Related papers: Complexity-based permutation entropies: from deter…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
We develop a theory of classical complexity. We study the relations between classical complexity and entropy, and conjecture that in an isolated system, classical absolute complexity always tends to grow, until it reaches its maximum. We…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
We study expected values of the polynomials $P_N^{}(z)=\prod_{1\leq n\leq N}(X_n^2+z^2)$ whose $2N$ zeros $\{\pm i X_k\}^{}_{k=1,...,N}$ are generated by $N$ identically distributed multi-variate mean-zero normal random variables…
Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been…
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…
Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…
In this paper, we propose to mix the approach underlying Bandt-Pompe permutation entropy with Lempel-Ziv complexity, to design what we call Lempel-Ziv permutation complexity. The principle consists of two steps: (i) transformation of a…
Recently it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and…
We provide a computational complexity lens to understand the power of machine learning models, particularly their ability to model complex systems. Machine learning models are often trained on data drawn from sampleable or more complex…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
Collective behavior, both in real biological systems as well as in theoretical models, often displays a rich combination of different kinds of order. A clear-cut and unique definition of "phase" based on the standard concept of order…
This article investigates the possibility to use the class entropy of the output of a connectionist phoneme recogniser to predict time boundaries between phonetic classes. The rationale is that the value of the entropy should increase in…
The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric…
This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…
We study the build up of complexity on the example of 1 kg matter in different forms. We start on the simplest example of ideal gases, and then continue with more complex chemical, biological, life and social and technical structures. We…
We present the discovery of a fundamental composition law governing conjugate observables in the Random Permutation Sorting System (RPSS). The law links the discrete permutation count Np and the continuous elapsed time T through a…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…
In automated complexity analysis, noninterference-based type systems statically guarantee, via soundness, the property that well-typed programs compute functions of a given complexity class, e.g., the class FP of functions computable in…