Survival in equilibrium step fluctuations

We report the results of analytic and numerical investigations of the time scale of survival or non-zero-crossing probability $S(t)$ in equilibrium step fluctuations described by Langevin equations appropriate for attachment/detachment and edge-diffusion limited kinetics. An exact relation between long-time behaviors of the survival probability and the autocorrelation function is established and numerically verified. $S(t)$ is shown to exhibit simple scaling behavior as a function of system size and sampling time. Our theoretical results are in agreement with those obtained from an analysis of experimental dynamical STM data on step fluctuations on Al/Si(111) and Ag(111) surfaces.Comment: RevTeX, 4 pages, 3 figure

Evaluation of SPARC as a candidate gene of juvenile-onset primary open-angle glaucoma by mutation and copy number analyses

Purpose: To investigate the involvement of SPARC (secreted protein acidic and rich in cysteine) mutations and copy number variation in juvenile-onset primary open-angle glaucoma (JPOAG). Methods: This study involved the 27 family members from the GLC1M (glaucoma 1, open angle, M)-linked Philippine pedigree with JPOAG, 46 unrelated Chinese patients with JPOAG and 95 controls. Mutation screening of the SPARC sequence, covering the promoter, 5′-untranslated region (UTR), entire coding regions, exon-intron boundaries, and part of the 3′-UTR, was performed using polymerase chain reaction and direct DNA sequencing. Copy number of the gene was analyzed by three TaqMan copy number assays. Results: No putative SPARC mutation was detected in the Philippine family. In the Chinese participants, 11 sequence variants were detected. Two were novel: IVS2+8G>T and IVS2+32C>T. For the 9 known SNPs, one was synonymous (rs2304052, p.Glu22Glu) and the others were located in noncoding regions. No individual SNP was associated with JPOAG. Five of the most common SNPs, i.e., rs2116780, rs1978707, rs7719521, rs729853, and rs1053411, were contained in a LD (linkage disequilibrium) block. Haplotype-based analysis showed that no haplotype was associated with the disorder. Copy number analysis revealed that all study subjects had two copies of the gene, suggesting no correlation between the copy number of SPARC and JPOAG. Conclusions: We have excluded SPARC as the causal gene at the GLC1M locus in the Philippine pedigree and, for the first time, revealed that the coding sequences, splice sites and copy number of SPARC do not contribute to JPOAG. Further investigations are warranted to unravel the involvement of SPARC in the pathogenesis of other forms of glaucoma

Large-Deviation Functions for Nonlinear Functionals of a Gaussian Stationary Markov Process

We introduce a general method, based on a mapping onto quantum mechanics, for investigating the large-T limit of the distribution P(r,T) of the nonlinear functional r[V] = (1/T)\int_0^T dT' V[X(T')], where V(X) is an arbitrary function of the stationary Gaussian Markov process X(T). For T tending to infinity at fixed r we find that P(r,T) behaves as exp[-theta(r) T], where theta(r) is a large deviation function. We present explicit results for a number of special cases, including the case V(X) = X \theta(X) which is related to the cooling and the heating degree days relevant to weather derivatives.Comment: 8 page

Survival-Time Distribution for Inelastic Collapse

In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a randomly forced particle which collides inelastically with a boundary can undergo inelastic collapse and come to rest in a finite time. Here we discuss the survival probability for the inelastic collapse transition. It is found that the collapse-time distribution behaves asymptotically as a power-law in time, and that the exponent governing this decay is non-universal. An approximate calculation of the collapse-time exponent confirms this behaviour and shows how inelastic collapse can be viewed as a generalised persistence phenomenon.Comment: 4 pages, RevTe

