Escape from attracting sets in randomly perturbed systems

The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed to have Gaussian distribution. In this paper, we address the problem of escape induced by bounded noise. We show that the dynamics of escape from an attractor's basin is equivalent to that of a closed system with an appropriately chosen "hole". Using this equivalence, we show that there is a minimum noise amplitude above which escape takes place, and we derive analytical expressions for the scaling of the escape rate with noise amplitude near the escape transition. We verify our analytical predictions through numerical simulations of a two-dimensional map with noise.Comment: up to date with published versio

Output functions and fractal dimensions in dynamical systems

We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the Output Function Evaluation (OFE) method. The OFE method is based on an efficient scheme for computing output functions, such as the escape time, on a one-dimensional portion of the phase space. We show analytically that the OFE method is much more efficient than the uncertainty method for boundaries with $D<0.5$, where $D$ is the dimension of the intersection of the boundary with a one-dimensional manifold. We apply the OFE method to a scattering system, and compare it to the uncertainty method. We use the OFE method to study the behavior of the fractal dimension as the system's dynamics undergoes a topological transition.Comment: Uses REVTEX; to be published in Phys. Rev. Let

Signatures of fractal clustering of aerosols advected under gravity

Aerosols under chaotic advection often approach a strange attractor. They move chaotically on this fractal set but, in the presence of gravity, they have a net vertical motion downwards. In practical situations, observational data may be available only at a given level, for example at the ground level. We uncover two fractal signatures of chaotic advection of aerosols under the action of gravity. Each one enables the computation of the fractal dimension $D_{0}$ of the strange attractor governing the advection dynamics from data obtained solely at a given level. We illustrate our theoretical findings with a numerical experiment and discuss their possible relevance to meteorology.Comment: Accepted for publication in Phys. Rev. E (Rapid Communications

Integrated stress response of Escherichia coli to methylglyoxal : transcriptional readthrough from the nemRA operon enhances protection through increased expression of glyoxalase I

© 2013 The Authors. Molecular Microbiology published by John Wiley & Sons Ltd.Peer reviewedPublisher PD

Finite-dimensional representations of twisted hyper loop algebras

We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the classification of the irreducible modules, the definition of the universal highest-weight modules, called the Weyl modules, and, under a certain mild restriction on the characteristic of the ground field, a proof that the simple modules and the Weyl modules for the twisted hyper loop algebras are isomorphic to appropriate simple and Weyl modules for the non-twisted hyper loop algebras, respectively, via restriction of the action

Genetic diversity in a germplasm bank of Oenocarpus mapora (Arecaceae).

Oenocarpus mapora is an Amazonian palm species commonly used by native populations for food and in folk medicine. We measured genetic variability, using RAPD markers, of material kept in a germplasm bank composed of accessions sampled from the Brazilian Amazon. These included 74 individuals from 23 accessions sampled from 9 localities in three States of the Brazilian Amazon. Jaccard genetic similarities were calculated based on 137 polymorphic bands, amplified by 15 primers. Dendrograms constructed based on the genetic similarities among individuals and sample localities demonstrated genetic separation of Acre State from the States of Amazonas and Pará. Two models in three hierarchical levels were considered for AMOVA: one considering the grouping of sampling sites in each state, and the other considering sampling sites in each subgroup formed by the dendrograms. The first model showed no significant genetic variation among states. On the other hand, genetic variation among subgroups was significant. In this model, the within-sample-site genetic diversity was 47.15%, which is considered to be low, since O. mapora is allogamous. By means of Bayesian analysis, the sample sites were clustered into five groups, and their distribution was similar to what we found in the dendrograms based on genetic similarity