相关论文: Which depth to use to construct functional boxplot…
Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the…
The smooth bootstrap for estimating copula functionals in small samples is investigated. It can be used both to gauge the distribution of the estimator in question and to augment the data. Issues arising from kernel density and distribution…
The recently defined concept of a statistical depth function for fuzzy sets provides a theoretical framework for ordering fuzzy sets with respect to the distribution of a fuzzy random variable. One of the most used and studied statistical…
Hausdorff dimension of level sets of generic continuous functions defined on fractals can give information about the "thickness/narrow cross-sections" "network" corresponding to a fractal set, $F$. This lead to the definition of the…
We explain an array of basic functional analysis puzzles on the way to general spectral flow formulae and indicate a direction of future topological research for dealing with these puzzles.
The purpose of this article is to investigate Bach-flat critical metrics of the volume functional on a compact manifold $M$ with boundary $\partial M.$ Here, we prove that a Bach-flat critical metric of the volume functional on a simply…
In this paper, we will consider subfractals of hyperbolic iterated function systems which satisfy the open set condition. The subfractals will consist of points associated with infinite strings from a subshift of finite type or sofic…
Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied from a combinatorial perspective. In this work, we give the…
Non-autonomous iterated function systems are a generalization of iterated function systems. If the contractions in the system are conformal mappings, it is called a non-autonomous conformal iterated function system, and its attractor is…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
We introduce the Integrated Dual Local Depth which is a local depth measure for data in a Banach space based on the use of one-dimensional projections. The properties of a depth measure are analyzed under this setting and a proper…
We improve both dimension compression and expansion bounds for homeomorphisms with $p$-exponentially integrable distortion. To the first direction we also introduce estimates for the compression multifractal spectra, which will be used to…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
Ground-truth depth, when combined with color data, helps improve object detection accuracy over baseline models that only use color. However, estimated depth does not always yield improvements. Many factors affect the performance of object…
We propose learning a depth covariance function with applications to geometric vision tasks. Given RGB images as input, the covariance function can be flexibly used to define priors over depth functions, predictive distributions given…
Identification of the center of a data cloud is one of the basic problems in statistics. One popular choice for such a center is the median, and several versions of median in finite dimensional spaces have been studied in the literature. In…
In this paper we present a method for constructing the continuous best fractal approximation in the space of bounded functions. We construct the finite-dimensional subspace of the space of bounded functions whose base consists of the…
This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral convexity under sums and compositions of multifunctions, the domains and ranges…
Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the…
The structure of exponential subspaces of finitely generated shift-invariant spaces is well understood and the role of such subspaces for the approximation power of refinable function vectors and related multi-wavelets is well studied. In…