相关论文: Inhomogeneity and complexity measures for spatial …

Cloudiness or formation is a concept routinely used in industry to address deviations from homogeneity in nonwovens and papers. Measuring a cloudiness index based on image data is a common task in industrial quality assurance. The two most…

The relative configurational entropy per cell as a function of length scale is a sensitive detector of spatial self-similarity. For Sierpinski carpets the equally separated peaks of the above function appear at the length scales that depend…

In this paper, we consider the problem of estimating Tsallis entropy from a given data set. We propose four different estimators for Tsallis entropy measure based on higher-order sample spacings, and then discuss estimation of Tsallis…

We investigate the dimension theory of inhomogeneous self-affine carpets. Through the work of Olsen, Snigireva and Fraser, the dimension theory of inhomogeneous self-similar sets is now relatively well-understood, however, almost no…

In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…

A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…

Measures of discordance between datasets have become an essential part of cosmological analyses. It is important to accurately evaluate the significance of such discordances when present. We propose here a Bayesian interpretation of…

An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…

We restrict our attention to space-time point pattern data for which we have a single realisation within a finite region. Second-order characteristics are used to analyse the spatio-temporal structure of the underlying point process. In…

The game-theoretical approach to non-extensive entropy measures of statistical physics is based on an abstract measure of complexity from which the entropy measure is derived in a natural way. A wide class of possible complexity measures is…

The experimental and theoretical challenges posed by the study of dynamically inhomogeneous systems are outlined in the context of cuprates and other oxides. Considering the pitfalls in the single-component approach to the analysis of…

In this paper we propose numerical measures for evaluating the aesthetic interest of simple patterns. The patterns consist of elements (symbols, pixels, etc.) in regular square arrays. The measures depend on two characteristics of the…

An extension of the ambient metric construction of Fefferman-Graham to infinite order in even dimensions is described. The main ingredients are the introduction of "inhomogeneous ambient metrics" with asymptotic expansions involving the…

We present a path toward determining the statistical origin of the thermodynamic limit for systems with long-range interactions. We assume throughout that the systems under consideration have thermodynamic properties given by the Tsallis…

A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…

We present a complexity measure for any finite time series. This measure has invariance under any monotonic transformation of the time series, has a degree of robustness against noise, and has the adaptability of satisfying almost all the…

A carpet is a metric space homeomorphic to the Sierpinski carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincar\'e inequalities. Our…

In this paper we construct a large family of examples of subsets of Euclidean space that support a 1-Poincar\'e inequality yet have empty interior. These examples are formed from an iterative process that involves removing well-behaved…

We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant,…

Several ways have been proposed in the literature to define a coherence measure based on Tsallis relative entropy. One of them is defined as a distance between a state and a set of incoherent states with Tsallis relative entropy taken as a…