Derive Dirichlet scalar curvature energy functional variation formula
problem Dirichlet scalar curvature energy functional
method First variation formula
result Introduce Dirichlet-Einstein metrics
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48 results for “Dirichlet”
Solves a specific Dirichlet problem on Hermitian manifolds.
problem Solving Dirichlet problem for Monge-Ampère type equations on Hermitian manifolds.
method Solves the Dirichlet problem for Monge-Ampère type equations for -plurisubharmonic functions on Hermitian manifolds.
result Solves a specific Dirichlet problem on Hermitian manifolds.
Trapezoids uniquely identified by their Dirichlet Laplace spectrum.
problem Identifying trapezoids based on their spectral properties.
method Analyzing the Dirichlet Laplace spectrum of non-obtuse trapezoids.
result Non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum.
Study classifies ruled surfaces critical to Dirichlet energy.
problem Identifying ruled surfaces critical to Dirichlet energy.
method Explicit parametrization of ruled surfaces.
result Classification of ruled surfaces as critical points of Dirichlet energy.
Study non-linear Dirichlet-to-Neumann map for Poincaré-Einstein fillings.
problem Non-linear Dirichlet-to-Neumann map for Poincaré-Einstein fillings.
method Description of range in terms of Dirichlet-to-Neumann tensor, construction of hypersurface invariants.
result Unique conformally invariant Dirichlet-to-Neumann hypersurface invariants for Poincaré-Einstein fillings.
LDTA expands LDA's topic modeling capacity with tree-structured priors.
problem Limited expressiveness of Dirichlet priors in LDA for complex topic relationships.
method Introduces Latent Dirichlet-Tree Allocation (LDTA) with Dirichlet-Tree (DT) priors, and develops universal mean-field variational inference and Expectation Propagation.
result LDTA enables expressive, tree-structured priors over topic proportions, expanding modeling capacity of LDA.
Solves a specific Dirichlet problem for Lagrangian mean curvature equations.
problem Solving the Dirichlet problem for Lagrangian mean curvature equations.
method Solves the Dirichlet problem for Lagrangian mean curvature equations on uniformly convex domains.
result Solves the Dirichlet problem for Lagrangian mean curvature equations.
The Dirichlet problem for degenerate fully nonlinear elliptic equations on Riemannian manifoldsmath.AP
Solves a specific Dirichlet problem on Riemannian manifolds.
problem Dirichlet problem for degenerate fully nonlinear elliptic equations on Riemannian manifolds.
method Derives existence of -solutions under appropriate assumptions.
result Existence of -solutions.
Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.
problem Comparing eigenvalues on spherically symmetric manifolds to Euclidean balls.
method Examines Dirichlet Laplace eigenvalues on balls of spherically symmetric manifolds and Euclidean space.
result Eigenvalues on spherically symmetric manifolds are smaller for small radii, but larger for hyperbolic spaces.
Enhances topic models to better handle polysemous words.
problem Lack of polysemy handling in Gaussian latent Dirichlet allocation.
method Introduces a hierarchical structure to capture polysemy in Gaussian latent Dirichlet allocation.
result Significantly improves polysemy detection and provides more parsimonious topic representations.
TPBS models improve robustness to overfitting with localized Dirichlet energy regularization.
problem Global Dirichlet energy-based regularization fails for TPBS models due to perfect interpolation.
method Propose local Dirichlet energy regularization and two inference estimators.
result TPBS models outperform neural networks in overfitting regimes and maintain competitive performance otherwise.
Study on geometry of Dirichlet distributions using Fisher-Rao metric.
problem Understanding the geometry of Dirichlet distributions.
method Analysis of Fisher-Rao metric on Dirichlet distribution parameter space.
result Geodesic completeness and negative sectional curvature of the space.
Graph Laplacians adapt to different manifold dimensions, while Dirichlet energies converge to a tensorized Dirichlet energy.
problem Understanding machine learning methods for data with varying intrinsic dimensions.
method Γ-convergence of graph Dirichlet energies and spectral convergence of graph Laplacians on intersecting manifolds of varying dimensions.
result Normalized Dirichlet energy converges to a tensorized Dirichlet energy that adapts to all dimensions simultaneously.
Discriminative classifier for compositional data using hierarchical mixture of Generalized Dirichlet models.
problem Classifying compositional data, especially in spam detection and color space identification.
method Hierarchical mixture of discriminative Generalized Dirichlet classifiers, using variational approximation for parameter learning.
result First time a variational upper-bound for Generalized Dirichlet mixture is proposed in literature.
The paper finds universal inequalities for eigenvalues on hyperbolic spaces.
problem Eigenvalues of the Dirichlet Laplacian on conformally flat Riemannian manifolds.
method Establishes universal inequalities for eigenvalues of the Dirichlet Laplacian on hyperbolic spaces.
result Establishes universal inequalities for eigenvalues of the Dirichlet Laplacian on hyperbolic spaces.
