Related papers: Inhomogeneity and complexity measures for spatial …
Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…
The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot…
Consider an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. In order to establish concentration properties for nonlinear functions $Z(A)$, it is standard to appeal to functional inequalities like Poincar\'e or…
We introduce two new concepts, local homogeneity and local L^q-spectrum, both of which are tools that can be used in studying the local structure of measures. The main emphasis is given to the examination of local dimensions of measures in…
Topological complexity is a numerical homotopy invariant that measures the instability of motion planning in a space. To study the topological complexity of non-simply connected spaces, Costa and Farber introduced a cohomology class whose…
We develop new tools to compute the index of symmetry in the context of homogeneous fibrations. As a consequence of our results, we determine the index of symmetry of every homogeneous space diffeomorphic to a compact rank-one symmetric…
Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis. In addtition, some matrix trace…
We propose here selected actual features of measurement problems based on our concerns in our respective fields of research. Their technical similarity in apparently disconnected fields motivate this common communication. Problems of…
Detecting spatial patterns is fundamental to scientific discovery, yet current methods lack statistical consensus and face computational barriers when applied to large-scale spatial omics datasets. We unify major approaches through a single…
Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on…
We present a new approach to study measures on ensembles of contours, polymers or other objects interacting by some sort of exclusion condition. For concreteness we develop it here for the case of Peierls contours. Unlike existing methods,…
Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…
Spatial phenomena in environmental and biological contexts often involve events that are unevenly distributed across space and carry attributes, whose associations/variations are space-dependent. In this paper, we introduce the class of…
Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply…
Performance evaluation of complex networks has traditionally focused on structural integrity or average transmission efficiency, perspectives that often overlook the dimension of functional fairness. This raises a central question: Under…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
We propose a method for testing cosmic homogeneity based on the Shannon entropy in Information theory and test the potentials and limitations of the method on Monte Carlo simulations of some homogeneous and inhomogeneous 3D point process in…
This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…
One considers linearly thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance and thermal…
Relative entropy of coherence can be written as an entropy difference of the original state and the incoherent state closest to it when measured by relative entropy. The natural question is, if we generalize this situation to Tsallis or…