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This paper is devoted to change-point detection using only the ordinal structure of a time series. A statistic based on the conditional entropy of ordinal patterns characterizing the local up and down in a time series is introduced and…

The identification of predictive biomarkers from a large scale of covariates for subgroup analysis has attracted fundamental attention in medical research. In this article, we propose a generalized penalized regression method with a novel…

Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…

This article reports on a new approach to properly analyze time series of dynamical systems which are spoilt by the simultaneous presence of dynamical noise and measurement noise. It is shown that even strong external measurement noise as…

We developed a new approach for the analysis of physiological time series. An iterative convolution filter is used to decompose the time series into various components. Statistics of these components are extracted as features to…

In this paper, we provide an overview of the research conducted in the context of structural systems since the latest survey by Dion et al. in 2003. We systematically consider all the papers that cite this survey as well as the seminal work…

Several applications in time series forecasting require predicting multiple steps ahead. Despite the vast amount of literature in the topic, both classical and recent deep learning based approaches have mostly focused on minimising…

We propose a new sequential procedure to detect change in the parameters of a process $ X= (X_t)_{t\in \Z}$ belonging to a large class of causal models (such as AR($\infty$), ARCH($\infty$), TARCH($\infty$), ARMA-GARCH processes). The…

In sequential change detection, existing performance measures differ significantly in the way they treat the time of change. By modeling this quantity as a random time, we introduce a general framework capable of capturing and better…

Causal discovery is challenging in general dynamical systems because, without strong structural assumptions, the underlying causal graph may not be identifiable even from interventional data. However, many real-world systems exhibit…

We discuss issues of structural and practical identifiability of partially observed differential equations which are often applied in systems biology. The development of mathematical methods to investigate structural non-identifiability has…

In recent years, change point detection for high dimensional data has become increasingly important in many scientific fields. Most literature develop a variety of separate methods designed for specified models (e.g. mean shift model,…

Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…

Analyzing sequential data is crucial in many domains, particularly due to the abundance of data collected from the Internet of Things paradigm. Time series classification, the task of categorizing sequential data, has gained prominence,…

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very…

Given a multivariate big time series, can we detect anomalies as soon as they occur? Many existing works detect anomalies by learning how much a time series deviates away from what it should be in the reconstruction framework. However, most…

Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…

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…

This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…

This paper deals with analyzing structural breaks in the covariance operator of sequentially observed functional data. For this purpose, procedures are developed to segment an observed stretch of curves into periods for which second-order…