Geodesic balls with non-negative Ricci curvature have a sharp lower bound on their first Dirichlet eigenvalue.
problem Finding a sharp lower bound for the first Dirichlet eigenvalue of geodesic balls.
method Quantitative explicit inequality linking the width of geodesic balls to the spectral gap.
result A quantitative inequality relating the width of geodesic balls to the spectral gap between the first Dirichlet eigenvalue and its lower bound.
Paper solves Dirichlet problem for -convex hypersurfaces with curvature constraints.
problem Solving the Dirichlet problem for -convex hypersurfaces with prescribed curvature.
method Proved existence of a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition, obtained an interior curvature estimate.
result Existence of a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition.
Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.
problem Recover stiffness tensor and density from Dirichlet-to-Neumann map.
method Analyze invariance under coordinate transformations and gauge freedoms.
result Present gauge freedoms in the Dirichlet-to-Neumann map for Riemannian elastic wave equation.
New portfolios outperform traditional methods by using factor weights.
problem Improving portfolio allocation in markets driven by factors.
method Factor-weighted Dirichlet portfolios outperform uniform Dirichlet portfolios.
result Factor-weighted portfolios outperform uniformly sampled portfolios in market returns.
Estimates eigenvalues of poly-Laplace operator on lattice subgraphs.
problem Estimating eigenvalues of poly-Laplace operator on subgraphs of lattice graphs.
method Introduced discrete poly-Laplace operator, derived upper and lower bounds for eigenvalues.
result Poly-Laplace eigenvalues are at least squares of lower-order poly-Laplace eigenvalues.
A new method detects outliers using ensembles of Dirichlet process mixtures.
problem Challenges in unsupervised outlier detection using Dirichlet process mixtures.
method Ensembles of Dirichlet process Gaussian mixtures with random subspace and subsampling.
result Empirically outperforms existing approaches in unsupervised outlier detection.
Dirichlet pruning compresses neural networks by removing unimportant units.
problem Compressing large neural network models without sacrificing performance.
method Assigns Dirichlet distribution over network layers' units and uses variational inference to estimate parameters.
result Achieves state-of-the-art compression performance on larger architectures like VGG and ResNet.
Solves Dirichlet problem for harmonic maps to give geodesic insights.
problem Asymptotic Dirichlet problem for harmonic maps.
method Holographic characterization using conformal geodesics.
result Characterizes conformal geodesics on the boundary.
We derive and approximate the conjugate prior of Dirichlet and beta distributions.
problem Intractability of conjugate prior for Dirichlet and beta distributions.
method Derive conjugate prior, define closed-form approximation, and provide algorithm.
result Closed-form approximation enables fully tractable Bayesian treatment.
Solves Dirichlet problem for prescribed scalar curvature in Anti-de Sitter space
problem Dirichlet problem for prescribed scalar curvature in Anti-de Sitter space
method Fully non-linear elliptic equation
result Solves if datas are strictly convex
Establishes log-concavity estimates for convex domains' first Dirichlet eigenfunctions.
problem Quantifying the Hessian of log-concave eigenfunctions on convex domains.
method Analyzes log-concavity properties of the first Dirichlet eigenfunction on convex domains.
result Obtains quantitative estimates for the Hessian of .
Some universal inequalities for Dirichlet eigenvalues of the Laplacian on a Euclidean convex domainmath.SP
Universal inequalities found for Laplacian eigenvalues on convex domains.
problem Finding bounds for Laplacian eigenvalues on convex domains.
method Established two universal inequalities.
result Found new bounds for Laplacian eigenvalues.
In this paper we address some problems concerning an approximate Dirichlet domain. We show that under some assumptions the approximate Dirichlet domain can work equally well as an exact Dirichlet domain. In particular, we consider a problem of tiling a hyperbolic ball with copies of the Dirichlet domain. This problem a…
Study uniquely determines Riemannian metric derivatives from boundary data.
problem Determining Riemannian metric derivatives from boundary data.
method Computing the full symbol of the elastic Dirichlet-to-Neumann map.
result The elastic Dirichlet-to-Neumann map uniquely determines all partial derivatives of the Riemannian metric on the boundary.
Solves Dirichlet problem for generalized Hitchin's equation on cyclic Higgs bundles.
problem Existence and uniqueness of solutions to the Dirichlet problem.
method Formulated using subharmonic functions; generalizes Hitchin's equation for diagonal harmonic metrics on cyclic Higgs bundles.
result Existence and uniqueness of solutions to the Dirichlet problem.
Paper solves Dirichlet problem at infinity for Riemannian cones.
problem Solvability of Dirichlet problem at infinity in Riemannian cones.
method Separation of variables and comparison arguments for ODE's.
result Sufficient condition for solvability related to Milnor's classification.
Solves Dirichlet problem for Lagrangian phase equation with critical and supercritical phase.
problem Solving Dirichlet problem for Lagrangian phase equation with critical and supercritical phase.
method Uses interior estimate.
result Result is sharp, showing existence of singular solutions in subcritical phase.
