Regularity for eigenfunctions of Schr\"odinger operators

We prove a regularity result in weighted Sobolev spaces (or Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\"odinger operator. More precisely, let K_{a}^{m}(\mathbb{R}^{3N}) be the weighted Sobolev space obtained by blowing up the set of singular points of the Coulomb type potential V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N} \frac{c_{ij}}{|x_i-x_j|}, x in \mathbb{R}^{3N}, b_j, c_{ij} in \mathbb{R}. If u in L^2(\mathbb{R}^{3N}) satisfies (-\Delta + V) u = \lambda u in distribution sense, then u belongs to K_{a}^{m} for all m \in \mathbb{Z}_+ and all a \le 0. Our result extends to the case when b_j and c_{ij} are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a<3/2.Comment: to appear in Lett. Math. Phy

Symmetries and observables in topological gravity

After a brief review of topological gravity, we present a superspace approach to this theory. This formulation allows us to recover in a natural manner various known results and to gain some insight into the precise relationship between different approaches to topological gravity. Though the main focus of our work is on the vielbein formalism, we also discuss the metric approach and its relationship with the former formalism.Comment: 34 pages; a few explanations added in subsection 2.2.1, published version of pape

Simultaneous Metabarcoding and Quantification of Neocallimastigomycetes from Environmental Samples:Insights into Community Composition and Novel Lineages

Anaerobic fungi from the herbivore digestive tract (Neocallimastigomycetes) are primary lignocellulose modifiers and hold promise for biotechnological applications. Their molecular detection is currently difficult due to the non-specificity of published primer pairs, which impairs evolutionary and ecological research with environmental samples. We developed and validated a Neocallimastigomycetes-specific PCR primer pair targeting the D2 region of the ribosomal large subunit suitable for screening, quantifying, and sequencing. We evaluated this primer pair in silico on sequences from all known genera, in vitro with pure cultures covering 16 of the 20 known genera, and on environmental samples with highly diverse microbiomes. The amplified region allowed phylogenetic differentiation of all known genera and most species. The amplicon is about 350 bp long, suitable for short-read high-throughput sequencing as well as qPCR assays. Sequencing of herbivore fecal samples verified the specificity of the primer pair and recovered highly diverse and so far unknown anaerobic gut fungal taxa. As the chosen barcoding region can be easily aligned and is taxonomically informative, the sequences can be used for classification and phylogenetic inferences. Several new Neocallimastigomycetes clades were obtained, some of which represent putative novel lineages such as a clade from feces of the rodent Dolichotis patagonum (mara)

Simultaneous Metabarcoding and Quantification of Neocallimastigomycetes from Environmental Samples:Insights into Community Composition and Novel Lineages

Anaerobic fungi from the herbivore digestive tract (Neocallimastigomycetes) are primary lignocellulose modifiers and hold promise for biotechnological applications. Their molecular detection is currently difficult due to the non-specificity of published primer pairs, which impairs evolutionary and ecological research with environmental samples. We developed and validated a Neocallimastigomycetes-specific PCR primer pair targeting the D2 region of the ribosomal large subunit suitable for screening, quantifying, and sequencing. We evaluated this primer pair in silico on sequences from all known genera, in vitro with pure cultures covering 16 of the 20 known genera, and on environmental samples with highly diverse microbiomes. The amplified region allowed phylogenetic differentiation of all known genera and most species. The amplicon is about 350 bp long, suitable for short-read high-throughput sequencing as well as qPCR assays. Sequencing of herbivore fecal samples verified the specificity of the primer pair and recovered highly diverse and so far unknown anaerobic gut fungal taxa. As the chosen barcoding region can be easily aligned and is taxonomically informative, the sequences can be used for classification and phylogenetic inferences. Several new Neocallimastigomycetes clades were obtained, some of which represent putative novel lineages such as a clade from feces of the rodent Dolichotis patagonum (mara)