Existence and approximation of Hunt processes associated with generalized Dirichlet forms

We show that any strictly quasi-regular generalized Dirichlet form that satisfies the mild structural condition D3 is associated to a Hunt process, and that the associated Hunt process can be approximated by a sequence of multivariate Poisson processes. This also gives a new proof for the existence of a Hunt process associated to a strictly quasi-regular generalized Dirichlet form that satisfies SD3 and extends all previous results.Comment: Revised, shortened and improved versio

Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms

Let E be an unbounded open (or closed) domain in Euclidean space of dimension greater or equal to two. We present conservativeness criteria for (possibly reflected) diffusions with state space E that are associated to fairly general perturbed divergence form operators. Our main tool is a recently extended forward and backward martingale decomposition, which reduces to the well-known Lyons-Zheng decomposition in the symmetric case.Comment: Corrected typos, minor modification

Invariant, super and quasi-martingale functions of a Markov process

We identify the linear space spanned by the real-valued excessive functions of a Markov process with the set of those functions which are quasimartingales when we compose them with the process. Applications to semi-Dirichlet forms are given. We provide a unifying result which clarifies the relations between harmonic, co-harmonic, invariant, co-invariant, martingale and co-martingale functions, showing that in the conservative case they are all the same. Finally, using the co-excessive functions, we present a two-step approach to the existence of invariant probability measures

Dynamics of Polyphosphate-Accumulating Bacteria in Wastewater Treatment Plant Microbial Communities Detected via DAPI (4′,6′-Diamidino-2-Phenylindole) and Tetracycline Labeling▿ †

Wastewater treatment plants with enhanced biological phosphorus removal represent a state-of-the-art technology. Nevertheless, the process of phosphate removal is prone to occasional failure. One reason is the lack of knowledge about the structure and function of the bacterial communities involved. Most of the bacteria are still not cultivable, and their functions during the wastewater treatment process are therefore unknown or subject of speculation. Here, flow cytometry was used to identify bacteria capable of polyphosphate accumulation within highly diverse communities. A novel fluorescent staining technique for the quantitative detection of polyphosphate granules on the cellular level was developed. It uses the bright green fluorescence of the antibiotic tetracycline when it complexes the divalent cations acting as a countercharge in polyphosphate granules. The dynamics of cellular DNA contents and cell sizes as growth indicators were determined in parallel to detect the most active polyphosphate-accumulating individuals/subcommunities and to determine their phylogenetic affiliation upon cell sorting. Phylotypes known as polyphosphate-accumulating organisms, such as a “Candidatus Accumulibacter”-like phylotype, were found, as well as members of the genera Pseudomonas and Tetrasphaera. The new method allows fast and convenient monitoring of the growth and polyphosphate accumulation dynamics of not-yet-cultivated bacteria in wastewater bacterial communities