Related papers: A Scale-Invariant Entropy Statistic for Distance D…
In this paper will be presented methodology of encoding information in valuations of discrete lattice with some translational invariant constrains in asymptotically optimal way. The method is based on finding statistical description of such…
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…
Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected…
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
Modeling sets is an important problem in machine learning since this type of data can be found in many domains. A promising approach defines a family of permutation invariant densities with continuous normalizing flows. This allows us to…
In this paper we introduce a new family of estimators for the parameters of shape and scale of the log-logistic distribution being robust when rank set sample method is used to select the data. Rank set sampling arises as a way to reduce…
Spatial organisation of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding…
Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies…
A system is invariant with respect to an input transformation if we can transform any dynamic input by this function and obtain the same output dynamics after adjusting the initial conditions appropriately. Often, the set of all such input…
This article extends results described in a recent article detailing a structural scale invariance property of the simulated annealing (SA) algorithm. These extensions are based on generalizations of the SA algorithm based on Tsallis…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
Entropy arises in strong interactions by a dynamical separation of ``partons'' from unobservable ``environment'' modes due to confinement. For interacting scalar fields we calculate the statistical entropy of the observable subsystem.…
We represent affine sub-manifolds of exponential family distributions as minimum relative entropy sub-manifolds. With such representation we derive analytical formulas for the inference from partial information on expectations and…
We advance scale-invariance arguments for systems that are governed (or approximated) by a $q-$Gaussian distribution, i.e., a power law distribution with exponent $Q=1/(1-q); q \in \mathbb{R}$. The ensuing line of reasoning is then compared…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
Discovery of a new scale-free law of earthquake phenomenon is reported. It is relevant to the structural and dynamical properties of the earthquake network proposed in a recent work [S. Abe and N. Suzuki, Europhys. Lett. 65, 581 (2004)].…