arXiv research

New conditions prevent gaps in optimal control problems.

Fundamental gap vanishes for convex domains in hyperbolic space.

The article explores the fundamental gap in Bakry-Emery geometry.

GACELA fills long gaps in musical audio with a GAN and context conditioning.

We prove the existence of metrics maximizing the first eigenvalue normalized by area on closed, non-orientable surfaces assuming two spectral gap conditions. These spectral gap conditions are proved by the authors in \cite{MS3}.

This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programm…

This work analyzes the gap between off-policy and on-policy policy gradient methods and provides conditions to reduce this gap.

Game-theoretic analysis of mining gaps in blockchain systems.

The paper classifies CMC free boundary hypersurfaces in rotational domains.

New spaces help connect manifold structures on equivariant Poincaré spaces.

The paper proves gap theorems for Yang-Mills on manifolds with positive Yamabe.

New method for spectral and Bergman kernels under local spectral gap condition.

Lu conjecture proven for minimal 2-spheres and surfaces under certain conditions.

Paper tackles fast convergence for non-convex strongly-concave min-max problems.

Estimates spectral gap for Brownian motion on sticky-reflecting domains.

New Dynkin condition for manifolds with boundary yields bi-Lipschitz equivalence and spectral properties.

We use the energy gap result of pure Yang-Mills equation [Feehan P.M.N., Adv. Math. 312 (2017), 547-587, arXiv:1502.00668] to prove another energy gap result of complex Yang-Mills equations [Gagliardo M., Uhlenbeck K., J. Fixed Point Theory Appl. 11 (2012), 185-198, arXiv:1401.7366], when Riemannian manifold $X$ of dim…

Estimates gaps between eigenvalues for elliptic operators on manifolds.

Develops finite-gap solutions for Pohlmeyer--Lund--Regge equation and Lund--Regge curve evolution.

In this paper, we extend the sharp lower bounds of spectal gap, due to Chen- Wang [10, 11], Bakry-Qian [6] and Andrews-Clutterbuck [5], from smooth Riemaniannian manifolds to general metric measure spaces with Riemannian curvature-dimension condition RCD*(K;N).

Study reveals a hidden cost in derivatives markets through option-implied discount factors.

Improves conditional coverage of regression models using conformal prediction.

Improved spectral gap for MwG with adaptive RWM proposals.

Paper establishes a universal growth rate for smooth surrogate losses in classification.

Characterizes Anosov representations and strongly convex cocompact groups with eigenvalue gaps.

We consider a rigidity problem for the spectral gap of the Laplacian on an $RCD(K,\infty)$-space (a metric measure space satisfying the Riemannian curvature-dimension condition) for positive $K$. For a weighted Riemannian manifold, Cheng--Zhou showed that the sharp spectral gap is achieved only when a $1$-dimensional G…

New estimates show spectral gap stability in RCD spaces, close to Beta distribution.

New algorithm reduces MDP regret by accounting for state suboptimality gaps and variance.

This work closes the theory-practice gap for distributed optimization methods by introducing a new regularity condition.

A new screening test for Lasso improves solution speed.

Researchers prove a spectral gap for Hecke covers of Schottky surfaces.

The study improves fundamental gap estimates for surfaces with non-constant positive curvature.

Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for manifolds with smooth group actions - isovariant and equivariant - often coincide under a condition called the Gap Hypothesis; the proofs use deep results in geometric topology. This paper analyzes the difference between th…

We study the spectrum of complete noncompact manifolds with bounded curvature and positive injectivity radius. We give general conditions which imply that their essential spectrum has an arbitrarily large finite number of gaps. In particular, for any noncompact covering of a compact manifold, there is a metric on the b…

In the present paper, by using estimates for the generalized Ricci curvature, we shall give some gap theorems for Ricci-harmonic solitons showing some necessary and sufficient conditions for the solitons to be harmonic-Einstein. Our results may be regarded as a generalization of recent works by H. Li, and M. Fernandez-…

For a second order operator on a compact manifold satisfying the strong Hörmander condition, we give a bound for the spectral gap analogous to the Lichnerowicz estimate for the Laplacian of a Riemannian manifold. We consider a wide class of such operators which includes horizontal lifts of the Laplacian on Riemannian s…

The paper derives upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.

Paper introduces a method to control early classification accuracy gaps.

Study gaps and clusters in eigenvalues of magnetic Laplacian on manifolds.

Log-concavity of eigenfunctions on curved surfaces is proven, leading to fundamental gap estimates.

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: $\displaystyle \sup_X |Ric|$ and $\displaystyle \sqrt{\sup_X |Rm|} \cdot \sqrt{\sup_X |R|}$ must blowup at least at the rate of type-I. Our estim…

Negative curvature restricts the gap between the first and second eigenvalues of convex domains.

Foundation models improve wage gap decomposition by capturing omitted career history factors.

This note removes technical assumptions and characterizes relatively dominated representations.

A novel method detects multiple mitosis events and mitigates annotation gaps in phase-contrast microscopy.

In this paper, we prove a gap result for a locally conformally flat complete non-compact Riemannian manifold with bounded non-negative Ricci curvature and a scalar curvature average condition. We show that if it has positive Green function, then it is flat. This result is proved by setting up new global Yamabe flow. Ot…

Mobile crowdsourcing has become easier thanks to the widespread of smartphones capable of seamlessly collecting and pushing the desired data to cloud services. However, the success of mobile crowdsourcing relies on balancing the supply and demand by first accurately forecasting spatially and temporally the supply-deman…

Fine-grained gap-dependent regret bounds for reinforcement learning.