Stochastic Sensitivity Analysis of Volcanic Activity

In the present paper, we study the stochastically induced behavior of a nonlinear volcanic model containing three prognostic variables: the plug velocity u, the pressure p under the plug, and the conduit volume V. The nouvelle phenomena of noise-induced transitions from the equilibrium to the cycle in the bistability parametric zone and noise-induced excitement with the generation of spike oscillations in the monostability zone are found in the presence of N-shaped friction force. To study these phenomena numerically, we used the computations of random solutions, the phase trajectories and time series, the statistics of interspike intervals, and the mean square variations. To study these phenomena analytically, we applied the stochastic sensitivity function technique and the confidence domains method. This approach is used to predict the noise-induced transition from a “dormant volcano” state to the “active volcano” mode. From the physical point of view, the volcano is capable to become active under the influence of external noises in the friction force, which model various compositions and properties of volcanic rocks. What is more, the volcanic plug can pop out when its slipping becomes heavy, and the volcano can erupt. © 2020 John Wiley & Sons, Ltd.This work was supported by the Ministry of Science and Higher Education of the Russian Federation (project number FEUZ‐2020‐0057)

Generalized empty-interval method applied to a class of one-dimensional stochastic models

In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models which cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called {\it interparticle distribution function} (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model which cannot be solved directly by the conventional IPDF method and which can be viewed as a generalization of the {\it voter} model and/or as an {\it epidemic} model. We also consider the {\it reversible} diffusion-coagulation model with input of particles and determine other reaction-diffusion models which can be mapped onto the latter via suitable {\it similarity transformations}. Finally we study the problem of the propagation of a wave-front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.Comment: 19 pages, no figure. To appear in Physical Review E (November 2001

The molecular function and clinical phenotype of partial deletions of the IGF2/H19 imprinting control region depends on the spatial arrangement of the remaining CTCF binding sites

At chromosome 11p15.5, the imprinting centre 1 (IC1) controls the parent of origin-specific expression of the IGF2 and H19 genes. The 5 kb IC1 region contains multiple target sites (CTS) for the zinc-finger protein CTCF, whose binding on the maternal chromosome prevents the activation of IGF2 and allows that of H19 by common enhancers. CTCF binding helps maintaining the maternal IC1 methylation-free, whereas on the paternal chromosome gamete-inherited DNA methylation inhibits CTCF interaction and enhancer-blocking activity resulting in IGF2 activation and H19 silencing. Maternally inherited 1.4-2.2 kb deletions are associated with methylation of the residual CTSs and Beckwith-Wiedemann syndrome, although with different penetrance and expressivity. We explored the relationship between IC1 microdeletions and phenotype by analysing a number of previously described and novel mutant alleles. We used a highly quantitative assay based on next generation sequencing to measure DNA methylation in affected families and analysed enhancer-blocking activity and CTCF binding in cultured cells. We demonstrate that the microdeletions mostly affect IC1 function and CTCF binding by changing CTS spacing. Thus, the extent of IC1 inactivation and the clinical phenotype are influenced by the arrangement of the residual CTSs. A CTS spacing similar to the wild-type allele results in moderate IC1 inactivation and is associated with stochastic DNA methylation of the maternal IC1 and incomplete penetrance. Microdeletions with different CTS spacing display severe IC1 inactivation and are associated with IC1 hypermethylation and complete penetrance. Careful characterization of the IC1 microdeletions is therefore needed to predict recurrence risks and phenotypical outcomes. © The Author 2012. Published by Oxford University Press