A Two-Step Certified Reduced Basis Method

In this paper we introduce a two-step Certified Reduced Basis (RB) method. In the first step we construct from an expensive finite element “truth” discretization of dimension N an intermediate RB model of dimension N≪N . In the second step we construct from this intermediate RB model a derived RB (DRB) model of dimension M≤N. The construction of the DRB model is effected at cost O(N) and in particular at cost independent of N ; subsequent evaluation of the DRB model may then be effected at cost O(M) . The DRB model comprises both the DRB output and a rigorous a posteriori error bound for the error in the DRB output with respect to the truth discretization. The new approach is of particular interest in two contexts: focus calculations and hp-RB approximations. In the former the new approach serves to reduce online cost, M≪N: the DRB model is restricted to a slice or subregion of a larger parameter domain associated with the intermediate RB model. In the latter the new approach enlarges the class of problems amenable to hp-RB treatment by a significant reduction in offline (precomputation) cost: in the development of the hp parameter domain partition and associated “local” (now derived) RB models the finite element truth is replaced by the intermediate RB model. We present numerical results to illustrate the new approach.United States. Air Force Office of Scientific Research (AFOSR Grant number FA9550-07-1-0425)United States. Department of Defense. Office of the Secretary of Defense (OSD/AFOSR Grant number FA9550-09-1-0613)Norwegian University of Science and Technolog

The Complete Genome of Propionibacterium freudenreichii CIRM-BIA1T, a Hardy Actinobacterium with Food and Probiotic Applications

Background: Propionibacterium freudenreichii is essential as a ripening culture in Swiss-type cheeses and is also considered for its probiotic use [1]. This species exhibits slow growth, low nutritional requirements, and hardiness in many habitats. It belongs to the taxonomic group of dairy propionibacteria, in contrast to the cutaneous species P. acnes. The genome of the type strain, P. freudenreichii subsp. shermanii CIRM-BIA1 (CIP 103027T), was sequenced with an 11-fold coverage. Methodology/Principal Findings: The circular chromosome of 2.7 Mb of the CIRM-BIA1 strain has a GC-content of 67% and contains 22 different insertion sequences (3.5% of the genome in base pairs). Using a proteomic approach, 490 of the 2439 predicted proteins were confirmed. The annotation revealed the genetic basis for the hardiness of P. freudenreichii, as the bacterium possesses a complete enzymatic arsenal for de novo biosynthesis of aminoacids and vitamins (except panthotenate and biotin) as well as sequences involved in metabolism of various carbon sources, immunity against phages, duplicated chaperone genes and, interestingly, genes involved in the management of polyphosphate, glycogen and trehalose storage. The complete biosynthesis pathway for a bifidogenic compound is described, as well as a high number of surface proteins involved in interactions with the host and present in other probiotic bacteria. By comparative genomics, no pathogenicity factors found in P. acnes or in other pathogenic microbial species were identified in P. freudenreichii, which is consistent with the Generally Recognized As Safe and Qualified Presumption of Safety status of P. freudenreichii. Various pathways for formation of cheese flavor compounds were identified: the Wood-Werkman cycle for propionic acid formation, amino acid degradation pathways resulting in the formation of volatile branched chain fatty acids, and esterases involved in the formation of free fatty acids and esters. Conclusions/Significance: With the exception of its ability to degrade lactose, P. freudenreichii seems poorly adapted to dairy niches. This genome annotation opens up new prospects for the understanding of the P. freudenreichii probiotic activity

On the design of a Nd

We report operation of a Nd3+-doped fiber-laser using a cholesteric liquid crystal acting as a narrow band reflector. The aim of this work is to apply to a fiber-laser the particular optical properties of an helical structure, whatever is the medium exhibiting this structure, either a liquid crystal or either any other material. The advantage of the use of these mediums in the design of fiber-lasers is that they can favourably take the place, in an easy and compact way, of several optical elements such as a polarizer and a quarter-wave plate at one and the same time. This technology promises to design rugged compact low cost tunable coherent sources the lasing range of which can easily be adjusted. We emphasize here the particular part played by the cholesteric liquid crystal-glass interface in the laser action of the fiber