New methods reduce bias in estimating optimality gaps for risk-averse stochastic programs.
problem Optimality gap estimation bias in risk-averse stochastic programs.
method Two independent samples, each estimating a different component of the optimality gap.
result Our method reduces bias in estimating optimality gaps for risk-averse problems.
Sharp spectral gap estimates on manifolds with integral curvature bounds.
problem Proving spectral gap estimates on manifolds with integral curvature bounds.
method Generalizing previous results to include integral curvature bounds.
result Confirms a conjecture about spectral gap estimates on manifolds with integral curvature bounds.
New estimates show spectral gap stability in RCD spaces, close to Beta distribution.
problem Stability of spectral gap bounds in metric-measure spaces.
method Combines L 1 L^1 L 1 -functional inequality and Stein's method. result Sharp quantitative estimate for spectral gap stability.
The article proves a conjecture about the fundamental gap for horoconvex domains in hyperbolic space.
problem Proving a conjecture about the fundamental gap for horoconvex domains in hyperbolic space.
method Establishing conformal log-concavity estimates for the first eigenfunction.
result Proves a conjecture about the fundamental gap for horoconvex domains in hyperbolic space.
We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator in the case when the potential is strongly convex. In particular, if the Hessian of the potential is bounded from below by a positive constant, the gap has a lower bound independent of the dimension. We also estimate the gap wh…
The paper proves lower bounds for Gaussian-weighted curvature integrals of self-shrinkers.
problem Proving lower bounds for Gaussian-weighted \(L^2\)-curvature integrals of self-shrinkers.
method Combining normal coordinate functions with weighted Poincaré inequalities and first-eigenvalue estimates.
result Explicit lower bounds in terms of entropy for closed self-shrinkers, leading to curvature gaps.
Estimates spectral gap for sub-Laplacian on compact manifolds.
problem Bounding the spectral gap of sub-Laplacian on compact manifolds.
method Lichnerowicz estimate adaptation for sub-Laplacian on compact manifolds.
result A bound for the spectral gap analogous to the Lichnerowicz estimate for the Laplacian.
The study improves fundamental gap estimates for surfaces with non-constant positive curvature.
problem Estimating the fundamental gap for surfaces with non-constant positive curvature.
method Using a two-point maximum principle, the study establishes log-concavity and fundamental gap estimates.
result Corresponding log-concavity and fundamental gap estimates for surfaces with non-constant positive curvature are derived.
A new algorithm estimates spectral gap of Markov chains efficiently.
problem Estimating the spectral gap of a Markov chain efficiently.
method UCPI (Upper Confidence Power Iteration) algorithm
result Estimates spectral gap in O ( n ) {\cal O}(n) O ( n ) time and O ( ( ln n ) 2 ) {\cal O}((\ln n)^2) O (( ln n ) 2 ) memory. Sharp spectral gap estimates for higher-order operators on hyperbolic spaces.
problem Estimating spectral gaps for higher-order operators on Cartan-Hadamard manifolds.
method Symmetrization-free proofs based on general functional inequalities.
result Solves a sharp asymptotic problem from Cheng and Yang and answers a question from Kristály.
Estimates spectral gap for Brownian motion on sticky-reflecting domains.
problem Estimating spectral gap for Brownian motion on sticky-reflecting domains.
method Interpolation method and novel applications of Reilly formula.
result Lower bounds for spectral gap derived for general domains.
Sharp fundamental gap estimate proved for convex domains on spheres.
problem Proving a sharp fundamental gap estimate for convex domains on spheres.
method Proving super log-concavity of the first eigenfunction.
result Sharp fundamental gap bound of 3 π 2 D 2 3\frac{π^2}{D^2} 3 D 2 π 2 for n ≥ 3 n \ge 3 n ≥ 3 . Estimates scalar curvature without nonnegativity, showing gap phenomenon on manifolds.
problem Estimating scalar curvature without curvature nonnegativity assumption.
method Derive estimates for scalar curvature and mean curvature on manifolds and domains.
result Show that metrics on even dimensional manifolds with nonzero Euler characteristic are ε-gap distance extremal.
Estimates generalization gap for overparameterized models using Langevin approximation.
problem Estimating the difference between training and generalization performance in overparameterized models.
method Functional variance and Langevin approximation of functional variance.
result Demonstrates efficient estimation of generalization gaps for overparameterized models.
Estimates gaps between eigenvalues for elliptic operators on manifolds.
problem Estimating the gaps between consecutive eigenvalues for elliptic differential operators.
method Analyzes a class of second-order elliptic differential operators in divergence form with Dirichlet boundary conditions.
result Estimates for the upper bound of gaps between eigenvalues, with results matching known best estimates for specific cases.
Estimates the mass gap for domains with integral Ricci curvature bounds.
problem Estimating the mass gap for domains with specific curvature conditions.
method Proving domains are John domains to estimate the first nonzero Neumann eigenvalue.
result Fundamental gap estimates for domains with integral Ricci curvature bounds.
