Two combinatorial models for moduli space are compared and homotopy equivalence proven.
problem Comparing and relating combinatorial models of moduli space.
method Using a critical graph map to produce an explicit homotopy equivalence between Bödigheimer's radial slit configurations and Godin's admissible fat graphs, and discussing natural compactifications.
result Induces a cellular homeomorphism between unilevel harmonic compactification and Sullivan diagrams.
Study calculates stable norm of slit tori using Farey sequence.
problem Computing the stable norm of slit tori.
method Explicit computations using the Farey sequence and gluing slit tori.
result Estimates the asymptotic counting of simple homology classes.
Formula for Laplacian determinants on polygonal domains with slits.
problem Determining the ζ-regularized determinant of the Laplacian on polygonal domains with slits. method Patchwork method for heat trace asymptotics, comparison formula for smooth conformal metrics.
result Polyakov-Alvarez type formula for Laplacian determinants on polygonal domains with slits.
The paper introduces new metrics on Finsler manifolds and characterizes associated vector fields.
problem Characterizing vector fields on Finsler manifolds with new metrics.
method Introducing F-natural metrics and characterizing conformal, homothetic, and Killing vector fields. result Characterization of vector fields on slit tangent bundles of Finsler manifolds.
The paper studies minimal resistance dynamics in radial fields, finding unique solutions for incompressible flows.
problem Nonlinear dynamics of minimal resistance in radial fields.
method Analysis of two non-equilibrium scenarios: scale-invariant free expansion and incompressible source flow.
result Incompressible flow acts as a structural regularizer, admitting unique, smooth, and strictly concave solutions.
Gradient-based training and pruning for radial basis function networks in materials physics.
problem Interpretable and robust machine learning for materials physics problems.
method Gradient-based training and pruning of radial basis function networks with closed-form optimization criteria.
result Pruned models provide compact and interpretable versions of larger models, offering insights into atom-level migration processes.
Introduces non-Archimedean metrics for pseudoeffective classes on Kähler manifolds.
problem Characterizing and approximating non-Archimedean metrics on pseudoeffective classes.
method Extending Ross-Witt Nyström correspondence to relative case, introducing flag configurations.
result Non-Archimedean finite energy metrics are approximable by flag configurations, and very general Ding energies are continuous.
New proof shows set of saddle connections has finite Cantor-Bendixson rank.
problem Characterizing saddle connections on meromorphic quadratic differentials.
method Introduced slit translation surfaces to study meromorphic quadratic differentials with higher order poles.
result Set of directions admitting saddle connections has finite Cantor-Bendixson rank.
Researchers prove long-time existence for two landmark Brownian motion.
problem Proving long-time existence of Brownian motion on configurations of two landmarks.
method Classification and analysis of long-time existence for configurations of exactly two landmarks, using a radial kernel.
result For configurations of exactly two landmarks, long-time existence is possible for certain kernels, but not for others.
A new method efficiently optimizes deep learning hyperparameters using deterministic RBF surrogates.
problem Efficiently optimizing hyperparameters of deep learning algorithms is crucial but computationally expensive.
method Proposes a deterministic hyperparameter optimization method using radial basis functions (RBFs).
result Significantly faster than existing methods (6 times faster on average for 19 hyperparameters).
A new method helps novices automatically set AutoDock's hyperparameters.
problem Helping novice users set optimal AutoDock hyperparameters.
method Surrogate based multi-objective algorithm using radial basis function model and non-dominated sorting.
result The method effectively helps novices set AutoDock hyperparameters.
New multi-spiral approach improves packaging of thick membranes.
problem Deploying thick membranes on curved surfaces efficiently.
method Multi-spiral folding approach with prismatic folding lines.
result Improved deployment performance of thick membranes on curved surfaces.
Researchers compute gap distributions for saddle connection directions on specific translation surfaces.
problem Computing gap distributions for saddle connection directions on translation surfaces.
method Translation to dynamical question of return times to a transversal under the horocycle flow.
result Gap distributions have support at 0 and quadratic tail decay.
Uniqueness of circle packings on certain translation surfaces is proven.
problem Proving the uniqueness of circle packings on specific translation surfaces.
method Using splitting bigons to characterize variations of circle packings.
result For certain circle packings on H(1,1) translation surfaces, there are only a finite number of ways the packing can vary without changing the contacts graph. On the slit tangent manifold of a Finsler manifold M are given the vertical and the Liouville foliations. In this paper we define some new types of vertical forms with respect to the Liouville foliation on TM^0. We define a cohomology group of TM^0 using these new forms. We prove a de Rham type theorem.
