Related papers: Scaling behaviour of entropy estimates
We present results of the numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy tailed probability distribution functions. Assuming that the distribution function of the random fluctuations…
We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use…
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…
Symbolic relative entropy, an efficient nonlinear complexity parameter measuring probabilistic divergences of symbolic sequences, is proposed in our nonlinear dynamics analysis of heart rates considering equal states. Equalities are not…
Unveiling universal non-equilibrium scaling laws has been a central theme in modern statistical physics, with recent attention increasingly directed toward non-equilibrium phases that exhibit rich dynamical phenomena. A striking example…
The out-of-equilibrium character of active systems is often twofold, arising from both the activity itself and from non-reciprocal couplings between constituents. A well-established measure to quantify the system's distance from equilibrium…
We study the mutual information between two lattice-blocks in terms of von Neumann entropies for one-dimensional infinite lattice systems. Quantum $q$-state Potts model and transverse field spin-$1/2$ XY model are considered numerically by…
On a fine grained scale the Gibbs entropy of an isolated system remains constant throughout its dynamical evolution. This is a consequence of Liouville's theorem for Hamiltonian systems and appears to contradict the second law of…
It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…
An explosive percolation transition is the abrupt emergence of a giant cluster at a threshold caused by a suppression of the growth of large clusters. In this paper, we consider the information entropy of the cluster size distribution,…
It has been shown that sufficiently well mixing dynamical systems with positive entropy have extreme value laws which in the limit converge to one of the three standard distributions known for i.i.d. processes, namely Gumbel, Fr\'echet and…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
Tries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP…
Due to the second principle of thermodynamics, the time dependence of entropy for all kinds of systems under all kinds of physical circumstances always thrives interest. The logistic map $x_{t+1}=1-a x_t^2 \in [-1,1]\;(a\in [0,2])$ is…
We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional $S_{BG}[p(x)]…
We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage…
We discuss the two-dimensional motion of a Brownian particle that is confined to a harmonic trap and driven by a shear flow. The surrounding medium induces memory effects modelled by a linear, typically nonreciprocal coupling of the…
Quantifying the similarity between symbolic sequences is a traditional problem in Information Theory which requires comparing the frequencies of symbols in different sequences. In numerous modern applications, ranging from DNA over music to…
The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…
We show that statistical criticality, i.e. the occurrence of power law frequency distributions, arises in samples that are maximally informative about the underlying generating process. In order to reach this conclusion, we first identify…