Convergence rates for rank-based models with applications to portfolio theory

We determine rates of convergence of rank-based interacting diffusions and semimartingale reflecting Brownian motions to equilibrium. Bounds on fluctuations of additive functionals are obtained using Transportation Cost-Information inequalities for Markov processes. We work out various applications to the rank-based abstract equity markets used in Stochastic Portfolio Theory. For example, we produce quantitative bounds, including constants, for fluctuations of market weights and occupation times of various ranks for individual coordinates. Another important application is the comparison of performance between symmetric functionally generated portfolios and the market portfolio. This produces estimates of probabilities of “beating the market”.     

Novel sucrose-based macrocyclic receptors for enantioselective recognition of chiral ammonium cations

A new synthetic route to macrocyclic sucrose-based receptors with different substituents at the ring nitrogen atom is described. Very good enantioselectivity toward phenylethylammonium chloride was observed [a much stronger complex with the cation of the (S)-amine was formed] although the K_a values were low. Much higher K_a (1.4 × 10⁴ M^?1 in CDCl₃/CD₃OD) values of the complexes with aminoacid derivatives (especially valine) were found although this time the enantioselectivities were moderate.     

Inhomogeneity of electron injection rates in dye-sensitized TiO2: comparison of the mesoporous film and single nanoparticle behavior

As it has been shown by pump-probe experiments electron injection at the interface between a dye molecule and mesoporous TiO2 proceeds with rates exceeding 1 x 10(13) s(-1). However, similar dye-TiO2 systems exhibit residual dye emission with lifetimes extending into the long nanosecond range. To address this inhomogeneity of injection rates time-correlated single photon counting microscopy was used to compare the emission behavior of dye-sensitized mesoporous films of TiO2 with that of individual anatase nanoparticles that had undergone extensive dialysis. The sensitized films produce intense residual emission with multiexponential decay components as long as 220 ns. The channels of mesoporous films contain physisorbed and trapped dye, which is the dominant source of the emission. It is likely that the wide range of lifetimes reflects the distribution of mean free paths experienced by the loose dye molecules diffusing within the film prior to undergoing oxidative quenching. In contrast, the intensity of emission from individual nanoparticles from which the loose dye was removed by dialysis is orders of magnitude lower. The lifetimes obtained from such particles are much shorter, with the primary component on a sub-nanosecond time scale. The presence of residual emission with a 230 ps lifetime shows that even on the surfaces of dialyzed nanoparticles there is a fraction of sensitizer molecules that do not inject electrons with the same high rate as is observed in ultrafast pump-probe experiments on films. Since the physisorbed dye was removed from these samples by dialysis, the residual emission is likely to originate from dye molecules bound to surface defects. Unusual collective emission bursts were observed in some of the measurements on sensitized nanoparticles. We attribute this behavior to stimulated emission from individual nanocrystallites.     

Studies of Interaction Between Cyanine Dye T-284 and Fibrillar Alpha-Synuclein

A key feature of Parkinson’s disease is the formation and accumulation of amyloid fibrils of the natively unfolded protein α-synuclein (ASN) inside neurons. Recently we have proposed novel sensitive monomethinecyanine dye T-284 as fluorescent probe for quantitative detection of ASN amyloid fibrils. In this study the T-284 dye complex with ASN fibril was characterized by means of fluorescence anisotropy, atomic force microscopy and time-resolved fluorescence techniques to give further insights into the mode of dye interaction with amyloid fibrils. The fluorescence anisotropy of T-284 was shown to noticeably increase upon addition of aggregated proteins indicating on stable dye/amyloid fibril complex formation. AFM imaging of fibrillar wild-type ASN revealed differences in heights between ASN fibrils alone and in presence of the T-284 dye (6.37 ± 1.0 nm and 8.0 ± 1.1 nm respectively), that is believed to be caused by embedding of T-284 dye molecules in the “binding channel” running along the fibril. Fluorescence decay analysis of the T-284 in complexes with fibrillar ASN variants revealed the fluorescence lifetime values for T-284/fibril complexes to be an order of magnitude higher as compared to the free dye. Also, the fluorescence decay of free T-284 was bi-exponential, while dye bound to protein yields tri-exponential decay. We suppose that in complexes with fibrillar ASN variants T-284 dye might exist in different “populations” due to interaction with fibrils in different conformers and ways. The exact binding mode of T-284 with ASN fibrils needs further studies. Studied parameters of dye/amyloid fibril complexes are important for the characterization and screening of newly-developed amyloid-sensitive dyes.     

Cyclic Carboxylic Anhydrides as New Reagents for Formation of Chromone Ring

The propensity of cyclic carboxylic anhydrides to undergo ring‐opening was exploited in a reaction with 2'‐hydroxy‐α‐heteroarylacetophenones leading to the formation of chromones. New simple method was developed for the synthesis of 2‐(ω‐carboxyalkyl)‐3‐heteroarylchromones without protecting either the phenolic or the carboxylic groups. Treatment with hydrazine led to the formation of 3(5)‐(ω‐carboxyalkyl)‐5(3)‐(2,4‐dihydroxyphenyl)‐4‐heteroarylpyrazoles.     

A Facile Synthesis of Functionalized 1,2,6,7-Tetrahydroimidazo[1,5-c]pyrimidine-3,5-diones

A Pd-mediated hydrogenation of ethyl 6-azidomethyl-1,2,3,4-tetrahydro-4-R-2-oxo-5-pyrimidinecarboxylates leads to the corresponding ethyl 6-aminomethyl1,2,3,4-tetrahydro-4-R-2-oxo-5-pyrimidinecarboxylates. The latter react with bis(trichloromethyl)carbonate, yielding the title ethyl 1,2,3,5,6,7-hexahydro-7-R-3,5-dioxoimidazo[1,5-c]pyrimidine-8-carboxylates.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

β-Chlorocinnamonitriles in a New Synthesis of 3-Functionally Substituted 6-amino-1,2-Dihydropyridin-2-ones

β-Chlorocinnamonitriles react with methylene-active compounds containing N-substituted carboxamide group in DMSO solution in the presence of potassium hydroxide, forming 3-functionally substituted 1,2-dihydropyridin-2-ones.     

Influence of anchoring at a nematic cell surface on threshold spatially periodic reorientation of a director

We have analysed the influence of surface director anchoring in a planar flexoelectric nematic cell on the threshold spatially periodic reorientation of the director in an external dc electric field. By minimizing the free energy of the nematic cell we obtained the equations for a director and numerically solved them in the one elastic constant approximation. The dependences of the threshold electric field and the spatial period of director structure on the azimuthal and polar anchoring energy, as well as the flexoelectric parameters, are determined. It is shown that the domain of the flexoelectric parameter values, at which the spatially periodic reorientation of a director takes place, increases with decreasing azimuthal anchoring energy and increasing polar anchoring energy.     

3D reconstruction of the complex dielectric function of glass during femtosecond laser micro-fabrication

We report on a new technique to reconstruct the 3D dielectric function change in transparent dielectric materials and the application of the technique for on-line monitoring of refractive index modification in BK7 glass during direct femtosecond laser microfabrication. The complex optical field scattered from the modified region is measured using two-beam, single-shot interferogram and the distribution of the modified refractive index is reconstructed by numerically solving the inverse scattering problem in Born approximation. The optical configuration suggested is further development of digital holographic microscopy. It takes advantage of high spatial resolution and almost the same optical paths for both interfering beams, and allows ultrafast time resolution.