Related papers: Entropic Measure on Multidimensional Spaces

Let $\Lambda$ be a complex manifold and let $(f_\lambda)_{\lambda\in \Lambda}$ be a holomorphic family of rational maps of degree $d\geq 2$ of $\mathbb{P}^1$. We define a natural notion of entropy of bifurcation, mimicking the classical…

We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…

Let $\mu$ be a Borel probability measure on a compact path-connected metric space $(X, \rho)$ for which there exist constants $c,\beta>1$ such that $\mu(B) \geq c r^{\beta}$ for every open ball $B\subset X$ of radius $r>0$. For a class of…

The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…

For continuous maps on a compact manifold M, particularly for those that do not preserve the Lebesgue measure m, we define the observable invariant probability measures as a generalization of the physical measures. We prove that any…

The maximum entropy principle (MEP) is one of the most prominent methods to investigate and model complex systems. Despite its popularity, the standard form of the MEP can only generate Boltzmann-Gibbs distributions, which are ill-suited…

The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature $T_c$. A number of methods exist for estimating the entropy of…

We introduce the entropic measure transform (EMT) problem for a general process and prove the existence of a unique optimal measure characterizing the solution. The density process of the optimal measure is characterized using a…

We define the concept of symmetric sensitivity with respect to initial conditions for the endomorphisms on Lebesgue metric spaces. The idea is that the orbits of almost every pair of nearby initial points (for the product of the invariant…

We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…

Dirichlet distributions are probability measures on the unit simplex. They are often used as prior distributions in modeling categorical data, such as in topic analysis of text data. Motivated by this application, we consider Monte Carlo…

The simple entropic method to statistical reconstructing of heterogeneous three-dimensional media from a single two-dimensional image is briefly reported. We apply the entropic descriptor quantifying spatial inhomogeneity that depends on…

The Hierarchical Dirichlet process is a discrete random measure serving as an important prior in Bayesian non-parametrics. It is motivated with the study of groups of clustered data. Each group is modelled through a level two Dirichlet…

From a combinatorial point of view, we consider the Earth Mover's Distance (EMD) associated with a metric measure space. The specific case considered is deceptively simple: Let the finite set [n] = {1,...,n} be regarded as a metric space by…

We introduce the Mass Migration Process (MMP), a conservative particle system on ${\mathbb N}^{{\mathbb Z}^d}$. It consists in jumps of $k$ particles ($k\ge 1$) between sites, with a jump rate depending only on the state of the system at…

We address the problem of testing hypotheses about a specific value of the Fr\'echet mean in metric spaces, extending classical mean testing from Euclidean spaces to more general settings. We extend an Euclidean testing procedure…

Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…

We obtain results on the asymptotic equidistribution of the pre-images of linear subspaces for sequences of rational mappings between projective spaces. As an application to complex dynamics, we consider the iterates $P_k$ of a rational…

In this paper we study the liftability property for piecewise continuous maps of compact metric spaces, which admit inducing schemes in the sense of Pesin and Senti [PS05, PS06]. We show that under some natural assumptions on the inducing…

In this paper, we use a biorthogonal approach (Appell system) to construct and characterize the spaces of test and generalized functions associated to the fractional Poisson measure $\pi_{\lambda,\beta}$, that is, a probability measure in…