Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators

In many works, the linearized non-cutoff Boltzmann operator is considered to behave essentially as a fractional Laplacian. In the present work, we prove that the linearized non-cutoff Boltzmann operator with Maxwellian molecules is exactly equal to a fractional power of the linearized Landau operator which is the sum of the harmonic oscillator and the spherical Laplacian. This result allows to display explicit sharp coercive estimates satisfied by the linearized non-cutoff Boltzmann operator for both Maxwellian and non-Maxwellian molecules.Comment: arXiv admin note: text overlap with arXiv:1111.042

Structural and biochemical characterization of the exopolysaccharide deacetylase Agd3 required for Aspergillus fumigatus biofilm formation

The exopolysaccharide galactosaminogalactan (GAG) is an important virulence factor of the fungal pathogen Aspergillus fumigatus. Deletion of a gene encoding a putative deacetylase, Agd3, leads to defects in GAG deacetylation, biofilm formation, and virulence. Here, we show that Agd3 deacetylates GAG in a metal-dependent manner, and is the founding member of carbohydrate esterase family CE18. The active site is formed by four catalytic motifs that are essential for activity. The structure of Agd3 includes an elongated substrate-binding cleft formed by a carbohydrate binding module (CBM) that is the founding member of CBM family 87. Agd3 homologues are encoded in previously unidentified putative bacterial exopolysaccharide biosynthetic operons and in other fungal genomes. The exopolysaccharide galactosaminogalactan (GAG) is an important virulence factor of the fungal pathogen Aspergillus fumigatus. Here, the authors study an A. fumigatus enzyme that deacetylates GAG in a metal-dependent manner and constitutes a founding member of a new carbohydrate esterase family.Bio-organic Synthesi