8,256 research outputs found
Spatial pattern formation induced by Gaussian white noise
The ability of Gaussian noise to induce ordered states in dynamical systems
is here presented in an overview of the main stochastic mechanisms able to
generate spatial patterns. These mechanisms involve: (i) a deterministic local
dynamics term, accounting for the local rate of variation of the field
variable, (ii) a noise component (additive or multiplicative) accounting for
the unavoidable environmental disturbances, and (iii) a linear spatial coupling
component, which provides spatial coherence and takes into account diffusion
mechanisms. We investigate these dynamics using analytical tools, such as
mean-field theory, linear stability analysis and structure function analysis,
and use numerical simulations to confirm these analytical results.Comment: 11 pages, 8 figure
Stable and fast semi-implicit integration of the stochastic Landau-Lifshitz equation
We propose new semi-implicit numerical methods for the integration of the
stochastic Landau-Lifshitz equation with built-in angular momentum
conservation. The performance of the proposed integrators is tested on the 1D
Heisenberg chain. For this system, our schemes show better stability properties
and allow us to use considerably larger time steps than standard explicit
methods. At the same time, these semi-implicit schemes are also of comparable
accuracy to and computationally much cheaper than the standard midpoint
implicit method. The results are of key importance for atomistic spin dynamics
simulations and the study of spin dynamics beyond the macro spin approximation.Comment: 24 pages, 5 figure
Invariant Causal Prediction for Nonlinear Models
An important problem in many domains is to predict how a system will respond
to interventions. This task is inherently linked to estimating the system's
underlying causal structure. To this end, Invariant Causal Prediction (ICP)
(Peters et al., 2016) has been proposed which learns a causal model exploiting
the invariance of causal relations using data from different environments. When
considering linear models, the implementation of ICP is relatively
straightforward. However, the nonlinear case is more challenging due to the
difficulty of performing nonparametric tests for conditional independence. In
this work, we present and evaluate an array of methods for nonlinear and
nonparametric versions of ICP for learning the causal parents of given target
variables. We find that an approach which first fits a nonlinear model with
data pooled over all environments and then tests for differences between the
residual distributions across environments is quite robust across a large
variety of simulation settings. We call this procedure "invariant residual
distribution test". In general, we observe that the performance of all
approaches is critically dependent on the true (unknown) causal structure and
it becomes challenging to achieve high power if the parental set includes more
than two variables. As a real-world example, we consider fertility rate
modelling which is central to world population projections. We explore
predicting the effect of hypothetical interventions using the accepted models
from nonlinear ICP. The results reaffirm the previously observed central causal
role of child mortality rates
Removing systematic errors for exoplanet search via latent causes
We describe a method for removing the effect of confounders in order to
reconstruct a latent quantity of interest. The method, referred to as
half-sibling regression, is inspired by recent work in causal inference using
additive noise models. We provide a theoretical justification and illustrate
the potential of the method in a challenging astronomy application.Comment: Extended version of a paper appearing in the Proceedings of the 32nd
International Conference on Machine Learning, Lille, France, 201
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