SNP rs1533428 at 2p16.3 as a marker for late-onset primary open-angle glaucoma

Purpose: To investigate the associations between gene variants in cholesterol 24S-hydroxylase (CYP46A1), LIM homeobox transcription factor 1-beta (LMX1B), plexin domain containing 2 (PLXDC2), toll-like receptor 4 (TLR4), transmembrane and tetratricopeptide repeat containing 2 (TMTC2), zona pellucida glycoprotein 4 (ZP4), chromosome 2p16.3, and primary open-angle glaucoma (POAG). Methods: We studied 462 POAG patients and 577 controls from three cohorts (Hong Kong, Shantou, and Beijing, China). Twelve single-nucleotide polymorphisms (SNPs) were genotyped in the Hong Kong cohort using TaqMan genotyping assay. Significant associations were validated in the Shantou and Beijing cohorts. Results: Association of POAG with TLR4 rs7037117, in a recessive model, was identified in the Hong Kong and Shantou cohorts (both southern Chinese, $p_{rec}$=0.0019) but not the Beijing cohort (northern Chinese). rs1533428 at chromosome 2p16.3 showed a consistent trend of age-specific association in all three cohorts. Genotypes TT + CT conferred a 2.16 fold of significantly increased risk to late-onset POAG ($p_{dom}$=0.00025), but no significant risk to POAG of younger ages of onset in the combined cohort. A joint effect was found between rs7037117 and rs1533428, with carriers of both higher-risk genotypes having a 4.53 fold of increased disease risk (p=0.00028). Conclusions: Our study reveals discrepant association patterns of 12 candidate SNPs in 7 genes/loci with POAG in Chinese, provides positive replications for POAG markers rs1533428 at 2p16.3 and TLR4 rs7037117, and suggests that rs1533428 is a putative risk variant for late-onset POAG. The identification of an age-specific association between rs1533428 and late-onset POAG highlights a new genotype-phenotype association in POAG. Further studies are warranted to confirm the age-specific association

Fraction of uninfected walkers in the one-dimensional Potts model

The dynamics of the one-dimensional q-state Potts model, in the zero temperature limit, can be formulated through the motion of random walkers which either annihilate (A + A -> 0) or coalesce (A + A -> A) with a q-dependent probability. We consider all of the walkers in this model to be mutually infectious. Whenever two walkers meet, they experience mutual contamination. Walkers which avoid an encounter with another random walker up to time t remain uninfected. The fraction of uninfected walkers is investigated numerically and found to decay algebraically, U(t) \sim t^{-\phi(q)}, with a nontrivial exponent \phi(q). Our study is extended to include the coupled diffusion-limited reaction A+A -> B, B+B -> A in one dimension with equal initial densities of A and B particles. We find that the density of walkers decays in this model as \rho(t) \sim t^{-1/2}. The fraction of sites unvisited by either an A or a B particle is found to obey a power law, P(t) \sim t^{-\theta} with \theta \simeq 1.33. We discuss these exponents within the context of the q-state Potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as U(t) \sim t^{-\phi}, where \phi \simeq 1.13 when infection occurs between like particles only, and \phi \simeq 1.93 when we also include cross-species contamination.Comment: Expanded introduction with more discussion of related wor

Random Walks in Logarithmic and Power-Law Potentials, Nonuniversal Persistence, and Vortex Dynamics in the Two-Dimensional XY Model

The Langevin equation for a particle (`random walker') moving in d-dimensional space under an attractive central force, and driven by a Gaussian white noise, is considered for the case of a power-law force, F(r) = - Ar^{-sigma}. The `persistence probability', P_0(t), that the particle has not visited the origin up to time t, is calculated. For sigma > 1, the force is asymptotically irrelevant (with respect to the noise), and the asymptotics of P_0(t) are those of a free random walker. For sigma < 1, the noise is (dangerously) irrelevant and the asymptotics of P_0(t) can be extracted from a weak noise limit within a path-integral formalism. For the case sigma=1, corresponding to a logarithmic potential, the noise is exactly marginal. In this case, P_0(t) decays as a power-law, P_0(t) \sim t^{-theta}, with an exponent theta that depends continuously on the ratio of the strength of the potential to the strength of the noise. This case, with d=2, is relevant to the annihilation dynamics of a vortex-antivortex pair in the two-dimensional XY model. Although the noise is multiplicative in the latter case, the relevant Langevin equation can be transformed to the standard form discussed in the first part of the paper. The mean annihilation time for a pair initially separated by r is given by t(r) \sim r^2 ln(r/a) where a is a microscopic cut-off (the vortex core size). Implications for the nonequilibrium critical dynamics of the system are discussed and compared to numerical simulation results.Comment: 10 pages, 1 figur