A Note on Local Asymptotics of Solutions to Singular Elliptic Equations via Monotonicity Methods

This paper concerns the asymptotic behavior of solutions and their gradients to linear and nonlinear elliptic equations with singular coefficients of fuchsian type.     

Isomerization and rearrangement of (E)‐ and (Z)‐phenylhydrazones of 3‐benzoyl‐5‐phenyl‐1,2,4‐oxadiazole: evidence for a ‘new’ type of acid‐catalysis by copper(II) salts in mononuclear rearrangement of heterocycles

A kinetic investigation in methanol of the title reaction has evidenced the occurrence of two processes: the 1‐ E 1‐ Z isomerization and the rearrangement of the (Z)‐isomer into the relevant 4‐benzoylamino‐2,5‐diphenyl‐1,2,3‐triazole ( 1‐ Z → T ). The latter reaction is in line with the ability of the (Z)‐phenylhydrazones of 3‐benzoyl‐1,2,4‐oxadiazoles to undergo the so called mononuclear rearrangement of heterocycles (MRH). The occurrence of both the examined reactions is dependent on a Lewis‐acid‐catalysis. The obtained results have shown the possibility of a ‘new’ type of acid‐catalysis (bifunctional catalysis by Lewis salts) in the MRH. This catalysis operates through a completely different mechanism with respect to the one recently observed, and deeply investigated, in the presence of protic acids for the (Z)‐phenylhydrazone of 5‐amino‐3‐benzoyl‐1,2,4‐oxadiazole, in both dioxane/water and toluene, for which the catalytic process was dependent on the protonation of N(4) ring‐nitrogen of the 1,2,4‐oxadiazole. As a matter of fact, the copper salts seem able to interact with the >C?N? NH? C₆H₅ moiety, yielding adducts which, in some cases, are prone to both isomerize and rearrange. Therefore, a similar behaviour in some manner parallel to that already observed in benzene in the presence of aliphatic amines (base‐catalysis) has been evidenced. Copyright © 2008 John Wiley & Sons, Ltd.     

The Glucosamine-derivative NAPA Suppresses MAPK Activation and Restores Collagen Deposition in Human Diploid Fibroblasts Challenged with Environmental Levels of UVB

The ultraviolet (UV) component of solar radiation is the driving force of life on earth, but it can cause photoaging and skin cancer. In this study, we investigated the effects of the glucosamine-derivative 2-(N-Acetyl)-L-phenylalanylamido-2-deoxy-β-D-glucose (NAPA) on human primary fibroblasts (FBs) stimulated in vitro with environmental levels of UVB radiation. FBs were irradiated with 0.04 J cm⁻² UVB dose, which resulted a mild dosage as shown by the cell viability and ROS production measurement. This environmental UVB dose induced activation of MAP kinase ERK 1/2, the stimulation of c-fos and at lower extent of c-jun, and in turn AP-1-dependent up-regulation of pro-inflammatory factors IL-6 and IL-8 and suppression of collagen type I expression. On the contrary, 0.04 J cm⁻² UVB dose was not able to stimulate metalloprotease production. NAPA treatment was able to suppress the up-regulation of IL-6 and IL-8 via the inhibition of MAP kinase ERK phosphorylation and the following AP-1 activation, and was able to attenuate the collagen type I down-regulation induced by the UVBs. Taken together, our results show that NAPA, considering its dual action on suppression of inflammation and stimulation of collagen type I production, represents an interesting candidate as a new photoprotective and photorepairing agents.     

Regularity of the nodal set of segregated critical configurations under a weak reflection law

We deal with a class of Lipschitz vector functions U?=?(u ₁, . . . , u _h ) whose components are nonnegative, disjointly supported and verify an elliptic equation on each support. Under a weak formulation of a reflection law, related to the Pohoz?aev identity, we prove that the nodal set is a collection of C ^1,α hyper-surfaces (for every 0?<?α?<?1), up to a residual set with small Hausdorff dimension. This result applies to the asymptotic limits of reaction–diffusion systems with strong competition interactions, to optimal partition problems involving eigenvalues, as well as to segregated standing waves for Bose–Einstein condensates in multiple hyperfine spin states.     

Integrated Information in the Spiking–Bursting Stochastic Model

Integrated information has been recently suggested as a possible measure to identify a necessary condition for a system to display conscious features. Recently, we have shown that astrocytes contribute to the generation of integrated information through the complex behavior of neuron–astrocyte networks. Still, it remained unclear which underlying mechanisms governing the complex behavior of a neuron–astrocyte network are essential to generating positive integrated information. This study presents an analytic consideration of this question based on exact and asymptotic expressions for integrated information in terms of exactly known probability distributions for a reduced mathematical model (discrete-time, discrete-state stochastic model) reflecting the main features of the “spiking–bursting” dynamics of a neuron–astrocyte network. The analysis was performed in terms of the empirical “whole minus sum” version of integrated information in comparison to the “decoder based” version. The “whole minus sum” information may change sign, and an interpretation of this transition in terms of “net synergy” is available in the literature. This motivated our particular interest in the sign of the “whole minus sum” information in our analytical considerations. The behaviors of the “whole minus sum” and “decoder based” information measures are found to bear a lot of similarity—they have mutual asymptotic convergence as time-uncorrelated activity increases, and the sign transition of the “whole minus sum” information is associated with a rapid growth in the “decoder based” information. The study aims at creating a theoretical framework for using the spiking–bursting model as an analytically tractable reference point for applying integrated information concepts to systems exhibiting similar bursting behavior. The model can also be of interest as a new discrete-state test bench for different formulations of integrated information.     

Nanotechnology as an experiment in democracy: how do citizens form opinions about technology and policy?

This article analyzes nanotechnology as an experiment in democratic deliberation, one that seems motivated both by a desire to improve deliberative democracy and to protect the technology from undue public interference. However, rather than involving amplified (overstated) risks, nanotechnology appears to involve attenuated (understated) risks. Results from a 3-year panel study are presented to illustrate the ways in which citizens form opinions about nanotechnology, supporting the assertion that public opinion about complex technology can be both reasonable and stable. Nevertheless, the authors also voice concern that, in the absence of public pressure, risk regulation may not evolve as swiftly as it should to protect both society and industry.