Related papers: Quantifying the irregularity of a time series
We study the topology of circularly ordered sets. While the algebraic notion is classical, the general topological theory has received comparatively little attention. In this work we provide a self-contained topological exposition and…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix calculated from time series with the adjacency matrix of a complex network, and apply measures for the characterisation of…
Recurrence plot based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the…
Time series classification (TSC) of biological signals has progressed from handcrafted, modality-specific approaches to deep architectures capable of representing the diverse waveform structures of underlying physiological processes (i.e.,…
Cellular phones are now offering an ubiquitous means for scientists to observe life: how people act, move and respond to external influences. They can be utilized as measurement devices of individual persons and for groups of people of the…
Dynamical processes on time-varying complex networks are key to understanding and modeling a broad variety of processes in socio-technical systems. Here we focus on empirical temporal networks of human proximity and we aim at understanding…
The understanding of complex systems has become a central issue because complex systems exist in a wide range of scientific disciplines. Time series are typical experimental results we have about complex systems. In the analysis of such…
The analysis of temporal networks heavily depends on the analysis of time-respecting paths. However, before being able to model and analyze the time-respecting paths, we have to infer the timescales at which the temporal edges influence…
Irregularly sampled multivariate time series are ubiquitous in various fields, particularly in healthcare, and exhibit two key characteristics: intra-series irregularity and inter-series discrepancy. Intra-series irregularity refers to the…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
Causal discovery problems use a set of observations to deduce causality between variables in the real world, typically to answer questions about biological or physical systems. These observations are often recorded at regular time…
Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates…
A notion of time is fundamental in the study of dynamical systems. Time arises as a standalone dynamical system and also in solutions or trajectories as a special kind of map between systems. We characterize time by a universal property and…
Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and…
The creativity and emergence of biological and psychological behavior are nonlinear. However, that does not necessarily mean only that the measurements of the behaviors are curvilinear. Furthermore, the linear model might fail to reduce…
Modeling biological rhythms helps understand the complex principles behind the physical and psychological abnormalities of human bodies, to plan life schedules, and avoid persisting fatigue and mood and sleep alterations due to the…
Characteristic formulae give a complete logical description of the behaviour of processes modulo some chosen notion of behavioural semantics. They allow one to reduce equivalence or preorder checking to model checking, and are exactly the…
In the prediction of oscillating time series, the interest is in the turning points of successive oscillations rather than the samples themselves. For this purpose a scheme has been proposed; the state space reconstruction is limited to the…
A finite-time singularity accompanied by log-periodic oscillations shaped the war dynamics and development of the International System during the period 1495 - 1945. The identification of this singularity provides us with a perspective to…