Quenched Invariance Principle for the Random Walk on the Penrose Tiling

We consider the simple random walk on the graph corresponding to a Penrose tiling. We prove that the path distribution of the walk converges weakly to that of a non-degenerate Brownian motion for almost every Penrose tiling with respect to the appropriate invariant measure on the set of tilings. Our tool for this is the corrector method.Comment: 15 pages, 1 figur

Local stability implies global stability for the 2-dimensional Ricker map

Consider the difference equation $x_{k+1}=x_k e^{\alpha-x_{n-d}}$ where $\alpha$ is a positive parameter and d is a non-negative integer. The case d = 0 was introduced by W.E. Ricker in 1954. For the delayed version d >= 1 of the equation S. Levin and R. May conjectured in 1976 that local stability of the nontrivial equilibrium implies its global stability. Based on rigorous, computer aided calculations and analytical tools, we prove the conjecture for d = 1.Comment: for associated C++ program, mathematica worksheet and output, see http://www.math.u-szeged.hu/~krisztin/ricke

White matter integrity is associated with gait impairment and falls in mild cognitive impairment. Results from the gait and brain study

© 2019 The Authors Background: Mild Cognitive Impairment (MCI) is an intermediate state between normal cognition and dementia that is associated with twice the risk of falls. It is unknown whether white matter integrity (WMI) is associated with increased risk of falls in MCI. The purpose of this study was to evaluate if early changes in WMI were associated with gait impairment and falls. Methods: Forty-three participants with MCI from the Gait and Brain Study underwent standardized assessment of cognition, gait performance under single and dual-task conditions (walking while talking), and WMI using 3 Tesla diffusion tensor imaging (DTI). Macro-structural imaging characteristics (white and grey matter morphology) as well as microstructural WMI parameters were examined for associations with falls and gait performance. Significantly associated WM tracts were then used to test the interplay between WMI and history of falls, after adjusting for other important covariates. Results: Multiple WM tracts (corpus callosum, forceps minor, and the left inferior fronto-occipital fasciculus) were significantly associated with history of falls and lower dual-task gait performance. A multivariable regression model showed that fall history was associated with the radial diffusivity in the forceps minor, even after adjusting for education, sex, BMI, MMSE scores, comorbidities, gait velocity and WMH volume as covariates. Conclusions: Multiple WM tracts that are known to be involved in executive and visuospatial functions were preferentially affected in MCI individuals with history of falls. Our preliminary findings support the notion that WMI in key brain regions may increase risk of falls in older adults with MCI

Flow correlated percolation during vascular network formation in tumors

A theoretical model based on the molecular interactions between a growing tumor and a dynamically evolving blood vessel network describes the transformation of the regular vasculature in normal tissues into a highly inhomogeneous tumor specific capillary network. The emerging morphology, characterized by the compartmentalization of the tumor into several regions differing in vessel density, diameter and necrosis, is in accordance with experimental data for human melanoma. Vessel collapse due to a combination of severely reduced blood flow and solid stress exerted by the tumor, leads to a correlated percolation process that is driven towards criticality by the mechanism of hydrodynamic vessel stabilization.Comment: 4 pages, 3 figures (higher resolution at http://www.uni-saarland.de/fak7/rieger/HOMEPAGE/flow.eps

Invasion impact is conditioned by initial vegetation states

Abstract Biological invasion is a crucial problem in the world because of its negative consequences for protected areas. The degradation stage of vegetation might affect the success of invasion. One of the most abundant and threatening invasive species is the common milkweed (Asclepias syriaca L.) which has invaded already 23 countries of Europe and in several habitat types its further spreading is promoted by climate change. Pannonian sand grassland is one of the most threatened habitat by common milkweed invasion. Therefore, invasion in sand grassland vegetation is an important issue. However, the effects of the invasive plant in the open sand grassland are rather controversial. In order to clarify the existing contradictory results, the study was carried out in a strictly protected area, near Fülöpháza (Hungary) in a reserve core area in a UNESCO biosphere reserve. Microcoenological study was applied to determinate the fine-scale community characteristics of non-invaded and invaded stands in natural and seminatural vegetation and data were processed by Juhász-Nagy's information theory models. Shannon diversity of species combinations (compositional diversity) which describes the ways of the coexistence of species, and the number of realized species combinations were used for measuring beta diversity. Differences between stands were analyzed by two-way ANOVA. The maximum compositional diversity of species and main life-forms (annuals, perennials and cryptogams) did not differ significantly between the non-invaded and invaded stands. In contrast, significantly larger characteristic areas of compositional diversity were detected in the invaded stands. Based on these results, it could be concluded that diversity of species combinations did not change but those values have shifted to coarser scales in case of invaded stands. The direction of this change suggests a kind of impoverishment in the presence of Asclepias. Thus, it is worth mentioning from the invasion management point of view that protection of the habitats against disturbance is a more cost-effective and successful way than protection against the establishment or extirpation of invasive species, since disturbance facilitates the invasions throughout the impoverishment of the community

Analysis of stop-gain and frameshift variants in human innate immunity genes.

Loss-of-function variants in innate immunity genes are associated with Mendelian disorders in the form of primary immunodeficiencies. Recent resequencing projects report that stop-gains and frameshifts are collectively prevalent in humans and could be responsible for some of the inter-individual variability in innate immune response. Current computational approaches evaluating loss-of-function in genes carrying these variants rely on gene-level characteristics such as evolutionary conservation and functional redundancy across the genome. However, innate immunity genes represent a particular case because they are more likely to be under positive selection and duplicated. To create a ranking of severity that would be applicable to innate immunity genes we evaluated 17,764 stop-gain and 13,915 frameshift variants from the NHLBI Exome Sequencing Project and 1,000 Genomes Project. Sequence-based features such as loss of functional domains, isoform-specific truncation and nonsense-mediated decay were found to correlate with variant allele frequency and validated with gene expression data. We integrated these features in a Bayesian classification scheme and benchmarked its use in predicting pathogenic variants against Online Mendelian Inheritance in Man (OMIM) disease stop-gains and frameshifts. The classification scheme was applied in the assessment of 335 stop-gains and 236 frameshifts affecting 227 interferon-stimulated genes. The sequence-based score ranks variants in innate immunity genes according to their potential to cause disease, and complements existing gene-based pathogenicity scores. Specifically, the sequence-based score improves measurement of functional gene impairment, discriminates across different variants in a given gene and appears particularly useful for analysis of less conserved genes