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Fitting concentric geometric objects to digitized data is an important problem in many areas such as iris detection, autonomous navigation, and industrial robotics operations. There are two common approaches to fitting geometric shapes to…
Geometric programming (GP) is a well-known optimization tool for dealing with a wide range of nonlinear optimization and engineering problems. In general, it is assumed that the parameters of a GP problem are deterministic and accurate.…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization as optimization on Riemannian shape manifolds. We consider…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon…
We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…
We propose a new method of constraining the redshifts of individual extragalactic sources based on celestial coordinates and their ensemble statistics. Techniques from integer linear programming are utilized to optimize simultaneously for…
We present a novel method for deciding whether a given n-dimensional ellipsoid contains another one (possibly with a different center). This method consists in constructing a particular concave function and deciding whether it has any value…
Algorithms for the computation of the real zeros of hypergeometric functions which are solutions of second order ODEs are described. The algorithms are based on global fixed point iterations which apply to families of functions satisfying…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
We discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic. Via the Vessiot theory of differential equations, geometric singularities can be…
We design an algorithm for control of a linear switched system by means of Geometric Algebra. More precisely, we develop a switching path searching algorithm for a two-dimensional linear dynamical switched system with non-singular matrix…
In this work, we introduce the 3D Gaussian Point Encoder, an explicit per-point embedding built on mixtures of learned 3D Gaussians. This explicit geometric representation for 3D recognition tasks is a departure from widely used implicit…
Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the…
In this brief communication a new method is outlined for modelling magnification patterns on an observer's plane using a first order approximation to the null geodesic path equations for a point mass lens. For each ray emitted from a…
An efficient technique to solve precision problems consists in using exact computations. For geometric predicates, using systematically expensive exact computations can be avoided by the use of filters. The predicate is first evaluated…
We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realisation of the Guruswami-Sudan algorithm by using state-of-the-art algorithms from computer algebra for…
This paper presents a novel system designed for 3D mapping and visual relocalization using 3D Gaussian Splatting. Our proposed method uses LiDAR and camera data to create accurate and visually plausible representations of the environment.…
In the lattice approach to Loop Quantum Gravity on a fixed graph computations tend to be involved and are rarely analytically manageable. But, when interested in the expectation values of coherent states on the lattice which are sharply…