Positive recurrence of reflecting Brownian motion in three dimensions

Consider a semimartingale reflecting Brownian motion (SRBM) $Z$ whose state space is the $d$-dimensional nonnegative orthant. The data for such a process are a drift vector $\theta$, a nonsingular $d\times d$ covariance matrix $\Sigma$, and a $d\times d$ reflection matrix $R$ that specifies the boundary behavior of $Z$. We say that $Z$ is positive recurrent, or stable, if the expected time to hit an arbitrary open neighborhood of the origin is finite for every starting state. In dimension $d=2$, necessary and sufficient conditions for stability are known, but fundamentally new phenomena arise in higher dimensions. Building on prior work by El Kharroubi, Ben Tahar and Yaacoubi [Stochastics Stochastics Rep. 68 (2000) 229--253, Math. Methods Oper. Res. 56 (2002) 243--258], we provide necessary and sufficient conditions for stability of SRBMs in three dimensions; to verify or refute these conditions is a simple computational task. As a byproduct, we find that the fluid-based criterion of Dupuis and Williams [Ann. Probab. 22 (1994) 680--702] is not only sufficient but also necessary for stability of SRBMs in three dimensions. That is, an SRBM in three dimensions is positive recurrent if and only if every path of the associated fluid model is attracted to the origin. The problem of recurrence classification for SRBMs in four and higher dimensions remains open.Comment: Published in at http://dx.doi.org/10.1214/09-AAP631 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Microstructures and mechanical properties of pure tantalum processed by high-pressure torsion

A body-centred cubic (BCC) structure metal, tantalum, was processed by high- pressure torsion (HPT) at room temperature with different numbers of rotations. The microstructural evolution was studied by electron backscatter diffraction (EBSD). The grain sizes were significantly refined at the disk edge area in the early stages of deformation (N = 0.5) but tended to attain saturation after the numbers of rotations was increased to N = 5. As the deformation continued, some coarse grains appeared in the disk edge areas and it appeared that there was structural recovery at the expense of grain boundary migration in the tantalum during HPT processing. Microhardness measurements showed the hardness gradually evolved towards a more homogenized level across the disk surfaces as the numbers of rotations increased. The hardness level after N = 10 turns was slightly lower than after N = 5 turns, thereby indicating the occurrence of a recovery process after 5 turn

Characterization of TrxC, an Atypical Thioredoxin Exclusively Present in Cyanobacteria

Cyanobacteria form a diverse group of oxygenic photosynthetic prokaryotes considered to be the antecessor of plant chloroplast. They contain four different thioredoxins isoforms, three of them corresponding to m, x and y type present in plant chloroplast, while the fourth one (named TrxC) is exclusively found in cyanobacteria. TrxC has a modified active site (WCGLC) instead of the canonical (WCGPC) present in most thioredoxins. We have purified it and assayed its activity but surprisingly TrxC lacked all the classical activities, such as insulin precipitation or activation of the fructose-1,6-bisphosphatase. Mutants lacking trxC or over-expressing it were generated in the model cyanobacterium Synechocystis sp. PCC 6803 and their phenotypes have been analyzed. The ΔtrxC mutant grew at similar rates to WT in all conditions tested although it showed an increased carotenoid content especially under low carbon conditions. Overexpression strains showed reduced growth under the same conditions and accumulated lower amounts of carotenoids. They also showed lower oxygen evolution rates at high light but higher Fv’/Fm’ and Non-photochemical-quenching (NPQ) in dark adapted cells, suggesting a more oxidized plastoquinone pool. All these data suggest that TrxC might have a role in regulating photosynthetic adaptation to low carbon and/or high light conditions.España, MINECO BIO2016-75634-PJunta de Andalucía P12-BIO-1119 , BIO-28

Grain growth in the envelopes and disks of Class I protostars

We present new 3 mm ATCA data of two Class I Young Stellar Objects in the Ophiucus star forming region: Elias29 and WL12. For our analysis we compare them with archival 1.1 mm SMA data. In the (u,v) plane the two sources present a similar behavior: a nearly constant non-zero emission at long baselines, which suggests the presence of an unresolved component and an increase of the fluxes at short baselines, related to the presence of an extended envelope. Our data analysis leads to unusually low values of the spectral index $\alpha_{\rm 1.1-3mm}$, which may indicate that mm-sized dust grains have already formed both in the envelopes and in the disk-like structures at such early stages. To explore the possible scenarios for the interpretation of the sources we perform a radiative transfer modeling using a Monte Carlo code, in order to take into account possible deviations from the Rayleigh-Jeans and optically thin regimes. Comparison between the model outputs and the observations indicates that dust grains may form aggregates up to millimeter size already in the inner regions of the envelopes of Class I YSOs. Moreover, we conclude that the embedded disk-like structures in our two Class Is are probably very compact, in particular in the case of WL12, with outer radii down to tens of AU.Comment: 12 pages, 8 figures, Accepted for publication in A&

Generalized Wasserstein distance and its application to transport equations with source

In this article, we generalize the Wasserstein distance to measures with different masses. We study the properties of such distance. In particular, we show that it metrizes weak convergence for tight sequences. We use this generalized Wasserstein distance to study a transport equation with source, in which both the vector field and the source depend on the measure itself. We prove existence and uniqueness of the solution to the Cauchy problem when the vector field and the source are Lipschitzian with respect to the generalized Wasserstein distance