The paper compares eigenvalues of Dirichlet, Neumann, and Laplacian on graphs.
problem Eigenvalue comparisons on graphs.
method Analytical comparisons and discussions of eigenvalues and their applications.
result Extensions of eigenvalue estimates for Dirichlet and Neumann eigenvalues.
Study solves complex Hessian equation on Hermitian manifolds.
problem Solving Hessian equations on Hermitian manifolds with mixed structure.
method Derive a priori estimates and solve Dirichlet problem under conditions.
result Solvability of the Dirichlet problem for mixed Hessian equations.
Researchers calculate spectral invariants from Dirichlet-to-Neumann map for Witten-Laplacian with potential.
problem Calculating spectral invariants from Dirichlet-to-Neumann map for Witten-Laplacian with potential.
method Established an effective procedure to calculate all coefficients of the spectral asymptotic formula of the Dirichlet-to-Neumann map.
result Explicitly provided the first four coefficients of the spectral asymptotic formula.
A Dirichlet problem on ballsmath.DG
We provide infinitely many solutions of a Dirichlet problem on balls.
Paper proves new inequalities for hyperbolic space Laplacian eigenvalues.
problem Universal inequalities for eigenvalues of the Dirichlet Laplacian.
method Proves new inequalities for eigenvalues on hyperbolic space.
result Verifies Cheng's conjecture up to a small loss.
In this paper, we first introduce higher order Dirichlet-to-Neumann maps on graphs which can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann maps on compact Riemannian manifolds with boundary and a higher order generalization of the Dirichlet-to-Neumann map on graphs introduced by Hua-Huang-W…
Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over Dirichlet parameters complicate the joint distribution of model parameters. This paper s…
The Dirichlet mechanism protects privacy while minimizing KL divergence.
problem Minimizing KL divergence while protecting sensitive data privacy.
method Using the exponential mechanism with the KL divergence loss function, resulting in the Dirichlet mechanism.
result Proved a probability tail bound on KL divergence and derived a lower bound for sample complexity.
Study on Dirichlet process mixtures for clustering consistency.
problem Consistency of clustering with Dirichlet process mixtures.
method Analysis of posterior distribution as sample size increases, focusing on consistency for the number of clusters.
result Consistency for the number of clusters can be achieved with a properly adapted concentration parameter in a Bayesian setting.
Estimates for eigenvalues on Riemannian manifolds using classical inequalities.
problem Estimating eigenvalues of the Dirichlet Laplacian on Riemannian manifolds.
method Building on Li-Yau's and Yang's inequalities, deriving upper and lower bounds.
result Explicit estimates on lower bounds for eigenvalues of the Dirichlet Laplacian on projective spaces and their minimal submanifolds.
Abstract: Expresses zeta-determinant of Dirichlet-to-Neumann operator on forms.
problem Express zeta-determinant of Dirichlet-to-Neumann operator on forms.
method Expresses zeta-determinant as difference of Laplacian determinants with boundary conditions.
result Computes terms explicitly for dimensions 2 and 3.
The paper defines Dirichlet domains for Anosov subgroups in Lie groups.
problem Finding finite-sided Dirichlet domains for Anosov subgroups in Lie groups.
method Introducing a sufficient condition for finite-sided Dirichlet domains in semisimple Lie groups for polyhedral Finsler metrics.
result Finitely generated subgroups of semisimple Lie groups can have finite-sided Dirichlet domains under certain conditions.
Study connects boundary geometry to symbol of Dirichlet-to-Neumann operator.
problem Determining geometric data from boundary symbol of connection Laplacian.
method Analyze symbol of Dirichlet-to-Neumann operator associated with connection Laplacian.
result Geometric data on boundary and normal derivatives are determined by symbol.
Paper calculates eigenvalues of a specific triangle on a sphere.
problem Computing eigenvalues of a specific triangle on a sphere.
method Computed first two Dirichlet eigenvalues and eigenfunctions of the equilateral Schwarz triangle (3/2 3/2 3/2) on the sphere.
result Computed the first two Dirichlet eigenvalues and eigenfunctions of the equilateral Schwarz triangle (3/2 3/2 3/2).
Solves Dirichlet problem for specific PSH functions on Hermitian manifolds.
problem Solving Dirichlet problem for Monge-Ampère equation for -PSH functions.
method Deriving a quantitative boundary estimate under -PSH subsolutions assumption.
result Quantitative boundary estimate confirmed for specific manifolds.
Paper solves Hessian quotient equations in Lorentz-Minkowski space with Dirichlet boundary conditions.
problem Existence and uniqueness of solutions to Hessian quotient equations in Lorentz-Minkowski space.
method Suitable settings to prove existence and uniqueness of solutions.
result Existence and uniqueness of solutions to the class of Hessian quotient equations.