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"Winkler, M"
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Microbial diversity differences within aerobic granular sludge and activated sludge flocs
In this study, we investigated during 400 days the microbial community variations as observed from 16S DNA gene DGGE banding patterns from an aerobic granular sludge pilot plant as well as the from a full-scale activated sludge treatment plant in Epe, the Netherlands. Both plants obtained the same wastewater and had the same relative hydraulic variations and run stable over time. For the total bacterial population, a similarity analysis was conducted showing that the community composition of both sludge types was very dissimilar. Despite this difference, general bacterial population of both systems had on average comparable species richness, entropy, and evenness, suggesting that different bacteria were sharing the same functionality. Moreover, multi-dimensional scaling analysis revealed that the microbial populations of the flocculent sludge system moved closely around the initial population, whereas the bacterial population in the aerobic granular sludge moved away from its initial population representing a permanent change. In addition, the ammonium-oxidizing community of both sludge systems was studied in detail showing more unevenness than the general bacterial community.
Nitrosomonas
was the dominant AOB in flocculent sludge, whereas in granular sludge,
Nitrosomonas
and
Nitrosospira
were present in equal amounts. A correlation analysis of process data and microbial data from DGGE gels showed that the microbial diversity shift in ammonium-oxidizing bacteria clearly correlated with fluctuations in temperature.
Journal Article
Permutation inference for the general linear model
Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. We present a generic framework for permutation inference for complex general linear models (glms) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. We also demonstrate how the inference on glm parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm – the “randomise” algorithm – for permutation inference with the glm.
•Permutation for the GLM in the presence of nuisance or non-independence.•A generalised statistic that performs well even under heteroscedasticity.•Permutation and/or sign-flipping, exchangeability blocks and variance groups.•The “randomise” algorithm, as well as various practical examples.
Journal Article
Faster permutation inference in brain imaging
Permutation tests are increasingly being used as a reliable method for inference in neuroimaging analysis. However, they are computationally intensive. For small, non-imaging datasets, recomputing a model thousands of times is seldom a problem, but for large, complex models this can be prohibitively slow, even with the availability of inexpensive computing power. Here we exploit properties of statistics used with the general linear model (GLM) and their distributions to obtain accelerations irrespective of generic software or hardware improvements. We compare the following approaches: (i) performing a small number of permutations; (ii) estimating the p-value as a parameter of a negative binomial distribution; (iii) fitting a generalised Pareto distribution to the tail of the permutation distribution; (iv) computing p-values based on the expected moments of the permutation distribution, approximated from a gamma distribution; (v) direct fitting of a gamma distribution to the empirical permutation distribution; and (vi) permuting a reduced number of voxels, with completion of the remainder using low rank matrix theory. Using synthetic data we assessed the different methods in terms of their error rates, power, agreement with a reference result, and the risk of taking a different decision regarding the rejection of the null hypotheses (known as the resampling risk). We also conducted a re-analysis of a voxel-based morphometry study as a real-data example. All methods yielded exact error rates. Likewise, power was similar across methods. Resampling risk was higher for methods (i), (iii) and (v). For comparable resampling risks, the method in which no permutations are done (iv) was the absolute fastest. All methods produced visually similar maps for the real data, with stronger effects being detected in the family-wise error rate corrected maps by (iii) and (v), and generally similar to the results seen in the reference set. Overall, for uncorrected p-values, method (iv) was found the best as long as symmetric errors can be assumed. In all other settings, including for familywise error corrected p-values, we recommend the tail approximation (iii). The methods considered are freely available in the tool PALM — Permutation Analysis of Linear Models.
•Permutation methods can be accelerated through additional statistical approaches.•Six approaches are described and assessed.•Methods can be 100 times faster than in the non-accelerated case.•Recommendations are provided for various common scenarios.
Journal Article
A positive-negative mode of population covariation links brain connectivity, demographics and behavior
Using data from the Human Connectome Project, a single holistic multivariate analysis identified one strong mode of population co-variation: subjects were predominantly spread along a single ‘positive-negative’ axis linking lifestyle, demographic and psychometric measures to each other and to a specific pattern of functional brain connectivity.
We investigated the relationship between individual subjects' functional connectomes and 280 behavioral and demographic measures in a single holistic multivariate analysis relating imaging to non-imaging data from 461 subjects in the Human Connectome Project. We identified one strong mode of population co-variation: subjects were predominantly spread along a single 'positive-negative' axis linking lifestyle, demographic and psychometric measures to each other and to a specific pattern of brain connectivity.
Journal Article
Factors influencing the density of aerobic granular sludge
In the present study, the factors influencing density of granular sludge particles were evaluated. Granules consist of microbes, precipitates and of extracellular polymeric substance. The volume fractions of the bacterial layers were experimentally estimated by fluorescent in situ hybridisation staining. The volume fraction occupied by precipitates was determined by computed tomography scanning. PHREEQC was used to estimate potential formation of precipitates to determine a density of the inorganic fraction. Densities of bacteria were investigated by Percoll density centrifugation. The volume fractions were then coupled with the corresponding densities and the total density of a granule was calculated. The sensitivity of the density of the entire granule on the corresponding settling velocity was evaluated by changing the volume fractions of precipitates or bacteria in a settling model. Results from granules originating from a Nereda reactor for simultaneous phosphate COD and nitrogen removal revealed that phosphate-accumulating organisms (PAOs) had a higher density than glycogen-accumulating organisms leading to significantly higher settling velocities for PAO-dominated granules explaining earlier observations of the segregation of the granular sludge bed inside reactors. The model showed that a small increase in the volume fraction of precipitates (1–5 %) strongly increased the granular density and thereby the settling velocity. For nitritation–anammox granular sludge, mainly granular diameter and not density differences are causing a segregation of the biomass in the bed.
Journal Article
Permutation inference for canonical correlation analysis
Canonical correlation analysis (CCA) has become a key tool for population neuroimaging, allowing investigation of associations between many imaging and non-imaging measurements. As age, sex and other variables are often a source of variability not of direct interest, previous work has used CCA on residuals from a model that removes these effects, then proceeded directly to permutation inference. We show that a simple permutation test, as typically used to identify significant modes of shared variation on such data adjusted for nuisance variables, produces inflated error rates. The reason is that residualisation introduces dependencies among the observations that violate the exchangeability assumption. Even in the absence of nuisance variables, however, a simple permutation test for CCA also leads to excess error rates for all canonical correlations other than the first. The reason is that a simple permutation scheme does not ignore the variability already explained by previous canonical variables. Here we propose solutions for both problems: in the case of nuisance variables, we show that transforming the residuals to a lower dimensional basis where exchangeability holds results in a valid permutation test; for more general cases, with or without nuisance variables, we propose estimating the canonical correlations in a stepwise manner, removing at each iteration the variance already explained, while dealing with different number of variables in both sides. We also discuss how to address the multiplicity of tests, proposing an admissible test that is not conservative, and provide a complete algorithm for permutation inference for CCA.
Journal Article