New bounds for knot distances using Khovanov homology.
problem Calculating precise distances between knots.
method Using Khovanov homology to refine existing bounds.
result Improved bounds for Gordian distances of knots.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “distance bounding”
Lower bounds on ribbon distance using Bar-Natan and α-Homology.
problem Calculating the minimum number of ribbon operations to unknot a knot.
method Bar-Natan Homology and α-Homology approaches.
result Lower bounds on ribbon distance via both Bar-Natan and α-Homology.
Sharp bounds found for distances between specific geometric shapes in hyperbolic space.
problem Finding effective distances between specific geometric shapes (tori) in hyperbolic 3-manifolds.
method Sharp, effective bounds on distances between tori of fixed injectivity radius.
result Effective bounds on distances between specific geometric shapes in hyperbolic space.
Upper bound for max-sliced 2-Wasserstein distance between measures.
problem Estimating distance between probability measures and their empirical counterparts.
method Same technique as previous work, upper bound approach.
result Upper bound for expected max-sliced 2-Wasserstein distance.
Paper finds the best way to estimate neural net distance from samples.
problem Estimating the neural net distance from samples.
method Developed minimax lower and upper bounds for the neural net distance.
result Lower and upper bounds match, validating the empirical neural net distance.
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 study improves PAC-Bayesian bounds for adversarial generative models.
problem Improving generalization bounds for adversarial generative models.
method Extending PAC-Bayesian theory to generative models, developing bounds for Wasserstein and total variation distances.
result New training objectives for Wasserstein and Energy-Based GANs.
Uniform distance distortion estimate for Ricci flows with bounded scalar curvature.
problem Analyzing Ricci flows with collapsing initial data.
method Uniform distance distortion estimate through renormalized metric-measure quantities.
result Uniform lower bounds of the renormalized heat kernel match with the lower bound of the renormalized volume ratio, proving distance distortion estimate.
Introduces spectral-domain Wasserstein distance and Gelbrich bound for elliptical processes.
problem Estimating distances and bounds for elliptical stochastic processes.
method Defines spectral-domain Wasserstein distance and Gelbrich bound.
result Develops new spectral-domain bounds for non-elliptical processes.
Estimating distances in simplicial complexes with applications to 3-manifolds and handlebody-knotsmath.GT
The study bounds distances in simplicial complexes and defines new invariants for 3-manifolds and handlebody-knots.
problem Estimating distances in simplicial complexes associated with low-dimensional manifolds.
method Obtained bounds on distances in simplicial complexes using topological conditions on vertices and curve complexes. Defined new invariants for 3-manifolds and handlebody-knots using splitting distances.
result Splitting distances in simplicial complexes are bounded from below under stabilizations, leading to converging invariants.
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.
Paper proposes Gini distance statistics for estimating feature-label dependence.
problem Identifying statistical dependence between features and categorical labels.
method Generalized Gini distance in RKHS for feature-label dependence estimation.
result Gini distance statistics converge faster and have tighter error bounds than distance covariance.
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, i…
Upper bound for Hausdorff distance between hyperbolic space and its medianization.
problem Calculating the Hausdorff distance between hyperbolic space and its medianization.
method Using de Sitter space to model finite-dimensional hyperbolic space and its medianization, calculating the Hausdorff distance.
result An upper bound for the Hausdorff distance between hyperbolic space and its medianization is calculated.
Upper bound found for distance degenerate curves in Heegaard splittings.
problem Distance degenerate curves in Heegaard splittings.
method Using diameter finite balls in curve complexes.
result Found an upper bound for distance degenerate curves.
Lower bounds on knot distortion related to bridge distance and number.
problem Finding lower bounds on knot distortion in 3D space.
method Extending Pardon's techniques to relate distortion to bridge distance and number.
result Lower bound on knot distortion proportional to minimum of bridge distance and bridge number.
This work provides guaranteed bounds on the total variation distance for univariate mixtures.
problem Lack of closed-form expressions for total variation distance between mixtures.
method Two methods: information monotonicity for lower bounds and geometric envelopes for upper bounds.
result Demonstrated tightness of bounds on Gaussian, Gamma, and Rayleigh mixtures.
