Related papers: Three Perspectives on Complexity $-$ Entropy, Comp…
In this work, we introduce metrics to evaluate the use of simplified time series in the context of interpretability of a TSC -- a Time Series Classifier. Such simplifications are important because time series data, in contrast to text and…
In this paper we carry out an information-theoretic analysis of the $D$-dimensional rigid rotator by studying the entropy and complexity measures of its wavefunctions, which are controlled by the hyperspherical harmonics. These measures…
A major challenge of interdisciplinary description of complex system behaviour is whether real systems of higher complexity levels can be understood with at least the same degree of objective, "scientific" rigour and universality as…
Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…
A measure for the complexity of a differentiable function f(x) on an interval is introduced. It is based on approximations of the function by piecewise constant functions. The measure takes into account the quality of the approximation and…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
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 investigate how to measure and define the entropy of a simple chaotic system, three hard spheres on a ring. A novel approach is presented, which does not assume the ergodic hypothesis. It consists of transforming the particles collision…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the…
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…
Entropic measures of complexity are able to quantify the information encoded in complex network structures. Several entropic measures have been proposed in this respect. Here we study the relation between the Shannon entropy and the Von…
We introduce an asymmetric distance in the space of learning tasks, and a framework to compute their complexity. These concepts are foundational for the practice of transfer learning, whereby a parametric model is pre-trained for a task,…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
In nonlinear dynamics, and to a lesser extent in other fields, a widely used measure of complexity is the Permutation Entropy. But there is still no known method to determine the accuracy of this measure. There has been little research on…
A unified combinatorial definition of the information content and entropy of different types of patterns, compatible with the traditional concepts of information and entropy, going beyond the limitations of Shannon information interpretable…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…