Related papers: Information-Geometric Equivalence of Transportatio…
The goal of this paper is to study the path-following method for univariate polynomials. We propose to study the complexity and condition properties when the Newton method is applied as a correction operator. Then we study the geodesics and…
One may associate several frames to a given polytope, such as its collection of vertices, edges, or facet normal vectors. In this note, we use these frames to generate geometric inequalities for the simplex in $\mathbb{R}^d$ and polytopes…
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical…
For a stationary Poisson hyperplane tessellation $X$ in ${\mathbb R}^d$, whose directional distribution satisfies some mild conditions (which hold in the isotropic case, for example), it was recently shown that with probability one every…
This paper presents two algorithms. In their simplest form, the first algorithm decides the existence of a pointed homotopy between given simplicial maps f, g from X to Y and the second computes the group $[\Sigma X,Y]^*$ of pointed…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
On the probability simplex, we can consider the standard information geometric structure with the e- and m-affine connections mutually dual with respect to the Fisher metric. The geometry naturally defines submanifolds simultaneously…
The mix of two maniplexes is the minimal maniplex that covers both. This construction has many important applications, such as finding the smallest regular cover of a maniplex. If one of the maniplexes is an abstract polytope, a natural…
Some information geometric structures concerning the Mercator projections are studied. It is known that a loxodrome on the surface of the globe is related to the straight line on a Mercator map by the Mercator projection. It is not well…
Quantiles are a fundamental concept in probability and theoretical statistics and a daily tool in their applications. While the univariate concept of quantiles is quite clear and well understood, its multivariate extension is more…
Kendall shape spaces are a widely used framework for the statistical analysis of shape data arising from many domains, often requiring the parallel transport as a tool to normalise time series data or transport gradient in optimisation…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional…
We characterize maps between $n$-dimensional N\"obeling manifolds that can be approximated by homeomorphisms.
We first give a characterization of the L^1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences.…
We study the vertices of the polytopes of all affine maps (a.k.a. hom-polytopes) between higher dimensional simplices, cubes, and crosspolytopes. Systematic study of general hom-polytopes was initiated in [3]. The study of such vertices is…
The total matching polytope generalizes the stable set polytope and the matching polytope. In this paper, we first propose new facet-defining inequalities for the total matching polytope. We then give an exponential-sized, non-redundant…
This article gives necessary and sufficient conditions for a relation to be the containment relation between the facets and vertices of a polytope. Also given here, are a set of matrices parameterizing the linear moduli space and another…
The problem of bi-equivariant extension of continuous maps of binary $G$-spaces is considered. The concept of a structural map of distributive binary $G$-spaces is introduced, and a theorem on the bi-equivariant extension of structural maps…
We introduce a natural notion of holomorphic map between generalized complex manifolds and we prove some related results on Dirac structures and generalized Kaehler manifolds.