Related papers: Random dynamical systems, entropies and informatio…

Here we define natural chaotic systems, like the earths weather and climate system, as chaotic systems which are open to the world so have constantly changing boundary conditions, and measurements of their states are subject to errors. In…

Algorithmic modeling relies on limited information in data to extrapolate outcomes for unseen scenarios, often embedding an element of arbitrariness in its decisions. A perspective on this arbitrariness that has recently gained interest is…

As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…

We explored the challenge of predicting and explaining the occurrence of events within sequences of data points. Our focus was particularly on scenarios in which unknown triggers causing the occurrence of events may consist of…

The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $\epsilon$…

A technique is introduced for estimating unknown parameters when time series of only one variable from a multivariate nonlinear dynamical system is given. The technique employs a combination of two different control methods, a linear…

Multiple metrics have been developed to detect causality relations between data describing the elements constituting complex systems, all of them considering their evolution through time. Here we propose a metric able to detect causality…

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…

Most research designing novel predictive models, or employing existing ones, assumes that training and testing data are independent and identically distributed. In practice, the data encountered at serving time often deviate from the…

Social robot navigation algorithms are often demonstrated in overly simplified scenarios, prohibiting the extraction of practical insights about their relevance to real-world domains. Our key insight is that an understanding of the inherent…

We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…

Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…

Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…

Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…

We define the notion of localizable property for a dynamical system. Then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the…

Here, we investigate the uncertainty of dynamical observables in classical systems manipulated by repeated measurements and feedback control; the precision should be enhanced in the presence of an external controller but limited by the…

We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions…

Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…

Reliable predictions from systems biology models require knowing whether parameters can be estimated from available data, and with what certainty. Identifiability analysis reveals whether parameters are learnable in principle (structural…