Related papers: Statistical Compactness
Depth is a concept that measures the `centrality' of a point in a given data cloud or in a given probability distribution. Every depth defines a family of so-called trimmed regions. For statistical applications it is desirable that with…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
We attempt to review all trustworthy and well-controlled de Sitter compactifications of string theory.
The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves more explicitly the symmetry between time and frequency…
We discuss general formation of complementary behaviors, functions and forms in biological species competing for resources. We call orthogonalization the related processes on macro and micro-level of a self-organized formation of…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
The connections between the objects mentioned in the title are used to give a short proof of the Cartan--Helgason theorem and a natural construction of the compactifications.
Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…
We give a definition of a functor compactifying the functor of bundles on a surfaces. Earlier different authors have defined similar spaces as either images under a morphism or a quotient by an equivalence relation. We use the technique of…
Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
In these notes, uniform convergence on compacta is studied on the space of functions taking values in the set of finite Borel measures. Related limit theorems, including L\'evy's continuity theorem and functional limit theorems for…
One of the nice properties of the first-order logic is the compactness of satisfiability. It state that a finitely satisfiable theory is satisfiable. However, different degrees of satisfiability in many-valued logics, poses various kind of…
Convergence theory is an extension of general topology. In contrast with topology, it is closed under some important operations, like exponentiation. With all its advantages, convergence theory remains rather unknown. It is an aim of this…
A revised version of the compactness criterion for families of quantum operations in the strong convergence topology (obtained previously) is presented, along with a more detailed proof and the examples showing the necessity of this…
Presented is a Julia meta-program that discovers compact theories from data if they exist. It writes candidate theories in Julia and then validates: tossing the bad theories and keeping the good theories. Compactness is measured by a…
Some types of statistical convergence such as statistical order and deferred statistical convergences have been studied and investigated in Riesz spaces, recently. In this paper, we introduce the concept of deferred statistical convergence…