Related papers: Parameter-free quantification of stochastic and ch…
There exist extensive studies on periodic and random perturbations of various continuous maps investigating their dynamics. This paper presents a random piecewise smooth map derived from a simple inductor-less switching circuit. The…
A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…
In this paper we suggest a new algorithm for determination of signal-to-noise ratio (SNR). SNR is a quantitative measure widely used in science and engineering. Generally, methods for determination of SNR are based on using of…
Controller synthesis for hybrid systems that satisfy temporal specifications expressing various system properties is a challenging problem that has drawn the attention of many researchers. However, making the assumption that such temporal…
Recent advances in stochastic differential equations (SDEs) have enabled robust modeling of real-world dynamical processes across diverse domains, such as finance, health, and systems biology. However, parameter estimation for SDEs…
In many stochastic dynamical systems, ordinary chaotic behavior is preceded by a full-dimensional phase that exhibits 1/f-type power-spectra and/or scale-free statistics of (anti)instantons such as neuroavalanches, earthquakes, etc. In…
The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…
Most of physical experiments are usually described as repeated measurements of some random variables. The experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared…
In this paper we employ methods from Statistical Mechanics to model temporal correlations in time series. We put forward a methodology based on the Maximum Entropy principle to generate ensembles of time series constrained to preserve part…
Due to the regularization effect of the stochastic noise, the quantitative entropy-cost type propagation of chaos for mean field interacting particle system is proposed. The result shows that the Kac's chaotic property measured in relative…
We compute the asymptotic temporal behavior of the dynamical complexity associated with the maximum probability trajectories on Gaussian statistical manifolds in presence of correlations between the variables labeling the macrostates of the…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
Periodic recurrence is a prominent behavioural of many biological phenomena, including cell cycle and circadian rhythms. Although deterministic models are commonly used to represent the dynamics of periodic phenomena, it is known that they…
In this paper, we show that the recent integration of statistical models with deep recurrent neural networks provides a new way of formulating volatility (the degree of variation of time series) models that have been widely used in time…
Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…
Conditional differential entropy provides an intuitive measure for relatively ranking time-series complexity by quantifying uncertainty in future observations given past context. However, its direct computation for high-dimensional…
Time-varying non-Euclidean random objects are playing a growing role in modern data analysis, and periodicity is a fundamental characteristic of time-varying data. However, quantifying periodicity in general non-Euclidean random objects…
We study a new class of chaotic systems with dynamical localization, where gain or loss mechanisms break the Hermiticity, while allowing for parity-time (PT) symmetry. For a value \gamma_PT of the gain or loss parameter the spectrum…
This work is inspired by a recent study of a two-dimensional stochastic fragmentation model. We show that the configurational entropy of this model exhibits log-periodic oscillations as a function of the sample size, by exploiting an exact…
A new method is introduced to obtain a strong signal by the interference of weak signals in noisy channels. The method is based on the interference of 1/f noise from parallel channels. One realization of stochastic interference is the…