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.
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.
169,291 papers · 148 categories
Trend · papers per month
48 results for “distance degenerate”
In infinite dimensional Heisenberg group, degenerate distances linked to unbounded curvature.
problem Degenerate distances and unbounded curvature in infinite dimensional Heisenberg group.
method Construct left invariant weak Riemannian and sub-Riemannian metrics, adapt sectional curvature definition.
result Degenerate distances coincide with unbounded sectional curvature.
We study one parameter degenerations of complex projective manifolds by introducing certain type of Hodge metrics coming from the pluricanonical forms. We show that degenerations with at most canonical singularities are all in the finite distance boundary of moduli spaces. We also propose the converse to be true in the…
Study on hypersurfaces with minimized distance between rulings.
problem Characterizing singularities and properties of two-ruled hypersurfaces.
method Characterization through striction curves and examination of pseudo-non-degenerate properties.
result Two-ruled hypersurfaces constructed from specific curves are pseudo-non-degenerate.
A new invariant captures geometric features of circle embeddings.
problem Capturing geometric features of circle embeddings invariantly.
method Chordal distance transform and persistent homology.
result Persistent homology of chordal distance transform is invariant.
The paper studies parallel surfaces of cuspidal cross caps and their degeneracy.
problem Investigating the geometry and singularities of parallel surfaces of cuspidal cross caps.
method Established a criterion for the degeneracy of the distance squared function using geometric invariants.
result Parallel surfaces degenerate into a degenerated cuspidal S1 singularity at specific distances.
The Lorentzian length, which is one of the most significant functions in Lorentzian geometry, is a complex-valued function. Its square gives a real-valued non-degenerate quadratic function. In this paper, we define naturally extended mappings of Lorentzian distance-squared functions, wherein each component is a Lorentz…
The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerat…
Study finite-energy metrics over complex manifold degenerations.
problem Finite-energy metrics on complex manifolds with singularities.
method Investigate spaces of plurisubharmonic metrics with finite-energy conditions.
result Complete and geodesic metric structure on finite-energy metrics space.
The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this p…
The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this p…
Defines Lorentzian distance on contactomorphisms, proving continuity and finite conditions.
problem Continuous distance function on contactomorphisms with finite intervals.
method Defining and analyzing Lorentzian distance functions, proving continuity and finite intervals.
result Distance function is continuous and finite if and only if contactomorphisms are orderable.
New method improves sampling efficiency in complex stochastic systems.
problem Sampling efficiency in nonconvex stochastic gradient cases.
method Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo.
result Quantitative Gaussian concentration bounds and convergence rates established.
We introduce an universum of the Polish (=complete separable metric) space - the convex cone of distance matrices and study its geometry. It happened that the generic Polish spaces in this sense of this universum is so called Urysohn spaces defined by P.S.Urysohn in 20-th, and generic metric triple (= metric space with…
The paper studies how hyperbolic surfaces degenerate along harmonic map rays.
problem The degeneration of hyperbolic surfaces along harmonic map rays.
method Using Teichmüller space and holomorphic quadratic differentials, the authors show convergence of rescaled distance functions to the intersection number with a vertical measured foliation.
result Hyperbolic surfaces along the ray converge to the dual R-tree of the vertical measured foliation in the sense of Gromov-Hausdorff.
Let be a genus Heegaard splitting with Heegaard distance : (1) Let , be two slopes in the same component of , such that the natural Heegaard splitting has distance less than , then the distance…
Study validates Michor-Mumford conjecture in infinite dimensional Hilbertian H-type groups.
problem Validation of Michor-Mumford conjecture in infinite dimensional Hilbertian H-type groups.
method Introduced infinite dimensional Hilbertian H-type groups with weak, graded, left invariant Riemannian metrics and proved the vanishing of geodesic distance and local unboundedness of sectional curvature.
result Validation of Michor-Mumford conjecture linking geodesic distance vanishing to local unboundedness of sectional curvature.
Study geodesics on neck-degenerate manifolds, focusing and winding behavior observed.
problem Geodesics behavior on neck-degenerate manifolds with cuspidal singularities.
method Detailed multiscale analysis, blow-up techniques.
result Geodesics exhibit focussing and winding behavior as the neck degenerates.
