Related papers: Robustly estimating the flow direction of informat…

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multi-frequency sparse phased or phaseless far field data. With the phased data,…

Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from bio-medical imaging to precision measurements. In all of these fields, the central aim is to gather as much information…

This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…

The information flow-based quantitative causality analysis has been widely applied in different disciplines because of its origin from first principles, its concise form, and its computational efficiency. So far the algorithm for its…

Investigation of the underlying physics or biology from empirical data requires a quantifiable notion of similarity - when do two observed data sets indicate nearly identical generating processes, and when they do not. The discriminating…

Quantification of complexity in neurophysiological signals has been studied using different methods, especially those from information or dynamical system theory. These studies revealed the dependence on different states of consciousness,…

Understanding causal relationships in time series is fundamental to many domains, including neuroscience, economics, and behavioral science. Granger causality is one of the well-known techniques for inferring causality in time series.…

From ancient philosophers to modern economists, biologists, and other researchers, there has been a continuous effort to unveil causal relations. The most formidable challenge lies in deducing the nature of the causal relationship: whether…

Causal analysis based on non-uniform embedding schemes is an important way to detect the underlying interactions between dynamic systems. However, there are still some obstacles to estimate high-dimensional conditional mutual information…

We provide a general formula, based on stochastic thermodynamics, that describes the flow of information between an arbitrary number of coupled complex-valued Langevin equations. This permits to describe the transfer of information in…

Experimentally observed networks of interacting dynamical systems are inferred from recorded multivariate time series by evaluating a statistical measure of dependence, usually the cross-correlation coefficient, or mutual information. These…

This paper proposes a novel feature called spectrum congruency for describing edges in images. The spectrum congruency is a generalization of the phase congruency, which depicts how much each Fourier components of the image are congruent in…

Transient phenomena play a key role in coordinating brain activity at multiple scales, however,their underlying mechanisms remain largely unknown. A key challenge for neural data science is thus to characterize the network interactions at…

Information flow between components of a system takes many forms and is key to understanding the organization and functioning of large-scale, complex systems. We demonstrate three modalities of information flow from time series X to time…

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

Phase-averaging is a fundamental approach for investigating periodic and non-stationary phenomena. In fluid dynamics, these can be generated by rotating blades such as propellers/turbines or by pulsed jets. Traditional phase-averaging…

We devised a measure based on the distributions of relative event timings of two coupled units. The measure dynamically evaluates temporal interdependencies between the two coupled units. Using this we show that even in the event of…

The entrainment between weakly-coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the…

This article investigates the causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and…

'Causal' direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between…