Given a triangulated surface , we use Ge-Xu's -flow \cite{Ge-Xu1} to deform any initial inversive distance circle packing metric to a metric with constant -curvature. More precisely, we prove that the inversive distance circle packing with constant -curvature is unique if , which generalize And…
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48 results for “constant time distance”
Proposes a Coulomb-like model for international trade flows, fitting real-world data.
problem Describing and predicting international trade flows between countries.
method Formulated a coulomb force model where GDP represents charge and distance is influenced by various factors.
result Developed a trade strength distribution equation that fits real-world data well.
The study finds new constant mean curvature surfaces in curved spaces.
problem Finding surfaces with constant mean curvature in curved spaces.
method Analyzing families of surfaces in and .
result New families of surfaces with constant mean curvature, including non-equivariant examples.
In this paper we prove that a properly embedded constant mean curvature surface in which has finite topology and stays at a finite distance from a vertical geodesic line is invariant by rotation around a vertical geodesic line.
Kaehler Metrics Generated by Functions of the Time-Like Distance in the Flat Kaehler-Lorentz Spacemath.DG
We prove that every Kaehler metric, whose potential is a function of the time-like distance in the flat Kaehler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kaehler manifolds with the above mentioned metrics. New examples o…
Dual volume bound linked to Weil-Petersson distance in quasi-Fuchsian manifolds.
problem Bounding dual volume in quasi-Fuchsian manifolds.
method Using dual Bonahon-Schläfli formula, proving bound on dual volume.
result Explicit constant bound on dual volume related to Weil-Petersson distance.
In this work an intrinsic projectively invariant distance is used to establish a new approach to the study of projective geometry in Finsler space. It is shown that the projectively invariant distance previously defined is a constant multiple of the Finsler distance in certain case. As a consequence, two projectively r…
New null distance bounds confirm Big Bang singularity in cosmological models.
problem Understanding the geometry of spacetime near Big Bang singularities.
method Developed a new null distance metric for temporal functions and applied it to cosmological models.
result Null distance is bounded by a constant multiple of Riemannian distance on level sets with constant gradient norm.
Paper bounds integral of distance function on compact manifolds.
problem Bounding integral of distance function on compact manifolds.
method Curvature assumptions on compact Riemannian manifolds.
result Integral is bounded below by diameter, volume, and a constant.
Complete Finsler spaces with negative Ricci curvature are reversible.
problem Characterizing Finsler spaces with constant negative Ricci curvature.
method Utilizing projectively invariant pseudo-distance and Schwarzian derivative.
result Every connected complete Finsler space with constant negative Ricci scalar is reversible.
This note improves correlation stress tests using geodesic distance.
problem Improving financial risk management through better covariance stress tests.
method Proposes a new geometrically invariant definition of correlation stress tests.
result Demonstrates a submanifold approach to stress testing covariance matrices.
Improved efficiency in HMC samplers reduces dissipative behavior.
problem Reducing dissipative behavior in HMC samplers.
method Variable integration time and partial velocity refreshment.
result Efficiency improved by a √κ factor in Wasserstein-2 distance.
Optimized parallel algorithms for identifying strong ties in data.
problem Identifying strong ties in data with varying distances and community sizes.
method Design and analysis of sequential and parallel algorithms for partitioned local depths.
result Optimized algorithms achieve up to 19.4x speedup in parallel execution.
Proves stability of cone-volume measure with nearly constant density.
problem Stability of cone-volume measure with near constant density.
method Proves stability of cone-volume measure with near constant density.
result Homothetic copy of the body is close to the unit ball in the -distance.
Study cobordism distances between 3-braid links and trefoil knots.
problem Understanding the geometric relationship between 3-braid links and trefoil knots.
method Determined cobordism distances between 3-braid links and trefoil knots, and explored limits of Coxeter's braid group result.
result Found cobordism distances between 3-braid links and trefoil knots, up to a constant error.
The isotropic 3-space I^3 which is one of the Cayley--Klein spaces is obtained from the Euclidean space by substituting the usual Euclidean distance with the isotropic distance. In the present paper, we give several classifications on the surfaces in I^3 with the constant relative curvature (analogue of the Gaussian cu…
Bounds on geodesic distances on Stiefel manifold derived from new metrics.
problem Improving geodesic computation algorithms and understanding Stiefel manifold.
method New geometric insights and Lipschitz constants for geodesic distances.
result Explicit bounds on geodesic distances and conditions for attaining bounds.
