Efficient rare-event simulation for perpetuities

We consider perpetuities of the form

D=_B1exp(_Y1)+_B2exp(_Y1+_Y2)+?,$D=B_{1}exp\left(Y_1\right)+B_{2}exp(Y_1+Y_2)+?\text{,}$

where the _Yj$Y_j$’s and _Bj$B_j$’s might be i.i.d. or jointly driven by a suitable Markov chain. We assume that the _Yj$Y_j$’s satisfy the so-called Cramér condition with associated root _θ∗∈(0,∞)${\theta }_{\ast }\in (0,\infty )$ and that the tails of the _Bj$B_j$’s are appropriately behaved so that D$D$ is regularly varying with index _θ∗${\theta }_{\ast }$. We illustrate by means of an example that the natural state-independent importance sampling estimator obtained by exponentially tilting the _Yj$Y_j$’s according to _θ∗${\theta }_{\ast }$ fails to provide an efficient estimator (in the sense of appropriately controlling the relative mean squared error as the tail probability of interest gets smaller). Then, we construct estimators based on state-dependent importance sampling that are rigorously shown to be efficient.     

Self-imaging of gratings with two roughness levels

In previous works, the authors have analyzed diffraction gratings with surface roughness on their strips. Appl. Opt. 46 (2007) 3668 determined the near field of a grating whose strips present two kinds of roughness, one of them so rough that the grating acts as an amplitude grating. On the other hand, in J. Opt. Soc. Am. A 25 (2008) 2390, a grating with roughness only in one of the grating levels is studied. In the present work, we extend our analysis to the general case where the strips of the grating present two finite roughness levels. As a consequence, the periodic modulation is only generated by random micro-topography of the strips. A statistical analysis is developed to obtain equations that predict the average intensity distribution after the grating. This general case presents differences with the previous works. For example, the maximum contrast of the self-images is given at a certain distance from the grating, that is, the contrast of the self images firstly increases with the distance of the observation plane and after, it decreases. Numerical simulations, based on Rayleigh–Sommerfeld approach, are performed which confirm the theoretical predictions.     

Silicene: compelling experimental evidence for graphenelike two-dimensional silicon

Because of its unique physical properties, graphene, a 2D honeycomb arrangement of carbon atoms, has attracted tremendous attention. Silicene, the graphene equivalent for silicon, could follow this trend, opening new perspectives for applications, especially due to its compatibility with Si-based electronics. Silicene has been theoretically predicted as a buckled honeycomb arrangement of Si atoms and having an electronic dispersion resembling that of relativistic Dirac fermions. Here we provide compelling evidence, from both structural and electronic properties, for the synthesis of epitaxial silicene sheets on a silver (111) substrate, through the combination of scanning tunneling microscopy and angular-resolved photoemission spectroscopy in conjunction with calculations based on density functional theory.     

Low-temperature synthesis of Zn2SiO4:Mn green photoluminescence phosphor

Zn₂SiO₄:Mn green phosphor having comparable photoluminescence (PL) efficiency with commercial phosphor has been synthesized at 1000 °C using solid state reactions involving ZnO, silicic acid and manganese acetate. The water of crystallization attached to SiO₂ in silicic acid whose dissociation at 1000 °C seem to promote the sintering efficiency of Zn₂SiO₄:Mn. Incremental ZnO addition and re-firing at 1000 °C promote the diffusion rate of ZnO and SiO₂. The formation of a single crystalline phase of willemite structure in the samples was confirmed by powder XRD measurements. The phosphor exhibit an intense excitation band centered around 275 nm and a relatively weak excitation centered around 380 nm while the broad band green emission peaks at 524 nm. Other parameters studied include PL spectra, grain morphology, ZnO/SiO₂ molar ratio, Mn concentration, co-dopant/flux and the effect of chemical forms of Mn dopant as well as silica on the PL efficiency.     

Early contrast enhancement of the liver: exact description of subphases using MRI

Purpose

The purpose of this study was to describe the subphases of early post-contrast enhancement of the liver, using vessel enhancement patterns, and correlate these findings with enhancement patterns of abdominal organs.