Study estimates gaps in semigroup products, proving embedding properties.
problem Estimating singular value gaps in semigroup products.
method Lower estimates for singular value gaps of free products of semigroups in ping-pong position.
result Groups generated by semigroups in ping-pong position are quasi-isometrically embedded.
Paper improves volume gap between minimal submanifolds and unit spheres.
problem Volume gap between minimal submanifolds and unit spheres.
method Modified Cheng-Li-Yau coefficients and applied Cheng-Yang eigenvalue estimate for Laplacian.
result Enhanced volume gap between minimal submanifolds and unit spheres.
Log-concavity of eigenfunctions on curved surfaces is proven, leading to fundamental gap estimates.
problem Proving log-concavity of eigenfunctions on curved surfaces.
method Analyzing the Laplacian eigenfunctions on positively curved surfaces.
result Strong log-concavity of the first eigenfunction on positively curved surfaces.
Probabilistic method proves gap estimates on sphere.
problem Proving fundamental gap estimates for Schrödinger operators on spheres.
method Reflection coupling method on Riemannian manifolds.
result Extends probabilistic proof to sphere, generalizing previous results.
A novel method detects multiple mitosis events and mitigates annotation gaps in phase-contrast microscopy.
problem Detecting multiple mitosis events and handling annotation gaps in closely placed cells.
method Estimating a spatiotemporal likelihood map via 3DCNN to detect multiple mitosis events and mitigate annotation gaps.
result Our method outperformed compared methods in terms of F1-score using a challenging dataset.
Paper generalizes Bakry-Émery calculus for curvature and applies to Markov chains.
problem Formulating both Bakry-Émery and entropic curvature simultaneously.
method Generalization of Bakry-Émery calculus, new measure optimality criterion, dimension parameter in entropic curvature.
result Diameter estimates for Markov chains with strictly positive entropic curvature and spectral gap.
Foundation models improve wage gap decomposition by capturing omitted career history factors.
problem Estimating wage disparities using incomplete career history data.
method Fine-tuning foundation models to mitigate omitted variable bias and estimate wage gaps.
result Foundation models can decompose gender wage gaps more accurately than traditional econometric methods.
We develop some estimates under the Ricci flow and use these estimates to study the blowup rates of curvatures at singularities. As applications, we obtain some gap theorems: sup X ∣ R i c ∣ \displaystyle \sup_X |Ric| X sup ∣ R i c ∣ and sup X ∣ R m ∣ ⋅ sup X ∣ R ∣ \displaystyle \sqrt{\sup_X |Rm|} \cdot \sqrt{\sup_X |R|} X sup ∣ R m ∣ ⋅ X sup ∣ R ∣ must blowup at least at the rate of type-I. Our estim…
We give a new lower bound for the first gap λ 2 − λ 1 λ_2 - λ_1 λ 2 − λ 1 of the Dirichlet eigenvalues of the Schr{ö}dinger operator on a bounded convex domain Ω Ω Ω in R n ^n n or S n ^n n and greatly sharpens the previous estimates. The new bound is explicit and computable.
Sharp curvature estimates for expanding Ricci solitons in various dimensions.
problem Estimating curvature bounds for expanding Ricci solitons.
method Sharp lower and upper bounds derived for scalar curvature under specific conditions.
result Sharp curvature estimates provided for expanding Ricci solitons in dimensions three and four.
Paper addresses eigenvector perturbation in small eigen-gap scenarios.
problem Fine-grained behavior of eigenvectors in the presence of small eigen-gaps.
method Develops de-biased estimators for linear functions of an unknown eigenvector.
result Achieves minimax lower bounds for a family of scenarios, even with small eigen-gaps.
Paper tackles small eigen-gap estimation and inference for noisy symmetric matrices.
problem Estimating eigenvectors with small eigen-gap and fine-grained statistical reasoning.
method Eigen-decomposition of asymmetric data matrix, distribution-free procedures, adaptive to heteroscedastic noise.
result Minimax optimal under Gaussian noise, confidence intervals for eigenvalues, small eigen-gap handling.
Detecting and recovering labels in binomial logistic mixtures is challenging due to an information gap.
problem Detecting and recovering labels in binomial logistic mixtures
method Propose two feasibility-aware inference procedures
result Avoid misleading component selections and improve label probability calibration
Proves spectral gap bounds for Teichmüller geodesics on flat surfaces.
problem Quantify spectral gaps for Teichmüller geodesics.
method Bounding spectral gaps in terms of geometric quantities on flat surfaces.
result Quantitative non-uniform hyperbolicity of Teichmüller geodesic flow.
Paper stabilizes DARTS algorithm for better neural architecture search.
problem Weak stability of DARTS algorithm leading to unreliable results.
method Amended gradient estimation method to bridge optimization gap.
result Significant improvement in search stability and larger search spaces explored.
