Structural Properties of Self-Attracting Walks

Self-attracting walks (SATW) with attractive interaction u > 0 display a swelling-collapse transition at a critical u_{\mathrm{c}} for dimensions d >= 2, analogous to the \Theta transition of polymers. We are interested in the structure of the clusters generated by SATW below u_{\mathrm{c}} (swollen walk), above u_{\mathrm{c}} (collapsed walk), and at u_{\mathrm{c}}, which can be characterized by the fractal dimensions of the clusters d_{\mathrm{f}} and their interface d_{\mathrm{I}}. Using scaling arguments and Monte Carlo simulations, we find that for u<u_{\mathrm{c}}, the structures are in the universality class of clusters generated by simple random walks. For u>u_{\mathrm{c}}, the clusters are compact, i.e. d_{\mathrm{f}}=d and d_{\mathrm{I}}=d-1. At u_{\mathrm{c}}, the SATW is in a new universality class. The clusters are compact in both d=2 and d=3, but their interface is fractal: d_{\mathrm{I}}=1.50\pm0.01 and 2.73\pm0.03 in d=2 and d=3, respectively. In d=1, where the walk is collapsed for all u and no swelling-collapse transition exists, we derive analytical expressions for the average number of visited sites and the mean time to visit S sites.Comment: 15 pages, 8 postscript figures, submitted to Phys. Rev.

Ising model on 3D random lattices: A Monte Carlo study

We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to 128,000 approx. 503 sites which are linked together according to the Voronoi/Delaunay prescription. For each lattice size quenched averages are performed over 96 realizations. By using reweighting techniques and finite-size scaling analyses we investigate the critical properties of the model in the close vicinity of the phase transition point. Our random lattice data provide strong evidence that, for the available system sizes, the resulting effective critical exponents are indistinguishable from recent high-precision estimates obtained in Monte Carlo studies of the Ising model and \phi^4 field theory on three-dimensional regular cubic lattices.Comment: 35 pages, LaTex, 8 tables, 8 postscript figure

Phospholipid oxidation and carotenoid supplementation in Alzheimer’s disease patients

Alzheimer's disease (AD) is a progressive, neurodegenerative disease, characterised by decline of memory, cognitive function and changes in behaviour. Generic markers of lipid peroxidation are increased in AD, therefore reactive oxygen species have been suggested to be involved in the aetiology of cognitive decline. Carotenoids are depleted in AD serum, therefore we have compared serum lipid oxidation between AD and age-matched control subjects before and after carotenoid supplementation. The novel oxidised phospholipid biomarker 1-palmitoyl-2-(5'-oxo-valeroyl)-sn-glycero-3-phosphocholine (POVPC) was analysed using electrospray ionization tandem mass spectrometry (MS) with multiple reaction monitoring (MRM), 8-isoprostane (IsoP) was measured by ELISA and ferric reducing antioxidant potential (FRAP) was measured by a colorimetric assay. AD patients (n=21) and healthy age-matched control subjects (n=16) were supplemented with either Macushield™ (10 mg meso-zeaxanthin, 10 mg lutein, 2 mg zeaxanthin) or placebo (sunflower oil) for six months. The MRM-MS method determined serum POVPC sensitively (from 10 µl serum) and reproducibly (CV=7.9%). At baseline, AD subjects had higher serum POVPC compared to age-matched controls, (p=0.017) and cognitive function was correlated inversely with POVPC (r=−0.37; p=0.04). After six months of carotenoid intervention, serum POVPC was not different in AD patients compared to healthy controls. However, POVPC was significantly higher in control subjects after six months of carotenoid intervention compared to their baseline (p=0.03). Serum IsoP concentration was unrelated to disease or supplementation. Serum FRAP was significantly lower in AD than healthy controls but was unchanged by carotenoid intervention (p=0.003). In conclusion, serum POVPC is higher in AD patients compared to control subjects, is not reduced by carotenoid supplementation and correlates with cognitive function