Test for low-dimensional determinism in electroencephalograms

We tested low-dimensional determinism in an electroencephalogram (EEG), based on the fact that smoothness (continuity) on an embedded phase space is enough to imply determinism within time series. A modified version of the method developed by Salvino and Cawley [Phys. Rev. Lett. 73, 1091 (1994)] was used. In our method, we chose a box randomly and then estimated the mean directional element in the box containing the d+1 data points, where d is the embedding dimension. The global average for the mean local directional elements over the boxes, W, is a measure for smoothness. The nonlinear noise reduction method developed by Sauer [Physica D 58, 193 (1992)] is then applied to the EEG. We also compared the results for the EEG with those for its surrogate data. We found that the W values for the noise-reduced EEG had stable values around 0.35, which means that the EEG is not a low-dimensional deterministic signal. However, this method may not be applicable to the time series generated from high-dimensional deterministic systems. We cannot exclude the possibility that the determinism in the EEG may be too high-dimensional to be detected with current methods.     

Economical Covers with Geometric Applications

A cover of a hypergraph is a collection of edges whose unioncontains all vertices. Let H = (V, E) be a k-uniform, D-regularhypergraph on n vertices, in which no two vertices are containedin more than o(D/e^2k log D) edges as D tends to infinity. Ourresults include the fact that if k = o(log D), then there isa cover of (1 + o(1))n/k edges, extending the known result thatthis holds for fixed k. On the other hand, if k 4 log D thenthere are k-uniform, D-regular hypergraphs on n vertices inwhich no two vertices are contained in more than one edge, andyet the smallest cover has at least (nk) log (k log D)) edges.Several extensions and variants are also obtained, as well asthe following geometric application. The minimum number of linesrequired to separate n random points in the unit square is,almost surely, (n^2/3 / (log n)^1/3). 2000 Mathematical SubjectClassification: 05C65, 05D15, 60D05.     

Highly efficient ortho-fluoro-dimeric cinchona-derived phase-transfer catalysts

A series of cinchona alkaloid-derived dimeric quaternary ammonium salts were prepared as chiral phase-transfer catalysts by the introduction of various functional groups on the phenyl ligand. Among them, the 2-F-substituted derivative 21 showed the highest enantioselectivity in the alkylation of the glycine anion equivalent 1 (97 to >99% ee).     

A pseudorotaxane-based molecular machine controlled by light and thermal stimuli

A new pseudorotaxane-based molecular machine exhibits extremely efficient switching between assembly and disassembly mode, controlled by the combination of light and thermal stimuli.     

Broad-spectrum radical cyclizations boosted by polarity matching. Carbonylative access to alpha-stannylmethylene lactams from azaenynes and CO

Free-radical mediated stannylcarbonylation of azaenynes provides a general [n + 1]-type annulation approach leading to alpha-stannylmethylene lactams. The cyclization is unusual in its breadth, covering 4-exo, 5-exo, 6-exo, 7-exo, and 8-exo modes.     

Simple and Sensitive Assay of Torasemide in Human Plasma by High-Performance Liquid Chromatography Using a Monolithic Silica Column

A rapid and sensitive method to assay torasemide in plasma was developed using a simple liquid-liquid extraction technique followed by high-performance liquid chromatography. Torasemide and the internal standard furosemide were extracted from 0.5 mL of plasma using ethyl acetate in the presence of 0.1M HCl. The analysis of the extracts was performed on a monolithic silica column with ultraviolet spectrophotometric detection. The calibration curve was linear over the concentration range of 0.05-5 μg mL^?1 in plasma. Recoveries were reasonable for routine analyses (>80%); the limit of quantification was 0.05 μg mL^?1 with a signal-to-noise ratio of 5. The coefficient of variation of the assay precision was less than 6.1%, and the accuracy exceeded 98%. This method was used to measure the torasemide concentration in plasma from healthy subjects after a single 20-mg oral dose of torasemide. This method provides a very simple, sensitive, and accurate way to determine torasemide concentrations in plasma.     

General and systematic synthetic entry to carotenoid natural products

A general synthetic method of carotenoid natural products has been developed, in which the systematic chain extension and termination processes were applied. The syntheses of the chain extension and termination units were greatly improved by the use of the common intermediate, 1-bromo-4-chloro-3-methyl-2-butene (8), in a short and highly efficient way. The C₁₀ chain initiation β-cyclogeranyl sulfone (3) was coupled with the C₅ chain extension unit to give the C₁₅ chain-extended allylic sulfone after chemoselective sulfide oxidation. This chain-extended C₁₅ allylic sulfone underwent the Julia olefination reaction with the C₅ and the C₁₀ chain termination units to give retinol (1) and β-carotene (2), respectively.