GPRNs accurately model stellar activity affecting RV measurements of exoplanets.
problem Stellar activity limits detection and characterisation of exoplanets.
method Gaussian Process Regression Networks (GPRNs) for joint analysis of RV data and stellar activity indicators.
result GPRNs accurately describe solar RV data, correlating with activity at separations of a few days.
Sharp bounds for Calabi energy derived from geodesic rays and Mabuchi K-energy.
problem Sharp lower bounds for Calabi energy in Kähler geometry.
method Using geodesic rays and Mabuchi K-energy, derived a sharp bound for Calabi energy.
result Sharp bound for Calabi energy derived from geodesic rays and Mabuchi K-energy is proven to be sharp.
The paper generalizes radial curvature bounds on manifolds.
problem Bounding radial curvature on Riemannian manifolds.
method Introducing a new class of manifolds with radial curvature constraints.
result New insights into curvature properties of manifolds.
Neural nets solve electric field in non-convex microfluidic devices.
problem Solving differential equations in non-convex geometries.
method Neural network approximation of electric potential and field.
result Deep neural networks outperform shallow networks in accuracy.
Proof of smooth radial sections in vector bundles.
problem Existence of smooth radial sections in vector bundles.
method Proof of existence using linear connection.
result Existence of smooth radial sections in vector bundles.
All radially symmetric connections on round spheres are parallel.
problem Classifying radially symmetric connections in vector bundles over spheres.
method Proving all such connections are parallel.
result Radially symmetric connections on round spheres are parallel.
Convexity properties are preserved under radial transformations in hyperbolic and spherical geometries.
problem Preserving convexity in hyperbolic and spherical geometries under radial transformations.
method Used Poincaré disk model for hyperbolic geometry and stereographic projection for spherical geometry to prove preservation of convexity under radial expansion and contraction.
result Radial expansion and contraction preserve hyperbolic and spherical convexity, respectively.
Study examines maximal domains of radial harmonic functions across different curvature types.
problem Understanding maximal domains of radial harmonic functions in various curvature settings.
method Analysis of harmonic spaces with positive, zero, and negative curvature.
result Characterization of maximal domains for radial harmonic functions in different curvature contexts.
New findings show Berwald Finsler spacetimes cannot be metrized.
problem Can Szabo's metrizability theorem be extended to Finsler spacetimes?
method Investigation of Berwald Finsler spacetimes and their properties.
result Found a class of Berwald spacetimes with asymmetric Ricci tensors.
Study geometry and topology of manifolds with radial curvature bounds.
problem Understanding manifolds with specific curvature constraints.
method Systematic investigation of manifolds with integral radial curvature bounds.
result Obtained many interesting and important conclusions about manifold geometry and topology.
Study on radial solutions in higher dimensions, finding special cases.
problem Analyzing radial solutions to Hamiltonian stationary equations in various dimensions.
method Examined smooth radial solutions defined away from the origin, focusing on dimensions two and higher.
result In higher dimensions, non-special Lagrangian radial solutions exist near the origin, with continuity conditions.
The study characterizes harmonic spaces and their radial eigen-functions and vector fields.
problem Characterizing harmonic spaces and their geometric properties.
method Examining radial eigen-spaces of Laplacians and using duality.
result Results extend to spaces harmonic with respect to a single point.
Data-driven method estimates urban MV and LV grid topology using smart meter data.
problem Reliability issues in urban distribution grids due to distributed energy resources.
method Probabilistic graphical model with group lasso regularization.
result Highly accurate topology estimation in various grid configurations.
No radial balanced metrics found on Kepler manifold unit ball with mild boundary conditions.
problem Finding radial balanced metrics on the unit ball of the Kepler manifold.
method Analyzing boundary behavior and weights of metrics.
result Explicit weights for radial metrics satisfying balanced condition identified.
Study complete gradient Ricci solitons with zero radial Weyl curvature.
problem Characterize complete gradient Ricci solitons with specific curvature properties.
method Classify complete gradient Ricci solitons with zero radial Weyl curvature for dimensions n≥4. result Completely classified complete gradient Ricci solitons with zero radial Weyl curvature.
Noting that the complete lift of a Rimannian metric defined on a differentiable manifold is not 0-homogeneous on the fibers of the tangent bundle . In this paper we introduce a new lift which is 0-homogeneous. It determines on slit tangent bundle a pseudo-Riemannian metric, which depends only on the metric . We study s…
Radial BNNs offer a scalable, continuous weight distribution for Bayesian deep learning.
problem Discrete support in Bayesian deep learning methods like MC dropout.
method Radial BNNs with full support over weight-space.
result Radial BNNs outperform discrete-support methods in real-world applications.
