On spacelike hypersurfaces with constant scalar curvature in the de Sitter space

We classify spacelike hypersurfaces of the de Sitter space with constant scalar curvature and with two principal curvatures. Moreover, we prove that if Mn is a complete spacelike hypersurface with constant scalar curvature n(n−1)R and with two distinct principal curvatures such that the multiplicity of one of the principal curvatures is n−1, then R<(n−2)c/n. Additionally, we prove several rigidity theorems for such hypersurfaces.     

Multivariate dynamic modeling for Bayesian forecasting of business revenue

Forecasting enterprise-wide revenue is critical to many companies and presents several challenges and opportunities for significant business impact. This case study is based on model developments to address these challenges for forecasting in a large-scale retail company. Focused on multivariate revenue forecasting across collections of supermarkets and product categories, hierarchical dynamic models are natural: these are able to couple revenue streams in an integrated forecasting model, while allowing conditional decoupling to enable relevant and sensitive analysis together with scalable computation. Structured models exploit multi-scale modeling to cascade information on price and promotion activities as predictors relevant across categories and groups of stores. With a context-relevant focus on forecasting revenue 12 weeks ahead, the study highlights product categories that benefit from multi-scale information, defines insights into when, how, and why multivariate models improve forecast accuracy, and shows how cross-category dependencies can relate to promotion decisions in one category impacting others. Bayesian modeling developments underlying the case study are accessible in custom code for interested readers.     

Single‐Molecule Methods to Study Membrane Receptor Oligomerization

Membrane receptors control fundamental cellular processes. Binding of a specific ligand to a receptor initiates communication through the membrane and activation of signaling cascades. This activation process often leads to a spatial rearrangement of receptors in the membrane at the molecular level. Single‐molecule techniques contributed significantly to the understanding of receptor organization and rearrangement in membranes. Here, we review four prominent single‐molecule techniques that have been applied to membrane receptors, namely, stepwise photobleaching, Förster resonance energy transfer, sub‐diffraction localization microscopy and co‐tracking. We discuss the requirements, benefits and limitations of each technique, discuss target labeling, present a selection of applications and results and compare the different methodologies.     

Degradation kinetics of poly(lactic-co-glycolic) acid block copolymer cast films in phosphate buffer solution as revealed by infrared and Raman spectroscopies

Poly(lactic-co-glycolic) acid (PLGA) is an important copolymer used in drug delivery platforms where controlled release is required. In this work we investigated the in vitro degradation of four PLGA copolymers with L/G molar compositions of 50/50, 65/35, 75/25 and 95/5. ATR-IR and Raman spectroscopies were used to differentiate and quantify the degradation rates of glycolic and lactic units. Both techniques were used to determine the polymer composition as a function of degradation time and the degradation rate constants for the hydrolysis of glycolic and lactic units were calculated using a 1st order kinetics approach. Our results revealed a two stage process for the degradation of PLGA cast films in PBS in agreement with our previous work. The degradation rate constant for glycolic unit was found to be 1.3 times higher than for lactic units. In addition the degradation rate constants for L and G units were shown to decrease proportionally with increasing initial lactic content of the copolymer used to prepare the films.     

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Ab initio quantum Monte Carlo study of the binding of a positron to alkali-metal hydrides

Quantum Monte Carlo methods are used to investigate the binding of a positron to the alkali-metal hydrides, XH (X = Na and K). We obtain positron affinities for the NaH and KH molecules of 1.422(10) eV and 2.051(39) eV, respectively. These are considerably larger than the previous results of 1.035 eV and 1.273 eV obtained from multireference single- and double-excitation configuration interaction calculations. Together with our previous results for [LiH;e(+)] [Y. Kita et al., J. Chem. Phys. 131, 134310 (2009)], our study confirms the strong correlation between the positron affinity and dipole moment of alkali-metal hydrides.