Related papers: Complexity-based permutation entropies: from deter…
We propose an operational definition of the entropy of cosmological perturbations based on a truncation of the hierarchy of Green functions. The value of the entropy is unambiguous despite gauge invariance and the renormalization procedure.…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
Time series models are ubiquitous in science, arising in any situation where researchers seek to understand how a system's behaviour changes over time. A key problem in time series modelling is \emph{inference}; determining properties of…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
In applications such as rank aggregation, mixture models for permutations are frequently used when the population exhibits heterogeneity. In this work, we study the widely used Mallows mixture model. In the high-dimensional setting, we…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…
We propose a novel tensor-based formalism for inferring causal structures from time series. An information theoretical analysis of transfer entropy, shows that transfer entropy results from transmission of information over a set of…
Distinguishing cause from effect is a scientific challenge resisting solutions from mathematics, statistics, information theory and computer science. Compression-Complexity Causality (CCC) is a recently proposed interventional measure of…
This article proposes a new approach to modeling high-dimensional time series by treating a $p$-dimensional time series as a nonsingular linear transformation of certain common factors and idiosyncratic components. Unlike the approximate…
Entropy plays a key role in statistical physics of complex systems, which in general exhibit diverse aspects of emergence on different scales. However, it still remains not fully resolved how entropy varies with the coarse-graining level…
We introduce a model of effective conformal quantum field theory in dimension $d=1+1$ coupled to stochastic noise, where Kardar-Parisi-Zhang (KPZ) class fluctuations can be observed. The analysis of the quantum dynamics of the scaling…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…
We introduce Extrema-Segmented Entropy (ExSEnt), a feature-decomposed framework for quantifying time-series complexity that separates temporal from amplitude contributions. The method partitions a signal into monotonic segments by detecting…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…
Instantaneous noise-based logic can avoid time-averaging, which implies significant potential for low-power parallel operations in beyond-Moore-law-chips. However, the universe (uniform superposition) will be zero with high probability…
This contribution investigates the computational complexity of simulating linear ordinary differential equations (ODEs) on digital computers. We provide an exact characterization of the complexity blowup for a class of ODEs of arbitrary…
Background: Transitioning from an old medical coding system to a new one can be challenging, especially when the two coding systems are significantly different. The US experienced such a transition in 2015. Objective: This research aims to…