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This paper introduces a novel spatial scalar-on-function quantile regression model that extends classical scalar-on-function models to account for spatial dependence and heterogeneous conditional distributions. The proposed model…
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…
In a recent paper we used a basic decomposition property of polyanalytic functions of order $2$ in one complex variable to characterize solutions of the classical $\overline{\partial}$-problem for given analytic and polyanalytic data. Our…
Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or…
Using the quadrature bases that incorporate the spatiotemporal degrees of freedom, we develop a Wigner functional theory for quantum optics, as an extension of the Moyal formalism. Since the spatiotemporal quadrature bases span the complete…
We introduce a novel framework for constructing scalable and flexible covariance kernels for Gaussian processes (GPs) by directly learning the covariance structure under a regression-type parameterization induced by Vecchia approximations,…
We covariantize calculations over the manifold of phase space, establishing Stokes' theorem for differential cross sections and providing new definitions of familiar observable properties like infrared and collinear safety. Through the…
In modelling time series data coming from different sources, frequencies can easily vary since some variable can be measured at higher frequencies, others, at lower frequencies. Given data measured over spatial units and at varying…
This paper introduces a new spatial scan statistic designed to adjust cluster detection for longitudinal confounding factors indexed in space. The functional-model-adjusted statistic was developed using generalized functional linear models…
Prominently used in support vector machines and logistic regressions, kernel functions (kernels) can implicitly map data points into high dimensional spaces and make it easier to learn complex decision boundaries. In this work, by replacing…
Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…
The discussion focuses on metric covariance, a new association measure between paired random objects in a metric space, developed by Dubey and M\"uller, and on its relationship with other similar concepts which have previously appeared in…
Our goal is to provide simple and practical algorithms in higher-order Fourier analysis which are based on spectral decompositions of operators. We propose a general framework for such algorithms and provide a detailed analysis of the…
This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…
In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will…
In recent years, samples of time-varying object data such as time-varying networks that are not in a vector space have been increasingly collected. These data can be viewed as elements of a general metric space that lacks local or global…
We study stochastic convolutions providing by fundamental solutions of a class of integrodifferential equations which interpolate the heat and the wave equations. We give sufficient condition for the existence of function--valued…