The Margulis constant for Kleinian groups is the smallest constant such that for each discrete group and each point in the upper half space , the group generated by the elements in which move less than distance c is elementary. We take a first step towards determining this constant by p…
The paper tightens bounds on distances between Reeb graphs.
problem Certifying quasi-universality of distances between Reeb graphs.
method Establishes tight bi-Lipschitz bounds for various distances.
result Proves strict universality of the functional contortion distance for contour trees and coincides with interleaving distance for merge trees.
We bound the value of the Casson invariant of any integral homology 3-sphere by a constant times the distance-squared to the identity, measured in any word metric on the Torelli group $\T$, of the element of $\T$ associated to any Heegaard splitting of . We construct examples which show this bound is asymptotica…
Algorithm learns affine transformations robustly from corrupted samples.
problem Learning affine transformations from corrupted samples.
method New geometric certificate and iterative improvement method.
result Total variation distance of between learned and original distributions.
Solves constant mean curvature Dirichlet problem on catenoids with improved estimates.
problem Solving constant mean curvature Dirichlet problem on catenoidal necks.
method Found solutions in exponentially weighted Hölder spaces with non-integer weight.
result Improved estimate to γ=1 by comparing solutions with their limits on the disk.
Study on diffusion in non-complete sub-Riemannian manifolds with specific conditions.
problem Analyzing diffusion in incomplete sub-Riemannian manifolds.
method Identifying conditions for Gaussian-type upper bounds and logarithmic asymptotics of heat kernels.
result Optimal constant in exponent for Gaussian-type upper bounds and concentration of diffusion bridge measures.
This paper introduces a fast algorithm for solving MDPs with sparse rewards.
problem Solving MDPs with large state and action spaces and sparse reward sources is computationally expensive.
method A novel algorithm that solves deterministic, continuous MDPs with sparse reward sources efficiently and exactly.
result The algorithm offers a time complexity of and a memory complexity of .
This article is about a natural distance function induced by smooth cobordisms between links. We show that the cobordism distance of torus links is determined by the profiles of their signature functions, up to a constant factor.
Optimizing dividend payments for an insurance company with bounded rates.
problem Maximizing expected exponential utility of discounted dividends under bounded dividend rates.
method Suboptimal strategies are evaluated using a new method to estimate the distance to the value function.
result The optimal strategy is of barrier type with a non-linear barrier.
Robust test for distributions under Hellinger distance, simpler than optimal tests.
problem Testing and estimating distributions robustly under Hellinger distance.
method Simple robust hypothesis test with optimal sample complexity, robust to Hellinger distance perturbations.
result Empirically demonstrated robustness and power of the test on canonical distributions.
The paper analyzes conditions for solving low-rank matrix recovery problems with noisy measurements.
problem Low-rank matrix recovery with corrupted measurements.
method Analysis of the restricted isometry property (RIP) and local search methods.
result Sharp bounds on the maximum distance between local minimizers and the ground truth.
We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the curve graphs and the mapping class groups.
Approximation of Riemannian Distances and Applications to Distance-Based Learning on Manifoldsmath.DG
Approximates distances on Riemannian manifolds efficiently.
problem High computational cost of pairwise distances on large Riemannian manifolds.
method Approximates distances using a two-dimensional model space with constant curvature.
result Linear number of geodesic boundary value problems required for approximation.
We announce the classification of complete, almost embedded surfaces of constant mean curvature, with three ends and genus zero: they are classified by triples of points on the sphere whose distances are the asymptotic necksizes of the three ends.
In the Engel group with its Carnot group structure we study subsets of locally finite subRiemannian perimeter and possessing constant subRiemannian normal. We prove the rectifiability of such sets: more precisely we show that, in some specific coordinates, they are upper-graphs of entire Lipschitz functions (with respe…
We extend techniques due to Pardon to show that there is a lower bound on the distortion of a knot in proportional to the minimum of the bridge distance and the bridge number of the knot. We also exhibit an infinite family of knots for which the minimum of the bridge distance and the bridge number is unb…
Algorithm learns Gaussian mixtures robust to outliers.
problem Efficiently learn high-dimensional Gaussian mixtures with outliers.
method Sum-of-Squares based proofs to algorithms approach.
result Polynomial time algorithm for -mixture with pairwise separated components.
