Elastic String in a Random Medium

We consider a one dimensional elastic string as a set of massless beads interacting through springs characterized by anisotropic elastic constants. The string, driven by an external force, moves in a medium with quenched disorder. We present evidence that the consideration of longitudinal fluctuations leads to nonlinear behavior in the equation of motion which is {\it kinematically} generated by the motion of the string. The strength of the nonlinear effects depends on the anisotropy of the medium and the distance from the depinning transition. On the other hand the consideration of restricted solid on solid conditions imposed to the growth of the string leads to a nonlinear term in the equation of motion with a {\it diverging} coefficient at the depinning transition.Comment: 9 pages, REVTEX, figures available upon request from [email protected]

Evaluation of Clustering and Genotype Distribution for Replication in Genome Wide Association Studies: The Age-Related Eye Disease Study

Genome-wide association studies (GWASs) assess correlation between traits and DNA sequence variation using large numbers of genetic variants such as single nucleotide polymorphisms (SNPs) distributed across the genome. A GWAS produces many trait-SNP associations with low p-values, but few are replicated in subsequent studies. We sought to determine if characteristics of the genomic loci associated with a trait could be used to identify initial associations with a higher chance of replication in a second cohort. Data from the age-related eye disease study (AREDS) of 100,000 SNPs on 395 subjects with and 198 without age-related macular degeneration (AMD) were employed. Loci highly associated with AMD were characterized based on the distribution of genotypes, level of significance, and clustering of adjacent SNPs also associated with AMD suggesting linkage disequilibrium or multiple effects. Forty nine loci were highly associated with AMD, including 3 loci (CFH, C2/BF, LOC387715/HTRA1) already known to contain important genetic risks for AMD. One additional locus (C3) reported during the course of this study was identified and replicated in an additional study group. Tag-SNPs and haplotypes for each locus were evaluated for association with AMD in additional cohorts to account for population differences between discovery and replication subjects, but no additional clearly significant associations were identified. Relying on a significant genotype tests using a log-additive model would have excluded 57% of the non-replicated and none of the replicated loci, while use of other SNP features and clustering might have missed true associations

Scaling properties of driven interfaces in disordered media

We perform a systematic study of several models that have been proposed for the purpose of understanding the motion of driven interfaces in disordered media. We identify two distinct universality classes: (i) One of these, referred to as directed percolation depinning (DPD), can be described by a Langevin equation similar to the Kardar-Parisi-Zhang equation, but with quenched disorder. (ii) The other, referred to as quenched Edwards-Wilkinson (QEW), can be described by a Langevin equation similar to the Edwards-Wilkinson equation but with quenched disorder. We find that for the DPD universality class the coefficient $\lambda$ of the nonlinear term diverges at the depinning transition, while for the QEW universality class either $\lambda = 0$ or $\lambda \to 0$ as the depinning transition is approached. The identification of the two universality classes allows us to better understand many of the results previously obtained experimentally and numerically. However, we find that some results cannot be understood in terms of the exponents obtained for the two universality classes {\it at\/} the depinning transition. In order to understand these remaining disagreements, we investigate the scaling properties of models in each of the two universality classes {\it above\/} the depinning transition. For the DPD universality class, we find for the roughness exponent $\alpha_P = 0.63 \pm 0.03$ for the pinned phase, and $\alpha_M = 0.75 \pm 0.05$ for the moving phase. For the growth exponent, we find $\beta_P = 0.67 \pm 0.05$ for the pinned phase, and $\beta_M = 0.74 \pm 0.06$ for the moving phase. Furthermore, we find an anomalous scaling of the prefactor of the width on the driving force. A new exponent $\varphi_M = -0.12 \pm 0.06$, characterizing the scaling of this prefactor, is shown to relate the values of the roughnessComment: Latex manuscript, Revtex 3.0, 15 pages, and 15 figures also available via anonymous ftp from ftp://jhilad.bu.edu/pub/abms/ (128.197.42.52

Statistical Analyses Support Power Law Distributions Found in Neuronal Avalanches

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to −1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling (“finite size” effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to −1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex

Single-Trait and Multi-Trait Genome-Wide Association Analyses Identify Novel Loci for Blood Pressure in African-Ancestry Populations

Hypertension is a leading cause of global disease, mortality, and disability. While individuals of African descent suffer a disproportionate burden of hypertension and its complications, they have been underrepresented in genetic studies. To identify novel susceptibility loci for blood pressure and hypertension in people of African ancestry, we performed both single and multiple-trait genome-wide association analyses. We analyzed 21 genome-wide association studies comprised of 31,968 individuals of African ancestry, and validated our results with additional 54,395 individuals from multi-ethnic studies. These analyses identified nine loci with eleven independent variants which reached genome-wide significance (P \u3c 1.25×10−8) for either systolic and diastolic blood pressure, hypertension, or for combined traits. Single-trait analyses identified two loci (TARID/TCF21 and LLPH/TMBIM4) and multiple-trait analyses identified one novel locus (FRMD3) for blood pressure. At these three loci, as well as at GRP20/CDH17, associated variants had alleles common only in African-ancestry populations. Functional annotation showed enrichment for genes expressed in immune and kidney cells, as well as in heart and vascular cells/tissues. Experiments driven by these findings and using angiotensin-II induced hypertension in mice showed altered kidney mRNA expression of six genes, suggesting their potential role in hypertension. Our study provides new evidence for genes related to hypertension susceptibility, and the need to study African-ancestry populations in order to identify biologic factors contributing to hypertension