The dimension of loop-erased random walk in 3D

We measure the fractal dimension of loop-erased random walk (LERW) in 3 dimensions, and estimate that it is 1.62400 +- 0.00005. LERW is closely related to the uniform spanning tree and the abelian sandpile model. We simulated LERW on both the cubic and face-centered cubic lattices; the corrections to scaling are slightly smaller for the face-centered cubic lattice.Comment: 4 pages, 4 figures. v2 has more data, minor additional change

Hurst's Rescaled Range Statistical Analysis for Pseudorandom Number Generators used in Physical Simulations

The rescaled range statistical analysis (R/S) is proposed as a new method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the RS analysis provides a very sensitive method to reveal hidden long run and short run correlations. Several widely used and also some recently proposed pseudorandom number generators are subjected to this test. In many generators correlations are detected and quantified.Comment: 12 pages, 12 figures, 6 tables. Replaces previous version to correct citation [19

Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model. I. Two Dimensions

We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to non-integer q \ge 1. We consider spatial dimension d=2 and 1.25 \le q \le 4 in steps of 0.25, on lattices up to 1024^2, and obtain estimates for the dynamic critical exponent z_{CM}. We present evidence that when 1 \le q \lesssim 1.95 the Ossola-Sokal conjecture z_{CM} \ge \beta/\nu is violated, though we also present plausible fits compatible with this conjecture. We show that the Li-Sokal bound z_{CM} \ge \alpha/\nu is close to being sharp over the entire range 1 \le q \le 4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.Comment: LaTeX2e, 75 pages including 26 Postscript figure

The effect of a preparation of minerals, vitamins and trace elements on the cardiac gene expression pattern in male diabetic rats

BACKGROUND: Diabetic patients have an increased risk of developing cardiovascular diseases, which are the leading cause of death in developed countries. Although multivitamin products are widely used as dietary supplements, the effects of these products have not been investigated in the diabetic heart yet. Therefore, here we investigated if a preparation of different minerals, vitamins, and trace elements (MVT) affects the cardiac gene expression pattern in experimental diabetes. METHODS: Two-day old male Wistar rats were injected with streptozotocin (i.p. 100 mg/kg) or citrate buffer to induce diabetes. From weeks 4 to 12, rats were fed with a vehicle or a MVT preparation. Fasting blood glucose measurement and oral glucose tolerance test were performed at week 12, and then total RNA was isolated from the myocardium and assayed by rat oligonucleotide microarray for 41012 oligonucleotides. RESULTS: Significantly elevated fasting blood glucose concentration and impaired glucose tolerance were markedly improved by MVT-treatment in diabetic rats at week 12. Genes with significantly altered expression due to diabetes include functional clusters related to cardiac hypertrophy (e.g. caspase recruitment domain family, member 9; cytochrome P450, family 26, subfamily B, polypeptide; FXYD domain containing ion transport regulator 3), stress response (e.g. metallothionein 1a; metallothionein 2a; interleukin-6 receptor; heme oxygenase (decycling) 1; and glutathione S-transferase, theta 3), and hormones associated with insulin resistance (e.g. resistin; FK506 binding protein 5; galanin/GMAP prepropeptide). Moreover the expression of some other genes with no definite cardiac function was also changed such as e.g. similar to apolipoprotein L2; brain expressed X-linked 1; prostaglandin b2 synthase (brain). MVT-treatment in diabetic rats showed opposite gene expression changes in the cases of 19 genes associated with diabetic cardiomyopathy. In healthy hearts, MVT-treatment resulted in cardiac gene expression changes mostly related to immune response (e.g. complement factor B; complement component 4a; interferon regulatory factor 7; hepcidin). CONCLUSIONS: MVT-treatment improved diagnostic markers of diabetes. This is the first demonstration that MVT-treatment significantly alters cardiac gene expression profile in both control and diabetic rats. Our results and further studies exploring the mechanistic role of individual genes may contribute to the prevention or diagnosis of cardiac complications in diabetes

The contributions of local and remote atmospheric moisture fluxes to East Asian precipitation and its variability

We investigate the contribution of the local and remote atmospheric moisture fluxes to East Asia (EA) precipitation and its interannual variability during 1979-2012. We use and expand the \citet{Brubaker_etal_JC_1993} method, which connects the area-mean precipitation to area-mean evaporation and the horizontal moisture flux into the region. Due to its large landmass and hydrological heterogeneity, EA is divided into five sub-regions: Southeast (SE), Tibetan Plateau (TP), Central East (CE), Northwest (NW) and Northeast (NE). For each region, we first separate the contributions to precipitation of local evaporation from those of the horizontal moisture flux by calculating the precipitation recycling ratio: the fraction of precipitation over a region that originates as evaporation from the same region. Then, we separate the horizontal moisture flux across the region's boundaries by direction. We estimate the contributions of the horizontal moisture fluxes from each direction, as well as the local evaporation, to the mean precipitation and its interannual variability. We find that the major contributors to the mean precipitation are not necessarily those that contribute most to the precipitation interannual variability. Over SE, the moisture flux via the southern boundary dominates the mean precipitation and its interannual variability. Over TP, in winter and spring, the moisture flux via the western boundary dominates the mean precipitation; however, variations in local evaporation dominate the precipitation interannual variability. The western moisture flux is the dominant contributor to the mean precipitation over CE, NW and NE. However, the southern or northern moisture flux or the local evaporation dominates the precipitation interannual variability over these regions, depending on the season. Potential mechanisms associated with interannual variability in the moisture flux are identified for each region. The methods and results presented in this study can be readily applied to model simulations, to identify simulation biases in precipitation that relate to the simulated moisture supplies and transport

