Related papers: Quantifying the irregularity of a time series
Cluster indices describe extremal behaviour of stationary time series. We consider runs estimators of cluster indices. Using a modern theory of multivariate, regularly varying time series, we obtain central limit theorems under conditions…
Granular simulations are used to probe the particle scale dynamics at short, intermediate, and long time scales for gravity driven, dense granular flows down an inclined plane. On approach to the angle of repose, where motion ceases, the…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
Resilience broadly describes a quality of withstanding perturbations. Measures of system resilience have gathered increasing attention across applied disciplines, yet existing metrics often lack computational accessibility and…
Network-theoretic tools contribute to understanding real-world system dynamics, e.g., in wildlife conservation, epidemics, and power outages. Network visualization helps illustrate structural heterogeneity; however, details about…
We propose a metric to characterize the complex behavior of a dynamical system and to distinguish between organized and disorganized complexity. The approach combines two quantities that separately assess the degree of unpredictability of…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
A stochastic model, the product of a circulant matrix and a random normal vector, is shown to produce an evolutive long memory time series with a power law spectral density. The distribution of the time series, a beta location scale family…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work…
Approaches for mapping time series to networks have become essential tools for dealing with the increasing challenges of characterizing data from complex systems. Among the different algorithms, the recently proposed ordinal networks stand…
Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be…
The recently introduced concept of dynamic communicability is a valuable tool for ranking the importance of nodes in a temporal network. Two metrics, broadcast score and receive score, were introduced to measure the centrality of a node…
When the discrete time-translation symmetry of isolated, periodically driven systems is spontaneously broken, a new phase of matter can emerge. We review some recent developments on both the theoretical underpinnings and experimental…
In temporal planning, many different temporal network formalisms are used to model real world situations. Each of these formalisms has different features which affect how easy it is to determine whether the underlying network of temporal…
Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning…
Distinguishing cause from effect is a scientific challenge resisting solutions from mathematics, statistics, information theory and computer science. Compression-Complexity Causality (CCC) is a recently proposed interventional measure of…
The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval),…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
Critical phase transitions have proven to be a powerful concept to capture the phenomenology of many systems, including deeply non-equilibrium ones like living systems. The study of these phase transitions has overwhelmingly relied on…