arXiv research

New infinite-dimensional representations with bounded multiplicity found for Lie groups.

A classical result by Cheng in 1976, improved later by Besson and Nadirashvili, says that the multiplicities of the eigenvalues of the Schrodinger operator with a smooth potential on a compact Riemannian surface M are bounded in terms of the eigenvalue index and the genus of M. We prove that these multiplicity bounds h…

We prove two explicit bounds for the multiplicities of Steklov eigenvalues $σ_k$ on compact surfaces with boundary. One of the bounds depends only on the genus of a surface and the index $k$ of an eigenvalue, while the other depends as well on the number of boundary components. We also show that on any given smooth Rie…

We find sharp upper bounds for the multiplicities and the numerical values of all the distinct eigenvalues on a surface of revolution diffeomorphic to the sphere.

Paper develops a framework to derive lower bounds on FDR and FNR in multiple testing.

The known upper bounds for the multiplicities of the Laplace-Beltrami operator eigenvalues on the real projective plane are improved for the eigenvalues with even indexes. Upper bounds for Dirichlet, Neumann and Steklov eigenvalues on the real projective plane with holes are also provided.

We present generalization bounds for the TS-MKL framework for two stage multiple kernel learning. We also present bounds for sparse kernel learning formulations within the TS-MKL framework.

The paper bounds eigenvalue multiplicities for hyperbolic surfaces using short geodesics.

Study on CMC hypersurfaces with bounded index and area, proving multiplicity one convergence and bounds on genus.

We determine the sample complexity of pure exploration bandit problems with multiple good answers. We derive a lower bound using a new game equilibrium argument. We show how continuity and convexity properties of single-answer problems ensures that the Track-and-Stop algorithm has asymptotically optimal sample complexi…

In the present paper several bounds on multiplicities of eigenvalues of the Laplacian operator on surfaces are generalized from the case of either closed surface or simply-connected planar domain to the case of a surface of positive genus with holes.

New PAC-Bayes bound controls multiple error types simultaneously.

We consider a continuous map $f :M\to N$ between two manifolds and try to estimate its multiplicity from below, i.e. find a $q$-tuple of pairwise distinct points $x_1,..., x_q\in M$ such that $f(x_1) = f(x_2) = ... = f(x_q)$. We show that there are certain characteristic classes of vector bundle $f^*TN-TM$ that guarant…

Paper finds efficient OPE estimator for multiple logging policies with minimum variance.

Study on singularity behavior of mean curvature flow with bounded curvature and index.

Develops a method for solving optimal stopping problems with multiple exercise rights.

Let $M$ be a compact Riemannian manifold not containing any totally geodesic surface. Our main result shows that then the area of any complete surface immersed into $M$ is bounded by a multiple of its extrinsic curvature energy, i.e. by a multiple of the integral of the squared norm of its second fundamental form.

Klein quartic maximizes the first positive Laplacian eigenvalue's multiplicity to 8.

Study on Kähler manifolds shows rigidity of eigenvalues with positive Ricci bound.

Establishes inequality for multiple black holes, proving mass lower bound.

Beta diffusion generates bounded data using multiplicative transitions.

Proposes a method to compute valid lower confidence bounds for multiple models selected based on their performance.

Study on geodesics proving index and intersection bounds, with examples of multiplicity.

We discuss a multiple-play multi-armed bandit (MAB) problem in which several arms are selected at each round. Recently, Thompson sampling (TS), a randomized algorithm with a Bayesian spirit, has attracted much attention for its empirically excellent performance, and it is revealed to have an optimal regret bound in the…

We present a data dependent generalization bound for a large class of regularized algorithms which implement structured sparsity constraints. The bound can be applied to standard squared-norm regularization, the Lasso, the group Lasso, some versions of the group Lasso with overlapping groups, multiple kernel learning a…

We derive an upper bound on the local Rademacher complexity of $\ell_p$-norm multiple kernel learning, which yields a tighter excess risk bound than global approaches. Previous local approaches aimed at analyzed the case $p=1$ only while our analysis covers all cases $1\leq p\leq\infty$, assuming the different feature …

Improved guarantees and multiple-descent curve for data approximations.

The paper proves unique geodesics on hyperbolic surfaces and finds lower bounds.

Study phase transitions with prescribed mean curvature in Riemannian manifolds.

We prove several results about the multiplicity of the first Steklov eigenvalues on compact surfaces with boundary. We improve some bounds on the multiplicity, especially for the first eigenvalue, and we prove they are sharp on some surfaces of small genus. In a previous article, we defined a new chromatic invariant of…

Paper develops upper-bounds for target general loss in multiple source DA and DG settings.

Proposes DEXP3.M for unknown delay in multi-arm bandit with multiple play.

Optimal best-arm identification with known number of optimal arms.

The paper finds lower bounds for volumes of complex geometric structures.

For a membrane in the plane the multiplicity of the $k$-th eigenvalue is known to be not greater than $2k-1$. Here we prove that it is actually not greater than $2k-3$, for $k\ge 3$.

We study a generalization of the multi-armed bandit problem with multiple plays where there is a cost associated with pulling each arm and the agent has a budget at each time that dictates how much she can expect to spend. We derive an asymptotic regret lower bound for any uniformly efficient algorithm in our setting. …

New bounds on ropelength for special alternating knots.

Proves a plumbing-multiplicative property of a Links-Gould invariant.

This paper proposes a simple approach to derive efficient error bounds for learning multiple components with sparsity-inducing regularization. We show that for such regularization schemes, known decompositions of the Rademacher complexity over the components can be used in a more efficient manner to result in tighter b…

Grimaldi-Pansu metrics are constructed for manifolds with multiple ends.

Optimizes profit in targeted marketing across multiple markets with varying marketing expenditures.

While domain adaptation has been actively researched in recent years, most theoretical results and algorithms focus on the single-source-single-target adaptation setting. Naive application of such algorithms on multiple source domain adaptation problem may lead to suboptimal solutions. As a step toward bridging the gap…

Paper adapts multiplicative weights method to Gaussian graphical models.

Improved uniform convergence bound with fat-shattering dimension reduces sample complexity gap.

The Allen-Cahn equation is a semilinear PDE which is deeply linked to the theory of minimal hypersurfaces via a singular limit. We prove curvature estimates and strong sheet separation estimates for stable solutions (building on recent work of Wang-Wei) of the Allen-Cahn equation on a 3-manifold. Using these, we are ab…

Proves unknottedness of certain 3D shapes with multiple ends.

In this paper, we study the spectrums of faithful dimension pairs on a closed Finsler manifold and obtain a Gromov type and a Buser type lower bounds for eigenvalues. Furthermore, for the Lusternik-Schnirelmann spectrum, we not only obtain a better lower bound, but also estimate the multiplicity of each eigenvalue.

Framework for controlling multiple risks in AI models.