Related papers: Information directionality in coupled time series …
We present a methodology to characterize synchronization in time series based on symbolic representations. A symbol is linked to a sequence of numbers through the rank-order of its values. A representation of a time series results after…
The concept of transcripts was introduced in 2009 as a means to characterize various aspects of the functional relationship between time series of interacting systems. Based on this concept that utilizes algebraic relations between ordinal…
Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…
The coupling complexity index is an information measure introduced within the framework of ordinal symbolic dynamics. This index is used to characterize the complexity of the relationship between dynamical system components. In this work,…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
The use of ordinal patterns (OPs) for analyzing the dependence structure of univariate and continuously distributed processes has gained popularity in recent years. This research goes one step further and considers the transcripts being…
Measures of information transfer have become a popular approach to analyze interactions in complex systems such as the Earth or the human brain from measured time series. Recent work has focused on causal definitions of information transfer…
Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the…
Algebraic representations of time series are symbolic representations whose symbols belong to a finite group. Precisely, the framework of the present paper is the analysis of coupled time series in algebraic representations and, more…
Temporal information conveyed by language describes how the world around us changes through time. Events, durations and times are all temporal elements that can be viewed as intervals. These intervals are sometimes temporally related in…
The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of…
We introduce Ordinal Synchronization ($OS$) as a new measure to quantify synchronization between dynamical systems. $OS$ is calculated from the extraction of the ordinal patterns related to two time series, their transformation into…
We describe and analyze different approaches to represent ordinal patterns. All of these can be found in the literature. The most important representations (plus sub-classes) are compared in terms of their applicability from different…
We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition…
We propose a straightforward extension of symbolic transfer entropy to enable the investigation of delayed directional relationships between coupled dynamical systems from time series. Analyzing time series from chaotic model systems, we…
Information flow or information transfer is an important concept in dynamical systems which has applications in a wide variety of scientific disciplines. In this study, we show that a rigorous formalism can be established in the context of…
We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…
We introduce a new methodology to analyze the evolution of epidemic time series, which is based on the construction of epidemic networks. First, we translate the time series into ordinal patterns containing information about local…
Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a…
The analysis of GPS trajectories is a well-studied problem in Urban Computing and has been used to track people. Analyzing people mobility and identifying the transportation mode used by them is essential for cities that want to reduce…