Noise has significant impact on nonlinear phenomena. Here we demonstrate that, in opposition to previous assumptions, additive noise interferes with the linear stability of scalar nonlinear systems when these are subject to time delay. We show this by performing a recently designed time-dependent delayed center manifold (DCM) reduction around a Hopf bifurcation in a model of nonlinear negative ...

We consider the problem of learning causal directed acyclic graphs from an observational joint distribution. One can use these graphs to predict the outcome of interventional experiments, from which data are often not available. We show that if the observational distribution follows a structural equation model with an additive noise structure, the directed acyclic graph becomes identifiable fro...

We apply a stochastic center manifold method to the calculation of noise-induced phase transitions in the stochastic Swift-Hohenberg equation. This analysis is applied to the reduced mode equations that result from Fourier decomposition of the field variable and of the temporal noise. The method shows a pitchfork bifurcation at lower perturbation order, but reveals a novel additive-noise-induce...

We provide sufficient conditions for synchronization by noise, i.e. under these conditions we prove that weak random attractors for random dynamical systems consist of single random points. In the case of SDE with additive noise, these conditions are also essentially necessary. In addition, we provide sufficient conditions for the existence of a minimal weak point random attractor consisting of...

The synchrony and variability of the coupled Langevin model subjected to spatially correlated additive and multiplicative noise are discussed. We have employed numerical simulations and the analytical augmented-moment method, which is the second-order moment method for local and global variables [H. Hasegawa, Phys. Rev. E 67, 041903 (2003)]. It has been shown that the synchrony of an ensemble i...

The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuous-valued data linear acyclic causal models with additive noise are often used because these models are well understood and there are well-known methods to fit them to data. In reality, of course, many causal relationships are more or less nonlinear, raising some doubts as ...

The process of information hiding is modeled in the context of additive noise. Under an independence assumption, the histogram of the stegomessage is a convolution of the noise probability mass function (PMF) and the original histogram. In the frequency domain this convolution is viewed as a multiplication of the histogram characteristic function (HCF) and the noise characteristic function. Lea...

We propose a method for inferring the existence of a latent common cause (“confounder”) of two observed random variables. The method assumes that the two effects of the confounder are (possibly nonlinear) functions of the confounder plus independent, additive noise. We discuss under which conditions the model is identifiable (up to an arbitrary reparameterization of the confounder) from the joi...