Related papers: Skyrmions, Rational Maps & Scaling Identities

We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of…

Static polarizabilities of the low--lying $1/2^+$ baryons are studied within the collective coordinate approach to the three flavor generalization of the Skyrme model; in particular, magnetic polarizabilities are considered. Predicted…

Skyrmion walls are topologically-nontrivial solutions of the Skyrme system which are periodic in two spatial directions. We report numerical investigations which show that solutions representing parallel multi-walls exist. The most stable…

The quantum Skyrme model is considered in non canonical bases SU(3) > SO(3) for the state vectors. A rational map ansatz is used to describe the soliton with the topological number bigger than one. The canonical quantization of the…

Magnetic skyrmions are topological magnetic spin structures exhibiting particle-like behaviour. They are of strong interest from a fundamental viewpoint and for application, where they have potential to act as information carriers in future…

This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…

When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…

This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…

We present an empirical study in the geometric task of learning interatomic potentials, which shows equivariance matters even more at larger scales; we show a clear power-law scaling behaviour with respect to data, parameters and compute…

For proper stacks, unlike schemes, there is a distinction between rational and integral points. Moreover, rational points have extra automorphism groups. We show that these distinctions exactly account for the lower order main terms…

Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of…

Rectangles are used to approximate objects, or sets of objects, in a plethora of applications, systems and index structures. Many tasks, such as nearest neighbor search and similarity ranking, require to decide if objects in one rectangle A…

This is the first report on Working Paper WP-RFM-14-01. The potential and capability of sparse representations is well-known. However, their (multivariate variable) vectorial form, which is completely fine in many fields and disciplines,…

We study determinantal Cremona maps, i.e. birational maps whose base ideal is the maximal minors ideal of a given matrix $\Phi$, via the resolution of the polynomials systems defined by $\Phi$. Using convex geometry, this approach leads in…

We study the problem of determining whether a given frame is scalable, and when it is, understanding the set of all possible scalings. We show that for most frames this is a relatively simple task in that the frame is either not scalable or…

\emph{Scalable spaces} are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are…

In this paper we present algorithms for computing the topology of planar and space rational curves defined by a parametrization. The algorithms given here work directly with the parametrization of the curve, and do not require to compute or…

We consider moduli spaces of dynamical systems of correspondences over the projective line as a generalization of moduli spaces of dynamical systems of endomorphisms on the projective line. We obtain the rationality of the moduli spaces.…

Let X be a complex, rationally connected, projective manifold. We show that X admits a modification X' that contains a quasi-line, ie a smooth rational curve whose normal bundle is a direct sum of copies of O_{P^1}(1). For manifolds…

This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…