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Previous work on three-point statistics of cosmic shear has mainly concentrated on the convergence, or on aperture measures of the shear. However, as has become clear recently for the two-point statistics of cosmic shear, the basic quantity…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images.…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…
Recent equivariant models have shown significant progress in not just chemical property prediction, but as surrogates for dynamical simulations of molecules and materials. Many of the top performing models in this category are built within…
Recent work by McClarren & Hauck [29] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
In this article, we introduce and study the concept of $\textit{spherical-vectors}$, which can be perceived as a natural extension of the arguments of complex numbers in the context of quaternions. We initially establish foundational…
This short paper is concerned with the use of spherical t-designs as optimal designs for the spherical harmonic regression model in three dimensions over a range of specified criteria. The nature of the designs is explored and their…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral decomposition of input data. We present several theoretical…
In this paper, we present a robust spherical harmonics approach for the classification of point cloud-based objects. Spherical harmonics have been used for classification over the years, with several frameworks existing in the literature.…
Recent attempts at introducing rotation invariance or equivariance in 3D deep learning approaches have shown promising results, but these methods still struggle to reach the performances of standard 3D neural networks. In this work we study…
It is common to have to process signals, whose values are points on the 3-D sphere. We consider a Tikhonov-type regularization model to smoothen or interpolate sphere-valued signals defined on arbitrary graphs. We propose a convex…
Currently, cortical surface registration techniques based on classical methods have been well developed. However, a key issue with classical methods is that for each pair of images to be registered, it is necessary to search for the optimal…
Relationships in scientific data, such as the numerical and spatial distribution relations of features in univariate data, the scalar-value combinations' relations in multivariate data, and the association of volumes in time-varying and…
Sheaf cohomology or, more generally, higher direct images of coherent sheaves along proper morphisms are central to modern algebraic geometry. However, the computation of these objects is a non-trivial and expensive task which easily…
We introduce a translational and rotational invariant local representation for vector fields, which can be employed in the construction of machine-learning energy models of solids and molecules. This allows us to describe, on the same…
We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces $Z=G/H$ attached to a real reductive Lie group $G$. A special emphasis is made to the case where $Z$ is real spherical.