Related papers: Convex lineability in copula and quasi-copula sets
In the paper we consider convex cones in infinite-dimensional real vector spaces which are endowed with no topology. The main purpose is to study an internal geometric structure of convex cones and to obtain an analytical description of…
The characterizations when two natural upper bounds of the set of copulas with a given diagonal section are copulas have been well studied in the literature. Given a curvilinear section, however, there is only a partial result concerning…
We construct a family of monotone and convex $C^1$ integro cubic splines under a strictly convex position of the dataset. Then, we find an optimal spline by considering its approximation properties. Finally, we give some examples to…
We introduce a new notion for geometric families called self-coverability and show that homothets of convex polygons are self-coverable. As a corollary, we obtain several results about coloring point sets such that any member of the family…
Copulas are known to satisfy a number of regularity properties, and one might therefore believe that their densities, when they exist, admit a certain degree of regularity themselves. We show that this is not true in general by constructing…
We introduce the notions of geometric height and graded (geometric) relative hyperbolicity in this paper. We use these to characterize quasiconvexity in hyperbolic groups, relative quasiconvexity in relatively hyperbolic groups, and convex…
The main goal of this paper is to study the extent of freedom one has in constructing quasi-copulas vs. copulas. Specifically, it exhibits three construction methods for quasi-copulas based on recent developments: a representation of…
In this article, the concept of copulas is generalised to infinite dimensional Hilbert spaces. We show one direction of Sklar's theorem and explain that the other direction fails in infinite dimensional Hilbert spaces. We derive a necessary…
In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are convergent in…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
In most of today's exactly solved classes of polyominoes, either all members are convex (in some way), or all members are directed, or both. If the class is neither convex nor directed, the exact solution uses to be elusive. This paper is…
Multivariate distributions are fundamental to modeling. Discrete copulas can be used to construct diverse multivariate joint distributions over random variables from estimated univariate marginals. The space of discrete copulas admits a…
We prove that every quasi-copula can be written as a uniformly converging infinite sum of multiples of copulas. Furthermore, we characterize those quasi-copulas which can be written as a finite sum of multiples of copulas, i.e., that are a…
This paper aims to give a further study on quasi-convex subsets in Alexandrov spaces with lower curvature bound which are introduced in [SSW]. We first provide new insights on quasi-convex subsets (Theorem A and Corollary C), and then as…
We show that the maximum cardinality of an anti-chain composed of intersections of a given set of n points in the plane with half-planes is close to quadratic in n. We approach this problem by establishing the equivalence with the problem…
We study some particular cases of the $n$-well problem in two-dimensional linear elasticity. Assuming that every well in $\mathcal{U}\subset\mathbb{R}^{2\times 2}_\text{sym}$ belong to the same two-dimensional affine subspace, we…
Bivariate copulas with prescribed diagonal section were first studied by Bertino. Their maximality was studied so far only from the point of view of upper bounds which brings quasi-copulas into the picture and limits the resulting set…
A problem posed by Erd\H{o}s in 1945 initiated the study of non-separable arrangements of convex bodies. A finite collection of convex bodies in Euclidean $d$-space is called a non-separable family (or NS-family) if every hyperplane…
We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are ``convex co-compact'' in a natural sense. We prove an infinitesimal rigidity statement when the angle around the singular lines is less than…