Related papers: Multidimensional exact classes, smooth approximati…
A theorem is proved concerning approximation of analytic functions by multivariate polynomials in the $s$-dimensional hypercube. The geometric convergence rate is determined not by the usual notion of degree of a multivariate polynomial,…
Massive classification, a classification task defined over a vast number of classes (hundreds of thousands or even millions), has become an essential part of many real-world systems, such as face recognition. Existing methods, including the…
Mathematical models are essential for understanding and making predictions about systems arising in nature and engineering. Yet, mathematical models are a simplification of true phenomena, thus making predictions subject to uncertainty.…
The shape of homogeneous, generic, smooth convex bodies as described by the Euclidean distance with nondegenerate critical points, measured from the center of mass represents a rather restricted class M_C of Morse-Smale functions on S^2.…
A map between manifolds induces stratifications of both the source and the target according to the occurring multisingularities. In this paper, we study universal expressions-called higher Thom polynomials-that describe the…
Relations between components of the effective tensors of composites that hold regardless of composite's microstructure are called exact relations. Relations between components of the effective tensors of all laminates are called lamination…
Let $G$ be a group with a metric $\mathrm{d}$ invariant under left and right translations, and let $\bar{\mathbb{D}}_r$ be the ball of radius $r$ around the identity. A $(k,r)$-metric approximate subgroup is a symmetric subset $X$ of $G$…
The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic…
We define fully exact module categories, a subclass of exact module categories over a finite braided tensor category that is stable under the relative Deligne product. In contrast, we demonstrate with examples in both zero and non-zero…
The classical theory of elliptic curves with complex multiplication is a fundamental tool for studying the arithmetic of abelian extensions of imaginary quadratic fields. While no direct analogue is available for real quadratic fields, a…
Machine learning models provide statistically impressive results which might be individually unreliable. To provide reliability, we propose an Epistemic Classifier (EC) that can provide justification of its belief using support from the…
This paper investigates a new property of formal languages called REG-measurability where REG is the class of regular languages. Intuitively, a language \(L\) is REG-measurable if there exists an infinite sequence of regular languages that…
While classical data analysis has addressed observations that are real numbers or elements of a real vector space, at present many statistical problems of high interest in the sciences address the analysis of data that consist of more…
Despite spectacular advances in defining invariants for simply connected smooth and symplectic 4-dimensional manifolds and the discovery of effective surgical techniques, we still have been unable to classify simply connected smooth…
We introduce the notion of large scale inductive dimension for asymptotic resemblance spaces. We prove that the large scale inductive dimension and the asymptotic dimensiongrad are equal in the class of r-convex metric spaces. This class…
Object of investigation are almost hypercomplex manifolds with Hermitian-Norden metrics of the lowest dimension. The considered manifolds are constructed on 4-dimensional Lie groups. It is established a relation between the classes of a…
In this paper we consider a special class of polymorphisms with invariant measure, - (cf.[1])- the algebraic polymorphisms of compact groups. A general polymorphism is -- by definition -- a many-valued map with invariant measure, and the…
A classical result of Carleman, based on the theory of quasianalytic functions, shows that polynomials are dense in $L^2(\mu)$ for any $\mu$ such that the moments $\int x^k d\mu$ do not grow too rapidly as $k \to \infty$. In this work, we…
In previous work, a class of noninvertible topological dynamical systems $f: X \to X$ was introduced and studied; we called these {\em topologically coarse expanding conformal} systems. To such a system is naturally associated a preferred…
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…