Related papers: On a comparative study between dependence scales d…
Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…
Real-world systems are characterized by complex interactions of their internal degrees of freedom, while living in ever-changing environments whose net effect is to act as additional couplings. Here, we introduce a paradigmatic interacting…
In principle, the probability of configurations, determined by the system's partition function or wave function, encapsulates essential information about phases and phase transitions. Despite the exponentially large configuration space, we…
Nonparametric and nonlinear measures of statistical dependence between pairs of random variables are important tools in modern data analysis. In particular the emergence of large data sets can now support the relaxation of linearity…
Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…
We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf 69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
We discuss the relevance of information contained in cross-correlations among different degrees of freedom, which is crucial in non-equilibrium systems. In particular we consider a stochastic system where two degrees of freedom $X_1$ and…
In this paper, we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains…
Isotropization occurs on time scales much shorter than the thermal equilibration time. This is a crucial ingredient for the understanding of collision experiments of heavy nuclei or other nonequilibrium phenomena in complex many body…
On the basis of local realism theory, nonlocal information is necessary for violation of Bell's inequality. From a theoretical point of view, nonlocal information is essentially the mutual information on distant outcome and measurement…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
It is presented a generalization of the von Neumann mutual information in the context of Tsallis' nonextensive statistics. As an example, entanglement between two (two-level) quantum subsystems is discussed. Important changes occur in the…
Evaluating large language models across many benchmarks is expensive, yet many benchmarks are highly correlated. We formalize the selection of a small, informative subset as submodular maximization under a multivariate Gaussian model.…
We measure the influence of different time-scales on the dynamics of financial market data. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying…
Systematic generalization remains challenging for current language models, which are known to be both sensitive to semantically similar permutations of the input and to struggle with known concepts presented in novel contexts. Although…
While the quantum mutual information is a fundamental measure of quantum information, it is only defined for spacelike-separated quantum systems. Such a limitation is not present in the theory of classical information, where the mutual…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
Three aspects of time series are uncertainty (dispersion at a given time scale), scaling (time-scale dependence), and intermittency (inclination to change dynamics). Simple measures of dispersion are the mean absolute deviation and the…
Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have…