Pluripolarity of Graphs of Denjoy Quasianalytic Functions of Several Variables

In this paper we prove pluripolarity of graphs of Denjoy quasianalytic functions of several variables on the spanning se

Sulphate-controlled Diversity of Subterranean Microbial Communities over Depth in Deep Groundwater with Opposing Gradients of Sulphate and Methane

The groundwater system in Olkiluoto, Finland, is stratified with a mixing layer at a depth of approximately 300m between sulphate-rich, methane-poor and sulphate-poor, methane-rich groundwaters. New sequence library data obtained by 454 pyrotag sequencing of the v4v6 16S rDNA region indicated that sulphate-reducing bacteria (SRB) dominated the mixing layer while SRB could not be detected in the deep sulphate-poor groundwater samples. With the indispensable support of the sequence data, it could be demonstrated that sulphate was the only component needed to trigger a very large community transition in deep sulphate-poor, methane-rich groundwater from a non-sulphate-reducing community comprising Hydrogenophaga, Pseudomonas, Thiobacillus, Fusibacter, and Lutibacter to a sulphate-reducing community with Desulfobacula, Desulfovibrio, Desufobulbaceae, Desulfobacterium, Desulfosporosinus, and Desulfotignum. Experiments with biofilms and planktonic microorganisms in flow cells under in situ conditions confirmed that adding sulphate to the sulphate-poor groundwater generated growth of cultivable SRB and detectable SRB-related sequences. It was also found that the 16S rDNA diversity of the biofilms was conserved over 103 d and that there was great similarity in diversity between the microorganisms in the biofilms and in the flowing groundwater. This work demonstrates that the presence/absence of only one geochemical parameter, i.e., sulphate, in the groundwater significantly influenced the diversity of the investigated subterranean microbial community

Complexity of multi-dimensional spontaneous EEG decreases during propofol induced general anaesthesia

Emerging neural theories of consciousness suggest a correlation between a specific type of neural dynamical complexity and the level of consciousness: When awake and aware, causal interactions between brain regions are both integrated (all regions are to a certain extent connected) and differentiated (there is inhomogeneity and variety in the interactions). In support of this, recent work by Casali et al (2013) has shown that Lempel-Ziv complexity correlates strongly with conscious level, when computed on the EEG response to transcranial magnetic stimulation. Here we investigated complexity of spontaneous high-density EEG data during propofol-induced general anaesthesia. We consider three distinct measures: (i) Lempel-Ziv complexity, which is derived from how compressible the data are; (ii) amplitude coalition entropy, which measures the variability in the constitution of the set of active channels; and (iii) the novel synchrony coalition entropy (SCE), which measures the variability in the constitution of the set of synchronous channels. After some simulations on Kuramoto oscillator models which demonstrate that these measures capture distinct ‘flavours’ of complexity, we show that there is a robustly measurable decrease in the complexity of spontaneous EEG during general anaesthesia