Materials and Methods

A total of 114 patients who underwent gadolinium-enhanced abdominal magnetic resonance imaging examinations constituted the final study group, of which 56 were women (age range, 3–94 years; mean, 50 years) and 58 were men (age range, 6–85 years; mean, 54 years). Early post-contrast sequences in all patients were evaluated retrospectively by two reviewers for the determination of the presence of contrast enhancement in predetermined major vessels of the abdomen and qualitative and quantitative extent of enhancement of the renal cortex, spleen, pancreas and liver. Based on the overall findings, subphases of early contrast enhancement of the liver were described and quantitative extent of enhancement of organs was correlated with subphases of early contrast enhancement of the liver. Mann–Whitney U test and one-way unbalanced analysis of variance tests were used for the comparisons.

Results

Early hepatic arterial phase was observed in 14/114 patients, mid-hepatic arterial phase in 23/114 patients, late hepatic arterial phase in 33/114 patients, splenic vein only hepatic arterial dominant phase in 20/114 patients and hepatic arterial dominant phase in 24/114 patients. There was an overall association between the subphases of enhancement and the quantitative extent of enhancement for all studied organs (P<.0001).

Conclusion

The evaluation of vessel and organ enhancement patterns has allowed the characterization of five different subphases in early post-contrast enhancement of the liver. The quantitative extent of enhancement of abdominal organs also demonstrated significant correlation with these five subphases.     

Diethyl 1‐(4‐fluoro­phenyl)‐3‐(2‐furyl)‐5‐oxopyrrolidine‐2,2‐di­carboxyl­ate and diethyl 1‐(3,4‐di­chloro­phenyl)‐3‐(2‐furyl)‐5‐oxopyrrolidine‐2,2‐di­carboxyl­ate

The title compounds, C₂₀H₂₀FNO₆ and C₂₀H₁₉Cl₂NO₆, respectively, may exhibit bioactivity. In these compounds, the pyrrolidine ring adopts a conformation intermediate between envelope and half‐chair. Only one of the two ethoxy­carbonyl side chains is nearly planar. Centrosymmetric pairs are formed, and the crystal structure is stabilized by weak C—H⋯O hydrogen bonds and van der Waals interactions.     

Natural Compounds Isolated from Stachybotrys chartarum Are Potent Inhibitors of Human Protein Kinase CK2

A large number of secondary metabolites have been isolated from the filamentous fungus Stachybotrys chartarum and have been described before. Fourteen of these natural compounds were evaluated in vitro in the present study for their inhibitory activity towards the cancer target CK2. Among these compounds, stachybotrychromene C, stachybotrydial acetate and acetoxystachybotrydial acetate turned out to be potent inhibitors with IC₅₀ values of 0.32 µM, 0.69 µM and 1.86 µM, respectively. The effects of these three compounds on cell proliferation, growth and viability of MCF7 cells, representing human breast adenocarcinoma as well as A427 (human lung carcinoma) and A431 (human epidermoid carcinoma) cells, were tested using EdU assay, IncuCyte^® live-cell imaging and MTT assay. The most active compound in inhibiting MCF7 cell proliferation was acetoxystachybotrydial acetate with an EC₅₀ value of 0.39 µM. In addition, acetoxystachybotrydial acetate turned out to inhibit the growth of all three cell lines completely at a concentration of 1 µM. In contrast, cell viability was impaired only moderately, to 37%, 14% and 23% in MCF7, A427 and A431 cells, respectively.     

Synthesis of BINOL derived phosphorodithioic acids as new chiral Brønsted acids and an improved synthesis of 3,3′-disubstituted H8-BINOL derivatives

Original phosphorodithioic acid diesters were prepared according to an improved synthesis of 3,3′-disubstituted H₈-BINOL derivatives. In preliminary experiments, these new Brønsted acids were tested as organocatalysts in three reactions. They promoted the Nazarov cyclisation with mixed selectivities, the Mannich reaction with good enantioselectivity and they catalyzed efficiently the alkylation of N-acyliminium with enol silyl ether.     

1/fα fractal noise generation from Grünwald–Letnikov formula

This communication presents a recursive algorithm for generating streams of 1/f^α fractal noise, by means of fractional integration/differentiation of a white noise signal. The quality of correlated and anticorrelated noise obtained by this approach is evaluated by applying detrended fluctuation analysis.