Related papers: Conditional mixing in deterministic chaos
We propose a stochastic model predictive control (MPC) framework for linear systems subject to joint-in-time chance constraints under unknown disturbance distributions. Unlike existing approaches that rely on parametric or Gaussian…
Assessing the synergistic high-order behaviors (HOBs) that emerge from underlying structural mechanisms is crucial to characterize complex systems. This work leverages the combined use of predictability and information measures to detect…
We consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long…
Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control…
All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…
Science and technology have a growing need for effective mechanisms that ensure reliable, controlled performance from black-box machine learning algorithms. These performance guarantees should ideally hold conditionally on the input-that is…
Restarting a stochastic search process can accelerate its completion by providing an opportunity to take a more favorable path with each reset. This strategy, known as stochastic resetting, is well studied in random processes. Here, we…
An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully…
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependance on initial conditions (SDIC). Unfortunately, numerical noises (such as truncation error and round-off error)…
The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally…
Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all space-time…
In this paper we apply the techniques of symbolic dynamics to the analysis of a labor market which shows large volatility in employment flows. In a recent paper, Bhattacharya and Bunzel \cite{BB} have found that the discrete time version of…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…
This work describes the way that topological mixing and chaos in continua, as induced by discrete dynamical systems, can or can't be understood through topological conjugacy with symbolic dynamical systems. For example, there is no symbolic…