fluctuations. (c) 2004 Elsevier Ltd. All rights reserved.

Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

Multivariate genetic analysis of academic skills of the Queensland Core Skills Test and IQ highlight the importance of genetic g

This study examined the genetic and environmental relationships among 5 academic achievement skills of a standardized test of academic achievement, the Queensland Core Skills Test (QCST; Queensland Studies Authority, 2003a). QCST participants included 182 monozygotic pairs and 208 dizygotic pairs (mean 17 years +/- 0.4 standard deviation). IQ data were included in the analysis to correct for ascertainment bias. A genetic general factor explained virtually all genetic variance in the component academic skills scores, and accounted for 32% to 73% of their phenotypic variances. It also explained 56% and 42% of variation in Verbal IQ and Performance IQ respectively, suggesting that this factor is genetic g. Modest specific genetic effects were evident for achievement in mathematical problem solving and written expression. A single common factor adequately explained common environmental effects, which were also modest, and possibly due to assortative mating. The results suggest that general academic ability, derived from genetic influences and to a lesser extent common environmental influences, is the primary source of variation in component skills of the QCST.

Beyond the sphere of the English facial approximation literature: Ramifications of German papers on western method concepts

In the English literature, facial approximation methods have been commonly classified into three types: Russian, American, or Combination. These categorizations are based on the protocols used, for example, whether methods use average soft-tissue depths (American methods) or require face muscle construction (Russian methods). However, literature searches outside the usual realm of English publications reveal key papers that demonstrate that the Russian category above has been founded on distorted views. In reality, Russian methods are based on limited face muscle construction, with heavy reliance on modified average soft-tissue depths. A closer inspection of the American method also reveals inconsistencies with the recognized classification scheme. This investigation thus demonstrates that all major methods of facial approximation depend on both face anatomy and average soft-tissue depths, rendering common method classification schemes redundant. The best way forward appears to be for practitioners to describe the methods they use (including the weight each one gives to average soft-tissue depths and deep face tissue construction) without placing them in any categorical classificatory group or giving them an ambiguous name. The state of this situation may need to be reviewed in the future in light of new research results and paradigms.

Assessing facial approximation accuracy: How do resemblance ratings of disparate faces compare to recognition tests?

In the past, the accuracy of facial approximations has been assessed by resemblance ratings (i.e., the comparison of a facial approximation directly to a target individual) and recognition tests (e.g., the comparison of a facial approximation to a photo array of faces including foils and a target individual). Recently, several research studies have indicated that recognition tests hold major strengths in contrast to resemblance ratings. However, resemblance ratings remain popularly employed and/or are given weighting when judging facial approximations, thus indicating that no consensus has been reached. This study aims to further investigate the matter by comparing the results of resemblance ratings and recognition tests for two facial approximations which clearly differed in their morphological appearance. One facial approximation was constructed by an experienced practitioner privy to the appearance of the target individual (practitioner had direct access to an antemortem frontal photograph during face construction), while the other facial approximation was constructed by a novice under blind conditions. Both facial approximations, whilst clearly morphologically different, were given similar resemblance scores even though recognition test results produced vastly different results. One facial approximation was correctly recognized almost without exception while the other was not correctly recognized above chance rates. These results suggest that resemblance ratings are insensitive measures of the accuracy of facial approximations and lend further weight to the use of recognition tests in facial approximation assessment. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

Studying phenotypic evolution using multivariate quantitative genetics

Quantitative genetics provides a powerful framework for studying phenotypic evolution and the evolution of adaptive genetic variation. Central to the approach is G, the matrix of additive genetic variances and covariances. G summarizes the genetic basis of the traits and can be used to predict the phenotypic response to multivariate selection or to drift. Recent analytical and computational advances have improved both the power and the accessibility of the necessary multivariate statistics. It is now possible to study the relationships between G and other evolutionary parameters, such as those describing the mutational input, the shape and orientation of the adaptive landscape, and the phenotypic divergence among populations. At the same time, we are moving towards a greater understanding of how the genetic variation summarized by G evolves. Computer simulations of the evolution of G, innovations in matrix comparison methods, and rapid development of powerful molecular genetic tools have all opened the way for dissecting the interaction between allelic variation and evolutionary process. Here I discuss some current uses of G, problems with the application of these approaches, and identify avenues for future research.

Using multivariate analysis to predict the behaviour of soils under effluent irrigation

Onsite wastewater treatment systems aim to assimilate domestic effluent into the environment. Unfortunately failure of such systems is common and inadequate effluent treatment can have serious environmental implications. The capacity of a particular soil to treat wastewater will change over time. The physical properties influence the rate of effluent movement through the soil and its chemical properties dictate the ability to renovate effluent. A research project was undertaken to determine the role that physical and chemical soil properties play in predicting the long-term behaviour of soil under effluent irrigation and to determine if they have a potential function as early indicators of adverse effects of effluent irrigation on treatment sustainability. Principal Component Analysis (PCA) and Cluster Analysis grouped the soils independently of their soil classifications and allowed us to distinguish the most suitable soils for sustainable long term effluent irrigation and determine the most influential soil parameters to characterise them. Multivariate analysis allowed a clear distinction between soils based on the cation exchange capacities. This in turn correlated well with the soil mineralogy. Mixed mineralogy soils in particular sodium or magnesium dominant soils are the most susceptible to dispersion under effluent irrigation. The soil Exchangeable Sodium Percentage (ESP) was identified as a crucial parameter and was highly correlated with percentage clay, electrical conductivity, exchangeable sodium, exchangeable magnesium and low Ca:Mg ratios (less than 0.5).