Graph-based weather prediction adapted for local models.
problem Applying neural weather prediction to limited area modeling.
method Adapting graph-based Neural Weather Prediction approach to local models.
result Validation of multi-scale hierarchical model extension for Nordic region.
Classifies central extensions for area-preserving diffeomorphisms and shows they are fuzzy sphere limits.
problem Classifying central extensions for area-preserving diffeomorphisms.
method Classifying central extensions and showing they are fuzzy sphere limits of Kac-Moody cocycles.
result Central extensions are fuzzy sphere limits of Kac-Moody cocycles for large k.
NeuroPaint infers missing brain area dynamics from multi-animal datasets.
problem Leveraging multi-animal datasets to understand interactions between brain areas.
method Masked autoencoding approach trained across animals with partial observations.
result Models can successfully reconstruct dynamics of unrecorded brain areas.
The paper shows how heat flow approximates area functional on specific geometric spaces.
problem Approximating the area functional on $\RCD(K,\infty)$ spaces.
method Using heat flow and properties of $\RCD(K,\infty)$ spaces.
result The area functional coincides with its relaxation in $\RCD(K,\infty)$ spaces.
New limits of minimal surface systems have surprising large interior parts.
problem Minimal surface system limits with large interior vertical and non-minimal portions.
method Construction of limits with smallest possible dimension and codimension.
result Limits of minimal surface systems can have surprising large interior parts.
Minimal surfaces in a ball have limited area.
problem Bounding the area of genus zero minimal surfaces in a unit ball.
method Proving an area inequality and showing convergence of saturating sequences.
result The area of each nonflat surface is less than its radial projection, with sharp asymptotic bounds.
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.
problem Preserving area while deforming plane curves.
method Non-local flow of convex closed plane curves.
result Limiting curve is a circle in the C∞ metric. We prove prove a bridge principle at infinity for area-minimizing surfaces in the hyperbolic space H3, and we use it to prove that any open, connected, orientable surface can be properly embedded in H3 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.
problem The reliability of limit order book representations under data perturbation.
method Experimental analysis of existing representations and guidelines for future research.
result Existing representations of limit order book data are vulnerable to data perturbation.
The paper studies minimal surfaces in 3D spheres and balls, confirming conjectures and identifying new surfaces.
problem Understanding minimal surfaces in 3D spheres and balls with low area.
method Equivariant optimization of Laplace and Steklov eigenvalues to construct minimal surfaces of prescribed topology.
result Sharp area estimates and varifold limits for minimal surfaces in large topology regimes.
Survey on strong convergence in random matrices and its applications.
problem Understanding convergence of random matrices to operators.
method Analysis of operator norms of noncommutative polynomials.
result New insights and applications in random graphs, geometry, and operator algebras.
New formulas limit minimal submanifolds' area in curved spaces.
problem Bounding minimal submanifolds' area in curved spaces.
method Developed new monotonicity formulae involving energy-like integrals over non-geodesic sets.
result Imply sharp area bounds for minimal submanifolds through a prescribed point.
New foliations found for critical surfaces of Hawking energy, resolving discrepancies.
problem Finding consistent critical surfaces for the Hawking energy in non-totally geodesic spacelike hypersurfaces.
method Constructing a unique local foliation of area constrained critical surfaces of the Hawking energy in the general case of non-totally geodesic spacelike hypersurfaces.
result Discrepancy found in the small sphere limit of the Hawking energy, explained and resolved.
Survey on Gaussian processes and their deep variants.
problem Limitations of Gaussian processes and their derivatives.
method Comprehensive review of existing methods and research themes.
result Advancements in Deep Gaussian Processes over the past decade.
PriorVAE uses VAEs to efficiently encode spatial priors for small-area estimation.
problem Efficiently encoding spatial priors for small-area estimation using Gaussian processes.
method Approximating Gaussian process priors with a variational autoencoder (VAE).
result Efficient spatial inference through a low-dimensional latent Gaussian space representation.
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.
problem Existence of area-minimizing homotopies between homotopic curves in the plane.
method Geometric and variational approach, lifting curves into higher co-dimension, applying Douglas's solution of the Plateau problem.
result Uniform convergence of Douglas minimizers and minimal homotopy area minimization.
This paper proves compactness of conformal Chern-minimal surfaces in Hermitian surfaces.
problem Compactness of conformal Chern-minimal surfaces in Hermitian surfaces.
method Proves compactness through bubble tree limit analysis.
result Compactness of conformal Chern-minimal surfaces is established with bounded area.
