Related papers: Parameter-free quantification of stochastic and ch…
We introduce a novel notion of invariance feedback entropy to quantify the state information that is required by any controller that enforces a given subset of the state space to be invariant. We establish a number of elementary properties,…
Statistical parameters are used in finance, weather, industrial, science, among other vast number of different fields to draw conclusions. New more efficient selection methods are mandatory to analyses the huge amount of astronomical data.…
We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition…
The entanglement evolution after a quantum quench became one of the tools to distinguish integrable versus chaotic (non-integrable) quantum many-body dynamics. Following this line of thoughts, here we propose that the revivals in the…
Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…
By making use of the concept of natural time, a simple model is proposed which exhibits the $1/f^a$ behavior with $a$ close to unity. The properties of the model are compared to those of the Seismic Electric Signals (SES) activities that…
Identifying the start time of a sequence of symbols received at the receiver, commonly referred to as \emph{frame synchronization}, is a critical task for achieving good performance in digital communications systems employing…
In this work we address the statistical periodicity phenomenon on a coupled map lattice. The study was done based on the asymptotic binary patterns. The pattern multiplicity gives us the lattice information capacity, while the entropy rate…
We introduce a new logic called Signal Convolution Logic (SCL) that combines temporal logic with convolutional filters from digital signal processing. SCL enables to reason about the percentage of time a formula is satisfied in a bounded…
This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…
Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…
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 {\em stochastic maximal inequality} derived by using the formula for…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
In this technical note, a recursive set-membership filtering algorithm for discrete-time nonlinear dynamical systems subject to unknown but bounded process and measurement noises is proposed. The nonlinear dynamics is represented in a…
State space models contain time-indexed parameters, termed states, as well as static parameters, simply termed parameters. The problem of inferring both static parameters as well as states simultaneously, based on time-indexed observations,…
In this work we introduce a method for estimating entropy rate and entropy production rate from finite symbolic time series. From the point of view of statistics, estimating entropy from a finite series can be interpreted as a problem of…
The long-term mean-field dynamics of coupled underdamped Duffing oscillators driven by an external periodic signal with Gaussian noise is investigated. A Boltzmann-type H-theorem is proved for the associated nonlinear Fokker-Planck equation…
In this article we study a relatively novel way of constructing chaotic sequences of probability measures supported on Kac's sphere, which are obtained as the law of a vector of $N$ i.i.d. variables after it is rescaled to have unit average…
We address the problem of signal denoising and pattern recognition in processing batch-mode time-series data by combining linear time-invariant filters, orthogonal multiresolution representations, and sparsity-based methods. We propose a…
Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture.…