Comment on "Influence of Noise on Force Measurements"

In a recent Letter [arXiv:1004.0874], Volpe et al. describe experiments on a colloidal particle near a wall in the presence of a gravitational field for which they study the influence of noise on the measurement of force. Their central result is a striking discrepancy between the forces derived from experimental drift measurements via their Eq. (1), and from the equilibrium distribution. From this discrepancy they infer the stochastic calculus realised in the system. We comment, however: (a) that Eq. (1) does not hold for space-dependent diffusion, and corrections should be introduced; and (b) that the "force" derived from the drift need not coincide with the "force" obtained from the equilibrium distribution.Comment: Comment submitted to a PRL letter; 1 page, 1 figur

Changes in the dynamical behavior of nonlinear systems induced by noise.

Weak noise acting upon a nonlinear dynamical system can have far-reaching consequences. The fundamental underlying problem - that of large deviations of a nonlinear system away from a stable or metastable state, sometimes resulting in a transition to a new stationary state, in response to weak additive or multiplicative noise - has long attracted the attention of physicists. This is partly because of its wide applicability, and partly because it bears on the origins of temporal irreversibility in physical processes. During the last few years it has become apparent that, in a system far from thermal equilibrium, even small noise can also result in qualitative change in the system's properties, e.g., the transformation of an unstable equilibrium state into a stable one, and vice versa, the occurrence of multistability and multimodality, the appearance of a mean field, the excitation of noise-induced oscillations, and noise-induced transport (stochastic ratchets). A representative selection of such phenomena is discussed and analyzed, and recent progress made towards their understanding is reviewed

Competition between noise and coupling in the induction of synchronisation.

We apply a Fokker-Planck analysis to investigate the relative influences of coupling strength and noise on the synchronisation of two phase oscillators. We go beyond earlier studies of noise-induced synchronisation (without couplings) and coupling-induced synchronisation (without common noise) to consider both effects together, and we obtain a result that is very different from a straightforward superposition of the effects of each agent acting alone: two regimes are possible depending on which agent is inducing the synchronisation. In each regime, one agent induces and the other hinders the synchronisation. In particular we show that, counterintuitively, coupling can sometimes inhibit synchronisation

Self-consistent analytic solution for the current and the access resistance in open ion channels.

A self-consistent analytic approach is introduced for the estimation of the access resistance and the current through an open ion channel for an arbitrary number of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved analytically in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved analytically in a one-dimensional approximation. An iterative procedure is used to match the two solutions together at the channel mouth in a self-consistent way. It is shown that the currentvoltage characteristics obtained are in good quantitative agreement with experimental measurements

Probit models for capture-recapture data subject to imperfect detection, individual heterogeneity and misidentification

As noninvasive sampling techniques for animal populations have become more popular, there has been increasing interest in the development of capture-recapture models that can accommodate both imperfect detection and misidentification of individuals (e.g., due to genotyping error). However, current methods do not allow for individual variation in parameters, such as detection or survival probability. Here we develop misidentification models for capture-recapture data that can simultaneously account for temporal variation, behavioral effects and individual heterogeneity in parameters. To facilitate Bayesian inference using our approach, we extend standard probit regression techniques to latent multinomial models where the dimension and zeros of the response cannot be observed. We also present a novel Metropolis-Hastings within Gibbs algorithm for fitting these models using Markov chain Monte Carlo. Using closed population abundance models for illustration, we re-visit a DNA capture-recapture population study of black bears in Michigan, USA and find evidence of misidentification due to genotyping error, as well as temporal, behavioral and individual variation in detection probability. We also estimate a salamander population of known size from laboratory experiments evaluating the effectiveness of a marking technique commonly used for amphibians and fish. Our model was able to reliably estimate the size of this population and provided evidence of individual heterogeneity in misidentification probability that is attributable to variable mark quality. Our approach is more computationally demanding than previously proposed methods, but it provides the flexibility necessary for a much broader suite of models to be explored while properly accounting for uncertainty introduced by misidentification and imperfect detection. In the absence of misidentification, our probit formulation also provides a convenient and efficient Gibbs sampler for Bayesian analysis of traditional closed population capture-recapture data.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS783 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths

We consider the Kuramoto model of an ensemble of interacting oscillators allowing for an arbitrary distribution of frequencies and coupling strengths. We define a family of traveling wave states as stationary in a rotating frame, and derive general equations for their parameters. We suggest empirical stability conditions which, for the case of incoherence, become exact. In addition to making new theoretical predictions, we show that many earlier results follow naturally from our general framework. The results are applicable in scientific contexts ranging from physics to biology.Comment: 5 pages, 1 figur

Enlargement of a low-dimensional stochastic web

We consider an archetypal example of a low-dimensional stochastic web, arising in a 1D oscillator driven by a plane wave of a frequency equal or close to a multiple of the oscillator’s natural frequency. We show that the web can be greatly enlarged by the introduction of a slow, very weak, modulation of the wave angle. Generalizations are discussed. An application to electron transport in a nanometre-scale semiconductor superlattice in electric and magnetic fields is suggested