This paper constructs Brownian motion on complex flag manifolds and finds joint distribution of stochastic areas.
problem Modeling stochastic areas on complex partial flag manifolds.
method Constructs Brownian motion on complex partial flag manifolds and uses it to find joint distribution of stochastic areas.
result Limit law of stochastic areas is a multivariate Cauchy distribution.
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.
problem Modeling quaternionic stochastic areas on quaternionic flag manifolds.
method Relating quaternionic Brownian motion to symplectic Brownian motion and using radial dynamics.
result Quaternionic stochastic areas follow a multivariate normal distribution.
Predictive policing models can be biased by differential crime reporting rates.
problem Bias in predictive policing models due to differential crime reporting.
method Simulation based on Bogotá, Colombia's victimization and crime reporting data.
result Differential crime reporting rates can lead to misallocation of police patrols.
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 T2, with standard uniform C/t curvature decay, and with initial metrics converging to the standard flat unit-area square torus g0 in the Gromov-Hausdorff sense, with the property that the flows themselves converge not to the static Ricci flow g(t)≡g0, 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 Rn≥2 as an sharp upper bound of the variational (1,n)∋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 W2,2 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.
problem Estimating population characteristics in small areas with limited data.
method Integrates multivariate spatial Fay-Herriot model with variational autoencoders to leverage spatial structure efficiently.
result Significant computational efficiency improvements for high-dimensional datasets.
We study quaternionic stochastic areas processes associated with Brownian motions on the quaternionic rank-one symmetric spaces HHn and HPn. 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.
problem Characterize area-minimizing hypersurfaces in manifolds with Ricci curvature bounds.
method Apply Cheeger-Colding theory and blow-up techniques to analyze hypersurfaces.
result Proves continuity of volume functions and existence of area-minimizing limits.
The paper proves prevalent existence and partially determines moduli space of area-minimizing surfaces with fractal singular sets.
problem Existence and moduli space of area-minimizing surfaces with fractal singular sets.
method Proof of prevalent existence, determination of moduli space, refinement of strata.
result Sharp results on moduli space and refinement of strata, showing fractal singularities do not completely dissolve under generic perturbations.
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.
problem Understanding the limits of Fuchsian surfaces in hyperbolic 3-manifolds.
method Analyzing asymptotically Fuchsian maps and their induced probability area measures.
result Weak-* limits of induced area measures are convex combinations of Haar and totally geodesic surface measures.
Study shows negatively curved manifolds' spherical volume equals minimal surface area.
problem Understanding the spherical volume of negatively curved manifolds.
method Combining metric currents theory and limits of hyperbolic groups' representations.
result Spherical volume of negatively curved manifolds equals minimal surface area.
We prove that capillary surfaces converge to a specific energy density as the angle approaches zero.
problem Understanding the limiting behavior of capillary surfaces as the angle approaches zero.
method Rigorous limiting analysis and application to curvature estimates.
result Capillary area-density converges to the Weiss energy density as the angle tends to zero.
Research aims to make fact-checking models more transparent.
problem Making fact-checking models explainable in a complex field.
method Combines fact-checking methods with explainable AI techniques.
result Developed initial solutions for explainable fact-checking.
The paper confirms a conjecture for 3D manifolds and extends it to 3-7D under specific conditions.
problem Confirming a conjecture about asymptotically flat Riemannian manifolds with nonnegative scalar curvature.
method Analyzing limits of isoperimetric surfaces to extend a 3D result to higher dimensions.
result The conjecture holds for 3D and is extended to 3-7D under certain 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.
problem Sparse sensor deployment and unreliable data in spatiotemporal kriging tasks.
method Graph transformer model with positional encoding and attention mechanisms.
result Kriformer excels in representing unobserved locations in spatiotemporal kriging tasks.
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.
problem Quantization of Willmore energy in bounded energy and area conditions.
method Uniform boundedness of Willmore energy and area, weak convergence of maps, and conformal structures in compact domain.
result Quantization of Willmore energy holds under specified conditions.
Paper introduces ILD algorithm to determine Bayes error for binary classification.
problem Determining the best possible performance in binary classification problems.
method Model-agnostic ILD algorithm to calculate Bayes error.
result Provides intrinsic limits of any binary classification algorithm.
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…
Formulates approach for guiding explanation types based on user specifications.
problem Creating explainable AI components from user-defined specifications.
method Develops a method for generating explanations based on user-defined specifications.
result Demonstrates feasibility of user-defined explanations for complex models like Bayesian networks and graph neural networks.