Related papers: Dually flat structure with escort probability and …
In many applications, the curvature of the space supporting the data makes the statistical modelling challenging. In this paper we discuss the construction and use of probability distributions wrapped around manifolds using exponential…
In this article, a new and natural topology on the prime spectrum is established which behaves completely as the dual of the Zariski topology. It is called the flat topology. The basic and also some sophisticated properties of the flat…
This study reports on the evolution of the probability distribution in the configuration space of the two-dimensional Toda system. The distribution is characterized by singularities, which predominantly take two forms: double-cusped…
The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult…
We formulate the Riemannian calculus of the probability set embedded with $L^2$-Wasserstein metric. This is an initial work of transport information geometry. Our investigation starts with the probability simplex (probability manifold)…
We propose a dynamic data structure for the distribution-sensitive point location problem. Suppose that there is a fixed query distribution in $\mathbb{R}^2$, and we are given an oracle that can return in $O(1)$ time the probability of a…
This article introduces strongly near smooth manifolds. The main results are (i) second countability of the strongly hit and far-miss topology on a family $\mathcal{B}$ of subsets on the Lodato proximity space of regular open sets to which…
We investigate the statistical properties of two dimensional random cellular systems (froths) in term of their shell structure. The froth is analyzed as a system of concentric layers of cells around a given central cell. We derive exact…
We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional…
Any system of bisectors (in the sense of abstract Voronoi diagrams) defines an arrangement of simple curves in the plane. We define Voronoi-like graphs on such an arrangement, which are graphs whose vertices are locally Voronoi. A vertex…
In this paper, we propose a novel space partitioning strategy for implicit hierarchy visualization such that the new plot not only has a tidy layout similar to the treemap, but also is flexible to data changes similar to the Voronoi…
Exponential families and mixture families are parametric probability models that can be geometrically studied as smooth statistical manifolds with respect to any statistical divergence like the Kullback-Leibler (KL) divergence or the…
The dually flat structure of statistical manifolds can be derived in a non-parametric way from a particular case of affine space defined on a qualified set of probability measures. The statistically natural displacement mapping of the…
We consider the Voronoi diagram generated by $n$ i.i.d. $\mathbb{R}^{d}$-valued random variables with an arbitrary underlying probability density function $f$ on $\mathbb{R}^{d}$, and analyse the asymptotic behaviours of certain geometric…
The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small…
Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry…
Given an original distribution, its statistical and probabilistic attributs may be scanned by the associated escort distribution introduced by Beck and Schlogl and employed in the formulation of nonextensive statistical mechanics. Here, the…
A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…
This article represents the computational model for spacial addresation of the sensors in the dynamically changing real-time internet of things system. The model bases on the Voronoi diagrams as a basic data structure. Problem - the correct…
We investigate the combinatorial complexity of geodesic Voronoi diagrams on polyhedral terrains using a probabilistic analysis. Aronov etal [ABT08] prove that, if one makes certain realistic input assumptions on the terrain, this complexity…