Related papers: Divergence Measure Between Chaotic Attractors
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean…
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
Hierarchy of one-parameter families of chaotic maps with an invariant measure have been introduced, where their appropriate coupling has lead to the generation of some coupled chaotic maps with an invariant measure. It is shown that these…
A well-interpretable measure of information has been recently proposed based on a partition obtained by intersecting a random sequence with its moving average. The partition yields disjoint sets of the sequence, which are then ranked…
Anomalies are strange data points; they usually represent an unusual occurrence. Anomaly detection is presented from the perspective of Wireless sensor networks. Different approaches have been taken in the past, as we will see, not only to…
This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged "statistical"…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…
We show that, in periodically perturbed chaotic systems, Phase Synchronization appears, associated to a special type of stroboscopic map, in which not only averages quantities are equal to invariants of the perturbation, the angular…
After Boltzmann and Gibbs, the notion of disorder in statistical physics relates to ensembles, not to individual states. This disorder is measured by the logarithm of ensemble volume, the entropy. But recent results about measure…
We are interested in time series of the form $y_{n} = x_{n} + \xi_{n}$ where ${x_{n}}$ is generated by a chaotic dynamical system and where $\xi_{n}$ models observational noise. Using concentration inequalities, we derive fluctuation bounds…
The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically…
Interferometric photon-correlation measurements, which correspond to the second-order intensity cross-correlations between the two output ports of an unbalanced Michelson interferometer, are sensitive to both amplitude and phase…
Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a non-chaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped…
Chirality refers to the property that an object and its mirror image cannot overlap each other by spatial rotation and translation, and can be found in various research fields. We here propose chiral chaos and construct a chiral chaotic…
We exhibit a class of singularly perturbed parabolic problems which the asymptotic behavior can be described by a system of ordinary differential equation. We estimate the convergence of attractors in the Hausdorff metric by rate of…
We propose a new method to define anomaly scores and apply this to particle physics collider events. Anomalies can be either rare, meaning that these events are a minority in the normal dataset, or different, meaning they have values that…
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum…
Information theoretic quantities play an important role in various settings in machine learning, including causality testing, structure inference in graphical models, time-series problems, feature selection as well as in providing privacy…
A new description of strange attractor systems through three geometrical and dynamical invariants is provided. They are the correlation dimension ($\mathcal{D}$) and the correlation entropy ($\mathcal{K}$), both having attracted attention…