The paper explores density of stable mappings and their properties.
problem Density of stable mappings in different dimensions.
method Infinitesimal and algebraic methods to prove density of proper stable and topologically stable mappings.
result Density of topologically stable mappings holds for any pair (n,p), and for proper stable mappings if (n,p) is in nice dimensions.
This paper shows stable mappings are never dense on non-compact manifolds.
problem Density of stable mappings on non-compact manifolds.
method Complementing Mather's theory, proving stability results for non-compact manifolds.
result The set of stable mappings is never dense on non-compact manifolds.
Non-compact manifolds prevent C0-stable mappings from being dense.
problem Density of C0-stable mappings on non-compact manifolds. method Using topologically critical points to show non-density.
result The set of C0-stable mappings is never dense on non-compact manifolds. New framework for learning KR maps from data, ensuring stable generalization.
problem Learning monotone triangular transport maps efficiently and accurately.
method General framework using invertible transformations of smooth functions, ensuring no spurious local minima.
result Unique global minimizer corresponds to the KR map under certain conditions.
New method for modeling densities on Riemannian manifolds with symmetries.
problem Modeling densities on Riemannian manifolds with known symmetry groups.
method Combining implicit neural layers and optimal transport theory to propose IRCPMs.
result IRCPMs are simpler to incorporate symmetries and less expensive than ODE-flows.
Study on stable Hamiltonian topology finds non-density of certain structures.
problem Non-density of stable hypersurfaces and Hamiltonian structures.
method Proving non-density results for stable hypersurfaces and Hamiltonian structures in various dimensions.
result Non-density of stable hypersurfaces and Hamiltonian structures in specific isotopy and homotopy classes.
We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, we deal with density transformations and compute their p-var…
Stable solutions to a specific equation are one-dimensional.
problem Stability and dimensionality of solutions to the Allen-Cahn equation.
method Analysis of stable solutions with bounded energy density.
result Stable solutions to the Allen-Cahn equation are one-dimensional.
The study proves that certain stable minimal hypersurfaces must be cylindrical.
problem Characterizing stable minimal hypersurfaces in Euclidean space.
method Analyzing the density at infinity and using stable area minimizing hypercone properties.
result Stable minimal hypersurfaces with specific conditions are cylindrical.
DenSNet learns electron densities for molecular dynamics, enabling accurate spectroscopic predictions.
problem Lack of accurate electronic observables in MLIPs for molecular dynamics.
method DenSNet uses SE(3)-equivariant neural networks to predict electron densities and total energy.
result DenSNet predicts infrared spectra with excellent agreement to experimental data.
Exponential growth of stable subgroups in Morse geodesics.
problem Growth rates of stable subgroups in complex groups.
method Theory of automatic structures on Morse geodesics.
result Exponential growth of stable subgroups is faster than their infinite index stable subgroups.
New sampling method for heavy-tailed distributions using Langevin Algorithm.
problem Sampling from heavy-tailed distributions efficiently.
method Transformed Unadjusted Langevin Algorithm on specific transformations.
result Polynomial-order oracle complexities for certain heavy-tailed densities.
Proves regularity for stable varifolds near cones, expanding previous work.
problem Understanding stable varifolds near singularities.
method Proves C1,α regularity for varifolds in SQ. result Furthers understanding of local structure near singularities.
Stable and consistent model alignment for language models without assuming human preference models.
problem Lack of statistical consistency in existing alignment methods.
method Relative density ratio optimization between preferred and mixture of preferred and non-preferred data distributions.
result Our approach achieves statistical consistency and stability, providing tighter convergence guarantees.
Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce stable graphical (SG) models, a class of multivariate st…
Stable density-based clustering via multiparameter persistence.
problem Density-based clustering stability to data perturbations.
method Degree-Rips construction, correspondence-interleaving distance, multiparameter stability analysis.
result Persistable pipeline yields stable, consistent density-based clustering.