Study on wave fronts' singularities and parallel surfaces.
problem Understanding singularities of wave fronts and their parallel surfaces.
method Using geometric invariants to analyze principal curvatures and singular points.
result Criteria for bounded principal curvatures at non-degenerate singular points.
Tight isoparametric hypersurfaces in spheres have minimal critical points.
problem Finding minimal critical points on isoparametric hypersurfaces.
method Münzner's work on isoparametric hypersurfaces in spheres.
result Isoparametric hypersurfaces in spheres are tight.
Optimal inequalities found between Riemannian and Hilbert metrics in convex projective domains.
problem Finding optimal bounds between Riemannian and Hilbert metrics in convex projective domains.
method Optimal control techniques applied to Riemannian metrics induced by centro-affine hypersurface immersions.
result Optimal inequalities between Riemannian and Hilbert metrics for a class of convex projective domains.
The paper studies knot densities under various constraints and degenerations.
problem Understanding knot densities under different constraints and their degenerations.
method Introduces and analyzes unconstrained and ropelength-windowed -densities of knot types.
result The degenerations in the unconstrained theory and the introduction of ropelength-windowed densities.
We study a natural intrinsic definition of geometric simplices in Riemannian manifolds of arbitrary dimension , and exploit these simplices to obtain criteria for triangulating compact Riemannian manifolds. These geometric simplices are defined using Karcher means. Given a finite set of vertices in a convex set on t…
A new distance metric for vMF distributions simplifies spherical data analysis.
problem Intractability of normalization constants and lack of suitable geometric metrics for comparing vMF distributions.
method Proposes a Wasserstein-like distance that decomposes vMF distribution discrepancies into angular and concentration components.
result The proposed distance metric induces a latent geometric structure on the space of non-degenerate vMF distributions.
New Langevin algorithm works well even for rough distributions.
problem Sampling from non-smooth distributions.
method Simple Langevin algorithm without smoothness assumptions.
result Algorithm performs well even with discontinuous gradients.
The study uncovers invariant features in healthcare models that traditional methods overlook.
problem Discovering overlooked invariant features in healthcare models.
method Empirical learning of transformations minimizing Wasserstein distance and adding similarity regularization.
result LSTM models and BioBERT reveal invariant features not previously recognized.
Quantitative estimates for -curvature near minimizing metrics on Riemannian manifolds.
problem Estimating the -curvature near minimizing metrics on Riemannian manifolds.
method Proving quantitative estimates for the total -th order -curvature functional near minimizing metrics.
result Existence of quantitative estimates for the -curvature deficit controlling higher powers of the distance to the minimizing set.
We prove Feynman-Kac formulas for solutions to elliptic and parabolic boundary value and obstacle problems associated with a general Markov diffusion process. Our diffusion model covers several popular stochastic volatility models, such as the Heston model, the CEV model and the SABR model, which are widely used as ass…
Proves stable degeneration preserves symplectic forms and confirms Kaledin's conjecture.
problem Symplectic singularities and their degenerations.
method Combining volume minimization, deformation theory, and rigidity results.
result Kaledin's conjecture confirmed for symplectic singularities.
Alternative proof of weak solutions to mean curvature flow using minimizing movements.
problem Existence of weak solutions to mean curvature flow and volume preserving mean curvature flow.
method Proposes a new existence proof using a minimizing movements scheme and a novel proxy for distance.
result Unconditional convergence towards a De Giorgi solution for the minimizing movements scheme.
Study on convergence of SDEs using entropy methods.
problem Analyzing convergence of stochastic differential equations.
method Applied Lyapunov method to Fokker-Planck equation with weighted relative Fisher information.
result Exponential convergence of probability density function to invariant distribution in distance.
We prove that the degenerate part of the distributive homology of a multispindle is determined by the normalized homology. In particular, when the multispindle is a quandle , the degenerate homology of is completely determined by the quandle homology of . For this case (and generally for two term homology of …
We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singula…
An n-dimensional submanifold X of a projective space P^N (C) is called tangentially degenerate if the rank of its Gauss mapping γ: X ---> G (n, N) satisfies 0 < rank γ< n. The authors systematically study the geometry of tangentially degenerate submanifolds of a projective space . By means of the foca…
Improves point-cloud reconstruction by optimizing projections with self-attention.
problem Inefficient and non-metric projection methods for sliced Wasserstein distances.
method Proposes distributional sliced Wasserstein distance with self-attention for permutation-invariant and metric optimization.
result Self-attention amortized distributional projection optimization achieves better performance in point-cloud reconstruction.