Evolution models for mass transportation problems

We present a survey on several mass transportation problems, in which a given mass dynamically moves from an initial configuration to a final one. The approach we consider is the one introduced by Benamou and Brenier in [5], where a suitable cost functional $F(\rho,v)$, depending on the density $\rho$ and on the velocity $v$ (which fulfill the continuity equation), has to be minimized. Acting on the functional $F$ various forms of mass transportation problems can be modeled, as for instance those presenting congestion effects, occurring in traffic simulations and in crowd motions, or concentration effects, which give rise to branched structures.Comment: 16 pages, 14 figures; Milan J. Math., (2012

The production of dense lead-ion beams for the CERN LHC

To reach the design luminosity for lead-ions in the LHC, the present Low Energy Antiproton Ring (LEAR) has to be converted into a Low Energy Ion Ring (LEIR). Since the present ECR lead-ion source does not provide sufficient intensity, the main goal of LEIR is to act as a low-energy (4.2MeV/u) accumulator where the ion beam is stacked and cooled (with the help of an electron-cooler) to reach the required intensity and emittances. An experimental program has been carried out at LEAR in recent years in order to test the cooling and stacking process with the present electron-cooler. A variety of results have been reported at previous conferences. This paper will focus on the electron cooling aspects resulting from the afore mentioned experiments. Taking into account the experienc

Electron cooling of PB54+^{54+} ions in the low energy ion ring (LEIR)

For the preparation of dense bunches of lead ions for the LHC, electron cooling will be essential for accumula tion in a storage ring at 4.2 MeV/u. Tests have been carried out on the LEAR ring (renamed LEIR for Low Energy Ion Ring) in order to determine the optimum parameters for a future state-of-the-art electron cooling device which would be able to cool linac pulses of lead ions in less than 100 ms. The experiments focused on the generation of a stable high intensity electron beam that is needed to free space in both longitudinal and transverse phase space for incoming pulses. Investigations on the ion beam lifetime in the presence of the electron beam and on the dependency of the cooling times on the optical settings of the storage ring will also be discussed. This paper concentrates on the cooling aspects with the multiturn injection, vacuum, and high intensity aspects discussed in a companion paper at this conference

urg1: a uracil-regulatable promoter system for fission yeast with short induction and repression times.

BACKGROUND: The fission yeast Schizosaccharomyces pombe is a popular genetic model organism with powerful experimental tools. The thiamine-regulatable nmt1 promoter and derivatives, which take >15 hours for full induction, are most commonly used for controlled expression of ectopic genes. Given the short cell cycle of fission yeast, however, a promoter system that can be rapidly regulated, similar to the GAL system for budding yeast, would provide a key advantage for many experiments. METHODOLOGY/PRINCIPAL FINDINGS: We used S. pombe microarrays to identify three neighbouring genes (urg1, urg2, and urg3) whose transcript levels rapidly and strongly increased in response to uracil, a condition which otherwise had little effect on global gene expression. We cloned the promoter of urg1 (uracil-regulatable gene) to create several PCR-based gene targeting modules for replacing native promoters with the urg1 promoter (Purg1) in the normal chromosomal locations of genes of interest. The kanMX6 and natMX6 markers allow selection under urg1 induced and repressed conditions, respectively. Some modules also allow N-terminal tagging of gene products placed under urg1 control. Using pom1 as a proof-of-principle, we observed a maximal increase of Purg1-pom1 transcripts after uracil addition within less than 30 minutes, and a similarly rapid decrease after uracil removal. The induced and repressed transcriptional states remained stable over 24-hour periods. RT-PCR comparisons showed that both induced and repressed Purg1-pom1 transcript levels were lower than corresponding P3nmt1-pom1 levels (wild-type nmt1 promoter) but higher than P81nmt1-pom1 levels (weak nmt1 derivative). CONCLUSIONS/SIGNIFICANCE: We exploited the urg1 promoter system to rapidly induce pom1 expression at defined cell-cycle stages, showing that ectopic pom1 expression leads to cell branching in G2-phase but much less so in G1-phase. The high temporal resolution provided by the urg1 promoter should facilitate experimental design and improve the genetic toolbox for the fission yeast community

A critical examination of pure tantalum processed by high-pressure torsion

Tantalum, a common refractory metal with body-centred cubic (BCC) crystalline structure, was processed by high-pressure torsion (HPT) at room temperature through different numbers of rotations. Significant grain refinement and high strength were achieved with a reduction in grain size from ?60 ?m to ?160 nm and an increase in strength from ?200 to >1300 MPa. Hardness measurements revealed a high level of homogeneity after 10 turns of HPT but the hardness after 10 turns was slightly lower than after 5 turns indicating the occurrence of some recovery. Tensile testing at a strain rate of 1.0×10?3 s?1 gave high strengths of ?1200 MPa but little or no ductility after processing through 1, 5 and 10 turns. The introduction of a short-term (15 min) anneal immediately after HPT processing led to significant ductility in all samples and a reasonable level of strength at ?800 MPa