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While 3D Gaussian Splatting (3DGS) excels in static scene modeling, its extension to dynamic scenes introduces significant challenges. Existing dynamic 3DGS methods suffer from either over-smoothing due to low-rank decomposition or feature…

A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results…

The orientation and stability of the reconnection x-line in asymmetric geometry is studied using three-dimensional (3D) particle-in-cell simulations. We initiate reconnection at the center of a large simulation domain to minimize the…

In the past decades, many graph drawing techniques have been proposed for generating aesthetically pleasing graph layouts. However, it remains a challenging task since different layout methods tend to highlight different characteristics of…

This is a comparative study of the traditional 3D computer graphics technique of geometric modelling and image-based rendering techniques that were surveyed and implemented.We have discussed the classifications and representative methods of…

This paper introduces Polynomial Graphical Lasso (PGL), a new approach to learning graph structures from nodal signals. Our key contribution lies in modeling the signals as Gaussian and stationary on the graph, enabling the development of a…

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…

Compression techniques for 3D Gaussian Splatting (3DGS) have recently achieved considerable success in minimizing storage overhead for 3D Gaussians while preserving high rendering quality. Despite the impressive storage reduction, the lack…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…

Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…

We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…

A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…

A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…

This paper gives a key definition, for a new approach to dessins and algebraic numbers. The distant goal is to construct from each dessin $D$ an algebraic number $\eta_D$, in a systematic and useful way. The algebra of balanced dessins is…

We propose a numerical method to solve the three-dimensional static Maxwell equations in a singular axisymmetric domain, generated by the rotation of a singular polygon around one of its sides. The mathematical tools and an in-depth study…

Recently, the application of machine learning models has gained momentum in natural sciences and engineering, which is a natural fit due to the abundance of data in these fields. However, the modeling of physical processes from simulation…

A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…

We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…

Existing diffusion-based text-to-3D generation methods primarily focus on producing visually realistic shapes and appearances, often neglecting the physical constraints necessary for downstream tasks. Generated models frequently fail to…