Paper finds best constants in Hardy inequalities on Finsler metric measure manifolds.
problem Finding best constants in Hardy inequalities on Finsler metric measure manifolds.
method Investigates Hardy inequalities with distance functions in the Finsler setting, considering flag curvature, Ricci curvature, reversibility, and S-curvature.
result Establishes optimal Hardy inequalities on both noncompact and closed Finsler metric measure manifolds.
The paper estimates distances between manifold boundaries based on scalar curvature.
problem Estimating distances between manifold boundaries based on scalar curvature.
method Using the Dirac operator and properties of spin manifolds.
result Proves a bound on the distance between boundary components of a manifold.
The study examines constant mean curvature tubes around geodesics in specific 3-manifolds.
problem Investigating constant mean curvature surfaces in homogeneous 3-manifolds.
method Analyzing horizontal tubes foliating spaces under certain conditions.
result Horizontal tubes foliate spaces under specific curvature conditions.
Develops discrete geometry for non-constant curvature surfaces.
problem Modeling surfaces of non-constant curvature, especially with non-constant negative curvature.
method Derived and numerically integrated Lelieuvre formulas for hyperbolic surfaces. Proposed iterative and fast marching methods for solving implicit equations and computing geodesic distances.
result Explicit construction of immersions is not provided, but equations are described implicitly.
Researchers compute the full spectrum of Laplace operator on distance spheres in symmetric spaces.
problem Computing the full Laplace spectrum on distance spheres in symmetric spaces.
method Lie-theoretic methods to explicitly compute the spectrum.
result Unified formula for the full spectrum of Laplace operator on distance spheres in symmetric spaces of rank one.
SGD with constant stepsize converges to a non-Gaussian limit near flat minima.
problem Behavior of SGD near flat minima with convex objectives.
method Analyzes SGD with Markovian noise and contractive driving chain.
result Invariant law concentrates on scale and converges weakly to a non-Gaussian stationary distribution.
We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens in the classical case, we show that the Lipschitz constant of the nonlocal mean curvature of such a boundary controls its -distance fro…
The paper proves a Schwarz lemma for weakly Kähler-Finsler manifolds.
problem Estimating distance functions and proving Schwarz lemma for weakly Kähler-Finsler manifolds.
method Establishing theorems about distance functions and applying them to prove the Schwarz lemma.
result Holomorphic mappings from weakly Kähler-Finsler manifolds to pseudoconvex Finsler manifolds are constant under certain conditions.
New distances defined between space-times, proving some definite.
problem Defining distances between space-times.
method Introducing causal-null-compactifiable space-times and using cosmological time and null distance.
result Various definite distances defined, proving convergence of space-times.
New protocols implement logical gates on encoded qubits with minimal overhead.
problem Efficiently performing universal logical gates on encoded qubits with minimal overhead.
method Using topological codes associated to hyperbolic surfaces, we introduce protocols to implement Dehn twists through constant depth unitary circuits.
result Demonstrated the possibility of applying universal logical gate sets on encoded qubits through constant depth unitary circuits and with constant space overhead.
Improved training boosts certified robustness of L-infinity distance nets.
problem Certified robustness of L-infinity distance nets is not as strong as conventional networks.
method Improved training process combining scaled cross-entropy and clipped hinge loss with a decaying mixing coefficient.
result Certified accuracy of L-infinity distance nets improved from 33.30% to 40.06% on CIFAR-10.
Push-forward models struggle to fit multimodal distributions due to high Lipschitz constants.
problem Expressivity of push-forward generative models in fitting multimodal distributions.
method Analyzing the Lipschitz constant and its relation to the total variation distance and Kullback-Leibler divergence.
result Push-forward models require high Lipschitz constants to approximate multimodal distributions, leading to a trade-off between expressivity and stability.
Let be the product of two complex manifolds of positive dimensions. In this paper, we prove that there is no complete Kähler metric on such that: either (i) the holomorphic bisectional curvature of is bounded by a negative constant and the Ricci curvature is bounded below by where …
This paper introduces a novel real-time Fuzzy Supervised Learning with Binary Meta-Feature (FSL-BM) for big data classification task. The study of real-time algorithms addresses several major concerns, which are namely: accuracy, memory consumption, and ability to stretch assumptions and time complexity. Attaining a fa…