Related papers: A new class of spatial covariance functions genera…
The Mat\'ern covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Mat\'ern class is that it is possible to get precise control over the degree of…
In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…
We develop a multiscale spatial kernel convolution technique with higher order functions to capture fine scale local features and lower order terms to capture large scale features. To achieve parsimony, the coefficients in the multiscale…
As a regression technique in spatial statistics, the spatiotemporally varying coefficient model (STVC) is an important tool for discovering nonstationary and interpretable response-covariate associations over both space and time. However,…
We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions of the complex variable.
Modern datasets are often in the form of matrices or arrays,potentially having correlations along each set of data indices. For example, data involving repeated measurements of several variables over time may exhibit temporal correlation as…
In this paper, we show that geometric functionals (e.g., excursion area, boundary length) evaluated on excursion sets of sphere-cross-time long memory random fields can exhibit fractional cointegration, meaning that some of their linear…
Superoscillating functions, i.e., functions that locally oscillate at a rate faster than their highest Fourier component, are of interest for applications from fundamental physics to engineering. Here, we develop a new method which allows…
We investigate the structure of the constraints on three-point correlation functions emerging when conformal invariance is imposed in momentum space and in arbitrary space-time dimensions, presenting a derivation of their solutions for…
We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…
In spatial statistics, kriging models are often designed using a stationary covariance structure; this translation-invariance produces models which have numerous favorable properties. This assumption can be limiting, though, in…
Fractional Sobolev spaces $\widehat{H}^s(\mathbb{R})$ have been playing important roles in analysis of many mathematical subjects. In this work, we re-consider fractional Sobolev spaces under the perspective of fractional operators and…
In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in…
The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The technique of applying Fourier's vector transform with discontinuous coefficients for solving problems of…
Convolution operation is indispensable in studying analog optical and digital signal processing. Equally important is the correlation operation. The time domain community often teaches convolution and correlation only with one dimensional…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
Differential equations may possess coefficients that vary on a spectrum of scales. Because coefficients are typically multiplicative in real space, they turn into convolution operators in spectral space, mixing all wavenumbers. However, in…
We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
Rapid developments in satellite remote-sensing technology have enabled the collection of geospatial data on a global scale, hence increasing the need for covariance functions that can capture spatial dependence on spherical domains. We…