Related papers: Causation entropy from symbolic representations of…

Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…

The application of the Shannon entropy to study the relationship between information and structures has yielded insights into molecular and material systems. However, the difficulty in directly observing and manipulating atoms and molecules…

Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy…

Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic…

Synthetic datasets generated by structural causal models (SCMs) are commonly used for benchmarking causal structure learning algorithms. However, the variances and pairwise correlations in SCM data tend to increase along the causal…

Entanglement measures find frequent application in the study of topologically ordered systems, where the presence of topological order is reflected in an additional contribution to the entanglement of the system. Obtaining this topological…

The ordinal approach to evaluate time series due to innovative works of Bandt and Pompe has increasingly established itself among other techniques of nonlinear time series analysis. In this paper, we summarize and generalize the theory of…

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…

By relating and ordering events, causality constitutes a pivotal feature of our world. On the one hand, there are information-theoretic notions of causality defined in terms of the information processing ability of agents and on the other…

Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data…

Causal discovery aims to extract qualitative causal knowledge in the form of causal graphs from data. Because causal ground truth is rarely known in the real world, simulated data plays a vital role in evaluating the performance of the…

This study addresses the problem of learning a summary causal graph on time series with potentially different sampling rates. To do so, we first propose a new causal temporal mutual information measure for time series. We then show how this…

In [Haruna, T. and Nakajima, K., 2011. Physica D 240, 1370-1377], the authors introduced the duality between values (words) and orderings (permutations) as a basis to discuss the relationship between information theoretic measures for…

We analyze spacetimes with horizons and study the thermodynamic aspects of causal horizons, suggesting that the resemblance between gravitational and thermodynamic systems has a deeper quantum mechanical origin. We find that the observer…

Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…

We study causal inference in settings characterized by interference with a bipartite structure. There are two distinct sets of units: intervention units to which an intervention can be applied and outcome units on which the outcome of…

The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…

Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…

Qualitative causal relationships compactly express the direction, dependency, temporal constraints, and monotonicity constraints of discrete or continuous interactions in the world. In everyday or academic language, we may express…

A key challenge in systems biology is the elucidation of the underlying principles, or fundamental laws, which determine the cellular phenotype. Understanding how these fundamental principles are altered in diseases like cancer is important…