3,164 research outputs found
Synchronization of spatio-temporal chaos as an absorbing phase transition: a study in 2+1 dimensions
The synchronization transition between two coupled replicas of
spatio-temporal chaotic systems in 2+1 dimensions is studied as a phase
transition into an absorbing state - the synchronized state. Confirming the
scenario drawn in 1+1 dimensional systems, the transition is found to belong to
two different universality classes - Multiplicative Noise (MN) and Directed
Percolation (DP) - depending on the linear or nonlinear character of damage
spreading occurring in the coupled systems. By comparing coupled map lattice
with two different stochastic models, accurate numerical estimates for MN in
2+1 dimensions are obtained. Finally, aiming to pave the way for future
experimental studies, slightly non-identical replicas have been considered. It
is shown that the presence of small differences between the dynamics of the two
replicas acts as an external field in the context of absorbing phase
transitions, and can be characterized in terms of a suitable critical exponent.Comment: Submitted to Journal of Statistical Mechanics: Theory and Experimen
Adaptive unknonwn-input observers-based synchronization of chaotic circuits for secure telecommunication
International audienceWe propose a robust adaptive chaotic synchronization method based on unknown-input observers for master-slave syn- chronization of chaotic systems, with application to secured com- munication. The slave system is modelled by an unknown input observer in which, the unknown input is the transmitted informa- tion. As in the general observer-based synchronization paradigm, the information is recovered if the master and slave systems ro- bustly synchronize. In the context of unknown-input observers, this is tantamount to estimating the master's states and the unknown inputs. The set-up also considers the presence of perturbations in the chaotic transmitter dynamics and in the output equations (the transmitted signal). That is, the estimator (slave system) must syn- chronize albeit noisy measurements and reject the effect of pertur- bations on the transmitter dynamics. We provide necessary and sufficient conditions for synchronization to take place. To highlight our contribution, we also present some simulation results with the purpose of comparing the proposed method to classical adaptive observer-based synchronization (without disturbance rejection). It is shown that additive noise is perfectly canceled and the encoded message is well recovered despite the perturbations
KalmanNet:Neural Network Aided Kalman Filtering for Partially Known Dynamics
Real-time state estimation of dynamical systems is a fundamental task in signal processing and control. For systems that are well-represented by a fully known linear Gaussian state space (SS) model, the celebrated Kalman filter (KF) is a low complexity optimal solution. However, both linearity of the underlying SS model and accurate knowledge of it are often not encountered in practice. Here, we present KalmanNet, a real-time state estimator that learns from data to carry out Kalman filtering under non-linear dynamics with partial information. By incorporating the structural SS model with a dedicated recurrent neural network module in the flow of the KF, we retain data efficiency and interpretability of the classic algorithm while implicitly learning complex dynamics from data. We numerically demonstrate that KalmanNet overcomes nonlinearities and model mismatch, outperforming classic filtering methods operating with both mismatched and accurate domain knowledge.</p
The power spectrum of systematics in cosmic shear tomography and the bias on cosmological parameters
Cosmic shear tomography has emerged as one of the most promising tools to
both investigate the nature of dark energy and discriminate between General
Relativity and modified gravity theories. In order to successfully achieve
these goals, systematics in shear measurements have to be taken into account;
their impact on the weak lensing power spectrum has to be carefully
investigated in order to estimate the bias induced on the inferred cosmological
parameters. To this end, we develop here an efficient tool to compute the power
spectrum of systematics by propagating, in a realistic way, shear measurement,
source properties and survey setup uncertainties. Starting from analytical
results for unweighted moments and general assumptions on the relation between
measured and actual shear, we derive analytical expressions for the
multiplicative and additive bias, showing how these terms depend not only on
the shape measurement errors, but also on the properties of the source galaxies
(namely, size, magnitude and spectral energy distribution). We are then able to
compute the amplitude of the systematics power spectrum and its scaling with
redshift, while we propose a multigaussian expansion to model in a
non-parametric way its angular scale dependence. Our method allows to
self-consistently propagate the systematics uncertainties to the finally
observed shear power spectrum, thus allowing us to quantify the departures from
the actual spectrum. We show that even a modest level of systematics can induce
non-negligible deviations, thus leading to a significant bias on the recovered
cosmological parameters.Comment: 19 pages, 5 tables, 4 figure
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