Related papers: Skyrmions, Rational Maps & Scaling Identities
We construct an explicit bijection between bipartite pointed maps of an arbitrary surface $\mathbb{S}$, and specific unicellular blossoming maps of the same surface. Our bijection gives access to the degrees of all the faces, and distances…
We investigate complete arcs of degree greater than two, in projective planes over finite fields, arising from the set of rational points of a generalization of the Hermitian curve. The degree of the arcs is closely related to the number of…
Topological defects play a key role in a variety of physical systems, ranging from high-energy to solid state physics. They yield fascinating emergent phenomena and serve as a bridge between the microspic and macroscopic world. A skyrmion…
Spatial reasoning is a crucial component of both biological and artificial intelligence. In this work, we present a comprehensive study of the capability of current state-of-the-art large language models (LLMs) on spatial reasoning. To…
The observation of skyrmions across diverse physical domains suggests that they are universal features of S$^{2}$-valued fields, reflecting the ubiquity of topology in the study of the natural world. In this paper, we develop an abstract…
The skyrmion, which is characterised by a topological integer, is a structure that is topologically stable against local disturbances. The huge potential of skyrmions for use in magnetic storage systems has drawn considerable research…
We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points.
The multiskyrmions with large baryon number B given by rational map (RM) ansaetze can be described reasonably well within the domain wall approximation, or as spherical bubbles with energy and baryon number density concentrated at their…
The statistical shape analysis called Procrustes analysis minimizes the distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This…
The present paper attempts to show an alternative approach with regards to rational Pythagorean-hodograph (PH) curves and especially more natural approach for rational PH helices (i.e. rational helices). It exploits geometric features of…
Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…
We study the local approximation properties in hierarchical spline spaces through multiscale quasi-interpolation operators. This construction suggests the analysis of a subspace of the classical hierarchical spline space (Vuong et al.,…
The existing algorithms for processing skyline queries cannot adapt to big data. This paper proposes two approximate skyline algorithms based on sampling. The first algorithm obtains a fixed size sample and computes the approximate skyline…
Skyrmions are important in topological quantum field theory for being soliton solutions of a nonlinear sigma model and in information technology for their attractive applications. Skyrmions are believed to be circular and stripy spin…
The iteration of rational maps is well-understood in dimension 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First we give some properties of…
A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there…
We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.
Any subset of the plane can be approximated by a set of square pixels. This transition from a shape to its pixelation is rather brutal since it destroys geometric and topological information about the shape. Using a technique inspired by…
Skyrmions are important topologically non-trivial fields characteristic of models spanning scales from the microscopic to the cosmological. However, the Skyrmion number can only be defined for fields with specific boundary conditions,…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…