Related papers: Parameter-free quantification of stochastic and ch…
One of the central problems in many-body physics, both classical and quantum, is the relations between different notions of chaos. Ergodicity, mixing, operator growth, the eigenstate thermalization hypothesis, and spectral chaos are defined…
This study addresses the problem of learning a summary causal graph on time series with potentially different sampling rates. To do so, we first propose a new causal temporal mutual information measure for time series. We then show how this…
The analysis of chaotic signals with time-frequency methods is considered. For this purpose, two new transformations are presented which consist in the decomposition of a signal onto an orthogonal set of respectively linear and hyperbolic…
Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of…
We propose a novel data-driven stochastic model predictive control framework for uncertain linear systems with noisy output measurements. Our approach leverages multi-step predictors to efficiently propagate uncertainty, ensuring chance…
For random matrix models, the parameter estimation based on the traditional likelihood functions is not straightforward in particular when we have only one sample matrix. We introduce a new parameter optimization method for random matrix…
It has recently been observed that a stochastic (infinite degree of freedom) time series with a $1/f^\alpha$ power spectrum can exhibit a finite correlation dimension, even for arbitrarily large data sets. [A.R. Osborne and A.~Provenzale,…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
Recurrence plots were introduced to help aid the detection of signals in complicated data series. This effort was furthered by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence…
Recurrent temporal dynamics is a phenomenon observed frequently in high-dimensional complex systems and its detection is a challenging task. Recurrence quantification analysis utilizing recurrence plots may extract such dynamics, however it…
We focus on a linear chain of $N$ first-neighbor-coupled logistic maps at their edge of chaos in the presence of a common noise. This model, characterised by the coupling strength $\epsilon$ and the noise width $\sigma_{max}$, was recently…
Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy system, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values.…
We study, using information quantifiers, the dynamics generated by a special Hamiltonian that gives a detailed account of the interaction between a classical and a quantum system. The associated, very rich dynamics displays periodicity,…
A classical dynamical system can be viewed as a probability space equipped with a measure-preserving time evolution map, admitting a purely algebraic formulation in terms of the algebra of bounded functions on the phase space. Similarly, a…
Symbolic relative entropy, an efficient nonlinear complexity parameter measuring probabilistic divergences of symbolic sequences, is proposed in our nonlinear dynamics analysis of heart rates considering equal states. Equalities are not…
The paper is devoted to synthesis of recurrent algorithms for detection of stochastic signals given in state space. The structure of the algorithms synthesized is shown to be close to that of the Kalman filter. Analysis of one of the…
We consider an agent trying to bring a system to an acceptable state by repeated probabilistic action. Several recent works on algorithmizations of the Lovasz Local Lemma (LLL) can be seen as establishing sufficient conditions for the agent…
We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using It\^o's formula and on a new…
We consider state and parameter estimation for a dynamical system having both time-varying and time-invariant parameters. It has been shown that the robustness of the Markov Chain Monte Carlo (MCMC) algorithm for estimating time-invariant…