7,389 research outputs found
Optimal embedding parameters: A modelling paradigm
Reconstruction of a dynamical system from a time series requires the
selection of two parameters, the embedding dimension and the embedding
lag . Many competing criteria to select these parameters exist, and all
are heuristic. Within the context of modeling the evolution operator of the
underlying dynamical system, we show that one only need be concerned with the
product . We introduce an information theoretic criteria for the
optimal selection of the embedding window . For infinitely long
time series this method is equivalent to selecting the embedding lag that
minimises the nonlinear model prediction error. For short and noisy time series
we find that the results of this new algorithm are data dependent and superior
to estimation of embedding parameters with the standard techniques
Reconstructing dynamical networks via feature ranking
Empirical data on real complex systems are becoming increasingly available.
Parallel to this is the need for new methods of reconstructing (inferring) the
topology of networks from time-resolved observations of their node-dynamics.
The methods based on physical insights often rely on strong assumptions about
the properties and dynamics of the scrutinized network. Here, we use the
insights from machine learning to design a new method of network reconstruction
that essentially makes no such assumptions. Specifically, we interpret the
available trajectories (data) as features, and use two independent feature
ranking approaches -- Random forest and RReliefF -- to rank the importance of
each node for predicting the value of each other node, which yields the
reconstructed adjacency matrix. We show that our method is fairly robust to
coupling strength, system size, trajectory length and noise. We also find that
the reconstruction quality strongly depends on the dynamical regime
Nonlinear time-series analysis revisited
In 1980 and 1981, two pioneering papers laid the foundation for what became
known as nonlinear time-series analysis: the analysis of observed
data---typically univariate---via dynamical systems theory. Based on the
concept of state-space reconstruction, this set of methods allows us to compute
characteristic quantities such as Lyapunov exponents and fractal dimensions, to
predict the future course of the time series, and even to reconstruct the
equations of motion in some cases. In practice, however, there are a number of
issues that restrict the power of this approach: whether the signal accurately
and thoroughly samples the dynamics, for instance, and whether it contains
noise. Moreover, the numerical algorithms that we use to instantiate these
ideas are not perfect; they involve approximations, scale parameters, and
finite-precision arithmetic, among other things. Even so, nonlinear time-series
analysis has been used to great advantage on thousands of real and synthetic
data sets from a wide variety of systems ranging from roulette wheels to lasers
to the human heart. Even in cases where the data do not meet the mathematical
or algorithmic requirements to assure full topological conjugacy, the results
of nonlinear time-series analysis can be helpful in understanding,
characterizing, and predicting dynamical systems
Sensor Based on Extending the Concept of Fidelity to Classical Waves
We propose and demonstrate a remote sensor scheme by applying the quantum
mechanical concept of fidelity loss to classical waves. The sensor makes
explicit use of time-reversal invariance and spatial reciprocity in a wave
chaotic system to sensitively and remotely measure the presence of small
perturbations. The loss of fidelity is measured through a classical wave-analog
of the Loschmidt echo by employing a single-channel time-reversal mirror to
rebroadcast a probe signal into the perturbed system. We also introduce the use
of exponential amplification of the probe signal to partially overcome the
effects of propagation losses and to vary the sensitivity.Comment: 4 pages, 2 figure
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