Lower bounds on Gordian distance using Blanchfield pairings.
problem Calculating the Gordian distance between knots.
method Using Blanchfield pairings to establish lower bounds.
result At least 195 pairs of knots have a Gordian distance of 3.
The paper converts metric bounds to distance function Hölder bounds and proves compactness theorems.
problem Proving geometric stability results with scalar curvature bounds.
method Transforming bounds to Hölder bounds for distance functions.
result Compactness theorems and convergence guarantees for Riemannian manifolds.
Logit distance bounds representational similarity of models.
problem Approximating linear similarity when distributions are close.
method Defined a logit distance and proved its relationship to representational dissimilarity.
result Logit distance bounds representational similarity, providing nontrivial control in practice.
Translation distances in fibered 3-manifolds with boundary are bounded and grow with complexity.
problem Bounding translation distances in fibered 3-manifolds with boundary.
method Using essential surfaces with non-zero slope and analyzing their complexity.
result Translation distances are bounded and grow with complexity, supporting a conjecture.
Sharp bounds for max-sliced Wasserstein distances derived for empirical distributions.
problem Estimating the expected max-sliced Wasserstein distance between a probability measure and its empirical distribution.
method Banach space version and operator norm approach for upper bounds.
result Upper bounds for max-sliced Wasserstein distances are essentially matching and sharp up to a log factor.
Lower bounds for handlebody-knots using Alexander biquandle colorings.
problem Calculating Gordian distance and unknotting number for handlebody-knots.
method Using Alexander biquandle colorings to construct and calculate handlebody-knots.
result Constructed handlebody-knots with specific distance and unknotting numbers.
This work tightens generalization error bounds using Wasserstein distance.
problem Improving expected generalization error bounds in machine learning.
method Introduces bounds based on Wasserstein distance for various settings.
result New, tighter bounds based on relative entropy and other information measures.
Study uses equivariant topology to measure distances between G metric spaces.
problem Measuring distances between G metric spaces.
method Equivariant topology methods to derive lower bounds.
result Sharp bounds on Gromov Hausdorff distance between spheres.
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.
In this paper we analyze the behavior of the distance function under Ricci flows whose scalar curvature is uniformly bounded. We will show that on small time-intervals the distance function is -Hölder continuous in a uniform sense. This implies that the distance function can be extended continuously up to the …
A new framework tightens risk measure confidence bounds.
problem Improving confidence bounds for various risk measures.
method Distribution optimization framework with two estimation schemes based on concentration bounds.
result Consistently tighter confidence bounds compared to previous methods.
Establishes a lower bound for Kähler-Einstein distance on certain domains.
problem Finding a lower bound for Kähler-Einstein distance on specific types of domains.
method Proves an analog of the Hopf lemma for Riemannian manifolds with Ricci curvature bounded from below.
result Establishes a lower bound for the Kähler-Einstein distance on pseudoconvex domains with positive hyperconvexity index.
The paper connects geometric and topological concepts to bound distances between metric spaces.
problem Bounding distances between metric spaces using Gromov-Hausdorff distance.
method Using Borsuk-Ulam theorems and Vietoris-Rips complexes, the paper obstructs the existence of certain continuous maps between complexes to bound discontinuities of functions.
result The paper provides new bounds on Gromov-Hausdorff distances between spheres of different dimensions.
The paper connects geodesic nets to distance function critical points.
problem Understanding the relationship between geodesic nets and distance function critical points.
method Established a relationship between geodesic nets and critical points of the distance function.
result Bounded the number of balanced points and the length of certain minimizing geodesic nets.
Upper bounds on Wasserstein distance for empirical measures in unbounded functional spaces.
problem Analyzing convergence and concentration of empirical measures in unbounded functional spaces.
method Generalized upper bounds using Wasserstein distance, covering large dimensional Euclidean spaces and Gaussian processes.
result Rate-optimal upper bounds for functional data distributions with specific decay rates.
Unified proof of knot unknotting bounds using Ma-Qiu index.
problem Finding bounds on the number of moves to unknot knots.
method Using the Ma-Qiu index to bound presentation distances and Gordian distances.
result Unified proof of various unknotting number bounds.
