Sharpness versus robustness of the percolation transition in 2D contact processes

We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in [17] for vegetation patterns in arid landscapes, we focus on percolation under invariant measures of such processes. We prove that the percolation transition is sharp (for one of our models this requires a reasonable assumption). This is shown to contradict a form of 'robust critical behaviour' with power law cluster size distribution for a range of parameter values, as suggested in [17].Comment: 31 pages, to appear in Stochastic Processes and their Application

Random graph asymptotics on high-dimensional tori. II. Volume, diameter and mixing time

For critical bond-percolation on high-dimensional torus, this paper proves sharp lower bounds on the size of the largest cluster, removing a logarithmic correction in the lower bound in Heydenreich and van der Hofstad (2007). This improvement finally settles a conjecture by Aizenman (1997) about the role of boundary conditions in critical high-dimensional percolation, and it is a key step in deriving further properties of critical percolation on the torus. Indeed, a criterion of Nachmias and Peres (2008) implies appropriate bounds on diameter and mixing time of the largest clusters. We further prove that the volume bounds apply also to any finite number of the largest clusters. The main conclusion of the paper is that the behavior of critical percolation on the high-dimensional torus is the same as for critical Erdos-Renyi random graphs. In this updated version we incorporate an erratum to be published in a forthcoming issue of Probab. Theory Relat. Fields. This results in a modification of Theorem 1.2 as well as Proposition 3.1.Comment: 16 pages. v4 incorporates an erratum to be published in a forthcoming issue of Probab. Theory Relat. Field

Alternatives to Outdoor Daylight Illumination for Photodynamic Therapy—Use of Greenhouses and Artificial Light Sources

Daylight-mediated photodynamic therapy (daylight PDT) is a simple and pain free treatment of actinic keratoses. Weather conditions may not always allow daylight PDT outdoors. We compared the spectrum of five different lamp candidates for indoor “daylight PDT” and investigated their ability to photobleach protoporphyrin IX (PpIX). Furthermore, we measured the amount of PpIX activating daylight available in a glass greenhouse, which can be an alternative when it is uncomfortable for patients to be outdoors. The lamps investigated were: halogen lamps (overhead and slide projector), white light-emitting diode (LED) lamp, red LED panel and lamps used for conventional PDT. Four of the five light sources were able to photobleach PpIX completely. For halogen light and the red LED lamp, 5000 lux could photobleach PpIX whereas 12,000 lux were needed for the white LED lamp. Furthermore, the greenhouse was suitable for daylight PDT since the effect of solar light is lowered only by 25%. In conclusion, we found four of the five light sources and the greenhouse usable for indoor daylight PDT. The greenhouse is beneficial when the weather outside is rainy or windy. Only insignificant ultraviolet B radiation (UVB) radiation passes through the greenhouse glass, so sun protection is not needed

Bioactive compounds in the stem bark of Albizia coriaria (Welw. ex Oliver)

Albizia coriaria was investigated for the bioactive compounds present in its stem bark. The plant was selected on the basis of its widespread use in traditional herbal medicine. Extraction of the plant material was done with ethyl acetate, methanol and water and the bioactivity of each extract was tested against  Pseudomonas aeruginosa and Escherichia coli. Separation and purification of the compounds in the most active (ethyl acetate) extract was done using a  combination of chromatographic techniques. The compounds were identified by 1D and 2D -1H and 13C NMR techniques as well as Mass spectrometry (MS). Six compounds, namely: Lupeol (1), Lupenone (2), Betulinic acid (3), Acacic acid lactone (4), (+) – Catechin (5) and Benzyl alcohol (6) were identified and  characterized from the ethyl acetate extract. The results of the bioactivity tests carried out in this study indicated that A. coriaria has potential antimicrobial activity. Four of the characterized compounds (1, 2, 3 & 5) have a wide range of biological activity reported in literature. This justifies the use of this plant in traditional medicine and indicates a promising potential for the development of medicinal agents from A. coriaria stem bark.Keywords: Biological activity, Lupeol, Lupenone, Betulinic acid, Acacic acid lactone, (+) – Catechin

Chemical constituents of the ethyl acetate extracts of the stem bark and fruits of Dichrostachys cinerea and the roots of Parkia bicolor

The antibacterial activities of ethyl acetate, methanol and aqueous extracts of the stem bark of Dichrostachys cinerea and the roots of Parkia bicolor have been evaluated. Ethyl acetate extracts have been investigated, studies that led to a series of known compounds, amongst which many are reported here for the very first time from both the species.  KEY WORDS: Dichrostachys cinerea, Parkia bicolor, Chemical constituents, Antibacterial activity Bull. Chem. Soc. Ethiop. 2004, 18(1), 111-115

Benzylic fluorination induced by a charge-transfer complex with a solvent-dependent selectivity switch

We present a divergent strategy for the fluorination of phenylacetic acid derivatives that is induced by a charge-transfer complex between Selectfluor and 4-(dimethylamino)pyridine. A comprehensive investigation of the conditions revealed a critical role of the solvent on the reaction outcome. In the presence of water, decarboxylative fluorination through a single-electron oxidation is dominant. Non-aqueous conditions result in the clean formation of α-fluoro-α-arylcarboxylic acids

Random walk on the high-dimensional IIC

We study the asymptotic behavior the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by [26]. We do this by obtaining bounds on the effective resistance between the origin and the boundary of these Euclidean balls. We show that the geometric properties of long-range percolation clusters are significantly different from those of finite-range clusters. We also study the behavior of random walk on the backbone of the IIC and we prove that the Alexander-Orbach conjecture holds for the incipient infinite cluster in high dimensions, both for long-range percolation and for finite-range percolation

High-dimensional incipient infinite clusters revisited

The incipient infinite cluster (IIC) measure is the percolation measure at criticality conditioned on the cluster of the origin to be infinite. Using the lace expansion, we construct the IIC measure for high-dimensional percolation models in three different ways, extending previous work by the second author and Jarai. We show that each construction yields the same measure, indicating that the IIC is a robust object. Furthermore, our constructions apply to spread-out versions of both finite-range and long-range percolation models. We also obtain estimates on structural properties of the IIC, such as the volume of the intersection between the IIC and Euclidean balls