Related papers: Skyrmions, Rational Maps & Scaling Identities
There are only three stable singularities of a differentiable map between three-dimensional manifolds, namely folds, cusps and swallowtails. A Skyrme configuration is a map from space to SU(2), and its singularities correspond to the points…
This is, mostly, a survey of results about the birational geometry of rationally connected manifolds, using rational curves analogous to lines in ${\mathbb P}^n$ ({\it quasi-lines}). Various characterizations of a Zariski neighbourhood of a…
We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…
Semantic mapping is the incremental process of "mapping" relevant information of the world (i.e., spatial information, temporal events, agents and actions) to a formal description supported by a reasoning engine. Current research focuses on…
In this paper we provide a computational approach to the shape of curves which are rational in polar coordinates, i.e. which are defined by means of a parametrization (r(t),\theta(t)) where both r(t),\theta(t) are rational functions. Our…
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
In this paper, we establish improved effective irrationality measures for certain numbers of the form $\sqrt[3]{n}$, using approximations obtained from hypergeometric functions. These results are very close to the best possible using this…
The papers shows an algorithm to search for approximations of reals to rationals of the form a/b^2 that runs on \sqrt(b) polynomial time steps.
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…
One distinguishing feature of rational curves is that they have algebraic parameterizations. Arc spaces are a way of describing approximations to parameterizations of all curves in some fixed space. Playing on these descriptions, this paper…
We present a procedure to approximate a plane contour by piecewise polynomial functions, depending on various parameters, such as degree, number of local patches, selection of knots. This procedure aims to be adopted to study how…
This paper is devoted to the investigation of selected situations when the computation of projective (and other) equivalences of algebraic varieties can be efficiently solved with the help of finding projective equivalences of finite sets…
We look at sequences of positive integers that can be realized as degree sequences of iterates of rational dominant maps of smooth projective varieties over arbitrary fields. New constraints on the degree growth of endomorphisms of the…
To produce cartographic maps, simplification is typically used to reduce complexity of the map to a legible level. With schematic maps, however, this simplification is pushed far beyond the legibility threshold and is instead constrained by…
By combining two different techniques to construct multi-soliton solutions of the (3+1)-dimensional Skyrme model, the generalized hedgehog and the rational map ansatz, we find multi-Skyrmion configurations in $AdS_{2}\times S_{2}$. We…
Let $X,Y$ be two irreducible subvarieties of the projective space $\mathbb{P}^n$, and $d\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\bf explicitly}, in terms of $d$ and the ideals defining $X$ and…
In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…
Axially symmetric gravitating multi-skyrmion configurations are obtained using the harmonic map ansatz introduced in [1]. In particular, the effect of gravity on the energy and baryon densities of the SU(3) non-gravitating multi-skyrmion…
Polarization skyrmions are usually characterized through a unit Stokes vector field, which defines a map from the transverse plane to the Poincar\'e (Bloch) sphere and allows one to assign a skyrmion number under appropriate boundary…
We use a simulated annealing algorithm to find the static field configuration with the lowest energy in a given sector of topological charge for generalized SU(2) Skyrme models. These numerical results suggest that the following conjecture…