Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs

We study homogeneous, independent percolation on general quasi-transitive graphs. We prove that in the disorder regime where all clusters are finite almost surely, in fact the expectation of the cluster size is finite. This extends a well-known theorem by Menshikov and Aizenman & Barsky to all quasi-transitive graphs. Moreover we deduce that in this disorder regime the cluster size distribution decays exponentially, extending a result of Aizenman & Newman. Our results apply to both edge and site percolation, as well as long range (edge) percolation. The proof is based on a modification of the Aizenman & Barsky method.Comment: Latex 2e; 25 pages (a4wide); small editorial corrections; one reference adde

Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method

A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated by the sign-indefinite single-site potential, which is however sign-definite at the boundary of its support. For this class of Anderson operators we establish a finite-volume criterion which implies that above mentioned the fractional moment decay property holds. This constructive criterion is satisfied at typical perturbative regimes, e. g. at spectral boundaries which satisfy 'Lifshitz tail estimates' on the density of states and for sufficiently strong disorder. We also show how the fractional moment method facilitates the proof of exponential (spectral) localization for such random potentials.Comment: 29 pages, 1 figure, to appear in AH

Perturbation of a lattice spectral band by a nearby resonance

A soluble model of weakly coupled "molecular" and "nuclear" Hamiltonians is studied in order to exhibit explicitly the mechanism leading to the enhancement of fusion probability in case of a narrow near-threshold nuclear resonance. We, further, consider molecular cells of this type being arranged in lattice structures. It is shown that if the real part of the narrow nuclear resonance lies within the molecular band generated by the intercellular interaction, an enhancement, proportional to the inverse width of the nuclear resonance, is to be expected.Comment: RevTeX, 2 figures within the file. In May 2000 the title changed and some minor corrections have been don

The sterlet sturgeon genome sequence and the mechanisms of segmental rediploidization.

Sturgeons seem to be frozen in time. The archaic characteristics of this ancient fish lineage place it in a key phylogenetic position at the base of the ~30,000 modern teleost fish species. Moreover, sturgeons are notoriously polyploid, providing unique opportunities to investigate the evolution of polyploid genomes. We assembled a high-quality chromosome-level reference genome for the sterlet, Acipenser ruthenus. Our analysis revealed a very low protein evolution rate that is at least as slow as in other deep branches of the vertebrate tree, such as that of the coelacanth. We uncovered a whole-genome duplication that occurred in the Jurassic, early in the evolution of the entire sturgeon lineage. Following this polyploidization, the rediploidization of the genome included the loss of whole chromosomes in a segmental deduplication process. While known adaptive processes helped conserve a high degree of structural and functional tetraploidy over more than 180 million years, the reduction of redundancy of the polyploid genome seems to have been remarkably random

An Improved Combes-Thomas Estimate of Magnetic Schr\"{o}dinger Operators

In the present paper, we prove an improved Combes-Thomas estimate, i.e., the Combes-Thomas estimate in trace-class norms, for magnetic Schr\"{o}dinger operators under general assumptions. In particular, we allow unbounded potentials. We also show that for any function in the Schwartz space on the reals the operator kernel decays, in trace-class norms, faster than any polynomial.Comment: 25 pages, some errors correcte

Functional Characterization of Promoter Variants of the Adiponectin Gene Complemented by Epidemiological Data

# These authors contributed equally to the work. *Corresponding author

Conditional Wegner Estimate for the Standard Random Breather Potential

We prove a conditional Wegner estimate for Schr\"odinger operators with random potentials of breather type. More precisely, we reduce the proof of the Wegner estimate to a scale free unique continuation principle. The relevance of such unique continuation principles has been emphasized in previous papers, in particular in recent years. We consider the standard breather model, meaning that the single site potential is the characteristic function of a ball or a cube. While our methods work for a substantially larger class of random breather potentials, we discuss in this particular paper only the standard model in order to make the arguments and ideas easily accessible

Age-related delay in information accrual for faces: Evidence from a parametric, single-trial EEG approach

Background: In this study, we quantified age-related changes in the time-course of face processing by means of an innovative single-trial ERP approach. Unlike analyses used in previous studies, our approach does not rely on peak measurements and can provide a more sensitive measure of processing delays. Young and old adults (mean ages 22 and 70 years) performed a non-speeded discrimination task between two faces. The phase spectrum of these faces was manipulated parametrically to create pictures that ranged between pure noise (0% phase information) and the undistorted signal (100% phase information), with five intermediate steps. Results: Behavioural 75% correct thresholds were on average lower, and maximum accuracy was higher, in younger than older observers. ERPs from each subject were entered into a single-trial general linear regression model to identify variations in neural activity statistically associated with changes in image structure. The earliest age-related ERP differences occurred in the time window of the N170. Older observers had a significantly stronger N170 in response to noise, but this age difference decreased with increasing phase information. Overall, manipulating image phase information had a greater effect on ERPs from younger observers, which was quantified using a hierarchical modelling approach. Importantly, visual activity was modulated by the same stimulus parameters in younger and older subjects. The fit of the model, indexed by R2, was computed at multiple post-stimulus time points. The time-course of the R2 function showed a significantly slower processing in older observers starting around 120 ms after stimulus onset. This age-related delay increased over time to reach a maximum around 190 ms, at which latency younger observers had around 50 ms time lead over older observers. Conclusion: Using a component-free ERP analysis that provides a precise timing of the visual system sensitivity to image structure, the current study demonstrates that older observers accumulate face information more slowly than younger subjects. Additionally, the N170 appears to be less face-sensitive in older observers

Meta-analysis of genome-wide association studies from the CHARGE consortium identifies common variants associated with carotid intima media thickness and plaque

Carotid intima media thickness (cIMT) and plaque determined by ultrasonography are established measures of subclinical atherosclerosis that each predicts future cardiovascular disease events. We conducted a meta-analysis of genome-wide association data in 31,211 participants of European ancestry from nine large studies in the setting of the Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE) Consortium. We then sought additional evidence to support our findings among 11,273 individuals using data from seven additional studies. In the combined meta-analysis, we identified three genomic regions associated with common carotid intima media thickness and two different regions associated with the presence of carotid plaque (P < 5 × 10 -8). The associated SNPs mapped in or near genes related to cellular signaling, lipid metabolism and blood pressure homeostasis, and two of the regions were associated with coronary artery disease (P < 0.006) in the Coronary Artery Disease Genome-Wide Replication and Meta-Analysis (CARDIoGRAM) consortium. Our findings may provide new insight into pathways leading to subclinical atherosclerosis and subsequent cardiovascular events