Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.

Euclidean geometric invariant of framed knots in manifolds

We present an invariant of a three dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. An important feature of our work is that we are not using any nontrivial representation of the manifold fundamental group or knot group.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

Gene amplification in Rhynchosciara (1955-1987)

A review is made of the evidence indicating the existence of gene amplification in Rhynchosciara, from the early cytological work to the more recent studies using cloned sequences from the DNA puffs. Mention is made of work still in progress which indicates that the transcription unit of a DNA puff is surprisingly complex.

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

"Vegeu el resum a l'inici del document del fitxer adjunt."

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Amplification of the housekeeping sigma factor in Pseudomonas fluorescens CHA0 enhances antibiotic production and improves biocontrol abilities.

Pseudomonas fluorescens CHA0 produces a variety of secondary metabolites, in particular the antibiotics pyoluteorin and 2,4-diacetylphloroglucinol, and protects various plants from diseases caused by soilborne pathogenic fungi. The rpoD gene encoding the housekeeping sigma factor sigma 70 of P. fluorescens was sequenced. The deduced RpoD protein showed 83% identity with RpoD of Pseudomonas aeruginosa and 67% identity with RpoD of Escherichia coli. Attempts to inactivate the single chromosomal rpoD gene of strain CHA0 were unsuccessful, indicating an essential role of this gene. When rpoD was carried by an IncP vector in strain CHA0, the production of both antibiotics was increased severalfold and, in parallel, protection of cucumber against disease caused by Pythium ultimum was improved, in comparison with strain CHA0.

Sobolev mappings: Lipschitz density is not an isometric invariant of the target

"Vegeu el resum a l'inici del document del fitxer adjunt."

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Evidences of gentamicin resistance amplification in Klebsiella pneumoniae isolated from faeces of hospitalized newborns

The intestinal microbiota, a barrier to the establishment of pathogenic bacteria, is also an important reservoir of opportunistic pathogens. It plays a key role in the process of resistance-genes dissemination, commonly carried by specialized genetic elements, like plasmids, phages, and conjugative transposons. We obtained from strains of enterobacteria, isolated from faeces of newborns in a university hospital nursery, indication of phenothypical gentamicin resistance amplification (frequencies of 10-3 to 10-5, compatible with transposition frequencies). Southern blotting assays showed strong hybridization signals for both plasmidial and chromossomal regions in DNA extracted from variants selected at high gentamicin concentrations, using as a probe a labeled cloned insert containing aminoglycoside modifying enzyme (AME) gene sequence originated from a plasmid of a Klebsiella pneumoniae strain previously isolated in the same hospital. Further, we found indications of inactivation to other resistance genes in variants selected under similar conditions, as well as, indications of co-amplification of other AME markers (amikacin). Since the intestinal environment is a scenario of selective processes due to the therapeutic and prophylactic use of antimicrobial agents, the processes of amplification of low level antimicrobial resistance (not usually detected or sought by common methods used for antibiotic resistance surveillance) might compromise the effectiveness of antibiotic chemotherapy.

Identification of planorbids from Venezuela by polymerase chain reaction amplification and restriction fragment length polymorphism of internal transcriber spacer of the RNA ribosomal gene

Snails of the genus Biomphalaria from Venezuela were subjected to morphological assessment as well as polymerase chain reaction and restriction fragment length polymorphism (PCR-RFLP) analysis. Morphological identification was carried out by comparison of characters of the shell and the male and female reproductive apparatus. The PCR-RFLP involved amplification of the internal spacer region ITS1 and ITS2 of the RNA ribosomal gene and subsequent digestion of this fragment by the restriction enzymes DdeI, MnlI, HaeIII and MspI. The planorbids were compared with snails of the same species and others reported from Venezuela and present in Brazil, Cuba and Mexico. All the enzymes showed a specific profile for each species, that of DdeI being the clearest. The snails were identified as B. glabrata, B. prona and B. kuhniana.

Polymerase chain reaction amplification of genomic fragments of bovine herpesvirus-1

Especial conditions were developed for the amplification of five DNA segments from US region of BHV-1 by polymerase chain reaction. In order to eliminate most nonspecific products it was found that addition of three cosolvents DMSO, glycerol and NP 40 was a simple method for increasing the specificity of amplification.