Errata: “Universality in Orthogonal and Symplectic Invariant Matrix Models with Quartic Potential”

The errata concern mainly the last computations for the universality of the local statistics of eigenvalues at the edge of the spectrum in parts (iii) of Theorems 2.3 and 2.4.     

Color Zone Map in Peripheral Vision at Various Illuminance Levels

We measured the entire region of mesopic and photopic vision to determine the color zone covering the visual field with unique red, yellow, green, and blue hue components. Eight kinds of test stimuli in the natural color system (NCS) color notation system were used. These stimuli were presented at horizontal and vertical meridians, and at meridians inclined at 45° angles. The illuminance level was set at six levels: 0.01 lx-1000 lx. The evaluation method measured chromatic, white, and black components as well as the hue component of the stimuli. Results show that the color zone of the retina extended further into the periphery with increasing illuminance; the response of opponent colors y-b was shown to be greater than that of the opponent colors r-g.     

A realistic coronary artery phantom for particle image velocimetry

Myocardial infarction results from the rupture of an atherosclerotic plaque, which occurs in response to both mechanical stress and inflammatory processes. In order experimentally observe flow into atherosclerotic coronary artery morphologies, a novel technique for molding realistic compliant phantom featuring injection-molded inclusions and multiple layers has been developed. This transparent phantom allows for particle image velocimetry (PIV) flow analysis and can supply experimental data to validate computational fluid dynamics algorithms and hypothesis.     

Real-time color holographic interferometry devoted to 2D unsteady wake flows

A new optical technique based on real time holographic interferometry in true colors has been implemented around the transonic wind tunnel of the ONERA-Lille center to analyze 2D unsteady wake flows. Tests realized in color interferometry, real time and double exposure, use simultaneously three wavelengths of a continuous waves laser (argon and krypton mixed) and holograms are recorded on silver-halide single-layer panchromatic Slavich PFG03c plates. The very principle of real-time true color holographic interferometry uses three primary wavelengths (red, green and blue) to record, under no-flow conditions, the interference among the three measurement beams and the three reference beams simultaneously on a single reference hologram. After the holographic plate is developed, it is placed on the test setup again in the position it occupied during exposure and the hologram is illuminated again by the three reference beams and three measurement beams. A flat, uniform color can then be observed behind the hologram. So a horizontal, vertical, or even circular fringe pattern can be formed and the achromatic central fringe can be made out very clearly. The single color is used to determine the path difference zero on the interferograms. The flow studied was the unsteady flow downstream of a cylinder placed crosswise in the test section. A sequence of hundred interferograms was recorded on the flow around the cylinder at Mach 0.37. The vortex formation and dissipation phases can be seen very clearly, along with the fringe beat to either side of the cylinder.     

New functionalized polyesters to achieve controlled architectures

Following our continued interest in the production of bioerodible and biodegradable functional polymers for biomedical applications, we synthesized and characterized new unsaturated polyesters. The presence of functional groups in the polymer backbone provided sites for chemical modification, and through a variation in the structure, the physical properties, such as the hydrophilicity and solubility, could be affected. With 1,1-di-n-butyl-stanna-2,7-dioxacyclo-4-heptene as the initiator in the ring-opening polymerization of polyesters, a new set of functionalized polyesters was created. The polymerization of ϵ-caprolactone resulted in poly(ϵ-caprolactone) with a double bond incorporated into the structure. The polymers were obtained in a controlled manner with low molecular dispersities. The double bond was previously incorporated into L -lactide polymers, and the two reactions were compared in this study. The conversion of ϵ-caprolactone, with a degree of polymerization of 50, was completed within 140 min, whereas for L -lactide, only a 45% conversion took place in the same period of time. The dispersities were somewhat higher with ϵ-caprolactone because of the higher reaction rate and, therefore, lower selectivity. The incorporated CC double bond in the polyesters provided a variety of opportunities for further modifications. In this case, the double bond of the L -lactide macromonomers was oxidized into epoxides. Epoxidation was carried out with m-chloroperoxybenzoic acid as a chemical reagent. The conversion of the double bonds into epoxides was completed, and the obtained yields were good (>95%). As a result of the mild reaction conditions, the epoxidation of the double bond was carried out quantitatively without any side reactions. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 444–452, 2004     

Synthesis of Organic-Inorganic Hybrid Particles by Sol-Gel Chemistry

The synthesis of ORganically MOdified SILica (ORMOSIL) particles has been carried out using both the hydrolytic and non-hydrolytic sol-gel routes. The hybrid (nano)composites are organically modified with an alkyl or aryl group covalently bonded to silicon. Hybrids have been synthesised in an aqueous sol-gel process by a modified Stöber route, producing spherical nanoparticles with diameters in the range 50–300 nm. The size of the particles can be controlled by control of certain reaction parameters. Smaller ormosil nanoparticles can be synthesised by a base-catalysed emulsion polymerisation route, by varying the type and concentration of surfactant and precursor feed rate. In this case, particles in the size range 3.5–10 nm can be obtained. Hybrids have been synthesised from hyperbranched polyesters by encapsulation in a silica matrix using the hydrolytic sol-gel route. Optimisation of the reaction conditions allows the hybrids to be produced as isolated sub-micron spherical particles. Ormosil particles have also been synthesised using the non-hydrolytic sol-gel route, which may lead to products of different morphologies because of the different polarity of the reaction medium. Different reaction conditions were studied in order to optimise the size and shape of the particles, including choice of solvent, use of surfactants and addition of polystyrene. Dimethylsulfoxide acts as a novel oxygen donor for the catalyst-free formation of colourless silsesquioxanes.     

On division rings with algebraic commutators of bounded degree

We shall answer several questions concerning additive or multiplicative commutators in a division ring which are algebraic of bounded degree over its center.     

Seizure warning algorithm based on optimization and nonlinear dynamics

There is growing evidence that temporal lobe seizures are preceded by a preictal transition, characterized by a gradual dynamical change from asymptomatic interictal state to seizure. We herein report the first prospective analysis of the online automated algorithm for detecting the preictal transition in ongoing EEG signals. Such, the algorithm constitutes a seizure warning system. The algorithm estimates STL_max, a measure of the order or disorder of the signal, of EEG signals recorded from individual electrode sites. The optimization techniques were employed to select critical brain electrode sites that exhibit the preictal transition for the warning of epileptic seizures. Specifically, a quadratically constrained quadratic 0-1 programming problem is formulated to identify critical electrode sites. The automated seizure warning algorithm was tested in continuous, long-term EEG recordings obtained from 5 patients with temporal lobe epilepsy. For individual patient, we use the first half of seizures to train the parameter settings, which is evaluated by ROC (Receiver Operating Characteristic) curve analysis. With the best parameter setting, the algorithm applied to all cases predicted an average of 91.7% of seizures with an average false prediction rate of 0.196 per hour. These results indicate that it may be possible to develop automated seizure warning devices for diagnostic and therapeutic purposes.Mathematics Subject Classification (1991):20E28, 20G40, 20C20