Related papers: A $K$-function for inhomogeneous random measures w…
We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a…
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…
Conventional analysis of in vitro assays of motor proteins rests on the assumption that all proteins with the same chemical composition function identically; however molecule-to-molecule variation is often seen even in well-controlled…
We develop further the consequences of the irreducible-Boolean classification established in Ref. [9]; which have the advantage of allowing strong statistical calculations in disordered Boolean function models, such as the…
Symmetry detection and morphological classification of anatomical structures play pivotal roles in medical image analysis. The application of kinematic surface fitting, a method for characterizing shapes through parametric stationary…
The intensity function and Ripley's K-function have been used extensively in the literature to describe the first and second moment structure of spatial point sets. This has many applications including describing the statistical structure…
We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory. Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which…
Heteroskedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression model with multiple covariates. It is based on a suitable…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
Let $K$ be a homogeneous self-similar set satisfying the strong separation condition. This paper is concerned with the quantitative recurrence properties of the natural map $T: K\rightarrow K$ induced by the shift. Let $\mu$ be the natural…
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…
We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…
We can, and should, do statistical inference on simulation models by adjusting the parameters in the simulation so that the values of {\em randomly chosen} functions of the simulation output match the values of those same functions…
We propose to homogenize a periodic (along one direction) structure, first in order to verify the quasi-static prediction of its response to an acoustic wave arising from mixing theory, then to address the question of what becomes of this…
K-frame theory was recently introduced to reconstruct elements from the range of a bounded linear operator K in a separable Hilbert space. This significant property is worthwhile especially in some problems arising in sampling theory. Some…
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…
Extracting meaningful information about unknown quantum states without performing a full tomography is an important task. Low-dimensional projections and random measurements can provide such insight but typically require careful crafting.…
A conception of inhomogeneous locally random distribution of microdefects in crystalline solids is proposed. A method to calculate some physical properties of solids, containing inhomogeneously distributed defects, is developed. A…
Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where moment conditions have zero derivative with respect to…
A stochastic method is introduced for geometric modeling aerosol surface roughness with random field and discrete differential geometry theory. Optical scattering properties are computed for randomly oriented spheroidal particles with…