Related papers: Skyrmions, Rational Maps & Scaling Identities
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Motivated by problems arising in the relative trace formula and arithmetic invariant theory we prove the existence of rational points on orbits arising from certain infinitesimal symmetric spaces. As an application, we prove analogous…
We present simple examples of rational maps of the complex projective plane with equal first and second dynamical degrees and no invariant foliation.
We construct discrete analogs of Skyrmions in nonlinear dynamical lattices. The Skyrmion is built as a vortex soliton of a complex field, coupled to a dark radial soliton of a real field. Adjusting the Skyrmion ansatz to the lattice setting…
Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…
We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space. This problem is first turned into the computation of the finite…
Spatial Reasoning from language is essential for natural language understanding. Supporting it requires a representation scheme that can capture spatial phenomena encountered in language as well as in images and videos. Existing spatial…
Using atomistic simulations, we show that new types of skyrmion states called skyrmion molecular crystals and skyrmion superlattices can be realized on triangular substrates when there are two or three skyrmions per substrate minimum. We…
Magnetic skyrmions are small swirling topological defects in the magnetization texture stabilized by the protection due to their topology. In most cases they are induced by chiral interactions between atomic spins existing in…
We consider the Skyrme model modified by the addition of mass terms which explicitly break chiral symmetry and pick out a specific point on the model's target space as the unique true vacuum. However, they also allow the possibility of…
We discuss the use of matrices for providing sequences of rationals that approximate algebraic irrationalities. In particular, we study the regular representation of algebraic extensions, proving that ratios between two entries of the…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, this input data can be analyzed in…
Skyrmions were originally introduced in Particle Physics as a possible mechanism to explain the stability of particles. Lately the concept has been applied in Condensed Matter Physics to describe the newly discovered topologically protected…
We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
Two birational subvarieties of P^n are called Cremona equivalent if there is a Cremona modification of P^n mapping one to the other. If the codimension of the varieties is at least 2 then they are always Cremona Equivalent. For divisors the…
It is well known that popular optimization techniques can lead to overfitting or even a lack of convergence altogether; thus, practitioners often utilize ad hoc regularization terms added to the energy functional. When carefully crafted,…