Related papers: The Reversibility Error Method (REM): a new, dynam…

In this review, we present a survey of the Lyapunov Error and Reversibility Error (\cite{Faranda2012}), and we propose a generalization to make them invariant to the choice of initial conditions. We first define a process as the evolution…

We use the Reversibility Error Method and the Fidelity to analyze the global effects of a small perturbation in a non-integrable system. Both methods have already been proposed and used in the literature but the aim of this paper is to…

We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity…

The Maximum Eccentricity Method (MEM) is a standard tool for the analysis of planetary systems and their stability. The method amounts to estimating the maximal stretch of orbits over sampled domains of initial conditions. The present paper…

This paper studies multistep methods for the integration of reversible dynamical systems, with particular emphasis on the planar Kepler problem. It has previously been shown by Cano & Sanz-Serna that reversible linear multisteps for…

This study applied machine learning models to estimate stellar rotation periods from corrected light curve data obtained by the NASA Kepler mission. Traditional methods often struggle to estimate rotation periods accurately due to noise and…

We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…

We consider a class of systems with time-varying parameters, which are written as linear regressions with bounded disturbances. The task is to estimate such parameters under the condition that the regressor is finitely exciting (FE).…

The NMR technique allows one to create a non-equilibrium local polarization and to detect its later evolution. By a change of the sign of the effective dipolar Hamiltonian, the apparently diffusive dynamics is reverted, generating a…

Space missions have discovered a large number of exoplanets evolving in (or close to) mean-motion resonances (MMRs) and resonant chains. Often, the published data exhibit very high uncertainties due to the observational limitations that…

Given that secular perturbations in a binary system not only excite high orbital eccentricities but also alter the planetary orbital inclination, the classical Keplerian orbital model is no longer applicable for orbital retrieval. The…

Analyses in high energy physics aim to put the Standard Model---the commonly accepted theory---to test. For convincing conclusions, analysis methods are needed which offer an unambiguous comparison between data and theory while allowing…

The ground truth for cascading failure in power system can only be obtained through a detailed dynamic model involving nonlinear differential and algebraic equations whose solution process is computationally expensive. This has prohibited…

Several phenomena are available representing market activity: volumes, number of trades, durations between trades or quotes, volatility - however measured - all share the feature to be represented as positive valued time series. When…

Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for…

Discovering governing equations that describe complex chaotic systems remains a fundamental challenge in physics and neuroscience. Here, we introduce the PEM-UDE method, which combines the prediction-error method with universal differential…

Pel-recursive motion estimation isa well-established approach. However, in the presence of noise, it becomes an ill-posed problem that requires regularization. In this paper, motion vectors are estimated in an iterative fashion by means of…

Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a mean-motion resonance (MMR),…

Extreme learning machine (ELM) as an emerging branch of shallow networks has shown its excellent generalization and fast learning speed. However, for blended data, the robustness of ELM is weak because its weights and biases of hidden nodes…

In this paper we consider trajectory tracking problem for robotic systems affected by unknown external perturbations. Considering possible solutions, we restrict our attention to composite adaptation, which, particularly, ensures parametric…