Almost periodic sets and subactions in topological dynamics

Let be a group with subgroup . We show, under certain conditions, that an almost periodic point for the action of is also almost periodic for . This is applied to obtain a theorem of Glasner.

     

Deconvolution with simple extrapolation for improved cerebral blood flow measurement in dynamic susceptibility contrast magnetic resonance imaging during acute ischemic stroke

Magnetic resonance (MR) perfusion imaging is a clinical technique for measuring brain blood flow parameters during stroke and other ischemic events. Ischemia in brain tissue can be difficult to accurately measure or visualize when using MR-derived cerebral blood flow (CBF) maps. The deconvolution techniques used to estimate flow can introduce a mean transit time-dependent bias following application of noise stabilization techniques. The underestimation of the CBF values, greatest in normal tissues, causes a decrease in the image contrast observed in CBF maps between normally perfused and ischemic tissues; resulting in ischemic areas becoming less conspicuous. Through application of the proposed simple extrapolation technique, CBF biases are reduced when missing high-frequency signal components in the MR data removed during deconvolution noise stabilization are restored. The extrapolation approach was compared with other methods and showed a statistically significant increase in image contrast in CBF maps between normal and ischemic tissues for white matter (P<.05) and performed better than most other methods for gray matter. Receiver operator characteristic curve analysis demonstrated that extrapolated CBF maps better-detected penumbral regions. Extrapolated CBF maps provided more accurate CBF estimates in simulations, suggesting that the approach may provide a better prediction of outcome in the absence of treatment.     

Total synthesis and biochemical characterization of mirror image barnase

In this study we synthesized and characterized mirror image barnase (B. amyloliquefaciens ribonuclease). d-Barnase was identical to l-barnase, when analyzed by liquid chromatography and mass-spectrometry. Proteolysis of the mirror image enzyme revealed that in contrast to its native counterpart, d-barnase was completely stable to digestive proteases. In enzymatic assays, d-barnase had the reciprocal chiral specificity and was fully active towards mirror image substrates. Interestingly, d-barnase also hydrolyzed the substrate of the native chirality, albeit 4000 times less efficiently. This effect was further confirmed by digesting a native 112-mer RNA with the enzyme. Additional studies revealed that barnase accommodates a range of substrates with various chiralities, but the prime requirement for guanosine remains. These studies point toward using mirror image enzymes as modern agents in biotechnology.     

Dimension Reduction for the Landau-de Gennes Model on Curved Nematic Thin Films

We use the method of \(\Gamma \)-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness. This paper generalizes the approach in Golovaty et al. (J Nonlinear Sci 25(6):1431–1451, 2015) where we considered a similar problem for a planar surface. Since the anchoring energy dominates when the thickness of the film is small, it is essential to understand its influence on the structure of the minimizers of the limiting energy. In particular, the anchoring energy dictates the class of admissible competitors and the structure of the limiting problem. We assume general weak anchoring conditions on the top and the bottom surfaces of the film and strong Dirichlet boundary conditions on the lateral boundary of the film when the surface is not closed. We establish a general convergence result to an energy defined on the surface that involves a somewhat surprising remnant of the normal component of the tensor gradient. Then we exhibit one effect of curvature through an analysis of the behavior of minimizers to the limiting problem when the substrate is a frustum.     

Assessment of intracellular methotrexate and methotrexate-polyglutamate metabolite concentrations in erythrocytes by ultrafast matrix-assisted laser desorption/ionization triple quadrupole tandem mass spectrometry

A new ultrafast quantitative and high‐throughput mass spectrometric method using matrix‐assisted laser desorption/ionization triple quadrupole tandem mass spectrometry has been developed and validated for determination of intracellular erythrocyte concentrations of the antifolate drug methotrexate (MTX) and its polyglutamate metabolites. The method consists of a solid‐phase extraction of MTX and MTX‐polyglutamate metabolites from deproteinized erythrocyte lysates spiked with aminopterin as internal standard. The newly developed method was validated according to the most recent FDA guidelines on linearity, recovery, within‐run and between‐run accuracy and precision and stability of the analytes. The low limit of quantification (LLOQ) was 10 nmol/L for all analytes while the limit of detection (LOD) determined at a signal‐to‐noise (S/N) ratio = 3:1 in drug‐ free erythrocyte lysate was on average 0.3 nmol/L. After validation, the new method was used in the measurement of intracellular erythrocyte concentrations of MTX and MTX‐polyglutamate metabolites (MTXPG2 to MTXPG7) in packed human erythrocyte samples collected from patients with rheumatoid arthritis receiving low‐dose oral methotrexate therapy. Mean (SD) intracellular erythrocyte concentrations observed in patient samples were 12.8 (12.6), 12.4 (9.4), 44.4 (30.0), 33.6 (35.9) and 9.4 (8.2) nmol/L for MTX to MTXPG5, respectively, in 10⁶ erythrocytes. The highest observed glutamylation degree of MTX was MTXPG5, the very long chain MTX‐polyglutamate metabolites MTXPG6 and MTXPG7 were not detected in the packed erythrocyte pellets collected from rheumatoid arthritis patients. Copyright © 2011 John Wiley & Sons, Ltd.     

Local likelihood estimation for nonstationary random fields

We develop a weighted local likelihood estimate for the parameters that govern the local spatial dependency of a locally stationary random field. The advantage of this local likelihood estimate is that it smoothly downweights the influence of faraway observations, works for irregular sampling locations, and when designed appropriately, can trade bias and variance for reducing estimation error. This paper starts with an exposition of our technique on the problem of estimating an unknown positive function when multiplied by a stationary random field. This example gives concrete evidence of the benefits of our local likelihood as compared to unweighted local likelihoods. We then discuss the difficult problem of estimating a bandwidth parameter that controls the amount of influence from distant observations. Finally we present a simulation experiment for estimating the local smoothness of a local Matérn random field when observing the field at random sampling locations in [0,1]². The local Matérn is a fully nonstationary random field, has a closed form covariance, can attain any degree of differentiability or Hölder smoothness and behaves locally like a stationary Matérn. We include an appendix that proves the positive definiteness of this covariance function.