arXiv research

Graph-based weather prediction adapted for local models.

Classifies central extensions for area-preserving diffeomorphisms and shows they are fuzzy sphere limits.

NeuroPaint infers missing brain area dynamics from multi-animal datasets.

The paper shows how heat flow approximates area functional on specific geometric spaces.

New limits of minimal surface systems have surprising large interior parts.

Minimal surfaces in a ball have limited area.

We consider the Willmore functional on graphs, with an additional penalization of the area where the curvature is non-zero. Interpreting the penalization parameter as a Lagrange multiplier, this corresponds to the Willmore functional with a constraint on the area where the graph is flat. Sending the penalization parame…

Study a flow preserving area of plane curves, ending in a circle.

We prove prove a bridge principle at infinity for area-minimizing surfaces in the hyperbolic space $\mathbb{H}^3$, and we use it to prove that any open, connected, orientable surface can be properly embedded in $\mathbb{H}^3$ as an area-minimizing surface. Moreover, the embedding can be constructed in such a way that t…

The excluded area between a pair of two-dimensional hard particles with given relative orientation is the region in which one particle cannot be located due to the presence of the other particle. The magnitude of the excluded area as a function of the relative particle orientation plays a major role in the determinatio…

We prove an isoperimetric inequality for the second non-zero eigenvalue of the Laplace-Beltrami operator on the real projective plane. For a metric of the unit area this eigenvalue is not greater than 20π. This value is attained in the limit by a sequence of metrics of area one on the projective plane. The limiting met…

The paper examines the reliability of limit order book representations in the face of data perturbation.

The paper studies minimal surfaces in 3D spheres and balls, confirming conjectures and identifying new surfaces.

Survey on strong convergence in random matrices and its applications.

New formulas limit minimal submanifolds' area in curved spaces.

New foliations found for critical surfaces of Hawking energy, resolving discrepancies.

Survey on Gaussian processes and their deep variants.

PriorVAE uses VAEs to efficiently encode spatial priors for small-area estimation.

We prove qualitative estimates on the total curvature of closed minimal hypersurfaces in closed Riemannian manifolds in terms of their index and area, restricting to the case where the hypersurface has dimension less than seven. In particular, we prove that if we are given a sequence of closed minimal hypersurfaces of …

The paper proves existence of minimal homotopies for immersed planar curves.

This paper proves compactness of conformal Chern-minimal surfaces in Hermitian surfaces.

This paper constructs Brownian motion on complex flag manifolds and finds joint distribution of stochastic areas.

Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with multiplicity, and we analyze what happens when one blows up the surfaces near a point where…

Quaternionic Brownian motion on flag manifold linked to sphere diffusion.

Predictive policing models can be biased by differential crime reporting rates.

We introduce notions of Cheeger constants for graphons and graphings. We prove Cheeger and Buser inequalities for these. On the way we prove co-area formulae for graphons and graphings.

We construct a sequence of smooth Ricci flows on $T^2$, with standard uniform $C/t$ curvature decay, and with initial metrics converging to the standard flat unit-area square torus $g_0$ in the Gromov-Hausdorff sense, with the property that the flows themselves converge not to the static Ricci flow $g(t)\equiv g_0$, bu…

We survey - by means of 20 examples - the concept of varifold, as generalised submanifold, with emphasis on regularity of integral varifolds with mean curvature, while keeping prerequisites to a minimum. Integral varifolds are the natural language for studying the variational theory of the area integrand if one conside…

Through using the semidiameter (in connection to: the mean radius and surface radius) of a convex closed hypersurface in $\mathbb R^{n\ge 2}$ as an sharp upper bound of the variational $(1,n)\ni p$-capacity radius, this paper settles a restriction/variant of S.-T. Yau's \cite[Problem 59]{Yau} from the surface area to t…

We develop a bubble tree construction and prove compactness results for $W^{2,2}$ branched conformal immersions of closed Riemann surfaces, with varying conformal structures whose limit may degenerate, in a compact Riemannian manifold with uniformly bounded areas and Willmore energies. The compactness property is appli…

Paper proposes efficient multivariate spatial Fay-Herriot models using variational autoencoders.

We study quaternionic stochastic areas processes associated with Brownian motions on the quaternionic rank-one symmetric spaces $\mathbb{H}H^n$ and $\mathbb{H}P^n$. The characteristic functions of fixed-time marginals of these processes are computed and allows for the explicit description of their corresponding large-t…

Study area-minimizing hypersurfaces in manifolds with controlled curvature.

The paper proves prevalent existence and partially determines moduli space of area-minimizing surfaces with fractal singular sets.

We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties: not on…

Study shows limits of Fuchsian surfaces in hyperbolic 3-manifolds.

Study shows negatively curved manifolds' spherical volume equals minimal surface area.

We prove that capillary surfaces converge to a specific energy density as the angle approaches zero.

Research aims to make fact-checking models more transparent.

The paper confirms a conjecture for 3D manifolds and extends it to 3-7D under specific conditions.

Intensive care clinicians are presented with large quantities of patient information and measurements from a multitude of monitoring systems. The limited ability of humans to process such complex information hinders physicians to readily recognize and act on early signs of patient deterioration. We used machine learnin…

The use of computational methods to evaluate aesthetics in photography has gained interest in recent years due to the popularization of convolutional neural networks and the availability of new annotated datasets. Most studies in this area have focused on designing models that do not take into account individual prefer…

Kriformer uses graph transformers to estimate data in sparse sensor areas.

We consider the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain or at a straight line. We give a criterion on initial curves that guarantees the appearance of a singularity in finite time. We prove that the singularity is of type II. Furthermore, if these initial c…

Quantizes Willmore energy in Riemannian manifolds with bounded energy and area.

Paper introduces ILD algorithm to determine Bayes error for binary classification.

State-of-the-art solutions in the areas of "Language Modelling & Generating Text", "Speech Recognition", "Generating Image Descriptions" or "Video Tagging" have been using Recurrent Neural Networks as the foundation for their approaches. Understanding the underlying concepts is therefore of tremendous importance if we …

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are multi-scattering effect…