arXiv research

The paper shows how label noise in training can lead to solutions that solve a Lasso program.

Researchers classify lattices in a specific four-dimensional group.

In this paper, we initiate the study of a parametrised version of Rieffel's strict deformation quantization. We apply it to give a classification of noncommutative principal torus bundles, in terms of parametrised strict deformation quantization of ordinary principal torus bundles. The paper also contains a putative de…

Develops parametrised Poincaré duality for equivariant fixed points.

In this paper, we use the parametrised strict deformation quantization of C*-bundles obtained in a previous paper, and give more examples and applications of this theory. In particular, it is used here to classify H_3-twisted noncommutative torus bundles over a locally compact space. This is extended to the case of gen…

New framework for analyzing games with multi-dimensional singular controls and non-linear jumps.

Combines ML and DA to infer unresolved scale parametrisation from noisy data.

A new approach to unsupervised learning using recognition-parametrised models.

Study uses actor-critic method for continuous-time mean-field control with entropy regularisation.

New method for handling multi-dimensional singular controls with jump costs in mean-field problems.

We show that, for certain families $φ_{\mathbf{s}}$ of diffeomorphisms of high-dimensional spheres, the commutator of the Dehn twist along the zero-section of $T^*S^n$ with the family of pullbacks $φ^*_{\mathbf{s}}$ gives a noncontractible family of compactly-supported symplectomorphisms. In particular, we find example…

The abstract proves every knot type can be parametrized by smooth functions and studies limit knot types.

We characterise completely when limit sets, as parametrised by Cannon-Thurston maps, move discontinuously for a sequence of algebraically convergent quasi-Fuchsian groups.

In this paper we are dealing with mean curvature flow with surgeries of two-convex hypersurfaces. The main focus is to expand on the discussion in Section $3$ of Mean Curvature Flow with Surgeries of Two-Convex Hypersurfaces by Huisken and Sinestrari. Firstly we wish to establish how the neck detection lemma allows us …

We introduce a new parameter to measure the inhomogeneity of training datasets.

We present a procedure which allows one to integrate explicitly the class of checkerboard IC-nets which has recently been introduced as a generalisation of incircular (IC) nets. The latter class of privileged congruences of lines in the plane is known to admit a great variety of geometric properties which are also pres…

Researchers extend parametrization of Margulis spacetimes using strip deformations.

The study characterizes quasiperiodic surfaces in pseudo-hyperbolic spaces with curvature conditions.

Biological systems are often modelled at different levels of abstraction depending on the particular aims/resources of a study. Such different models often provide qualitatively concordant predictions over specific parametrisations, but it is generally unclear whether model predictions are quantitatively in agreement, …

Proposes a new Gaussian factor for probabilistic inference with degenerate settings.

Study on deformations of Einstein and nearly G2 structures in 3-Sasaki manifolds.

In this article we introduce a definition for the moduli space of equivariant minimal immersions of the Poincaré disc into a non-compact symmetric space, where the equivariance is with respect to representations of the fundamental group of a compact Riemann surface of genus at least two. We then study this moduli space…

For a given bundle $ξ\colon E \to M$ over a manifold, configuration-section spaces on $ξ$ parametrise finite subsets $z \subseteq M$ equipped with a section of $ξ$ defined on $M \smallsetminus z$, with prescribed "charge" in a neighbourhood of the points $z$. These spaces may be interpreted physically as spaces of fiel…

Study computability of real numbers from group properties.

By studying the Higgs bundle equations with the gauge group replaced by the group of symplectic diffeomorphisms of the 2-sphere we encounter the notion of a folded hyperkaehler 4-manifold and conjecture the existence of a family of such metrics parametrised by an infinite-dimensional analogue of Teichmueller space.

We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class $C^k$. The conditions allow for the probability densities to approach zero towards the boundary of the manifold. We also formulate two obstructions to regular …

Investigates second-order conditions for Cayley forms in eight dimensions.

New unknots with geometric constraints exist, proving a long-standing conjecture.

Convolutional Neural Processes improve data efficiency in neural processes.

We re-examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather than parametrising our basic degrees of freedom by a specified Grassmann algebra, w…

Universal geometry organizes heterotic moduli spaces.

Paper analyzes convergence of dynamic policy gradient for MDPs, improving performance in finite-time problems.

New approach predicts under latent shifts using high-dimensional images.

New CMC surfaces with dihedral symmetry constructed from Darboux transforms.

New discrete models for constant mean curvature surfaces and tori.

Rolling two hyperboloid surfaces is described using a Monge normal form.

Quantum models can approximate any function if data encoding allows for a rich enough frequency spectrum.

In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This equation reduces to studying the curve diffusion flow for the profile curve of the ribbon. We provide: (1) a complete classification of stationary solutions; (2) qualitative results on shrinkers, tr…

We study the degree of polynomial representations of knots. We give the lexicographic degree of all two-bridge knots with 11 or fewer crossings. First, we estimate the total degree of a lexicographic parametrisation of such a knot. This allows us to transform this problem into a study of real algebraic trigonal plane c…

Conservation laws vanishing along characteristic directions of a given system of PDEs are known as characteristic conservation laws, or characteristic integrals. In 2D, they play an important role in the theory of Darboux-integrable equations. In this paper we discuss characteristic integrals in 3D and demonstrate that…

In this note, we extend the theory of Chern-Cheeger-Simons to construct canonical invariants for a one-parameter family of flat connections on a smooth manifold. These invariants lie in degrees $(2p-2)$-cohomology with $\C/\Z$-cohomology, for $p\geq 2$. Furthermore, they are shown to be rigid in a variation of paths (p…

The paper describes a parametrisation of harmonic maps from a 2-torus to the 3-sphere.

New method for foliated bundles using holonomy groupoids.

Deep model predicts shapes of curves with multiple covariates.

We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which a well known triviality result exists, the Miura equivalence class…

Study strip deformations of hyperbolic polygons with decorated vertices.

We obtain the Weierstrass-Enneper representation for maximal graphs(whose Gauss map is one-one) in Lorentz-Minkowski space. For this we use the method of Barbishov and Chernikov, which they have used to find the solutions of Born-Infeld equation in hodographic coordinates. We could use their method in our case, because…

New method linearizes Darboux transformations of discrete curves.