This paper classifies special ends of real projective orbifolds.
problem Understanding the structures of ends of real projective orbifolds.
method Theoretical tools from affine manifolds and Riemannian foliations.
result Convex but non-properly convex and non-complete-affine radial ends are quasi-joins of horospheres and totally geodesic radial ends.
We determine a 2-codimensional CR-structure on the slit tangent bundle T0M of a Finsler manifold (M,F) by imposing a condition regarding the almost complex structure Ψ associated to F when restricted to the structural distribution of a framed f-structure. This condition is satisfied when (M,F) is of scal…
New topologies for star-shaped sets without boundedness.
problem Defining convergence for unbounded star-shaped sets.
method Introducing radial distance functionals and new topologies.
result New topologies τWr and τAWr for star-shaped sets. New algorithm radVI improves variational inference by optimizing radial profiles.
problem Gaussian approximations often fail to capture the radial profile of complex distributions.
method Optimizes over radial profiles in variational inference, providing theoretical guarantees.
result Theoretical convergence guarantees for radVI, improving over existing VI methods.
New capillary surface found without radial limits at corner.
problem Existence of capillary surfaces with no radial limits at corners.
method Investigated a convex corner domain with bounded contact angle.
result Found a capillary surface with no radial limits at (0,0) with bounded contact angle. The aim of this article is to establish a Toponogov type triangle comparison theorem for Finsler manifolds, in the manner of radial curvature geometry. We consider the situation that the radial flag curvature is bounded below by the radial curvature function of a non-compact surface of revolution, the edge opposite to …
Proves conditions for radial Kaehler metrics to be Kaehler-Einstein.
problem Characterizing radial Kaehler metrics as Kaehler-Einstein.
method Analyzes conditions for radial Kaehler metrics to be Kaehler-Einstein.
result Conditions for radial Kaehler metrics to be Kaehler-Einstein are provided.
Study radial processes in sub-Riemannian Brownian motions, proving stochastic completeness and eigenvalue estimates.
problem Analyzing sub-Riemannian Brownian motions and their radial processes.
method Application of Itô's formula and sub-Laplacian comparison theorems to prove stochastic completeness and eigenvalue estimates.
result Proved Cheng's type estimates for Dirichlet eigenvalues of sub-Riemannian metric balls.
Study on gradient ρ-Einstein solitons with radially nonnegative Bach tensor.
problem Characterizing gradient ρ-Einstein solitons with specific tensor properties.
method Analyzing the properties of Bach tensor and using local warping to classify solitons.
result Gradient ρ-Einstein solitons with radially nonnegative Bach tensor are locally warped products of an interval and an Einstein manifold.
Radial graphs with constant mean curvature found in Euclidean space.
problem Existence of hypersurfaces with constant mean curvature.
method Radial graphs over domains of the unit sphere, Dirichlet problem.
result Existence of hypersurfaces with positive constant mean curvature.
Let us fix two different radial eigenfunctions of a hyperbolic Laplacian and assume that both of them have the same value at the origin. Both eigenvalues can be complex numbers. The main goal of this paper is to estimate the lower bound for the interval (0,T], where these two eigenfunctions must assume different values…
Study proves radial symmetry in convex cones using subharmonic functions.
problem Proving radial symmetry in convex cones with boundary conditions.
method Using maximum principle and integral identities for subharmonic functions.
result Proves radial symmetry and Serrin-type results for partially overdetermined problems.
We generalize the maximal diameter sphere theorem due to Toponogov by means of the radial curvature. As a corollary to our main theorem, we prove that for a complete connected Riemannian n-manifold M having radial sectional curvature at a point bounded from below by the radial curvature function of an ellipsoid of …
Classifies radial scalar flat metrics with a constant third coefficient.
problem Classifying radial scalar flat metrics with a specific coefficient.
method Analyzing the TYZ expansion and Simanca's scalar flat metric.
result Characterization of Simanca's scalar flat metric as a byproduct.
The paper finds hypersurfaces with constant curvature and prescribed boundary in Euclidean space.
problem Finding hypersurfaces of constant curvature and prescribed boundary in Euclidean space.
method Using the theory of fully nonlinear elliptic equations, proving the existence of radial graphs.
result Radial graphs of constant curvature and prescribed boundary can be found if the given data admits a suitable radial graph as a subsolution.
Sharp inequalities for radial functions on hyperbolic spaces without boundary conditions.
problem Establishing inequalities for radial functions on hyperbolic spaces without zero boundary conditions.
method Novel approach considering both bounded and unbounded domains, focusing on weighted Sobolev and Adams-Trudinger-Moser embeddings.
result Theorems 1.2, 1.3, and 1.4 for weighted Sobolev embedding theorems, and Theorems 1.5 and 1.6 for Adams-Trudinger-Moser type embedding theorems.