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Feedback control (based on the quantum continuous measurement) of quantum systems inevitably suffers from estimation delays. In this paper we give a delay-dependent stability criterion for a wide class of nonlinear stochastic systems…
Four different Granger causality-based methods - one linear and three nonlinear (Granger Causality, Kernel Granger Causality, large-scale Nonlinear Granger Causality, and Neural Network Granger Causality) were used for assessment and…
Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions…
In this letter we discuss use of Granger causality to the analyze systems of coupled circular variables, by modifying a recently proposed method for multivariate analysis of causality. We show the application of the proposed approach on…
That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger causality, which allows us to more reliably and…
Language Models (LMs) have shown promising performance in natural language generation. However, as LMs often generate incorrect or hallucinated responses, it is crucial to correctly quantify their uncertainty in responding to given inputs.…
Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this…
We analyze a neural system which mimics a sensorial cortex, with different input characteristics, in presence of transmission delays. We propose a new measure to characterize collective behavior, based on the nonlinear extension of the…
Inferring nonlinear and asymmetric causal relationships between multivariate longitudinal data is a challenging task with wide-ranging application areas including clinical medicine, mathematical biology, economics and environmental…
The description of the dynamics of complex systems, in particular the capture of the interaction structure and causal relationships between elements of the system, is one of the central questions of interdisciplinary research. While the…
A transformation relation between multivariate ARMA and CARMA processes is derived through a discretization procedure. This gives a direct relationship between the discrete time and continuous time analogues, serving as the basis for an…
Assessing the magnitude of cause-and-effect relations is one of the central challenges found throughout the empirical sciences. The problem of identification of causal effects is concerned with determining whether a causal effect can be…
Distinguishing between cause and effect using time series observational data is a major challenge in many scientific fields. A new perspective has been provided based on the principle of Independence of Causal Mechanisms (ICM), leading to…
In this paper we test for Granger causality in high-dimensional vector autoregressive models (VARs) to disentangle and interpret the complex causal chains linking radiative forcings and global temperatures. By allowing for high…
We introduce a rigorous mathematical framework for Granger causality in extremes, designed to identify causal links from extreme events in time series. Granger causality plays a pivotal role in uncovering directional relationships among…
Kernel-based methods are used in the context of Granger Causality to enable the identification of nonlinear causal relationships between time series variables. In this paper, we show that two state of the art kernel-based Granger Causality…
Granger causality (GC) is undoubtedly the most widely used method to infer cause-effect relations from observational time series. Several nonlinear alternatives to GC have been proposed based on kernel methods. We generalize kernel Granger…
In a recent paper entitled "Inconsistencies of Recently Proposed Citation Impact Indicators and how to Avoid Them," Schreiber (2012, at arXiv:1202.3861) proposed (i) a method to assess tied ranks consistently and (ii) fractional attribution…
Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can yield significant insights into the…
We explore the hypothesis that the relative abundance of feedback loops in many empirical complex networks is severely reduced owing to the presence of an inherent global directionality. Aimed at quantifying this idea, we propose a simple…