Related papers: Simplicial complex entropy for time series analysi…

We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…

Discovering causal relations from observational time series without making the stationary assumption is a significant challenge. In practice, this challenge is common in many areas, such as retail sales, transportation systems, and medical…

When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real-world, we need a top-down approach to complexity. In this approach one may start with the desire to understand general…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

This paper proposes a new method for anomaly detection in time-series data by incorporating the concept of difference subspace into the singular spectrum analysis (SSA). The key idea is to monitor slight temporal variations of the…

We present a study of the equilibration process of nonequilibrium systems by means of molecular dynamics simulation technique. The nonequilibrium conditions are achieved in systems by defining velocity components of the constituent atoms…

We introduce a segmentation algorithm to probe temporal organization of heterogeneities in human heartbeat interval time series. We find that the lengths of segments with different local values of heart rates follow a power-law…

Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…

We consider continuum ensembles of linear time-invariant control systems with single inputs. A sparsity pattern is said to be structurally averaged controllability if it admits an averaged controllable linear ensemble system. We provide a…

The description of complex systems requires a progressively larger number of parameters. However, in practice, it often happens that a small subset of parameters suffices to describe the dynamics of the system itself: these combinations are…

Patients at high risk for sudden death often exhibit complex heart rhythms in which abnormal heartbeats are interspersed with normal heartbeats. We analyze such a complex rhythm in a single patient over a 12-hour period and show that the…

Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of…

Coarse-grained measurements offer a scalable alternative to full state tomography for characterizing complex quantum dynamics. We show that observational entropy (OE), an information-theoretic entropy defined directly from finite-resolution…

Active faults release elastic strain energy via a whole continuum of modes of slip, ranging from devastating earthquakes to Slow Slip Events and persistent creep. Understanding the mechanisms controlling the occurrence of rapid, dynamic…

Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…

We measure the influence of different time-scales on the dynamics of financial market data. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying…

Understanding causality is challenging and often complicated by changing causal relationships over time and across environments. Climate patterns, for example, shift over time with recurring seasonal trends, while also depending on…

Graph based entropy, an index of the diversity of events in their distribution to parts of a co-occurrence graph, is proposed for detecting signs of structural changes in the data that are informative in explaining latent dynamics of…

Shapelets are discriminative time series subsequences that allow generation of interpretable classification models, which provide faster and generally better classification than the nearest neighbor approach. However, the shapelet discovery…

We apply renormalized entropy as a complexity measure to the logistic and sine-circle maps. In the case of logistic map, renormalized entropy decreases (increases) until the accumulation point (after the accumulation point up to the most…