Transcriptomic alterations in the heart of non-obese type 2 diabetic Goto-Kakizaki rats

BACKGROUND: There is a spectacular rise in the global prevalence of type 2 diabetes mellitus (T2DM) due to the worldwide obesity epidemic. However, a significant proportion of T2DM patients are non-obese and they also have an increased risk of cardiovascular diseases. As the Goto-Kakizaki (GK) rat is a well-known model of non-obese T2DM, the goal of this study was to investigate the effect of non-obese T2DM on cardiac alterations of the transcriptome in GK rats. METHODS: Fasting blood glucose, serum insulin and cholesterol levels were measured at 7, 11, and 15 weeks of age in male GK and control rats. Oral glucose tolerance test and pancreatic insulin level measurements were performed at 11 weeks of age. At week 15, total RNA was isolated from the myocardium and assayed by rat oligonucleotide microarray for 41,012 genes, and then expression of selected genes was confirmed by qRT-PCR. Gene ontology and protein-protein network analyses were performed to demonstrate potentially characteristic gene alterations and key genes in non-obese T2DM. RESULTS: Fasting blood glucose, serum insulin and cholesterol levels were significantly increased, glucose tolerance and insulin sensitivity were significantly impaired in GK rats as compared to controls. In hearts of GK rats, 204 genes showed significant up-regulation and 303 genes showed down-regulation as compared to controls according to microarray analysis. Genes with significantly altered expression in the heart due to non-obese T2DM includes functional clusters of metabolism (e.g. Cyp2e1, Akr1b10), signal transduction (e.g. Dpp4, Stat3), receptors and ion channels (e.g. Sln, Chrng), membrane and structural proteins (e.g. Tnni1, Mylk2, Col8a1, Adam33), cell growth and differentiation (e.g. Gpc3, Jund), immune response (e.g. C3, C4a), and others (e.g. Lrp8, Msln, Klkc1, Epn3). Gene ontology analysis revealed several significantly enriched functional inter-relationships between genes influenced by non-obese T2DM. Protein-protein interaction analysis demonstrated that Stat is a potential key gene influenced by non-obese T2DM. CONCLUSIONS: Non-obese T2DM alters cardiac gene expression profile. The altered genes may be involved in the development of cardiac pathologies and could be potential therapeutic targets in non-obese T2DM

Multi-model evaluation of the sensitivity of the global energy budget and hydrological cycle to resolution

This study undertakes a multi-model comparison with the aim to describe and quantify systematic changes of the global energy and water budgets when the horizontal resolution of atmospheric models is increased and to identify common factors of these changes among models. To do so, we analyse an ensemble of twelve atmosphere-only and six coupled GCMs, with different model formulations and with resolutions spanning those of state-of-the-art coupled GCMs, i.e. from resolutions coarser than 100 km to resolutions finer than 25 km. The main changes in the global energy budget with resolution are a systematic increase in outgoing longwave radiation and decrease in outgoing shortwave radiation due to changes in cloud properties, and a systematic increase in surface latent heat flux; when resolution is increased from 100 to 25 km, the magnitude of the change of those fluxes can be as large as 5 W m−2. Moreover, all but one atmosphere-only model simulate a decrease of the poleward energy transport at higher resolution, mainly explained by a reduction of the equator-to-pole tropospheric temperature gradient. Regarding hydrological processes, our results are the following: (1) there is an increase of global precipitation with increasing resolution in all models (up to 40 × 103 km3 year−1) but the partitioning between land and ocean varies among models; (2) the fraction of total precipitation that falls on land is on average 10% larger at higher resolution in grid point models, but it is smaller at higher resolution in spectral models; (3) grid points models simulate an increase of the fraction of land precipitation due to moisture convergence twice as large as in spectral models; (4) grid point models, which have a better resolved orography, show an increase of orographic precipitation of up to 13 × 103 km3 year−1 which explains most of the change in land precipitation; (5) at the regional scale, precipitation pattern and amplitude are improved with increased resolution due to a better simulated seasonal mean circulation. We discuss our results against several observational estimates of the Earth's energy budget and hydrological cycle and show that they support recent high estimates of global precipitation