The aim of this paper is twofold. On the one hand, the study of gradient Schrödinger operators on manifolds with density φ. We classify the space of solutions when the underlying manifold is φ−parabolic. As an application, we extend the Naber-Yau Liouville Theorem, and we will prove that a complete manifold with de…
MAFLA improves sampling from heavy-tailed distributions using MH-inspired corrections.
problem Sampling from heavy-tailed and multimodal distributions when neither target nor proposal densities can be evaluated.
method Metropolis-Adjusted Fractional Langevin Algorithm (MAFLA) with Score Balance Matching.
result MAFLA significantly improves finite-time sampling accuracy over unadjusted fractional Langevin dynamics.
Unified framework for robust, stable, and efficient density ratio estimation.
problem Density-chasm and support-chasm problems in density ratio estimation.
method Dequantified diffusion-Schrödinger bridge (D3RE) framework with DDBI and DSBI.
result Offers uniform approximation and bounded time scores in theory and empirical performance.
Characterizes hyperbolic links with stable maps to the plane.
problem Understanding hyperbolic links through stable maps.
method Characterization of hyperbolic links via stable maps to the plane.
result Complete characterization of hyperbolic links with specific stable maps.
Defines Φ-harmonic maps and studies their unstable manifolds.
problem Characterizing unstable manifolds of Φ-harmonic maps. method Extrinsic average variational method in calculus of variations.
result Every compact Φ-superstrongly unstable manifold is Φ-strongly unstable. Classifies non-linear Fredholm maps linking to stable homotopy groups of spheres.
problem Classifying non-linear proper Fredholm maps between Hilbert spaces.
method Using stable homotopy groups of spheres to classify maps up to proper homotopy.
result Determines the non-trivial kernel of the map from stable homotopy groups to non-linear proper Fredholm maps.
Develops spherical density-equalizing maps for closed surfaces.
problem Lack of methods for genus-0 closed surfaces.
method Conformal parameterization onto unit sphere, density equalization, quasi-conformal theory, harmonic energy, landmark constraints.
result Landmark-aligned spherical density-equalizing maps balancing different distortion measures.
New method uses SoS densities and α-divergences for efficient sequential transport maps.
problem Efficiently generating samples from approximated densities.
method Sequential transport maps using Sum-of-Squares (SoS) densities and α-divergences.
result Convex optimization problems with efficient semidefinite programming solutions.
Defines super stable maps and proves quotient superorbifolds for genus zero.
problem Defines stable supercurves and super stable maps of genus zero.
method Uses labeled trees and slice theorem for super Lie groups.
result Proves moduli space of stable supercurves and super stable maps are quotient superorbifolds.
Authors create stable proper biharmonic maps from unit ball to spheres.
problem Constructing stable proper biharmonic maps from compact domains.
method Established second variation formula of bienergy, examined stability of previously constructed maps.
result Existence of an explicit family of stable proper biharmonic maps to Euclidean spheres.
Generative models learn smoother densities to sample from unknown distributions.
problem Sampling from unknown distributions in high-dimensional spaces.
method Formalizes sampling problem, introduces multimeasurement noise model, derives Bayes estimator, and uses underdamped Langevin MCMC.
result Formulation leads to efficient sampling methods and theoretical connections with denoising autoencoders.
Turaev's shadow can be seen locally as the Stein factorization of a stable map. In this paper, we define the notion of stable map complexity for a compact orientable 3-manifold bounded by (possibly empty) tori counting, with some weights, the minimal number of singular fibers of codimension 2 of stable maps into the re…
Visual construction of maps linking to two-bridge links.
problem Understanding stable maps and their properties for two-bridge links.
method Visual construction and analysis of stable maps from 3-sphere to plane.
result Determination of stable map complexities for some two-bridge link exteriors.
No stable discrete maps into certain curved spaces exist.
problem Stability of discrete maps into curved spaces.
method Analysis of weighted length or energy functionals on graphs.
result Non-existence of stable discrete minimal immersions or harmonic maps into specific homogeneous spaces.
Developed an ellipsoidal density-equalizing map for genus-0 closed surfaces.
problem Large geometric distortion when using spherical domain for genus-0 closed surfaces.
method Developed a novel method for ellipsoidal density-equalizing maps and combined with quasi-conformal maps.
result Significantly improved surface remeshing performance for genus-0 closed surfaces.
