Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations

We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these objects. As consequence, we give some applications to holomorphic foliations tangent to real-analytic Levi-flat hypersurfaces with singularities in \(\mathbb {P}^2\).     

Mechanistic insights into dopaminergic and serotonergic neurotransmission – concerted interactions with helices 5 and 6 drive the functional outcome

Brain functions rely on neurotransmitters that mediate communication between billions of neurons. Disruption of this communication can result in a plethora of psychiatric and neurological disorders. In this work, we combine molecular dynamics simulations, live-cell biosensor and electrophysiological assays to investigate the action of the neurotransmitter dopamine at the dopaminergic D₂ receptor (D₂R). The study of dopamine and closely related chemical probes reveals how neurotransmitter binding translates into the activation of distinct subsets of D₂R effectors (i.e.: G_i2, G_oB, G_z and β-arrestin 2). Ligand interactions with key residues in TM5 (S5.42) and TM6 (H6.55) in the D₂R binding pocket yield a dopamine-like coupling signature, whereas exclusive TM5 interaction is typically linked to preferential G protein coupling (in particular G_oB) over β-arrestin. Further experiments for serotonin receptors indicate that the reported molecular mechanism is shared by other monoaminergic neurotransmitter receptors. Ultimately, our study highlights how sequence variation in position 6.55 is used by nature to fine-tune β-arrestin recruitment and in turn receptor signaling and internalization of neurotransmitter receptors.

Neurotransmitter contacts within the receptor binding site differentially contribute to the overall functional response: transmembrane helix (TM) 5 contacts promote G protein coupling whereas concerted TM5–TM6 contacts enhance β-arrestin recruitment.     

In situ studies of the active sites for the water gas shift reaction over Cu-CeO2 catalysts: complex interaction between metallic copper and oxygen vacancies of ceria

New information about the active sites for the water gas shift (WGS) reaction over Cu-CeO2 systems was obtained using in-situ, time-resolved X-ray diffraction (TR-XRD), X-ray absorption spectroscopy (TR-XAS, Cu K and Ce L3 edges), and infrared spectroscopy (DRIFTS). Cu-CeO2 nanoparticles prepared by a novel reversed microemulsion method (doped Ce1-xCuxO2 sample) and an impregnation method (impregnated CuOx/CeO2 sample) were studied. The results from all of the samples indicate that both metallic copper and oxygen vacancies in ceria were involved in the generation of active sites for the WGS reaction. Evidence was found for a synergistic Cu-Ovacancy interaction. This interaction enhances the chemical activity of Cu, and the presence of Cu facilitates the formation of O vacancies in ceria under reaction conditions. Water dissociation occurred on the Ovacancy sites or the Cu-Ovacancy interface. No significant amounts of formate were formed on the catalysts during the WGS reaction. The presence of strongly bound carbonates is an important factor for the deactivation of the catalysts at high temperatures. This work identifies for the first time the active sites for the WGS reaction on Cu-CeO2 catalysts and illustrates the importance of in situ structural studies for heterogeneous catalytic reactions.     

Microscopic and Spectroscopic Methods Applied to the Measurements of Nanoparticles in the Environment

Abstract: Currently, thousands of commercially available products contain engineered nanoparticles (ENPs). Because numerous nanoparticles (NPs) are being used in products that will be in contact with water or directly used in water treatment processes, these materials will undoubtedly reside, at least temporarily, in bodies of water. Given the widespread use of NPs and ENPs in consumer goods, a large portion of these materials will soon go into the waste stream, potentially to soil and sediments or added directly to agricultural lands via biosolids. Possible impacts of ENPs on aquatic and terrestrial ecosystems are of great concern. Preliminary data from several research groups have shown that ENPs may have a direct impact on food safety and the food chain. However, our knowledge about detection and characterization of NPs in the environment, especially aquatic environments, is still in its infancy. This review includes the most recent literature about the methods applied to the measurement of NPs and ENPs in the environment. The review covers methods to determine size distribution, shape, structure, surface charge, chemical composition, surface area, agglomeration, surface chemistry, porosity, and solubility.     

Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population

We analytically derived and confirmed by empirical data the following three relations from the quasi-time-reversal symmetry, Gibrat’s law, and the non-Gibrat’s property observed in the urban population data of France. The first is the relation between the time variation of the power law and the quasi-time-reversal symmetry in the large-scale range of a system that changes quasi-statically. The second is the relation between the time variation of the log-normal distribution and the quasi-time-reversal symmetry in the mid-scale range. The third is the relation among the parameters of log-normal distribution, non-Gibrat’s property, and quasi-time-reversal symmetry.     

Classical versus Bayesian risks in acceptance sampling: a sensitivity analysis

Assuming a beta prior distribution on the fraction defective, $p$ , failure-censored sampling plans for Weibull lifetime models using classical (or average) and Bayesian (or posterior) producer’s and consumer’s risks are designed to determine the acceptability of lots of a given product. The average risk criterion provides a certain assurance that good (bad) lots will be accepted (rejected), whereas the posterior risk criterion provides a determined confidence that an accepted (rejected) lot is indeed good (bad). The performance of classical and Bayesian risks are analyzed in developing sampling plans when the lifetime variable follows the Weibull distribution. Several figures and tables illustrate the sensitivity of the risks and optimal sample sizes for selected censoring levels and specifications according to the available prior information on $p$ . The analysis clarifies the distinction among the different risks for a given sampling plan, and the effect of the prior knowledge on the required sample size. The study shows that, under uncertainty in the prior variance of $p$ , the designs using Bayesian risks are more appropriate.     

Smoothness of the Distribution of the Supremum of a Multi-dimensional Diffusion Process

In this article we deal with a multi-dimensional diffusion whose corresponding diffusion vector fields are commutative, and study its joint distribution at the time when a component attains its maximum on finite time interval. Under regularity and ellipticity conditions we shall show the smoothness of this joint distribution.     

Estimates for the density of functionals of SDEs with irregular drift

We obtain upper and lower bounds for the density of a functional of a diffusion whose drift is bounded and measurable. The argument consists of using Girsanov’s theorem together with an Itô–Taylor expansion of the change of measure. One then applies Malliavin calculus techniques in a non-trivial manner so as to avoid the irregularity of the drift. An integration by parts formula for this set-up is obtained.