This paper improves Q-learning bounds using reference-advantage decomposition.
problem Improving Q-learning bounds in MDPs with positive suboptimality gaps.
method Develops a novel error decomposition framework to prove gap-dependent regret bounds.
result Establishes logarithmic gap-dependent regret bounds for Q-learning.
The paper estimates the gap between eigenvalues of a clamped plate problem.
problem Estimating the gap between eigenvalues of a clamped plate problem.
method Using the asymptotic formula of Agmon and Pleijel, the paper gives an estimate for the gap between eigenvalues.
result The gap between eigenvalues is bounded by a term with a lower order $k^{ rac1n}$ .
In this paper, we give an easy proof of the main results of Andrews and Clutterbuck's paper [J. Amer. Math. Soc. 24 (2011), no. 3, 899--916], which gives both a sharp lower bound for the spectral gap of a Schröinger operator and a sharp modulus of concavity for the logarithm of the corresponding first eigenfunction. We…
Study fourth-order geometric problems on Willmore surfaces.
problem Fourth-order geometric problems on Willmore surfaces.
method Local energy estimates and global gap lemma derivation.
result Proved several local energy estimates and derived a global gap lemma.
Improved EXP3++ algorithm reduces regret in stochastic bandits.
problem Stochastic and adversarial multiarmed bandits.
method New gap estimation strategy combined with EXP3++.
result Regret reduced from ( ln t ) 3 (\ln t)^3 ( ln t ) 3 to ( ln t ) 2 (\ln t)^2 ( ln t ) 2 in stochastic regime. Uniform spectral gap found for stable commutator length in hyperbolic 2-orbifolds.
problem Understanding stable commutator length in 3-manifolds.
method Explicit quasimorphisms for generic case, hyperbolic geometry for exceptional case.
result Explicit uniform gap of 1/36 for all orbifolds except a sphere with three cone points.
New technique reduces imitation learning performance gap in finite samples.
problem Imitation learning performance gap in finite samples.
method Replay estimation to reduce empirical variance in finite samples.
result Achieves optimal performance gap of $\widetilde{O} \left( \min({H^{3/2}} / {N}, {H} / {\sqrt{N}}
ight)$ .
Paper shows statistical-computational gaps in learning sparse mixtures and robust estimation.
problem Statistical-computational gaps in learning sparse mixtures and robust estimation.
method Average-case reduction techniques, Imbalanced Sparse Gaussian Mixtures, and algorithmic change of measure.
result New hardness results for robust sparse mean estimation, semirandom planted dense subgraph, and universality principle for sparse mixture problems.
Paper uses 2-step Gradient Boosting to predict VAT tax gap.
problem Estimating tax evasion and revenue loss from tax avoidance.
method 2-steps Gradient Boosting model to correct selection bias.
result Significantly improved prediction of VAT tax gap.
Estimates Markov chain mixing time from a single trajectory.
problem Estimating mixing time of Markov chains from a single trajectory.
method Contraction with respect to total variation, inspired by Wolfer's contraction coefficient.
result Improved confidence intervals and instance-dependent rates for estimating Markov chains.
Uniform curvature estimates for homogeneous Ricci flows proved.
problem Uniform curvature estimates for Ricci flows on homogeneous spaces.
method Uniform curvature estimates proved using a gap theorem for Ricci-flatness on homogeneous spaces, by contradiction.
result Uniform curvature estimates for Ricci flows on homogeneous spaces.
The study provides energy estimates for Willmore surfaces and derives a gap statement.
problem Analyzing the tracefree curvature of Willmore surfaces.
method Proves ε-regularity result for tracefree curvature with bounded second fundamental form.
result Derives a gap statement for surfaces of the specified type.
A new method is proposed to compute connectivity measures on multivariate time series with gaps. Rather than removing or filling the gaps, the rows of the joint data matrix containing empty entries are removed and the calculations are done on the remainder matrix. The method, called measure adapted gap removal (MAGR), …
In the previous work [35], the second and third authors established a Bochner type formula on Alexandrov spaces. The purpose of this paper is to give some applications of the Bochner type formula. Firstly, we extend the sharp lower bound estimates of spectral gap, due to Chen-Wang [9, 10] and Bakry-Qian [6], from smoot…
Proves a fundamental gap lower bound for horoconvex domains in hyperbolic space.
problem Proving a fundamental gap lower bound for horoconvex domains in hyperbolic space.
method Reduces the problem to a radial-height problem, compares Dirichlet forms with angular operators, and uses Green estimates.
result Establishes a polynomial \(D^{-3}\) scale fundamental gap lower bound.
We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator with a nonconvex potential in terms of a distance associated with the potential. The results here can be applied to the double well potential.
The paper provides estimates for eigenvalues of elliptic differential problems.
problem Computing eigenvalue estimates for elliptic differential problems.
method Analytical computation of eigenvalues for specific types of elliptic differential equations.
result Universal estimates of eigenvalues and gaps between consecutive eigenvalues are derived.