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The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our…
The goal of this primer is to provide a relatively short exposition of the basics of multigrid methods, simplified by focusing on fundamental concepts in a variational setting. This is done by way of a quadratic energy minimization…
We present a framework for constructing Generalized Parton Distributions (GPDs) using holographic QCD in the large $N_c$ limit, with a focus on low-x and finite skewness. Our approach utilizes holographic amplitudes for exclusive…
We show how two-dimensional mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical cores for numerical weather prediction on pseudo-uniform…
For a group $G$, the generating graph $\Gamma(G)$ is defined as the graph with the vertex set $G$, and any two distinct vertices of $\Gamma(G)$ are adjacent if they generate $G$. In this paper, we study the generating graph of $D_n,$ where…
We introduce a layered random spin model, equivalent to the Generalized Random Energy Model (GREM). In analogy with diluted spin systems, a diluted GREM (DGREM) is introduced.It can be applied to calculate approximately thermodynamic…
We summarize recent developments in understanding the concept of generalized parton distributions (GPDs), its relation to nucleon structure, and its application to high-Q2 electroproduction processes. Following a brief review of QCD…
Turbulence is still one of the main challenges for accurately predicting reactive flows. Therefore, the development of new turbulence closures which can be applied to combustion problems is essential. Data-driven modeling has become very…
We introduce a new family of Generalised Parton Distribution models able to fulfil by construction all the theoretical properties imposed by QCD. These models are built on standard Parton Distribution Functions and extended to off-forward…
We present Gradient Gating (G$^2$), a novel framework for improving the performance of Graph Neural Networks (GNNs). Our framework is based on gating the output of GNN layers with a mechanism for multi-rate flow of message passing…
In many numerical schemes, the computational complexity scales non-linearly with the problem size. Solving a linear system of equations using direct methods or most iterative methods is a typical example. Algebraic multi-grid (AMG) methods…
We use grid diagrams to present a unified picture of braids, Legendrian knots, and transverse knots.
Digital twin worlds with realistic interactive dynamics presents a new opportunity to develop generalist embodied agents in scannable environments with complex physical behaviors. To this end, we present GDGen (Generalized Representation…
Simulation has become the evaluation method of choice for many areas of distributing computing research. However, most existing simulation packages have several limitations on the size and complexity of the system being modeled. Fine…
The purpose of this paper is to develop a simplified model as the modeling of the magnetized plasmas. The starting point is an assumption that the distribution of the ensemble of charged particles in the same species is homogeneous over…
A grid polygon is a polygon whose vertices are points of a grid. We define an injective map between permutations of length n and a subset of grid polygons on n vertices, which we call consecutive-minima polygons. By the kernel method, we…
Gyrokinetics is a rich and rewarding playground to study some of the mysteries of modern physics. In this thesis I present work, motivated by the quest for fusion energy, which seeks to uncover some of the inner workings of turbulence in…
3D Gaussian Splatting (3D-GS) has emerged as a significant advancement in the field of Computer Graphics, offering explicit scene representation and novel view synthesis without the reliance on neural networks, such as Neural Radiance…
In image anomaly detection, significant advancements have been made using un- and self-supervised methods with datasets containing only normal samples. However, these approaches often struggle with fine-grained anomalies. This paper…