Related papers: SpinorHelicity4D: a Mathematica toolbox for the fo…

Automated formalization of mathematics enables mechanical verification but remains limited to isolated theorems and short snippets. Scaling to textbooks and research papers is largely unaddressed, as it requires managing cross-file…

In this article, we extend the %Weyl-van der Waerden spinor technique for calculating helicity amplitudes to general massive fields of half-integer spins. We find that the little group generators can be represented as first-order…

We use on-shell methods to compute all three-point interactions of massive spin-3/2 particles involving a graviton and particles of spin $\leq 1$. By employing the massive spinor-helicity formalism we identify the interactions which have a…

With current trends in sensors (cheaper, more volume of data) and applications (increasing affordability for new tasks, new ideas in what 3D data could be useful for); there is corresponding increasing interest in the ability to…

We present a new framework for defining fuzzy approximations to geometry in terms of a cutoff on the spectrum of the Dirac operator, and a generalization of it that we call the Dirac-Flux operator. This framework does not require a…

This work puts forth low-complexity Riemannian subspace descent algorithms for the minimization of functions over the symmetric positive definite (SPD) manifold. Different from the existing Riemannian gradient descent variants, the proposed…

This text is addressed to mathematicians who are interested in generalized functions and unbounded operators on a Hilbert space. We expose in detail (in a "formal way" - as done by Heisenberg and Pauli - i.e. without mathematical…

We are concerned with rigid analytic geometry in the general setting of Henselian fields $K$ with separated analytic structure, whose theory was developed by Cluckers--Lipshitz--Robinson. It unifies earlier work and approaches of numerous…

We explore differential and algebraic operations on the exterior product of spinor representations and their twists that give rise to cohomology, the spin cohomology. A linear differential operator $d$ is introduced which is associated to a…

In the field of computational fluid dynamics, direct numerical simulations generate highly detailed data for the analysis of turbulent flows by resolving all relevant physical scales. Yet their large size, complexity, and heterogeneity make…

Lorentzian 4-metrics are expressed in spinorial coordinates. In these coordinates the metric components can be factorized into a product of complex conjugate quantities. The linearized theory and Einstein's vacuum field equations are…

The pure spinor formalism for the superstring has the advantage over the more conventional Ramond-Neveu-Schwarz formalism of being manifestly spacetime supersymmetric, which simplifies the computation of multiparticle and multiloop…

Accurately perceiving and tracking instances over time is essential for the decision-making processes of autonomous agents interacting safely in dynamic environments. With this intention, we propose Mask4Former for the challenging task of…

A data structure and toolkit are presented here that allow for the description and manipulation of mathematical models of three-manifolds and their interactive display from multiple viewpoints via the OpenGL 3D graphics package. The data…

Semantic segmentation of LiDAR points has significant value for autonomous driving and mobile robot systems. Most approaches explore spatio-temporal information of multi-scan to identify the semantic classes and motion states for each…

Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher…

Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal control of differential equations. These models are…

Many areas of science and engineering encounter data defined on spherical manifolds. Modelling and analysis of spherical data often necessitates spherical harmonic transforms, at high degrees, and increasingly requires efficient computation…

Large language models have demonstrated promising capabilities upon scaling up parameters. However, serving large language models incurs substantial computation and memory movement costs due to their large scale. Quantization methods have…

Micro- and mesostructures of multiphase materials obtained from tomography and image acquisition are an ever more important database for simulation analyses. Huge data sets for reconstructed 3d volumes typically as voxel grids call for…