Discuss folklore statements about manifolds with curvature bounds.
problem Distance functions in manifolds with curvature bounds.
method Regularity, subsets of positive reach, and cut locus.
result Folklore statements about manifolds with curvature bounds are discussed.
Estimates mixture entropy using pairwise distances.
problem Computing mixture entropy is challenging due to lack of closed-form solutions.
method Proposes a family of estimators based on pairwise distances.
result The proposed estimators are efficient, differentiable, and provide tight bounds on mixture entropy.
Novel distances between distributions using conditional ground distances.
problem Quantifying distances between statistical multivariate distributions.
method Optimal transport with entropic regularization and ground distance on conditionals.
result Upper bounds for jointly convex distances and improved GMM learning.
Develops bounds on Bayesian posterior approximations using Fisher distance.
problem Lack of finite-sample theory for scalable inference methods.
method Bounding Wasserstein distance via generalized Fisher distance.
result Derives bounds on Wasserstein error for various approximations.
Exact 1-Wasserstein distance between location-scale distributions derived, with privacy effects studied.
problem Calculating the 1-Wasserstein distance between location-scale distributions and its impact on differential privacy.
method Exact expressions and special functions for 1-Wasserstein distance, new upper bounds, and asymptotic analysis.
result New linear upper bound and detailed asymptotic bounds for Gaussian case, effect of differential privacy studied.
The paper studies the distance from calibration in sequential prediction, proving upper and lower bounds.
problem The challenge is to measure and minimize the deviation from perfect calibration in sequential binary prediction.
method The approach involves proving an upper bound and an lower bound, using structural results and minimax arguments.
result An upper bound on the calibration distance is achieved, with an lower bound showing the inherent difficulty.
Study distance maps on spaces with curvature bound, proving regularity and sphere theorem.
problem Regularity of distance maps on geodesically complete spaces with curvature bound above.
method Define and prove regularity of distance maps as Hurewicz fibrations.
result Sphere theorem for geodesically complete CAT(1) spaces.
The paper bounds distances and transformations between pants decompositions and triangulations on surfaces.
problem Finding bounds on distances and transformations between pants decompositions and triangulations.
method Using pre-triangulations, train tracks, and Agol-Hass-Thurston algorithm.
result Upper bounds on distances and transformations between pants decompositions and triangulations.
Study lower bounds for connectivity of distance function level sets in convex sets.
problem Understanding connectivity of distance function level sets in convex sets.
method Lower bound calculation using critical points of the distance function.
result Provide a lower bound for the range of connectivity.
New PAC-Bayesian bounds improve Sliced-Wasserstein distances.
problem Improving statistical properties of Sliced-Wasserstein distances.
method Leveraging PAC-Bayesian theory to provide bounds and learning procedures.
result PAC-Bayesian generalization bounds for adaptive SW distances.
Improved UCB method for stochastic bandits using distance tuning.
problem Improving performance in stochastic bandit problems.
method Tuning confidence bounds based on bandit distance.
result Empirically shows increased performance compared to existing methods.
Study exact Lagrangian cobordisms in cotangent bundles, proving bounds on sheaf interleaving distance and shadow distance.
problem Understanding Lagrangian cobordisms and their properties in cotangent bundles.
method Use microlocal theory of sheaves, sheaf quantization, and cone decompositions.
result Interleaving distance of sheaves is bounded by the shadow distance of the cobordism.
Sharp inequality between TV and Hellinger distances for Gaussian mixtures.
problem Understanding the relationship between total variation and Hellinger distances for Gaussian mixtures.
method Established a general upper bound on Hellinger distance in terms of TV distance raised to a power, demonstrating sharpness with specific examples.
result The Hellinger distance between two Gaussian mixtures is bounded by the TV distance raised to a power , where is of order .
New bounds for average graph distance using curvature and centrality.
problem Finding bounds for average graph distance.
method Using weighted average Ollivier curvature with edge betweenness centrality.
result Equality in bounds achieved for specific reflective graphs.
New method relaxes TV distance for two-sample testing without distributional assumptions.
problem Challenges in certifying equality or providing tight bounds on TV distance for two distributions.
method Examined blurred total variation distance, a relaxation of TV distance.
result Provided theoretical guarantees for upper and lower bounds on blurred TV distance.