Gaussian Mixture Model with unknown diagonal covariances via continuous sparse regularizationmath.ST
Paper estimates GMMs with unknown covariances using sparse regularization.
problem Estimating GMMs with unknown diagonal covariances from samples.
method Employed Beurling-LASSO (BLASSO) for sparse estimation of component means, covariances, and weights.
result Established non-asymptotic recovery guarantees with nearly parametric convergence rates.
Study degenerate Bianchi transformations for pseudo-spherical submanifolds in 5D space.
problem Characterize three-dimensional pseudo-spherical submanifolds with degenerate Bianchi transformations.
method Complete description through holonomically degenerate Bianchi transformations.
result Obtained a complete description of degenerate pseudo-spherical submanifolds.
New stabilization found in planar elasticae with degenerate diffusion.
problem Existence of local minimizers in degenerate -elasticae.
method Analysis of pinned planar -elasticae with degenerate diffusion.
result Uncountably many local minimizers with diverging energy in degenerate regime.
Classifies homogeneous Levi non-degenerate hypersurfaces in complex 3-space.
problem Classifying specific types of complex hypersurfaces.
method Analyzing hypersurfaces with symmetry algebra of dimension at least 6.
result All such hypersurfaces are classified.
Uniform estimates for Calabi-Yau degenerations proved.
problem Calabi-Yau degenerations of polarised algebraic manifolds.
method Uniform Skoda and -estimates for Kähler potentials.
result Uniform Skoda type estimate and -estimate for Calabi-Yau Kähler potentials proved.
Let be a geometrically bounded symplectic manifold, a closed, regular (i.e. "fibering") coisotropic submanifold, and a Hamiltonian diffeomorphism. The main result of this article is that the number of leafwise fixed points of is bounded below by the sum of the -Betti numbers o…
Sharp diameter bounds for Calabi-Yau degenerations proved.
problem Bounding the diameter of Calabi-Yau metrics during degeneration.
method Sharp upper and lower bounds derived for Ricci-flat Kahler metrics.
result Conjecture confirmed by obtaining precise diameter bounds.
This paper proposes a new AL method that directly uses geometric sampling over clusters.
problem Performance degeneration in uncertainty evaluation for AL with insufficient labeled data.
method Divide-and-conquer approach to AL, transferring it to geometric sampling over clusters.
result The proposed GAL method significantly outperforms state-of-the-art baselines.
New finding on K-semistability in optimal degenerations.
problem Understanding K-semistability in optimal degenerations.
method Analyzing K-unstable varieties and their optimal degenerations.
result Optimal degenerations of K-unstable varieties are relatively K-semistable.
Paper solves degenerated circle pattern metric problem in spherical geometry.
problem Existence and rigidity of (degenerated) circle pattern metrics with prescribed total geodesic curvatures.
method Defined prescribed combinatorial Ricci flows and studied their convergence.
result First degenerated result for total geodesic curvatures in spherical background geometry.
Paper studies degenerated circle packings in hyperbolic geometry and finds conditions for their existence.
problem Whether a prescribed total geodesic curvature can be realized by a degenerated circle packing.
method Introduced combinatorial Ricci flow to find the desired degenerated circle packed surface, analogous to Chow-Luo and Takatsu methods.
result Fully characterized sufficient and necessary conditions for the existence of degenerated circle packings and showed their uniqueness.
Proves unique degeneration of log Fano fibration germs.
problem Stable degeneration of log Fano fibration germs.
method Introduced the H-invariant for filtrations over log Fano fibration germs and used a unique quasi-monomial valuation to achieve the degeneration.
result Unique K-polystable special degeneration of log Fano fibration germs.
New insights on solutions to Allen-Cahn equation with degenerate minimal hypersurfaces.
problem Existence and rigidity of solutions to the Allen-Cahn equation.
method Analysis of degenerate minimal hypersurfaces as limit interfaces.
result New observations and examples of solutions to the Allen-Cahn equation.