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Introducing angular dispersion into a pulsed field associates each frequency with a particular angle with respect to the propagation axis. A perennial yet implicit assumption is that the propagation angle is differentiable with respect to…

We introduce the space of grid functions, a space of generalized functions of nonstandard analysis that provides a coherent generalization both of the space of distributions and of the space of Young measures. We will show that in the space…

Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…

A systematic fieldtheoretic description of critical adsorption on curved objects such as spherical or rodlike colloidal particles immersed in a fluid near criticality is presented. The temperature dependence of the corresponding order…

Researchers have now achieved great success on dealing with 2D images using deep learning. In recent years, 3D computer vision and Geometry Deep Learning gain more and more attention. Many advanced techniques for 3D shapes have been…

This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to…

We introduce the concept of entanglement width as measure of the spatial distribution of entanglement in multiparticle systems. We develop criteria to detect the width of entanglement using global observables such as energy and magnetic…

The coordinate projective line over a field is seen as a groupoid with a further `projection' structure. We investigate conversely to what extent such an, abstractly given, groupoid may be coordinatized by a suitable field constructed out…

This work presents a systematic investigation into how alternative LiDAR-to-image projections affect metric place recognition when coupled with a state-of-the-art vision foundation model. We introduce a modular retrieval pipeline that…

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…

A routine crystallography technique, crystal structure analysis, is rarely performed in computational condensed matter research. The lack of methods to identify and characterize crystal structures reliably in particle simulation data…

Although it is important both in theory as well as in applications, a theory of Birkhoff interpolation with main emphasis on the shape of the set of nodes is still missing. Although we will consider various shapes (e.g. we find all the…

The Erd\H{o}s distinct distance problem is a ubiquitous problem in discrete geometry. Somewhat less well known is Erd\H{o}s' distinct angle problem, the problem of finding the minimum number of distinct angles between $n$ non-collinear…

This article is dedicated to the anisotropic sparse grid quadrature for functions which are analytically extendable into an anisotropic tensor product domain. Taking into account this anisotropy, we end up with a dimension independent error…

Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…

This book is devoted to an informal discussion of patterns constructed for treating physical problems. Such patterns, when sufficiently formalized, are usually referred as "models", and tents to be applied not only in physics, but conquer…

Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…

Projection pursuit is used to find interesting low-dimensional projections of high-dimensional data by optimizing an index over all possible projections. Most indexes have been developed to detect departure from known distributions, such as…

A new method for analyzing the morphological features of point patterns is presented. The method is taken from the study of molecular liquids, where it has been introduced for making a statistical description of anisotropic distributions.…