A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite divisible distribution, and particularly elliptical tempered stable distribution, w…
Study on infinite-type surfaces shows stable commutator length is continuous and defines open subgroups.
problem Understanding stable commutator length on infinite-type surfaces.
method Analyzing mapping class groups of infinite-type surfaces, showing continuity and openness of commutator subgroups.
result Stable commutator length defines a continuous function on commutator subgroups of infinite-type mapping class groups.
Constructs stable maps from 3-manifolds to surfaces without cusps.
problem Creating stable maps from 3-manifolds to surfaces without problematic points.
method Visual construction of stable maps with specific properties.
result Obtains stable maps with no cusps and specific fiber structures.
New LP method recovers MAP solution from noisy stable instances.
problem MAP inference on noisy stable instances.
method Designing an algorithm to find nearby perturbation stable instances and using LP relaxation.
result LP approximately recovers the MAP solution from noisy stable instances.
We investigate how Viro's integral calculus applies for the study of the topology of stable maps. We also discuss several applications to Morin maps and complex maps.
The paper proves stability of certain graph types in Euclidean space with specific densities.
problem Stability of vertical and radial graphs in Euclidean space with certain densities.
method Techniques of calibrations used to prove stability and minimization.
result Vertical and radial graphs are strongly stable for specific densities.
Adapts a short argument to derive a stability theorem for smooth maps.
problem Proving stability of smooth proper maps.
method Adapting a short argument from Golubitsky and Guillemin to derive the Mather stability theorem.
result Derives the Mather stability theorem from the Mather stability theorem in [MaII].
New bounds on specific torsion lengths for periodic mapping classes.
problem Understanding specific torsion lengths in periodic mapping classes.
method Introduced stable specific torsion length and used it to bound Dehn twists.
result Bounded the stable specific torsion length of Dehn twists by six.
The paper explores symmetry in solutions of semilinear PDEs on Riemannian domains.
problem Symmetry phenomena in solutions of semilinear PDEs on Riemannian domains.
method General framework for formulating the symmetry problem; evidence from stable solutions; consideration of manifolds with density.
result Evidence that the framework is natural, with results for stable solutions.
We give new upper bounds on the stable commutator lengths of Dehn twists in mapping class groups and new lower bounds on the stable commutator lengths of Dehn twists in hyperelliptic mapping class groups. In particular, we show that the stable commutator lengths of Dehn twists about a nonseparating and a separating cur…
The study provides homological characterizations for Q-manifolds and l2-manifolds.
problem Density of maps in characterizing Q-manifolds and l2-manifolds. method Investigates weakening the density of Zn-maps and Z-maps to homological maps. result Obtains homological characterizations for Q-manifolds and l2-manifolds. Extends p-harmonic map theory for new properties.
problem No specific problem stated; extends existing theory.
method Extended p-harmonic and biharmonic map definitions.
result New properties of generalized stable p-harmonic maps.
Locally stable maps S3→R4 are classified up to homotopy through locally stable maps. The equivalence class of a map f is determined by three invariants: the isotopy class σ(f) of its framed singularity link, the generalized normal degree ν(f), and the algebraic number of cusps κ(f) of any extensi…
We introduce a scalar invariant on manifolds with density which is analogous to the renormalized volume coefficient v3 in conformal geometry. We show that this invariant is variational and that shrinking gradient Ricci solitons are stable with respect to the associated W-functional.
In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in R3. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By var…
Extends a Liouville theorem for stable minimal hypersurfaces.
problem Stable minimal hypersurfaces in cylindrical cones.
method Analyzes the density and foliation of minimal hypersurfaces.
result Shows that stable minimal hypersurfaces are cylindrical.
Algorithm aligns 3D density maps using Wasserstein distance.
problem Aligning 3D density maps in cryogenic electron microscopy.
method Minimizing 1-Wasserstein distance after rigid transformation using Bayesian optimization.
result Improved accuracy and efficiency in protein molecule alignment.