Infinitesimal Gribov copies in gauge-fixed topological Yang-Mills theories

We study the Gribov problem in four-dimensional topological Yang-Mills theories following the Baulieu-Singer approach in the (anti-)self-dual Landau gauges. This is a gauge-fixed approach that allows to recover the topological spectrum, as first constructed by Witten, by means of an equivariant (or constrained) BRST cohomology. As standard gauge-fixed Yang-Mills theories suffer from the gauge copy (Gribov) ambiguity, one might wonder if and how this has repercussions for this analysis. The resolution of the small (infinitesimal) gauge copies, in general, affects the dynamics of the underlying theory. In particular, treating the Gribov problem for the standard Landau gauge condition in non-topological Yang-Mills theories strongly affects the dynamics of the theory in the infrared. In the current paper, although the theory is investigated with the same gauge condition, the effects of the copies turn out to be completely different. In other words: in both cases, the copies are there, but the effects are very different. As suggested by the tree-level exactness of the topological model in this gauge choice, the Gribov copies are shown to be inoffensive at the quantum level. To be more precise, following Gribov, we discuss the path integral restriction to the Gribov horizon. The associated gap equation, which fixes the so-called Gribov parameter, is however shown to only possess a trivial solution, making the restriction obsolete. We relate this to the absence of radiative corrections in both gauge and ghost sectors. We give further evidence by employing the renormalization group which shows that, for this kind of topological model, the gap equation indeed forbids the introduction of a massive Gribov parameter.Comment: 21 pages. Final version accepted for publication in Physics Letters

Quantitative image analysis for the characterization of microbial aggregates in biological wastewater treatment : a review

Quantitative image analysis techniques have gained an undeniable role in several fields of research during the last decade. In the field of biological wastewater treatment (WWT) processes, several computer applications have been developed for monitoring microbial entities, either as individual cells or in different types of aggregates. New descriptors have been defined that are more reliable, objective, and useful than the subjective and time-consuming parameters classically used to monitor biological WWT processes. Examples of this application include the objective prediction of filamentous bulking, known to be one of the most problematic phenomena occurring in activated sludge technology. It also demonstrated its usefulness in classifying protozoa and metazoa populations. In high-rate anaerobic processes, based on granular sludge, aggregation times and fragmentation phenomena could be detected during critical events, e.g., toxic and organic overloads. Currently, the major efforts and needs are in the development of quantitative image analysis techniques focusing on its application coupled with stained samples, either by classical or fluorescent-based techniques. The use of quantitative morphological parameters in process control and online applications is also being investigated. This work reviews the major advances of quantitative image analysis applied to biological WWT processes.The authors acknowledge the financial support to the project PTDC/EBB-EBI/103147/2008 and the grant SFRH/BPD/48962/2008 provided by Fundacao para a Ciencia e Tecnologia (Portugal)

New insights into the key microbial phylotypes of anaerobic sludge digesters under different operational conditions

Analyses on bacterial, archaeal communities at family level and methane-production metabolism were conducted in thirteen full-scale and pilot-scale anaerobic sludge digesters. These digesters were operated at different conditions regarding solids concentration, sludge retention time, organic loading rate and feedstock composition, seeking to optimize digester capacity. Correlations between process parameters and identified microbial phylotypes were evaluated based on relative abundance of these phylotypes determined by Quantitative PCR and 16S rDNA amplicon sequencing. Results showed that, Total Solids concentration (TS), among the evaluated operational parameters, demonstrated the most positive correlation with chemical parameters (including NH3 and VFAs) and significant impact on the abundance of key microbial phylotypes regardless of other factors. Digesters were grouped into 'Higher-TS' with higher stress (TS > 44 g/L, NH3 > 90 mg/L, VFAs > 300 mg/L) and 'Lower-TS' under easier status (TS <= 44 g/L, NH3 < 120 mg/L, VFAs < 525 mg/L) in this study. We identified the key microbial phylotypes, i.e. the most abundant and discriminating populations, in 'Higher-TS' digesters with high biogas production rate, which were the class Clostridia, the family Methanosarcinaceae and the order Methanobacteriales. Thermoanaerobacteraceae and Syntrophomonadaceae were identified as key families of Clostridia. Methane was produced both from acetoclastic and hydrogenotrophic methanogenesis. By contrast, in 'Higher-TS' digesters with low biogas production rate, the classes Alpha-, Beta- and Gamma-proteobacteria were detected in higher percentages, of which Rhodobacteraceae, Comamonadaceae and Xanthomonadaceae were the most abundant families respectively, and Methanomicrobiales was the prevailing methanogen order. Consistently, hydrogenotrophic pathway was predominant for methanogenesis, indicating existence of syntrophic acetate oxidation in such 'high-stress', low biogas production rate digesters. These microbial phylotypes were therefore considered to be associated to 'Higher-TS' operation. In 'Lower-TS' digesters, the abundance of the class Delta-proteobacteria, the families Anaerolineaceae, Rikenellaceae, Candidatus Cloacamonas and Methanosaetaceae was obviously higher compared with those in 'Higher-TS' digesters, which were thus considered to be marker phylotypes of easy status. The influence of TS and NH3 on the microbiome should be considered when a 'TS-increasing' strategy is applied to increase digester capacity